Collapsing Radiative Shock Experiments on the

Omega Laser

by

Amy B. Reighard

A dissertation submitted in partial fulfillmentof the requirements for the degree of

Doctor of Philosophy(Physics)

in The University of Michigan2007

Doctoral Committee:

Professor R. Paul Drake, Co-ChairProfessor Fred C. Adams, Co-ChairProfessor Carl W. AkerlofProfessor James Paul HollowayProfessor Gregory Tarle

c© Amy B. Reighard 2007All Rights Reserved

To Robert L. Cooper, who helped at every step along the way with love, support, and a firmgrasp of reality; I hope I am just as helpful when it is your turn. To Mom and Dad, who never

doubted that I should or could do this.

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ACKNOWLEDGEMENTS

I would first like to thank my graduate research advisor, Paul Drake, for guid-

ing me on this exciting project. Thank you for allowing me to present at a dozen

conferences, for encouraging me to pursue somewhat-related tangents, for flying me

across the country to “see who will wander by”, for letting me do the fun stuff while

you handled the unpleasant things, and for always knowing when not to tell me the

answer.

Thank you also to the graduate students, past and present, in the Drake research

group; Carolyn Kuranz, Eric Harding, Tony Visco, Korbie Killebrew Dannenberg,

and Kelly Korreck for many useful discussions, brainstorming sessions, homework

arguments, and your enduring friendship, fellowship, and support. I feel lucky to

have such wonderful peers.

I would like to acknowledge the extensive contributions of the Target Fabrication

Team in the Drake group at the University of Michigan, especially Michael Grosskopf,

Douglas Kremer, Christine Krauland, and Trisha Donajkowski, who built, trans-

ported, organized, and filled my targets. Eduardo Mucino also helped extensively

with 1D simulation work on beryllium, and Dave Leibrandt simulated the experiment

using Zeus 2D.

Thank you also to the technical staff at the Omega Laser facility, without whom

none of these experiments could have been executed. Thank you especially to Keith

Thorp, Steve Stagnitto, Jack Armstrong, and Chuck Source.

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I have also had many helpful discussions with an international group of collabora-

tors, which includes Tom Boehly, Laurent Boireau, Serge Bouquet, Michel Busquet,

Dustin Froula, Gail Glendinning, Siegfried Glenzer, Freddy Hansen, Jim Knauer,

Michel Koenig, Ted Perry, Bruce Remington, Steven Ross, and Russell Wallace.

Lastly, thank you to my committee, whose extensive input helped shape this thesis

in a very positive way.

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TABLE OF CONTENTS

DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

LIST OF APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

CHAPTER

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 High-Energy-Density Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 A Brief History of HED physics . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Laboratory Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Tools of the Trade: High-Energy-Density Facilities . . . . . . . . . . . . . . . 6

1.4.1 High-powered laser facilities . . . . . . . . . . . . . . . . . . . . . . 71.4.2 Z-pinches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4.3 Petawatt Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

II. Radiation Hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 Single-Fluid Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 The Equation of Radiative Transfer and Radiative Hydrodynamics . . . . . 13

2.2.1 Threshold for Radiative Shocks . . . . . . . . . . . . . . . . . . . . 152.2.2 Classification for Meaningful Comparison . . . . . . . . . . . . . . 162.2.3 Formation of a Cooling Layer and a Collapsed Shock . . . . . . . . 172.2.4 Energy Balance in a Thick/Thin Shock . . . . . . . . . . . . . . . . 21

2.3 A Brief History of Radiation Hydrodynamics Experiments . . . . . . . . . . 22

III. Experiment Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1 Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3 Backlighters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.4 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4.1 Microchannel Plates and Framing Cameras . . . . . . . . . . . . . 403.4.2 Velocity Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . 433.4.3 Thomson scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

IV. Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

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4.1 Radiographic Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . 524.2 X-ray Radiographic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2.1 Single-strip framing camera data from 40 µm beryllium drive disks 574.2.2 Single-strip framing camera data from 20 µm, beryllium drive disks 574.2.3 Single-strip framing camera data from 10 µm beryllium drive disk . 614.2.4 Single-strip framing camera data from 80 µm polyimide drive disk 624.2.5 Four-strip framing camera data . . . . . . . . . . . . . . . . . . . . 64

4.3 Dual Radiographic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.4 Odd Radiographic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.5 Fringe Shifts from a Velocity Interferometry System for Any Reflector . . . . 77

V. Radiographic Image Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.1 Shot-to-Shot Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.2 Shock Position as a Function of Time . . . . . . . . . . . . . . . . . . . . . . 855.3 Shock Thickness as a Function of Time . . . . . . . . . . . . . . . . . . . . . 865.4 Structure in the Cooling Layer . . . . . . . . . . . . . . . . . . . . . . . . . . 88

VI. Thomson Scattering Experiment in Argon Gas . . . . . . . . . . . . . . . . . 94

VII. Radiation Hydrodynamic Simulations . . . . . . . . . . . . . . . . . . . . . . . 110

7.1 One-Dimensional Hyades Simulations . . . . . . . . . . . . . . . . . . . . . . 1107.1.1 Production of a radiatively collapsed shock . . . . . . . . . . . . . 1117.1.2 Drive disk thickness variation . . . . . . . . . . . . . . . . . . . . . 1177.1.3 Late-time effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.2 Two-Dimensional Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 1217.2.1 FCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1227.2.2 Zeus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.3 Issues Between Simulation and Experiment . . . . . . . . . . . . . . . . . . . 1267.4 One-Dimensional Simulations in Argon Gas . . . . . . . . . . . . . . . . . . . 1327.5 Summary of Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 135

VIII. Conclusions and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . 136

8.1 Radiative Shocks in Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . 1378.1.1 Shocks Emerging from Supernovae . . . . . . . . . . . . . . . . . . 1388.1.2 Cooling of Stellar Atmospheres . . . . . . . . . . . . . . . . . . . . 141

8.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1468.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

8.3.1 Flux Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 1478.3.2 Short-Pulse Backlighters and Ungated Imaging Diagnostics . . . . 148

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

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LIST OF FIGURES

Figure

1.1 Hubble Space Telescope picture of the Cyngus Loop. False coloring shows differentmetal line emissions. Credit: NASA, HST, Jeff Hester. . . . . . . . . . . . . . . . . 4

1.2 Hubble Space Telescope image of SN 1987a, taken in 2003 with WFPC2. Here, aring of circumstellar material lights up as the shockwave driven by the explosionheats it. Image credit: NASA and R. Kirshner. . . . . . . . . . . . . . . . . . . . . 5

1.3 Diagram of the planned laser facility at the Naval Research Laboratory in Wash-ington, D.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 Outside of the NIF target chamber. Square protrusions are where bundles of fourbeams, called quads, will enter the target chamber. . . . . . . . . . . . . . . . . . . 9

1.5 Beampath of one of the NIF beams. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6 Cutaway schematic of the Z-machine’s latest upgrade, now referred to as Z-R.Implosions happen near the axis of this large cylinder. . . . . . . . . . . . . . . . . 11

2.1 Diagram of general structure of a collapsing radiative shock. After an initial tem-perature and density jump at the shock front, radiative cooling causes a decreasein electron temperature (which cools the ions collisionally), and a correspondingincrease in density. The extent of this layer is dictated by energy balance of thesources of energy into and out of this transitional region, or “cooling layer”. . . . 19

2.2 Radiation flow in a thick-thin shock. Radiation at the boundary between theoptically thick upstream region and the transition region must be equal, and atmust equal twice the flux from the transition region at the shock front on the otherside of the transition region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 Photos of the University of Michigan Target Fabrication Center. a) System ismounted on an optics table in clean room to minimize dust and debris on op-tics and in stage mechanics. b) Two sets of coordinate systems aid holding andindependently positioning two pieces during fabrication. . . . . . . . . . . . . . . . 29

3.2 2D schematic of gas-filled target and 3D CAD drawing of target with attachedbacklighter foil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 (a) Metrology photo of target with area backlighter foil attached. Area backlightingis discussed further in section 3.3. (b) Metrology photo of gold grid attached totarget. Note notches on the grid near the target body, that served as spatialindicators. Increasingly large notches were cut farther from the drive surface. (c)Metrology photo of target with no area backlighter attached. . . . . . . . . . . . . 32

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3.4 (a) Diagram of spherical target chamber at the Omega Laser facility. Numberedcircles indicate beams, while larger circles numbered with H, P, and TIM labelsare ports for both fixed and removable diagnostics. (b) Schematic of beam pathsleading through charging banks and into the target chamber. Both images fromthe National Laser Users Facility User’s Guide. . . . . . . . . . . . . . . . . . . . . 34

3.5 Equivalent target plane images of beams spots integrated over a 1-ns pulse width.(a) An unsmoothed spot of a frequency-tripled Omega beam. (b) Beam spotsmoothed with a continuous phase plate. (c) Beam spot smoothed with SSD.From the National Laser Users Facility User’s Guide. . . . . . . . . . . . . . . . . 35

3.6 Xenon transmission spectrum in the range of 3-8 keV and argon spectum in therange of 1-6 keV, as calculated for cold material. . . . . . . . . . . . . . . . . . . . 38

3.7 Diagram of backlit pinhole backlighting setup, not to scale. In the Omega chamber,with the target at target chamber center, the backlighter target was 12 mm fromthe target axis, while the detector was 229 mm from the target axis on the oppositeside, for an image magnification of 20. . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.8 Target schematic for pinhole backlighter target . Measured details for each targetare filled in during fabrication and metrology. . . . . . . . . . . . . . . . . . . . . 41

3.9 Metrology photos of pinholebacklighter targets. a) Face-on view of backlightertarget. The large rectangle is the 5 mm square tantalum substrate. The darksquare seen is a feature on the tantalum, while close inspection shows the 2 mmpolyimide square. The dotted-line crosshairs shown are features of the viewingsystem, and the center of the crosshair is positioned on the 20 µm pinhole. b)XTVS view of backlit pinhole target, imaged in metrology at same angle as one ofthe cameras on Omega when the target is correctly positioned. . . . . . . . . . . . 42

3.10 Cartoon of framing camera components. An x-ray source on the right side of thecartoon shines through a target. The photons then hit a microchannel plate, whichturns x-ray photons into a cascade of electrons. These electrons are then directedonto a phosphor plate via an applied potential, which emits visible photons uponelectron impact. These visible photons are then imaged on film or a CCD camera.The microchannel plate can be coated with a material to increase its gain. Imagecourtesy Eric Harding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.11 Simulation of VISAR fringes from a steady-state target on a streak camera, wheretime is the vertical axis and position is the horizontal axis. Image from Forsman,2001 [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.12 Target setup for use with the VISAR diagnostic. The shock moves from left toright down the main cylinder, while the interferometer beams pass through thearm perpendicular to the main body tube. . . . . . . . . . . . . . . . . . . . . . . . 48

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4.1 a) Data captured by framing camera. Data from a framing camera are recordedon film, then digitized. A wedge file is created to help calibrate scanned exposurelevels to x-ray illumination. b) Calibrated image. Pre-shot metrology measures theposition of features on the target, to give axes in target coordinates. The gold gridshown in images provides not only a vehicle for introducing these features onto adata image, but also provides a reliable way to measure the actual image magnifica-tion. c) Data smoothed over a resolution element. Source-limited resolution limitsthe level at which useful data can be gathered. By smoothing over a resolutionelement, we remove small variations due to noise from the data image. d) Imagewith background variations subtracted out. Image is smoothed over a large fractionof the image, so only large scale variations remain, and then subtracted from theoriginal image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.2 Diagram of source limited resolution. Smear from photons passing through the samepart of the target but hitting different parts of the detector is calculated using thesize of the pinhole source and similar triangles. The extent of the smear on thedetector is then divided by the magnification of the image (image distance/objectdistance) to get the size of a source-resolution-limited element in target coordinates. 56

4.3 Single-strip framing camera from a shock driven with a 40 µm beryllium disk. a)t = 10 ns. b) t = 10ns. c) 20 ns. d) 12 ns. . . . . . . . . . . . . . . . . . . . . . . . 58

4.4 Single-strip framing camera from a shock driven with a 40 µm beryllium disk at20 ns after drive beams turn on. a) Image smoothed over a resolution element. b)Image background smoothed and subtracted. This piece of data is also displayedin Figure 4.3c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.5 Single-strip framing camera from a shock driven with a 20 µm beryllium disk at a)8 ns, b) 10 ns, c) 14 ns, d) 14ns, and e) 15 ns. All of these images show evidenceof some clumpy structure, though in images a and e it is not nearly so pronouncedas the other three images. Image e also shows a relatively curved front comparedto the rest, which have more planar structure. . . . . . . . . . . . . . . . . . . . . . 60

4.6 Plot of shock from 20 µm beryllium driver. a) Calibrated data smoothed over aresolution element. While the collapsed layer is visible, the contrast in the image ispoor, and features in the shock are not clearly defined. b) Image smoothed over 250µm, subtracted from original image, then once again smoothed over a resolutionelement. Not only is the collapsed layer more clearly defined, but some structureemerges on the back side of the dense layer, as well as possibly repeating structurenear the top of the front side of the shock, across from features on the backside.For comparison, the large white pixels are dead pixels smoothed to a source-limitedresolution element, which is smaller than the structure observed. . . . . . . . . . . 61

4.7 Single-strip framing camera from a shock driven with a 10 µm beryllium disk.a) Data smoothed over a resolution element. b) Smoothed data was large scalevariations subtracted out, showing more structure on both sides of the collapsedlayer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.8 Single-strip framing camera from a shock driven in xenon gas with a 80 µm poly-imide drive disk. This image shows only part of the shock, as the diagnostic wastimed too early. The shock is just entering the field of view of this diagnostic. Theshock is also obscured by a bright stripe across the image, which is from interferencefrom another diagnostic. This is described further in the Dual Radiography section. 63

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4.9 Raw four-strip framing camera data for a shock in argon at 12 ns, launched with a50 µm beryllium drive disk. This particular image was backlit using x-rays from L-shell transitions of tin. While grid features are visible, target walls are not, makingit difficult to confirm radial position of the shock. On this image, only four frameshave any image of the gold grid, and only one has a grid edge, the position of whichwas measured in metrology. Each strip is delayed 200 ps, with time beginning atthe upper-left corner. Within each strip, each cell is delayed by 60 ps. . . . . . . . 65

4.10 Blow-up of one cell of four-strip framing camera data from August, 2002, shown inFigure 4.9. This cell is in the second column, first row as measured from the lowerleft corner of the image, at time t = 12.4 ns. . . . . . . . . . . . . . . . . . . . . . 66

4.11 Raw four-strip framing camera data for a shock in xenon at 18 ns, launched with a50 µm beryllium drive disk. This particular image was backlit with a material moresuited to a shock in argon gas, but shock features are still visible, if not optimal.While grid features are visible, target walls are not, making it difficult to confirmradial position of the shock. All frames image the shock and the grid. . . . . . . . 67

4.12 Blow-up of one cell of the four-strip framing camera data from December, 2002,shown in Figure 4.11. This cell, in the second column, second row as measuredfrom the lower left corner of the image, at time t = 18.4 ns . . . . . . . . . . . . . 68

4.13 Raw four-strip framing camera data for a shock in xenon at 13 ns, launched with a80 µm plastic driver. Unlike previous four-strip framing camera data, one wall ofthe tube is visible in this image, as is trailing xenon gas along the wall. The otherwall is obscured by a grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.14 Blow-up of one cell of the four-strip framing camera data from April, 2004, shown inFigure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadiumsource. This cell, in the fourth column, second row as measured from the lower leftcorner of the image, at time t = 13.4 ns . . . . . . . . . . . . . . . . . . . . . . . . 70

4.15 Raw four-strip framing camera data for a shock in xenon at 15 ns, launched witha 40 µm beryllium driver. One wall of the tube is visible in this image, but theplacement of the shock on the image cuts out any possible traces of xenon trailingalong the wall of the tube. The other wall is obscured by a grid. . . . . . . . . . . 71

4.16 Blow-up of one cell of the four-strip framing camera data from April, 2004, shown inFigure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadiumsource. This cell, in the fourth column, second row as measured from the lower leftcorner of the image, at time t = 15.4 ns . . . . . . . . . . . . . . . . . . . . . . . . 72

4.17 CAD drawing of dual radiography setup. Pinhole and area backlighters were 80 or100 degrees apart, imaging areas of the tube separated by approximately 1 mm atdifferent times relative to the drive beam pulse. . . . . . . . . . . . . . . . . . . . . 73

4.18 Raw single-strip framing camera data, washed out by high-energy noise. Noticesignal outside of the active area of the microchannel plate. The bright strip presentin the center of this image was present on other pieces of single-strip framing cameradata taken in the dual radiography setup. On some pieces of data that were washedout, a faint image of the grid on the target is still visible. . . . . . . . . . . . . . . 74

4.19 Unusual data. This data was recorded 9 ns after the drive beams turned on, anddoes not show the normal thin, dense layer of xenon showed in most data images. . 75

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4.20 Unusual data. This piece of data showed an exaggerated tilt of the collapsed layerfrom the target axis. Dotted lines show the deviation to be about 10 degrees. . . . 76

4.21 Target for experiments using the VISAR diagnostic. Arms through the radius ofthe target were capped on one end with a quartz window, and on the other with acoated mirror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.22 Representative piece of VISAR data. Note the fringes from the interferometercease before the drive beams turn off. Also note late time signal with no fringes,corresponding to the passage of the shock through the VISAR path. . . . . . . . . 78

4.23 Only VISAR data which showed any fringe shift. The total signal length wasapproximately 2 ns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.1 Darkest radiographic image and horizontal lineouts showing intensity. a) Shot40706, taken at t = 20 ns with a 40 µm thick drive disk. This piece of data had thelowest relative intensity measurement taken. b) Horizontal lineout of the the shock.The lineout is taken over the center 400 µm of the shock, with the x-coordinategiven in the figure. c) Horizontal lineout of the grid. The lineout is taken over 60µm. The valleys of the grid wires in the image are not well resolved, as shown bythe lack of a flat feature at the lowest transmission point. . . . . . . . . . . . . . . 82

5.2 Two images showing shot to shot variability in the data, taken at 10 ns ± 0.25 ns.Sources of the variability are discussed in the text. a) Shot number 37033, using a38 µm drive disk. b) Shot number 37034, using a 44 µm drive disk. . . . . . . . . . 84

5.3 Plot of position data from experiments using 20 and 40 µm thick drive disks, andfrom simulations of those experiments using a 1D radiation hydrodynamics codeHYADES. The simulations overestimate the shock position for both drive diskthicknesses, seemingly from an error in the first few nanoseconds of the experiment.The experimental data also hints that at a late times the shock may slow, possiblyfrom the loss of a significant driving force from the beryllium piston. . . . . . . . 85

5.4 Plot of imaged thickness of dense collapsed xenon as a function of the distance theshock has traveled. Data are shown as points, with the position error bar fromuncertainty estimates from metrology, and the thickness error bar from uncertaintyfrom the density at which the collapsed layer “begins”. Though the data shows ageneral trend towards thicker shocks as more ground is covered by the shock, thismeasurement is highly susceptible to overestimating the thickness of the shock dueto slight departures from perfect side-on imaging. Note that only one data pointlies on the simulation curve, and the rest for both drive disk thicknesses lie wellabove. This effect is some combination of imaging a tilted shock and radiationtreatment in Hyades, discussed in the next chapter. . . . . . . . . . . . . . . . . . . 87

5.5 Images of shock from shot 39927, t = 14.6 ns launched with a 20 µm berylliumdriver. a) Calibrated data smoothed over a resolution element. b) Image smoothedover 200 µm, subtracted from original image, then once again smoothed over aresolution element. c) Image smoothed over 100 µm, subtracted from originalimage, then once again smoothed over a resolution element. Notice how smoothingover a shorter distance emphasizes the darkest parts of the shock, showing that theshock image is actually somewhat knotted. . . . . . . . . . . . . . . . . . . . . . . 89

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5.6 Images of shock from shot 38983, t = 15 ns using a 20 µm beryllium driver. a)Calibrated data smoothed over a resolution element. b) Image smoothed over200 µm, subtracted from the original image, and smoothed over a source-limitedresolution element. Smoothing in this image seems to enhance the contrast betweenthe shock and the surrounded gas. Structure emerges in the smoothed image, aswell, on both the front and back sides of the image. These structures are larger thana source-limited resolution element. The white pixel near the top edge of the shockis a dead pixel smoothed over a resolution element, showing the size comparison. . 90

5.7 Images of shock from shot 39925, t = 4 ns using a 10 µm beryllium driver. a)Calibrated data smoothed over a resolution element. b) Image smoothed over200 µm, subtracted from the original image, and smoothed over a source-limitedresolution element. In these images, the light and dark diagonal stripes are scratcheson the film. While some structure emerges in the smoothed image, the front sideof the shock is obscured by a scratch. . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.8 Images of shock from shot 40706, t = 20 using a 40 µm beryllium driver. a)Calibrated data smoothed over a resolution element. b) Image smoothed over200 µm, subtracted from the original image, and smoothed over a source-limitedresolution element. This image shows quite a bit of structure, and shows the largestfeatures on the front side of the shock. . . . . . . . . . . . . . . . . . . . . . . . . 92

6.1 2D diagram of the target used in the Thomson scattering measurement of the drivenradiative shock. It is very similar to the target discussed for earlier experiments,with an extra arm and inlet and outlet holes for the probe beam and scattered lightdiagnostic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.2 Metrology photos of targets used in Thomson scattering experiments. . . . . . . . . 99

6.3 Streak camera image of collected scattered light data from TS experiment. Early intime, the detector captures light from the destroyer beam blowing off the cover onthe target that points towards the collection diagnostic, which then fades. A shorttime later, the characteristic two-peaked spectrum of collective Thomson-scatteringbehavior appears. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.4 Results from atomic models, giving Z and ZTe as a function of Te. . . . . . . . . . 105

6.5 Best fit and error bars to Thomson scattered data. a) Lineout from data (purple)and best fit to data (black), with Ti = 300 eV, Te = 250 eV, and Z = 13.7, basedon average atom model. b) Lineout (purple, solid) and Te error bars from fluidlimit. Dashed line is Ti = 300 eV, Te = 285 eV, Z = 14.2. Dotted line is Ti = 300eV, Te = 215 eV, Z = 13.2. These lines obviously lie well outside the lineout of thedata. c) Lineout (purple, solid) and Ti error bars from fitting the data. Dashedline is Ti = 500 eV, Te = 250 eV, and Z = 13.7, while the minimum of the iontemperature is the same as the minimum of the electron temperature. That curvedoes not lie significantly outside the data points. . . . . . . . . . . . . . . . . . . . 106

7.1 Two 1D hyades simulations of density. The solid line shows the density profileof a beryllium-driven shock in xenon using a multigroup treatment of radiation.The vertical line shows the boundary between these two materials, with the xenonfeature being the rightmost dense feature. The dashed line shows the same ex-perimental setup in a Hyades run with radiation transport turned off. Again, thevertical line shows the boundary between the driving beryllium plasma and thexenon plasma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

xii

7.2 Profile of radiatively collapsed layer in xenon gas. This simulation was done with a20 µm beryllium drive disk in 1.1 ATM of xenon. The solid line is mass density, thedashed line is ion temperature, and the dotted line is electron temperature. Thespike in ion temperature marks the position of the shock front. . . . . . . . . . . . 114

7.3 Formation of a collapsed shock in the first few nanoseconds after the drive beamsturn on. Note the different peak density of collapsed plasma, which is the rightmostdense feature for each plotted curve. . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.4 Density profiles from multigroup simulation at three times for a shock launchedwith a 40 µm drive disk. Note that as the shock moves farther, the thickness of theshock increases, and the maximum density decreases slightly. . . . . . . . . . . . . 116

7.5 Density profiles from three multigroup simulations at the same time, 10 ns afterthe drive beams turn on. Each simulation used a different thickness of drive disk,pictured from left to right on the plot, 40 µm, 20 µm, and 10 µm. . . . . . . . . . 119

7.6 a) Density and b) velocity profiles at 6, 12, 18, and 24 ns after the drive lasers turnon for an experiment using a 20 µm thick beryllium drive disk. . . . . . . . . . . . 120

7.7 Density simulation in two dimensions using the FCI-2 code at 8 ns after the drivebeams turn on. The shock moves from left to right. The leftmost dense feature isthe beryllium pusher, separated by a low-density region from the rightmost densexenon feature. The coloring of the graph reflects the density expressed in units ofthe initial xenon gas density. Peak compression of the xenon gas is 45 times overinitial density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.8 a) FCI-2 density profile at 8ns, shown also in Figure 7.7. b) Simulated radiographfrom data in that 2D density profile. This simulated radiograph shows an imageof the collapsed xenon layer slightly thicker than that shown in the simulation,approximately 50 µm thick. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.9 Data points are experimentally measured positions of the beryllium/xenon inter-face for experiments using a 20 µm thick drive disk. The lines represent interfacepositions in simulations with full laser intensity and scaled laser intensities. Thelaser intensity must be reduced by approximately 25% to match the data. . . . . . 127

7.10 Simulations of laser driven beryllium into 0.006 g/cm3 helium gas. These simula-tions are identical to simulations done of the experimental setup described, exceptusing a weakly radiating fluid. Solid lines are simulations with diffusive multigroupradiative transport, while the dotted lines are simulations with radiation artificiallysuppressed. Note the marked difference in the density profile of the beryllium at10 ns between the two simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7.11 Multigroup simulations of a beryllium disk driven into xenon (solid lines) and he-lium (dashed lines). At 2.5 ns, the difference in the beryllium structure and interfaceposition between the two simulations is minimal. By 10 ns, the difference in thestructure of the beryllium is quite different. At this time, the beryllium/xenoninterface has moved 250 µm further than the beryllium/helium interface. Theberyllium in the xenon simulation at this time also has significantly more materialto the right of the density peak, suggesting flow of beryllium ablated by the xenonradiation source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

xiii

7.12 Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM(1 mg/cm3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.13 Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM(1 mg/cm3), showing mass density, ion temperature, and electron temperature. . . 134

8.1 Optical depth and mass profiles from 1D simulation of the supernova explosion of1987a Most of the mass is within the inner 350 zones. Optical depth is calculatedfrom the surface (zone 500) inward, and 22 zones are at an optical depth less than1. The rise in optical depth in zone 40 marks the location of the shock front. FromEnsman and Burrows, 1992. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

8.2 Temperature and mass density profiles from (a) Ensman and Burrows, 1992 and(b) 1D radhydro simulations of driven radiative shock experiment in xenon. Whilethe scales are different, both the density and temperature profiles are qualitativelysimilar. Note the spike in temperature, followed by rapid cooling and a significantincrease in the density in a thin layer. This similarity will last until the supernovashock moves into a regime where the material behind the shock becomes opticallythin, farther away from the exploding star. . . . . . . . . . . . . . . . . . . . . . . . 141

8.3 Shock structure from computational analysis of a radiative shock in a stellar atmo-sphere. The solid line structure was adopted for analysis of the temperature anddensity structure in the radiative wake. From Fokin et. al, 2004. . . . . . . . . . . 142

8.4 Temperature, mean molecular weight, and mass density profile of a stationaryshock in a stellar atmosphere. The x-axis is the distance from the shock front. Thevertical line marks a change in scale, as quantities change more slowly farther fromthe shock front. From Fokin et. al, 2004. . . . . . . . . . . . . . . . . . . . . . . . . 143

8.5 Effect on cooling rates from different contributions. This log plot gives both heatingand cooling of the system, with zero on the y-scale corresponding to no heating orcooling. From Fokin et. al, 2004. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

8.6 Calculated cooling rate from experiment in xenon. Radiation was assumed to bethermal radiation from the cooling layer in the shocked plasma. This plot is insimilar units to the cooling rate of Fokin, with cooling rates reported as negative.a) Cooling profile of most of the experiment, including beryllium driver. b) Coolingprofile of just xenon, near the shock front. . . . . . . . . . . . . . . . . . . . . . . 145

8.7 Targets for new generation of radiative shock experiments. Targets are gas tightwith view up the back end of the target into cylinder. A large acrylic shield withgold wedges facing the diagnostics surrounds the drive surface. a) Three-D CADimage of target. b) Shadowed image of target prototype roughly positioned in theOmega chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

xiv

LIST OF TABLES

Table

2.1 Comparison of experimental quantities in Reighard et al. and other recent radiationhydrodynamics research. Reighard et al. produces the fastest, hottest shock in thehighest density xenon gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1 Target feature tolerances as a function of shot day. Items listed as unknown wereeither not measured (if built at U. MI) or had no measured details on the documentaccompanying finished targets (if built at LLNL). . . . . . . . . . . . . . . . . . . . 34

C.1 Table of facility setup at the Omega laser facility for each shot day. . . . . . . . . . 163

C.2 Summary of all shots taken on the August, 2005 shot day. See table of acronymsfor more details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

C.3 Summary of all shots taken on the May, 2005 shot day. See table of acronyms formore details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

C.4 Summary of all shots taken on the February, 2005 shot day. See table of acronymsfor more details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

C.5 Summary of all shots taken on the August, 2004 shot day. Much of the data onthis shot day were victim to dual radiography washout (see Chapter Four). Seetable of acronyms for more details. . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

C.6 Summary of all shots taken on the April, 2004 shot day. Much of the data on thisshot day were victim to dual radiography washout (see Chapter Four). See tableof acronyms for more details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

C.7 Summary of all shots taken on the November, 2003 shot day. This shot day pro-duced no usable data. See table of acronyms for more details. . . . . . . . . . . . . 169

C.8 Summary of all shots taken on the July, 2003 shot day. This shot day produced nousable data, and was the first day that used University of Michigan. See table ofacronyms for more details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

C.9 Summary of all shots taken on the December, 2002 shot day. Though the fill gaswas xenon on this day, a tin backlighter was used. See table of acronyms for moredetails. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

C.10 Summary of all shots taken on the August, 2002 shot day. This was the first shotday for the radiative gas experiments. Laser energy information both in an onlinearchive and personal notes is unavailable. See table of acronyms for more details. . 172

xv

C.11 Target feature tolerances as a function of shot day. Items listed as unknown wereeither not measured (if built at U. MI) or had no measured details on the documentaccompanying finished targets (if built at LLNL). . . . . . . . . . . . . . . . . . . . 173

C.12 Acronyms used to describe radiative shock experiments, both in the above tablesand in the text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

xvi

LIST OF APPENDICES

Appendix

A. “Observation of collapsing radiative shocks in laboratory experiments,” [43]. . . . . 151

B. “Thomson scatttering from a shock front,” [44]. . . . . . . . . . . . . . . . . . . . . . 157

C. Shot data, diagnostics, and metrology tolerances . . . . . . . . . . . . . . . . . . . . . 161

xvii

CHAPTER I

Introduction

With the development of lasers to advance fusion technology, a tool became ac-

cessible with which to take a step beyond observation of stars, and move to creating

controlled experiments with ramifications for astrophysical systems. The types of ex-

periments capable of extending our understanding of the most dynamic and energetic

processes in the universe are getting broader at a rapid pace.

This thesis involves physics in the specific subfield of high energy density physics,

with an eye towards future applications to laboratory astrophysics. High-energy-

density laboratory astrophysics is a relatively new field, using the tools of plasma

physics and fusion energy studies to understand astrophysics problems in the high-

energy-density regime. This first chapter will provide a general introduction to high-

energy-density physics, present some examples of high-energy-density astrophysical

phenomena, and list some of the tools used to address the specific field of high-

energy-density physics. The second chapter will treat the physics of radiation hy-

drodynamics, including a causal explanation of the formation of a radiative cooling

layer and collapsed shock. We will describe the experiment setup, the laser facility,

target fabrication, and diagnostics used in Chapter Three. The fourth chapter cov-

ers results from experiments, while Chapter Five focuses on analysis of radiographic

1

2

data. An additional experiment using Thomson scattering techniques is described

in Chapter Six. Chapter Seven is devoted to discussion of simulation work in one-

and two-dimensional radiation hydrodynamic codes done for this experiment. In

Chapter Eight, we discuss the conclusions we can make from this experiment, draw

attention to astrophysical systems with similar optical depth profiles, and discuss

the experiment’s future in upcoming campaigns.

1.1 High-Energy-Density Physics

High-energy-density (HED) physics is defined as the physics that happens at

pressures greater than 1 million atmospheres, usually involving shock waves moving

through a medium over a wide range of densities. In different units, this is a pressure

of 1 Mbar, 1011 Pascals (N/m3), or 1012 ergs/cm3. The preferred unit in this field

and this thesis is a Mbar, where 1 bar = 1 ATM.

In these high-pressure systems, which are often also marked by high temperature

and/or high density, the material in question is ionized, and therefore does not behave

like an ensemble of neutral particles. By high density, I am referring to densities that

can be much higher than those covered by traditional plasma theory. These densities

can reach a few times solid density, on the order of 1 g/cm3. By high temperature,

I’m referring to temperatures as high as several kilo-electron volts (keV). At these

temperatures, even low-density material can support pressures of 1 Mbar.

1.2 A Brief History of HED physics

One of the first paths of high-energy-density physics research pursued simulation

and understanding of the nuclear bombs tested in the United States in the 1940s.

While the physics that happened in those explosions was most certainly in the high-

energy-density regime, the focus in these tests was not a controlled scientific exper-

3

iment. Adding control and diagnosis to the creation of high-energy-density systems

happened decades later. While work began towards fusion and high-energy-density

experiments in the 1970s, it was not until the 1980s that many of the modern diag-

nostics were capable of recording relevant information (such as images, time histories,

or spectra) on a sub-nanosecond timescale. This decade also saw the advent of facil-

ities with independently controlled and timed lasers, a crucial component in many

modern HED experiments [13]. A more complete review of radiation hydrodynamics

experiments is given in Chapter Two.

1.3 Laboratory Astrophysics

In the mid-1990s, high-energy-density physicists begin to turn their attention to

astrophysical problems. At the first “Workshop on Laboratory Astrophysics Exper-

iments with Large Lasers” in 1996 hosted by Lawrence Livermore National Lab-

oratory, astrophysicists weighed in on the areas that could benefit from controlled,

scaled experiments. At about this time, a wealth of x-ray data was imminent from the

Chandra satellite, probing phenomena where hydrodynamic quantities were affected

by radiation transport. From this, among other things, astrophysicists asked for

more controlled experiments involving radiation hydrodynamics. Study of radiation

hydrodynamics in a controlled environment would aid in both basic understanding

of radiation hydrodynamics (rarely seen and not much studied in Earth-based sys-

tems), and give a benchmark as more and better radiation treatment was added

to astrophysics codes. Challenges associated with meeting these scientific needs are

discussed in Chapter Two and briefly in Chapter Eight.

This request is not unusual, when one considers how many astrophysical systems

involve radiation hydrodynamic phenomena. High powered explosions, fast shock

4

waves, and low astrophysical densities make it easy for radiation to play a significant

factor in the heating, cooling, and dynamics of an astrophysical system.

For example, old supernova remnants like the Cygnus Loop, shown in Figure

1.1, can radiatively collapse into a thin shell, making them susceptible to thin-shell

instabilities, which is one possible origin of clumpy, irregular structure in supernova

remnants.

Figure 1.1: Hubble Space Telescope picture of the Cyngus Loop. False coloring shows differentmetal line emissions. Credit: NASA, HST, Jeff Hester.

Astrophysical jets at high speeds can cool significantly through radiation. This

cooling lowers their internal pressure and causes increased compression along the axis

of the jet, resulting in increased density and collimation of the jet. This phenomenon

is generally seen in high mach-number jets, which have flow speeds much larger than

their internal sound speed.

Supernova explosions also go through a radiation hydrodynamic phase at least

until the shock breaks out of the denser layers of the star. Of specific relevance here,

a simulation of shock breakout in SN 1987a shows the formation of a radiatively

5

collapsed shock [17] This and other relevant examples are discussed in Chapter Eight.

Figure 1.2: Hubble Space Telescope image of SN 1987a, taken in 2003 with WFPC2. Here, a ringof circumstellar material lights up as the shockwave driven by the explosion heats it.Image credit: NASA and R. Kirshner.

An obvious problem exists to the unschooled observer: the evolution of astro-

physical phenomena often involve vast distances, large total masses, and long time

scales. Making exact replicas of these systems is impossible, even if the power were

available in advanced facilities.

Fortunately, it is not necessary to replicate a system in its full size and scope

to study one a specific part of the phenomenon. As shown in Ryutov (1999) [45],

equations describing the hydrodynamic evolution of a system can be scaled in space

and time if radiation flux, viscosity, and heat flow can be neglected. Therefore,

studying a specific phase or part of an astrophysical object or event can be possible

on smaller length scales and shorter time scales if other factors are scaled as well.

When radiation flux becomes important, this scaling becomes complicated. While

exact comparison to an astrophysical system is no longer possible, meaningful com-

parisons are still possible. In these systems, comparison of the optical depth structure

reveals systems that can be described by similar physics. If the optical depth profile

6

of two systems is similar, radiation should have similar effects in each. The other

important parameter is the appropriately normalized rate of radiative emission. In

the present context this is related to the strength of the shock wave. This is discussed

in further detail in Chapter Two.

1.4 Tools of the Trade: High-Energy-Density Facilities

Though the scope and scale of these experiments can be many orders of magni-

tude smaller than their astrophysical counterparts, it still takes impressive facilities

to generate the power and intensity needed to create megabars of pressure in a con-

trolled environment. So before we discuss the physics involved in these experiments,

let us briefly review some of the facilities available for high-energy-density physics

experiments.

Most of the laser facilities listed below focus on the study of laser-driven fusion.

This problem is approached in two ways: direct drive and indirect drive. Direct drive

laser fusion involves irradiating a spherical capsule directly. This direct irradiation

causes the capsule to implode, creating the compression needed to cause the internal

fuel to ignite and burn. This method is hampered by the growth of non-spherical

structure through hydrodynamic instabilities, which reduces the energy gain. Indi-

rect drive laser fusion focuses the laser energy on a high-Z cylinder (usually gold).

A spherical, fuel-containing capsule is placed at the center of this cylinder. The

lasers heat the cylinder (called a hohlraum), which then emits radiation that com-

presses the target. This method creates fewer instabilities than direct drive, but is

less efficient.

7

1.4.1 High-powered laser facilities

Laboratory for Laser Energetics and the Omega laser facility

The Omega laser facility at the University of Rochester is a 60 beam neodynium:glass

laser, operating at λ = 351 nm. It is capable of delivering a total of 30 kJ at 30

terawatts of power using all 60 beams, which are oriented symmetrically around the

target chamber. Omega was designed to implode inertial fusion targets via direct

drive, where lasers directly implode a caspsule [5].

Recently, work has begun to add a high-energy pettawatt laser system next to

the main Omega laser system. The Omega EP (extended performance) laser will

add two short pulse beams (pulse lengths of 10-100 ps), with energy of 2.6 kJ/beam.

These beams can provide focused intensities of up to 6 ×1020 W/cm2 for fast ignition

experiments and ultrafast backlighting.

Naval Research Laboratory and the Nike, Electra and FTF laser facilities

The Nike facility at the Naval Research Laboratory is a KrF eximer laser facility

(λ = 248 nm), delivering several (3-4) kJ of energy to a target in 56 beams. The

Nike laser was designed for testing of hydrodynamic behavior relevant to direct-drive

fusion targets, and boasts a very uniform beam spot; this is ideal for fusion targets,

in which a hot spot on the beam can severely limit the efficiency of the compression.

The 700 J Electra facility at the Naval Research Laboratory is a testbed for high-

repetition rate laser technology. It has been successfully tested for operation at 5 Hz

for several thousand shots, and for longer duration at lower repetition rates. High

repetition rates are vital to the application of fusion power to power plants.

The Naval Research Laboratory has also proposed the building of a high-repetition-

rate KrF facility for direct drive fusion (where fusion fuel capsules are irradiated

directly with the lasers), with the hopes of using it as the first fusion power plant,

8

Figure 1.3: Diagram of the planned laser facility at the Naval Research Laboratory in Washington,D.C

9

called the Fusion Test Facility, or FTF [42]. This facility would have a 5 Hz repetition

rate, and would be dedicated to creating the maximum amount of fusion power with

minimum laser power requirements. This is the first facility to focus on creating a

commercial-grade fusion power plant.

Lawrence Livermore National Laboratory and the National Ignition Facility

The National Ignition Facility (NIF) at Lawrence Livermore National Laboratory

is the newest addition to this set of facilities. Though it is not yet fully operational,

with 192 lasers, the facility hopes to achieve 1 MJ of UV light on target by FY

2008 [25]. Delivering 500 terawatts of power to millimeter scale fusion targets, NIF

will be capable of both direct and indirect drive fusion experiments, and help forge

new paths into research of processes applicable to astrophysics. The technological

advances required to complete this facility at a reasonable cost were numerous, and

tested on prototype of four lasers called “Beamlet” in the early parts of this decade.

Figure 1.4: Outside of the NIF target chamber. Square protrusions are where bundles of fourbeams, called quads, will enter the target chamber.

10

Figure 1.5: Beampath of one of the NIF beams.

Laser MegaJoule and LULI

CEA in France is also building a very large laser facility in Bordeaux, call Laser

MegaJoule, or “LMJ”, which will be just about as large and powerful as the NIF

facility at LLNL. It is currently under construction, and expected to be finished

in 2010. It will have 240 lasers, and is designed to deliver 1.8 MJ of UV light on

target [9]. The eight-beam cluster “Ligne D’Integration Laser”, or “LIL” became

operational in 2003 to test the technology developed for this facility.

Currently in operation in France is the Laboratoire pour l’Utilisation des Lasers

Intenses, or “LULI” facility. This facility has two laser beams delivering a total of

2 kJ of UV light to a target. There is also an ultrafast laser facility housed here,

delivering 30 J in 0.3 ps in its main laser, with other, short-pulse lasers that are less

energetic. These lower-energy beams are used for diagnostics.

1.4.2 Z-pinches

The Z-machine at Sandia National Laboratory in Albuquerque is unique on this

list in that it is not a laser, but a Z-pinch machine. Running currents through

parallel wires forces them to implode, leading to stagnation on the cylindrical axis or

delivering an impact to a target situated inside of the wire cluster. The Z-machine

can produce 1.8 MJ of x-rays and draws tens of MA of current. In 2003 it became the

first Z-pinch facility to create and diagnose the production of thermonuclear fusion

11

neutrons from the implosion of fuel within a hohlraum. At the time of this writing,

it is currently undergoing an upgrade aimed at delivering even higher currents and

voltages ([38]). Other Z-pinches are located at Cornell University in Ithaca, NY,

Imperial College in the UK, and University of Nevada, Reno.

Figure 1.6: Cutaway schematic of the Z-machine’s latest upgrade, now referred to as Z-R. Implo-sions happen near the axis of this large cylinder.

1.4.3 Petawatt Lasers

As ultrafast lasers are built with higher energy output, the power output in short

pulses also increases. It is possible to generate petawatts or terawatts of power for

a few picoseconds or femtoseconds. This leads to very high intensities, up to 1022

W/cm2, with these short pulse lasers. With this capability, one can study even

relativistic phenomena in the high-energy-density regime. Ultrafast lasers capable

of creating these conditions include those located in facilities at the University of

Michigan Center for Ultrafast Optical Science (CUOS), at Los Alamos National

Laboratory, Lawrence Livermore National Laboratory, the University of Texas at

Austin [12], and other sites around the world.

CHAPTER II

Radiation Hydrodynamics

It is notoriously difficult to achieve controlled radiation hydrodynamic conditions.

Facilities are required to deliver a high laser irradiance or x-ray flux to a small target;

enough energy must be present to heat moderate density material to tens of eV.

This must also happen in a system with sufficient optical depth for radiation and

matter to interact. If radiation does not significantly affect the system, usually by

heating or cooling in laboratory systems, then the system can be treated with purely

hydrodynamic equations.

Some of the facilities capable of creating these conditions were listed in the Intro-

duction, and the facility used for the experiment that was the focus of this dissertation

research, the Omega Laser facility, is described in more detail in the Experimental

Methods chapter.

The radiative hydrodynamic experiments presented in the next chapters focus on

creating a radiatively collapsed shock by launching a piston into a gas-filled target.

This launches a shock fast enough and hot enough to begin to radiate away its energy.

To understand this system and how it differs from purely hydrodynamic systems, let

us look at the equations that govern hydrodynamic shocks, and then explore how

the inclusion of radiative effects alters them. This leads to a discussion of how to

12

13

scale laboratory radiative shocks to astrophysical ones.

2.1 Single-Fluid Euler Equations

If the mean free path of a particle in a gas is much smaller than the size of the

system of particles, it makes sense to treat the system as a fluid, with fluid elements

that are much larger than a mean free path of a particle, but much smaller than the

system size.

The single fluid Euler equations follow by taking moments of the Boltzmann

Equation, and describe the conservation of mass, momentum, and energy of a fluid:

(2.1a)∂ρ

∂t+∇ · (ρu) = 0,

(2.1b) ρ(∂u

∂t+ u · ∇u) = −∇p,

(2.1c)∂

∂t

(ρε +

ρu2

2

)= −∇ ·

[ρu

(ε +

u2

2

)+ pu

],

where ρ is density, u is velocity, p is scalar pressure, and ε is specific internal energy.

The energy equation here is expressed in conservative form.

These equations are valid in the regime where the viscosity is low, as is the heat

conduction, along with the contribution of the radiative flux to the dynamics. These

equations admit disturbances in pressure, density,and velocity (and implicitly, tem-

perature) as solutions. When such disturbances move faster than the sound speed

(c2s = γp/ρ for a polytropic gas), these quantities can become discontinuous, forming

a shock wave. Let’s describe how to modify these equations to account for significant

effects from radiation.

2.2 The Equation of Radiative Transfer and Radiative Hydrodynamics

Though megabar material pressures are impressive, there can be one other source

of significant dynamic influence in high-energy density systems. As temperatures

14

increase in these systems, the radiative flux σT 4 becomes comparable to the material

energy flux, and we must consider how the first moment of the equation of radiative

transfer begins to factor into our equations. One form of the radiative transfer

equation is:

(2.2)

[1

c

∂

∂t+

∂

∂s

]Iν(x, t,n, ν) = ην(x, t,n, ν)− χν(x, t,n, ν)Iν(x, t,n, ν),

where ds is the length of a path element, Iν is the mean spectral intensity, which

is the energy radiated per unit time-frequency-area-solid angle, in a direction n, ην

is the total spectral emissivity (which includes the effects of both absorption and

scattering) , and χν is the total opacity.

In these equations, we consider only non-relativistic systems, as in this limit the

contribution of the radiation to the Euler equations is relatively simple. In this limit,

the contribution of momentum of the system by radiation is negligible. With the

exception of some petawatt lasers, this is true of the regimes accessed by all the

currently available laser user facilities mentioned in the previous chapter. We need

not count photons in the mass continuity equation, so Equ. 2.1a remains unchanged.

The momentum equation (Equ. 2.1b) becomes

(2.3) ρ(∂u

∂t+ u · ∇u) = −∇(p + prad),

where prad is the radiation pressure in the system,

(2.4) prad =4σ

3cT 4,

and is included for completeness.

If the radiation were not isotropic, one might need to include a pressure tensor

term instead of a scalar. In this regime, the most important quantity is the magnitude

of the radiative flux, Frad, as a term in the energy conservation equation. This

15

quantity is not affected by whether the radiation field is isotropic, though the ratio

of radiative flux to radiative pressure may be affected by the isotropicness of the

field. Additional forces, such as gravity, would contribute terms on the right-hand

side of this equation. To modify the energy equation, we use the conservative form

of the energy equation (equation 2.1c), and continue to neglect viscosity. Adding

in contributions from the radiative pressure, flux, and energy density, but excluding

outside sources of heat,

(2.5)

∂

∂t

(ρu2

2+ ρε + Erad

)+∇ ·

[ρu

(ε +

u2

2

)+ (Erad + p + prad)u

]= −∇ · (Frad) ,

where Erad is the radiation energy density, prad is the radiation pressure, and Frad is

the radiation flux.

2.2.1 Threshold for Radiative Shocks

Without putting any restriction on the dependence of radiation on density and

pressure, we would still like to understand when radiative effects will become im-

portant. It is not yet possible to create systems in the laboratory with significant

radiative pressure, so we will limit our discussion to shocks where radiative flux lev-

els are important. Systems with megabar radiation pressures may be accessible in

the relatively near future by the National Ignition Facility and Laser MegaJoule.

Let us consider a system with a high Mach number shock wave (where the speed of

the shock is more than a few times of the sound speed of the unshocked material).

As will be discussed further later in this chapter, shock waves heat and compress

material, and a faster shock wave means more heating. When the temperature in a

system increases, the blackbody radiation a system would have if it were optically

thick increases faster than the energy flux carried into the shock by the material.

16

Let us consider the ratio of the energy flux lost to radiation in an optically thick

system at the immediate postshock temperature T to the energy flux carried in by

the material at the shock front:

(2.6) Rrad =σT 4

ρouscvT∝ u5

s

ρo

,

where us is the shock velocity, cv is the specific heat of the gas, and ρo is the density

of the of the unshocked, upstream material. The proportionality is only true for

strong shocks, where

(2.7) kBTi =Amp

1 + Z

(2γ − 1)

(γ + 1)2u2

s.

The ratio in Equ. 2.6 depends on the details of the radiative transport to and in the

cooling region. As Rrad approaches and exceeds 1, the system must adjust to allow

the radiation to escape and cool the post-shock region. As temperature goes up, the

opacity of the material typically goes down. The heated region becomes optically

thin, allowing the radiation to escape. The system can then cool, allowing this ratio

to pass below 1, and then again to become optically thick.

This ratio is only strictly valid for material that is optically thick and radiating in

a continuum. If instead the heated material emits from spectral lines, this ratio would

be somewhat less. In an optically thick system, the intensity of these lines would

become maximum at the blackbody level for that temperature, so many lines would

fill in the blackbody curve. In that case, Rrad would still be valid if the numerator of

the ratio included a quantity that accounted for the fraction of the blackbody curve

filled by emitting lines.

2.2.2 Classification for Meaningful Comparison

While the transition region discussed in section 2.2.1 in all radiative shocks spews

photons in all directions (both upstream and downstream of the shock) from an op-

17

tically thin layer, what happens to those photons depends greatly on the material

on either side of the shock. Therefore, there can be four different types of radiative

shocks, where either region can either be optically thick or optically thin. Exam-

ples of at least three of these types of radiative shocks can be found in astrophysics.

For example, a thick downstream-thick upstream shock could be found inside the

dense layers of a star as a consequence of core collapse. As shocks from core-collapse

supernova emerge into lower-density outer layers of the star and low density circum-

stellar material, the upstream region can become optically thin, and the shock can be

classified as a thick downstream-thin upstream radiative shock. Shocks that emerge

from supernova continue through the circumstellar material, and can evolve back

to radiative shock after behaving as a Taylor-Sedov type blast wave. Surrounded

by diffuse material, these radiative shocks are thin downstream-thin upstream. At

present, this author has no example of a thin downstream-thick upstream shock,

either in astrophysics or in laboratory experiments.

The regime that applies to the experiment discussed in following chapters as

well as to the specific astrophysical systems discussed in Chapter Eight is that of

an optically thick downstream region and optically thin upstream material. In this

regime, a cooling layer can form that loses energy through the optically thin upstream

region, which produces a very thin, dense region we will call a “radiatively collapsed

shock”. This situation applies to the experiment discussed in later chapters, as well

as thick-thin systems that heat electrons via collisions with shock-heated ions.

2.2.3 Formation of a Cooling Layer and a Collapsed Shock

The following explanation describes the experiment that will be discussed further

in the next few chapters. It also describes any collisional system with an optically

thin upstream region and an optically thick downstream region. We assume that the

18

optically thin upstream gas is a uniform plasma with constant initial temperature,

and that most of the radiation entering this region escapes. This type of system

supports a cooling layer, an optically thin transition layer between the upstream and

downstream region. Because the unshocked gas is optically thin, radiation from the

hot, shocked gas can escape, carrying energy flux with it. As the shocked material

cools via radiation, other quantities respond. This can result in a large increase in the

compression of the gas over the cooling layer, as explained further below, which we

call “radiative collapse.” As the material cools and becomes more dense, the material

will become optically thick, and radiation will no longer cool the material efficiently.

Compression of the shocked material will stop and ion and electron temperatures

will level off at some post-shock value, marking the end of the cooling layer. It is

in this way that the structure of the shock is dictated by the cooling layer; as the

layer radiates and heats the upstream gas, the system is being pushed towards a

steady state, where the upstream and downstream layers equilibrate to some final

temperature dictated by the energy output of the cooling layer [13]. Below, we

describe the steps causing radiative collapse in a shocked system which is optically

thin upstream. A cartoon of the general structure of the mass density, electron

temperature, and ion temperature is shown in Figure 2.1.

As a shock moves through a material, it creates a quick jump in pressure, density,

and ion temperature, as it accelerates all material. This happens over the course of

a few ion-ion mean free paths. Though the electrons are also accelerated, they are

heated only slightly, as most of the energy goes into heating the much heavier ions.

Electrons gain energy from collisions with the warm ions, according to

(2.8)∂Tion

∂t= −νie(Tion − Te),

19

Position

den

sity

, tem

per

atu

re

Figure 2.1: Diagram of general structure of a collapsing radiative shock. After an initial tempera-ture and density jump at the shock front, radiative cooling causes a decrease in electrontemperature (which cools the ions collisionally), and a corresponding increase in den-sity. The extent of this layer is dictated by energy balance of the sources of energy intoand out of this transitional region, or “cooling layer”.

where νie is the ion-electron collision rate, given by

(2.9) νie = 3.2× 10−9niZ3 ln Λ

AT 1.5e

for Te in eV and ni in cm−3, where ni is the ion density, Z is the average ionization

state, ln Λ is the Coulomb logarithm, A is the atomic weight of the material, and

Te is the electron temperature. The energy lost from each ion goes into heating (on

average) Z electrons, so the decrease in ion temperature is proportional to in the

increase in electron temperature. Electron and ion temperatures can equilibrate this

way. As electrons get warmer, they are capable of radiating away a more significant

fraction of the energy in the system. The fractional energy radiation rate is given by

νrad;

(2.10) νrad =2Frad

ρdcvT=

2κdρσT 4e

ρdcvT

In the approximation that T = ZTe + Ti = (Z + 1)Te if Te ∼ Ti, which is true

20

after the collisional temperature equilibriation process, the fractional radiation rate

simplifies to

(2.11) ν∗rad = 2.2

A

(Z + 1)κT 3

e

in sec−1 for Te in eV and the specific opacity κ in cm2/g, where A is the atomic

weight of the material in amu.

If collisional electron heating happens quickly, this can be treated as a two-step

process. If electron heating happens more slowly, cooling via radiation can begin

before the ion and electron temperature equilibrate. As the electron temperature

changes via radiation, collisions sap the ion temperature, and both the ions and

electrons cool.

As the system cools, conservation equations must still hold, and other quantities

must adjust in response to the lost energy. The pressure conservation equation is

(2.12) p1(ρ, T ) + ρ1u21 = p2(ρ, T ) + ρ2u

22,

where p = ρRTi from the ideal gas equation. The quantity R is the gas constant,

which is

(2.13) R =(Z + 1)kB

Amp

.

In this equation, Z is the average ionization state, kB is Boltzmann’s constant, A is

the atomic weight of the material, and mp is the mass of a proton. We can use these

conservation equations to predict the effect of radiative loss on compression. Since

the system in question is driven, the pressure is set, and the compression must be

the quantity to respond.

Because the average ionization state Z depends on T , we must estimate it’s be-

havior as a function of Te to estimate the effect of cooling on compression. As a

21

convenient approximation, we can use the Saha equation to get Z as a function of

Te. The Saha equation is only strictly valid in equilibrium systems, as it relies on

detailed balance to estimate level populations, which may not be strictly true in the

experimental system in question. Z from this equation will be designated Zbal, and

is:

(2.14) Zbal = 19.7

√√√√Te

(1 + 0.19 ln

(T

3/2e

n24

))− 1

2

with Te in eV and n24 is the electron density in units of 1024 cm−3. In this system,

equilibration times are shorter than the dominant ionization mechanism, which is by

collisions with electrons.

2.2.4 Energy Balance in a Thick/Thin Shock

Figure 2.2: Radiation flow in a thick-thin shock. Radiation at the boundary between the opticallythick upstream region and the transition region must be equal, and at must equal twicethe flux from the transition region at the shock front on the other side of the transitionregion.

Consideration of the sources of radiation flux at each boundary yields information

about the structure of the shock transition and the extent of the cooling layer. At the

boundary of the downstream region and the cooling layer, the flux from the cooling

layer flowing into the downstream region must balance the blackbody radiation from

the shock-heated gas flowing into the cooling layer. The cooling layer is optically

thin to this radiation, and so at the boundary of the cooling layer at the shock

22

transition, flux is flowing from the cooling layer, as is the blackbody radiation from

the downstream region (see figure 2.2). By noting that at the shock transition

there is no contribution to flux from the upstream region, one can find the inverse

compression just after the shock transition in terms of the final inverse compression:

(2.15)ρo

ρi

=γ − 1

γ + 1+

2γ

γ + 1

ρo

ρf

,

where ρo is the density of matter in the upstream region, ρi is the density of matter

immediately after the shock transition (at the edge of the cooling layer), and ρf is

the density of matter in the downstream region.

The energy supplying the radiated flux comes from the shocked material, and so

the radiation lost from the system must equal the energy flux lost from the cooling

layer. Balancing fluxes results in the final inverse compression of the gas:

(2.16)ρo

ρf

=

√√1 + 8Q− 1

4Q,

where Q = 2u5sσ/(R4ρo), the radiative strength parameter, and R is the gas constant.

This shows that the faster the shock is launched, the greater the compression (ρf/ρo)

of the shocked gas [13].

2.3 A Brief History of Radiation Hydrodynamics Experiments

Extensive work on laser-driven fusion to produce ignition and high gain begin-

ning in the 1970s. Much of the work done in the United States was classified until

the 1990s, at which point certain elements of the laser-driven fusion program were

declassified. A summary of the declassified work is given by John Lindl, first in a

review paper in Physics of Plasmas [35], and then in greater detail in his 1998 book

[36].

“Directly driven” means that lasers are incident on a target capsule with fusion

fuel at its center, and that the laser energy is used to compress the fuel. In contrast,

23

“indirectly-driven” targets have lasers incident on a high-z material surrounding a

target capsule, which creates a radiation source to implode the fusion fuel. Early

calculations predicted that laser energies as low as 1 kJ could achieve energy gains

of larger than unity [41] on a directly driven bare drop of deuterium-tritium fuel,

but that laser energies on the order of 1 MJ would be required for high gain. Later,

simulations showed that instabilities grew at a much higher rate in directly driven

targets than was predicted, and that hot-electron production and reduced laser ab-

sorption also severely hampered successful ignition for lasers in the energy range of

1-100 kJ, and so higher laser energies were required for ignition. Beam quality and

uniformity were also issues for early lasers. The challenge of controlling hot electron

production prompted a move to shorter wavelength lasers.

Hohlraums produce an environment which must be examined using radiation hy-

drodynamics. Successes and failures of early hohlraum experiments shaped fusion

research in the 1980s. Hohlraums designed to scale to larger ignition experiments

were used to assess coupling efficiency, hot electron losses, and parametric instabili-

ties on the largest lasers available, including Nova, Gekko, and Omega. Experiments

assessed the value of using a double-shelled target to increase implosion velocity, and

found that hydrodynamic instabilities were amplified. The need for more complete

diagnosis resulted in extensive research. Advances in laser technology gave higher

quality beams which could sacrifice beam coherence for beam uniformity, and when

coupled with with overlapping beam spots could produce very uniform illumination.

In 1985, experiments on Nova achieved a hohlraum temperature of 200 eV while

maintaining low levels of hot-electron preheat, which refers to heating of the fuel

by hot electrons before the target is shocked and compressed. The experiments

that followed, along with extensive modeling, investigated beam symmetry control,

24

quantitative Rayleigh-Taylor instability studies, pulse shaping benefits, and drive

temperature scaling. Successes in these experiments gave confidence that a larger

laser (1-2 MJ) would have a chance for ignition and modest gain.

Scientists from Germany and Japan also began to study indirectly driven inertial

fusion, using the Gekko XII laser in at the Institute for Laser Engineering in Osaka,

Japan. In the 1990s, these scientists began to publish work on laser-irradiated gold

cavities, which would become hohlraums for indirect-drive fusion experiments. In a

series of papers in 1991 and 1992, R. Sigel and coworkers reported on laser-driven

radiation hydrodynamics experiments in gold cavities on the Gekko XII laser facility

in Osaka, Japan ([48], [49], [40]), and reported initial success creating high levels

of radiation in a gold hohlraum. Work built on that, with scientists measuring the

x-ray re-emission of materials initially heated with hohlraum x-rays ([19], [16]), and

launching high-pressure shocks using hohlraum x-ray sources [37]. These radiation-

cavity-driven targets were fielded on the Nova laser [26], and will be used on the

National Ignition Facility [30].

Experiments using complex targets called “dynamic hohlraums” are currently

being tested on Z-pinch machines. These targets seek to use the smooth radiation

source of a hohlraum in a converging geometry. A cylindrical array of high-Z wires

is imploded onto a low-density foam, with a fuel cell at the center, filled with a low-

density argon gas tracer for diagnostic purposes. This setup uses the radiation from

the high-Z walls as an imploding radiation source. To ensure uniform heating, the

foam must not be optically thick, but must have enough material present to convert

the radiation to thermal energy. This technique has successfully produced hot dense

capsule implosions [4], and measurable neutron yields [32]. Laser-driven dynamic

hohlraum investigations are also underway, where a xenon-filled capsule is directly

25

imploded, launching a radiative shock wave in gas surrounding a central fuel cell in

a spherically converging geometry.

While radiation hydrodynamics played a significant role in the dynamics of these

indirectly driven targets, they did not involve radiative shocks. Laser heating in an

optically thick shell created very warm plasma, but not a fast-moving shock wave.

One can launch a radiative heating wave without launching a radiative shock, as

has been observed in several experiments. Experiments in laser-driven plastic foam

showed the presence of a supersonic heat wave through a radiogram of an ioniza-

tion front [1]. A laser-driven shock experiment in foam which inferred a temperature

profile from K-shell absorption spectra produced significant amounts of radiative pre-

heating [24]. A radiation wave, or Marshak wave [54], was detected diffusing through

a radiatively heated foam that was a few optical depths in extent in experiments by

Back et al. ([3], [2]). Bozier [7] saw evidence of a radiation wave in xenon gas.

Work on radiative shocks in the literature generally focus on one of two types of

radiative phenomena. The first is that of a radiative blast wave in a low-density gas,

where a strong shock is launched in gas, but not driven after the initial laser pulse.

The second launches a strong shock, driven or not, and studies the behavior of a

radiative precursor in the unshocked gas. The threshold shock velocity for creating

a radiative precursor is lower than the threshold for creating a radiatively collapsed

shock.

Blast wave studies were generally done in xenon gas. Shigemori [47] launched

cylindrically divergent shock waves in xenon gas, which showed signs of increased

density and a radiative precursor. In 1999, Budil et. al [8] suggested that the

Petawatt laser facility at the University of Texas could be used as a radiation hy-

drodynamics testbed, and specifically suggested supernova blast wave experiments.

26

Experiments to reproduce and reanalyze the Shigemori results, discussed by Edwards

et al. [15] produced us ∼ 8 km/s in a cylindrical blast wave produced with an ul-

trafast laser, and observed radiative cooling effects that resulted from heating of the

shocked gas by electron heat conduction. Experiments by Hansen et al. showed the

formation of a second shock wave ahead of a quasi-spherical radiative blast wave in

xenon gas ([22], [23]).

At higher us, experiments can exceed the threshold for the formation of a thermal

radiative precursor, in which thermal radiation from matter heated by the shock

itself heats the matter ahead of (“upstream of) the shock. Radiative precursors have

been observed in experiments by Bozier et al. [7], Grun et al. [21], Keiter et al. [27],

and Koenig, Bouquet, and coworkers ([28], [6], [39], [50]). The experiment of Grun

et. al. produced a quasi-spherical radiative blast wave, in which radiation during

the shock transition is calculated to play a key role [29]. Experiments by Edens et

al. [14] in nitrogen gas studied the polytropic index of shocked gases, which could

play an important role in linking the Grun experiments to the Vishniac instability

([51], [52]).

This dissertation research revolves around an experiment that is performed in

xenon gas, like many of these experiments, but at a higher density. These experiments

are of a shock driven by an ablatively-launched piston, and so will not evolve like

a blast wave, which is the focus of many of these studies. While some diagnostics

performed on the experiment confirm the existence of a precursor, the propagation

and evolution of that radiative precursor is not the main radiation hydrodynamic

effect studied. The experiment discussed in the next few chapters is that of a driven,

radiatively collapsed shock wave in xenon gas. In this experimental setup, a very

fast (i.e., strong) shock in launched in 6 mg/cm3 xenon gas, in a planar geometry.

27

This shock heats the gas to very high temperatures (∼ 250 eV), and the gas radiates

away a significant amount of energy. The gas then becomes highly compressed as

a response to this energy loss, as explained in earlier sections of this chapter. The

shocks in these systems are much faster and hotter than the shocks reported in prior

contemporary research in xenon. Very fast, hot shocks are launched in the case

of a dynamic hohlraum in CH foam, but much faster, hotter shocks are needed to

make CH radiative [13]. For comparison, the experimental conditions reported in

this dissertation are compared with results in Hansen et al. [22], Edwards et al. [15],

Grun et al. [21], Keiter et al. [27], Koenig et al. [28], and Bailey et al. [4] in Table

2.1.

Geometry ShockedMaterial

Initial Den-sity

Shock Ve-locity

Estimatedpeak Te

Reighard et al. Driven, pla-nar

Xenon gas 6 mg/cm3 <100km/sec

250 eV

Hansen et al. Sphericalblast wave

Xenon gas .07mg/cm3

10km/sec

5 eV

Grun et al. Sphericalblast wave

Xenon gas .04mg/cm3

10km/sec

none re-ported

Edwards et al. Cylindricalblast wave

Xenon gas .2-2mg/cm3

8 km/sec 1 eV in pre-cursor

Keiter et al. Planar SiO2 aero-gel foam

∼10mg/cm3

70km/sec

30 eV in pre-cursor

Koenig et al. Planar Xenon gas .5-1mg/cm3

40-80km/sec

15-20 eV inprecursor

Bailey et al. Cylindrical Tungsteninto CHfoam

14 mg/cm3 350km/sec

220eV

Table 2.1: Comparison of experimental quantities in Reighard et al. and other recent radiationhydrodynamics research. Reighard et al. produces the fastest, hottest shock in thehighest density xenon gas.

CHAPTER III

Experiment Description

This chapter is devoted to the description of experiments designed to create and

diagnose a driven, planar, radiative shock through a gas-filled target for observation

of the structure of the shocked layer. These designs were modified from an origi-

nal design conceived in collaboration with, and constructed at Lawrence Livermore

National Laboratory. As of July 2003, target specification and modeling, including

2D building schematics and 3D CAD models, were done by me and built by the

University of Michigan Target Fabrication team. An example of a 3D CAD diagram

of the target is shown below in Figure 3.2. Target design and modification were done

collaboratively between the target fabrication team and myself.

The U of M target fabrication and metrology facility was built and managed by

Korbie Killebrew Dannenberg, under the supervision of Paul Drake, and is currently

managed by Michael Grosskopf. It consists of 11 motorized stages with µm precision.

These stages are arranged into two separate coordinate systems; one set of stages

is used for holding and positioning a target, while the second set of stages is used

to hold and position a target component while it is affixed to the main target. The

fabrication process is aided by the use of three orthogonal viewers. Pictures of the

system and clean room surrounding it are shown in Figure 3.1.

28

29

Detailed pre-shot target characterization, or “metrology”, was done by me for

each target for the purpose of accurate positioning of the target in the Omega Laser

facility target chamber. This characterization was also vital in the interpretation of

data after the experiment, as each target was destroyed as the shock passed through

it. This was done on one set of precision stages also used for fabrication, using two

of the three orthogonal views. Measurements were aided by crosshairs on the views,

allowing measurements with approximately 25 µm precision. Generally, metrology

measurements included positions of relevant features for data analysis, examination

of targets from diagnostic views, imaging of the target from target chamber viewer

angles, and measurement of angular deviations from nominal.

Figure 3.1: Photos of the University of Michigan Target Fabrication Center. a) System is mountedon an optics table in clean room to minimize dust and debris on optics and in stagemechanics. b) Two sets of coordinate systems aid holding and independently positioningtwo pieces during fabrication.

3.1 Targets

The basic construction of the target consisted of a planar disk attached to a cylin-

der to form a gas-tight assembly. Other features were added to facilitate diagnostic

use or to speed the alignment process. The basic design and structure of the radiative

gas experiment targets are shown in Figure 3.2.

30

A crucial component was the planar disk, usually made of solid beryllium. In the

first experiments, this disk was initially 40 ± 10% µm thick and 2.5 mm in diameter.

The thickness of this disk was varied in later experiments, to 20 ± 10% µm and 10

± 20% µm thick and 2 mm in diameter. This thickness was measured as part of the

fabrication process with calipers, and was known to within 2 µm. It was essential

that this surface be a solid, low-density material, to launch a faster piston for a given

laser ablation pressure. To this end, some early disks were also made with 80 µm

thick polyimide overcoated with approximately 20 µm of PVA. This thickness gave

the same areal density as 40 µm of beryllium, with fewer risks than working with

beryllium.

This disk was centered on a polyimide tube, ID 575 µm, OD 625 µm, and ap-

proximately 5 mm in length. The polyimide tube was faced with a microlathe, to

ensure a right angle edge on the face upon which the beryllium disk was fixed. This

joint was inspected to measure concentricity of the disk and tube on the fabrication

system, with measured deviations from concentricity being less than 50 µm for ac-

ceptable assemblies by the final shot day. A step in the inspection process at this

point in the construction ensured that little or no glue from the joint seeped into the

target, onto the beryllium opposite the side on which the laser was incident, or the

“driven side.” This would have affected the time of shock propagation through the

drive disk, as well as the total amount of material launched by the laser pressure,

slowing the initial acceleration of the material into the gas cell. The driven surface

of the beryllium disk was also free of any glue.

A gold grid was also placed radially on the target facing an imaging diagnostic

as a spatial and magnification fiducial. The separation of the wires on any grid

square was 63.5 µm. The total length of the grid was approximately 2.5 mm on most

31

Figure 3.2: 2D schematic of gas-filled target and 3D CAD drawing of target with attached back-lighter foil.

targets. Regular, individual features were built into the grid on the side nearest the

target tube, giving several points of reference as spatial indicators. These features

were hand-cut, by removing wires from individual squares on an edge of the grid

approximately every 0.5 mm down its length. Gold was chosen because it is opaque

to x-ray photons in the range we discuss for backlighting later in this chapter, and

therefore provides a reliably dark feature on data images. When the target was

ideally positioned in the laser chamber, this opaque feature blocked little to no area

inside the target tube, and by extension blocked little to no data from the shocked

material. A metrology photo showing the grid and fiducials is shown in Figure 3.3b.

The target assembly was gas tight, with a stainless steel hypodermic tube in the

back end for evacuating the target of air and filling the target with gas. The steel tube

was fitted with a length of plastic tubing which ended in a voltage transducer. The

target was filled through this transducer, which measured the gas pressure inside the

target. In this way, the gas pressure of the target could be monitored up until about

32

(a) (b) (c)

Figure 3.3: (a) Metrology photo of target with area backlighter foil attached. Area backlighting isdiscussed further in section 3.3. (b) Metrology photo of gold grid attached to target.Note notches on the grid near the target body, that served as spatial indicators. In-creasingly large notches were cut farther from the drive surface. (c) Metrology photoof target with no area backlighter attached.

10 seconds before it was destroyed by the laser pulse. Most targets had a gas-leak

rate of about 1 torr/minute from a volume nominally at 835 torr, so the 10 second

blackout just before the laser pulse lead to a negligible error in the measurement of

the gas pressure at the time of the experiment. The leak rate on each target was

measured, and targets were overfilled to accommodate the time between gas fill and

the laser pulse. As a step in the fabrication, targets were pressure tested to up to 4

ATM, which is approximately 3000 torr, to test glue bond strength and leak rates.

Targets were routinely test filled again to more than 2 ATM on shot day, equivalent

to 1520 torr. Steel hypodermic tubing blocked the last 0.5 mm to 1 mm of the length

of the plastic tube from the diagnostics, so experiments were confined to the first 4

mm of the target as measured from the drive disk position. Two metrology photos

of targets are shown in Figures 3.3a and 3.3c.

This target was filled with 99.99% xenon or argon gas. After assessing the leak

rate on each target on shot day, it was evacuated and then overfilled to shoot at

approximately 1.1 ATM of gas, corresponding to 6 mg/cc of xenon, or 1.5 × 1019

33

atoms cm−3. For targets filled with argon gas, this corresponds to a mass density

of 1 mg/cc. This evacuation-and-refill process limited the amount of gas other than

the intended gas in the final target. Other gases could have diffused out from the

materials in the target, which had been stored in air and previously filled with

nitrogen. On shot day, targets were regularly overfilled to accommodate more than

an hour of time between fill and experiments, usually amounting to an extra 100 torr

of gas over the nominal 1.1 ATM.

Targets at built at LLNL were built by experienced fabrication professionals to

a high standard of accuracy. Tolerances on the construction of these targets were

inferred from documents accompanying finished targets with final angle and distance

measurement of features. When the fabrication was taken over by the staff and

students at the University of Michigan, it was not possible to initially build targets

to equally high accuracy. As the fabrication team became more adept at building

targets and I became more conscious of the need for quality checking, the accuracy of

the features of the targets improved. The tolerances for these targets were based on

checks done during the build process and during metrology. A list of the tolerances

of targets for each shot day are listed in Table 3.1, and can also be found in Appendix

C.

3.2 Lasers

These experiments were performed at the Omega Laser facility at the University

of Rochester’s Laboratory for Laser Energetics in Rochester, NY. This 60-laser beam

system is capable of delivering up to 30 kJ of laser energy to a target. The laser is

a Nd:glass laser operated at its frequency-tripled wavelength, λ3ω = 0.351 µm. The

configuration of the lasers at this facility are shown in Figure 3.4a. The full facility,

34

Table 3.1: Target feature tolerances as a function of shot day. Items listed as unknown were ei-ther not measured (if built at U. MI) or had no measured details on the documentaccompanying finished targets (if built at LLNL).

including target bay and capacitor banks, are shown in Figure 3.4b.

Figure 3.4: (a) Diagram of spherical target chamber at the Omega Laser facility. Numbered circlesindicate beams, while larger circles numbered with H, P, and TIM labels are ports forboth fixed and removable diagnostics. (b) Schematic of beam paths leading throughcharging banks and into the target chamber. Both images from the National LaserUsers Facility User’s Guide.

Ten beams of the 60 total beams of the Omega Laser facility struck the beryllium

drive surface of the target, the midpoint of the rising edge of the beam pulse defining

t = 0 in the experiment. These beams each had an energy which varied between

350 - 450 J, just below 400 J/beam for most shots. These beams used Distributed

Phase Plates (DPPs) to help smooth them. This involves using a removable optic

35

Figure 3.5: Equivalent target plane images of beams spots integrated over a 1-ns pulse width. (a)An unsmoothed spot of a frequency-tripled Omega beam. (b) Beam spot smoothedwith a continuous phase plate. (c) Beam spot smoothed with SSD. From the NationalLaser Users Facility User’s Guide.

that reduces spatial non-uniformities in the far field of the frequency-tripled beams

of the facility. This is done by modifying the beam’s near field coherence, changing

focusing properties, and shifting energy towards higher spatial frequencies, which

can then be rapidly blurred by temporal beam smoothing techniques. This temporal

blurring technique is called Smoothing by Spectral Dispersion (SSD), and was also

employed to create a more uniform time-averaged irradiance. The relative effect of

different smoothing techniques is shown in Figure 3.5.

The beryllium disk was accelerated much like a piston into the xenon gas via laser

ablation pressure. Ablation pressure is the consequence of momentum conservation

as material is heated and flows away from the target surface. As a drive laser boils

off material from a surface, the remaining material feels a force equal and opposite

to the flow of momentum from the surface. We can estimate the pressure on the

drive surface with a few assumptions. First, we use a flux-limited model for heat

conduction from the laser. We also assume that as the material boils off, part of the

laser energy goes into heating the lower-density material, while the rest penetrates to

the critical surface. In addition, we assume that the full laser irradiance is absorbed

36

by the material, which is a good assumption for UV lasers, but is less accurate at

longer wavelengths. The generated ablation pressure is equal and opposite of the

flow of momentum from the critical surface. If this flow happens at√

2 times the

sound speed, as is a common estimate in the literature for a UV-laser absorption

profile [13], then

(3.1) Pabl = 2M

√ZkBTe + 3kBTi

M× nc

Z

√ZkBTe + 3kBT1

M.

For typical laser coronae values of Z = 3 and Ti = Te/3 simplifies to

(3.2) Pabl = 2nckBTeZ + 1

Z= 8.0I

2/314 λ−2/3

µ ,

where the second equality gives pressures in Mbars. In Equations 3.1 and 3.2, M is

the ion mass, Z is the average ionization state of the plasma (again, approximated

as Z = 3 for the second equality in Equation 3.2), kB is Boltzmann’s constant, Te is

electron temperature, Ti is ion temperature, nc is critical density of the plasma, I14

is the irradiance on target in units of 1014 W/cm2, and λµ is the laser wavelength in

units of µm.

In this experiment, the force from laser ablation pressure first launches a shock

through the material, heating and compressing the beryllium disk with a strong

shock. Once the shock passes through the thickness of the material, this disturbance

from the laser is then subsonic. This force can then accelerate the bulk of the material

for the remainder of the length of the laser pulse. When the laser turns off, the

beryllium continues to move with the momentum imparted by the ablation pressure,

with material from the drive side expanding in a rarefaction wave. This accelerated

beryllium drives a strong shock in the xenon gas, as described in the Radiation

37

Hydrodynamics chapter. Radiation from the xenon layer helps drive a supersonic

flow at the boundary between the beryllium and xenon, which can initially outrun

the rarefaction wave. As the shock moves through the xenon and builds up more

material, the system will slow, and the rarefaction wave will overcome the flow layer.

Eventually, the rarefaction wave will overtake the xenon layer as well, at which point

the system is no longer driven by the beryllium plasma.

3.3 Backlighters

An additional, sometimes separate target was necessary to provide x-rays for

illumination of the primary target to image the shock. These x-rays were produced

by illuminating a thin metal foil with additional lasers. These lasers shocked and

heated the metal, producing a hot coronal plasma. Helium-α-like transitions in the

coronal plasma produce x-rays with energy of several keV. The backlighter metal was

chosen such that the emission provided a good contrast on the features of interest.

In this experiment, we wished to see absorption features from dense xenon or argon.

Xenon absorbs efficiently in the range of 4.75- 5.3 keV due to L-shell transitions,

while argon absorbs efficiently in the range of 3-4 keV. The absorption spectra for

xenon and argon are shown in Figure 3.6 for a volume of cold xenon that is 600 µm

thick and density of 0.06 g/cm3. This density is 10 times the initial gas density in

the target in question. Vanadium has He-α-like emission at 5.2 keV, making the

emission from this metal highly absorptive by xenon. In contrast, the absorption

of this wavelength by both beryllium and polyimide is very low. Therefore, there

were no absorption features on radiography images of beryllium, and the only plastic

visible on these images was the target wall at the very edge of the target, due to limb

darkening.

38

Figure 3.6: Xenon transmission spectrum in the range of 3-8 keV and argon spectum in the rangeof 1-6 keV, as calculated for cold material.

Two methods were used to backlight the target. On early targets, the method

used was called “area backlighting.” Area backlighting used a thin metal foil with

large area (usually 4 mm square) which was suspended off the side of the main target

using a metal wire. This foil was hung approximately 4 mm along the radius of the

cylinder of the main target. This foil was then illuminated with several laser beams

to make a large laser spot on the foil, usually approximately 1 mm in diameter. This

created a sea of x-ray photons into 4π steradians, some of which pass through the

target. Those x-rays were then passed through a 16-pinhole mask, which created 16

images of the target on a framing camera using a microchannel plate with four active

strips, as discussed below. This foil can be seen in Figure 3.1b.

The second method, called “pinhole backlighting”, was developed over the course

of this experiment, and is illustrated in Figure 3.7. This method used tantalum

as a high-Z substrate to block the x-rays from the illuminated foil except those

which passed through a small pinhole in the substrate. This tantalum piece was

5 mm square and 80 µm thick. The pinhole in the center was nominally 20 µm in

39

diameter. A small foil (usually 1 mm square), was placed on one side of the tantalum

substrate, centered over the small pinhole in the center of the substrate, offset from

the tantalum by approximately 100 µm by a plastic spacer foil. A plastic piece was

also placed on the side of the substrate opposite the foil to reduce solid spall launched

towards expensive diagnostic equipment. This package was mounted on a separate

target, and positioned independently from the main target. Two to six laser beams

illuminated the metal foil, which also created a sea of x-ray photons. Those which

moved in the general direction of the target were blocked, except those which passed

through the pinhole. Those photons that made it through the pinhole passed through

the target and were imaged on a framing camera using a single active strip across

most of its area. In this way, using a backlit pinhole allowed detection of images

that were of much higher magnification. The resolution of the image created by this

method was limited by the size of the effective source through the pinhole. The size

of the effective source was somewhat smaller than the actual size of the pinhole, as

the thickness of the substrate caused vignetting.

A backlighter target schematic is shown in Figure 3.8. Metrology photos are shown

in Figure 3.9. When correctly positioned in the Omega target chamber, these targets

are placed 12 mm away from the main target, well away from the center of the target

chamber. Viewers used to position targets in the target chamber can clearly image

features on targets when they are within approximately 4 mm of the center of the

target chamber, but objects positioned farther from the center will be out of focus

in the viewers. Careful metrology of features that are still well distinguishable even

out of focus was used to correctly position the target. In particular, the four corners

of the rectangular substrate can still be seen somewhat distinctly, allow for accurate

positioning of the backlighter target. For better accuracy, rotational alignment of

40

Vanadium-backed pinhole sandwich

Xenon-filledTarget Detector

5 keV x-rays

Dense shock

Figure 3.7: Diagram of backlit pinhole backlighting setup, not to scale. In the Omega chamber,with the target at target chamber center, the backlighter target was 12 mm from thetarget axis, while the detector was 229 mm from the target axis on the opposite side,for an image magnification of 20.

these targets is performed at target chamber center, before positioning in space.

Fabrication tolerances for backlighter targets are listed in Table 3.1.

3.4 Diagnostics

Several diagnostics were used on each shot to gather data and ensure that beams

were properly placed on targets. Below, we discuss the primary diagnostics used on

shot days. A summary of shot day diagnostics set up as well as laser information is

included in Table 2 in Appendix C.

3.4.1 Microchannel Plates and Framing Cameras

The main diagnostic tool used in these experiments was x-ray radiography. Using

the backlighting schemes just described, an x-ray source was created and photons

were allowed to pass through the main target. On successful shots, dense features

in the gas absorbed photons from the source, while x-rays passing through other

41

Target Date Completed Assembler Metrologist

Use Omega Mount Tin foil: 1mm x 1mm, 5 µm thickTa Pinhole substrate: 5 mm x 5mm, 50 µm thick, 20 µm pinholeCH squares: 2 X 100 µm thick X 2 mm dia.Exposed Ta coated with PVA

stalk

Ta substrate

CH

foil towardsTIM 4

TIM 6 view

H2

20 µm pinholeon center line

CH

stalk

5mm

Tinfoil

Ta substrate

2mm

1mm

H2H2

Thickness of totalpackage before adding foil=___________µm

79.20°

Figure 3.8: Target schematic for pinhole backlighter target . Measured details for each target arefilled in during fabrication and metrology.

42

Figure 3.9: Metrology photos of pinholebacklighter targets. a) Face-on view of backlighter target.The large rectangle is the 5 mm square tantalum substrate. The dark square seen is afeature on the tantalum, while close inspection shows the 2 mm polyimide square. Thedotted-line crosshairs shown are features of the viewing system, and the center of thecrosshair is positioned on the 20 µm pinhole. b) XTVS view of backlit pinhole target,imaged in metrology at same angle as one of the cameras on Omega when the target iscorrectly positioned.

features were not absorbed. In this way, important features in the gas were imaged

as absorption features.

An x-ray framing camera detected and amplified x-ray light and converted it to

visible light, which was then recorded on a piece of film or CCD camera. An x-

ray framing camera consists of a gating mechanism, a microchannel plate, and a

phosphor, behind which the image recording device is placed. A cartoon showing

the setup of these components is shown in Figure 3.10.

When an x-ray enters one of these channels, it may free an electron from the

material. This electron is accelerated down the pore by the electric field. When

the electron hits the wall of the pore as it passes through, it frees more electrons,

which are accelerated down the tube, and whose collisions with the pore walls will

free even more electrons, amplifying the signal. Eventually, the freed electrons exit

the tube in a spray, where they are accelerated towards a phosphor plate. This

43

Figure 3.10: Cartoon of framing camera components. An x-ray source on the right side of thecartoon shines through a target. The photons then hit a microchannel plate, whichturns x-ray photons into a cascade of electrons. These electrons are then directedonto a phosphor plate via an applied potential, which emits visible photons uponelectron impact. These visible photons are then imaged on film or a CCD camera.The microchannel plate can be coated with a material to increase its gain. Imagecourtesy Eric Harding.

spray of electrons has some finite shape and distribution, and produces a smear of

electrons. The voltage applied between the microchannel plate and the phosphor

helps minimize the spread of the spot as it travels towards the phosphor. When the

electrons impact the phosphor, they release visible photons, which are then focused

onto the film or CCD camera situated behind the phosphor.

3.4.2 Velocity Interferometry

Velocity interferometry is an active diagnostic generally used to time shock break-

out from a material, or to record the changes in the velocity of a reflective surface via

the Doppler shift. This is accomplished by recording fringe shifts due to changing

optical path lengths of the arms of the interferometer. In principle, any process that

44

changes the optical path length of the interferometer beams will cause fringe shifts,

such as a physical change of the path length from a moving, reflective surface, or a

changing index of refraction along the beam path.

The arms of the interferometer have almost identical beam paths; both arms of the

interferometer probe the same physical path (through a plasma or off of a mirror).

But one arm, referred to below as the “long” arm, passes through an extra optical

component called an “etalon”. The etalon has a different index of refraction than

the other components of the system, and can vary in length. It is the time difference

of the propagation of a disturbance in the system between the arms due to the etalon

that causes fringe shifts. In the discussion below, the etalon ranged from 3-30 mm

in thickness. Because of this, a VISAR system is sensitive to the rate of change of

the optical path, instead of to instantaneous differences in the optical path like a

standard interferometer.

If the mirrors in the interferometer are a small angle to the probe beam in the

plane of the interferometer, the electric fields of the two plane waves are

(3.3a) E1 = E0ei(ω0t−k1·r) = E0e

i(ω0t−kx)

(3.3b) E2 = E0ei(ω0t−k2·r) = E0e

i(ωt−kx cos α−ky sin α),

where ‖k‖ = ‖k1‖ = ‖k2‖, and α is the tilt of the mirror.

The intensity pattern of the interference of these two beams is

I = (E1 + E2)(E1 + E2)∗(3.4)

= 2E20(1 + cos ((k − kx)x− kyy)),(3.5)

45

where kx = k cos α and ky = k sin α. In the plane of the beam splitter (the y-z plane

in this coordinate system), the spatial profile of the intensity is

(3.6) Iseparation(y) = 2E20 (1 + cos (ky sin α)) .

This fringe pattern is shown in Figure 3.11.

Figure 3.11: Simulation of VISAR fringes from a steady-state target on a streak camera, wheretime is the vertical axis and position is the horizontal axis. Image from Forsman, 2001[20].

If a disturbance in the system affects the phase of the interferometer, the effective

change in the frequency of the light in the interferometer is

(3.7) ω = ω0 +dΦ

dt= ω0 + Φ′

In this equation, Φ′ changes slowly compared to 1/ω0. The electric fields will change:

(3.8a) E1 = E0ei(ω0t+Φ′t−kx)

(3.8b) E2 = E0ei([ω0+Φ′](t−τ)−kxx−kyy),

46

In this case, the intensity pattern is

(3.9) I = 2E20 (1 + cos [ω0 + Φ′(t− τ)) τ + ky sin α]

In the short arm of the interferometer, the optical path length L1 at some time t

is

(3.10) L1(t) = L1(0) + 2d (n(t)− n(0)) ,

and in the long arm of the interferometer the optical path length L2 is

(3.11) L2(t− τ) = L2(τ) + 2d (n(t− τ)− n(0))

where d is the width of the argon plasma, n is the refractive index, given by

(3.12) n(t) = n(0)

√1− Ne(t)

Nc

,

Ne is the electron density, Nc is the critical electron density, described in Chapter

Two, and τ is the time delay caused by the etalon. The difference in these optical

path lengths L(t), given by

(3.13) L(t) = L2(t− τ)− L1(t) =2d

λ(n(t− τ)− n(t))

gives a fringe shift, F (t), of

(3.14) F (t) =

(L(t)− L(0)

λ

)=

2d

λ(n(t− τ)− n(t)) .

47

For electron densities much lower than critical density, Ne � Nc, the expression

for fringe shift becomes

(3.15) F (t) =dn(0)

λNc

(Ne(t− τ)−Ne(t)) ,

so the fringe shift gives an electron density change,

(3.16) Ne(t) = Ne(t− τ)− λNc

dn(0)F (t).

The total phase change (assuming the change in the laser wavelength is small) is

(3.17) ∆Φ(t) =2π

λ

∫ t

0

[dL(t′ − τ)

dt′− dL(t′)

dt′

]dt′,

where

(3.18)dL(t)

dt= n(0) ∗ 2d

d

dt

√1− Ne(t)

Nc

=n(0)d

dtNe(t)

If Ne/Nc is small (we expect it to be less than 1%), then we are left with an expression

for phase change as a function of changing electron density:

(3.19) ∆Φ(t) = 2πF (t) = 2πdn(0)

λNc

(Ne(t− τ)−Ne(t)) .

This diagnostic was implemented to probe possible density changes in the radiative

shock experiments in a side-on setup. A diagram of the target used with the VISAR

(Velocity Interferometry System for Any Reflector) diagnostic is shown in Figure

3.12. As the material ahead of the shock was preheated and ionized, we hoped to

detect a change in electron density, which would change the index of refraction of

48

Figure 3.12: Target setup for use with the VISAR diagnostic. The shock moves from left to rightdown the main cylinder, while the interferometer beams pass through the arm perpen-dicular to the main body tube.

the plasma. The VISAR diagnostic at the Laboratory for Laser Energetics, used on

the Omega laser system, employs a Mach-Zender style interferometer at small angles

using a laser beam with λ = 532 nm. The beam probed a distance approximately 2

mm from the driven surface, radially along the main target axis.

3.4.3 Thomson scattering

Another diagnostic employed on a small number of experiments was a Thomson

scattering diagnostic, with the scattering spectrum recorded onto a UV streak cam-

era. The changes in the experimental setup are discussed extensively in the Thomson

Scattering chapter.

CHAPTER IV

Experimental Results

The experiment described in the previous chapter has been successfully fielded

on nine separate shot days over the last four years, which includes 4 half-days and 5

full days of shots on the Omega laser. Success of these shot days depended on target

quality and availability, target alignment speed, diagnostic understanding, and laser

performance, among other things.

The bulk of the useable data came from a single-strip framing camera diagnostic,

illuminating a shock in xenon gas by a pinhole backlighter. Some data came from a

four-strip framing camera, in experiments that used either xenon gas or argon gas.

One remarkable piece of data came from a spectrometer coupled with an UV streak

camera, which will be discussed in detail in the Thomson Scattering Experiment

chapter.

Another distinguishing characteristic between pieces of data is the composition

and thickness of the piston launched into the gas to drive the shock. A large fraction

of the data is from either 40 µm or 20 µm thick beryllium drive disks. One piece of

data is from a 10 µm beryllium disk. A small amount of data is from approximately

80 µm thick polyethelyne, or thicker (50 µm) beryllium. These characteristics will

be spelled out for each reported result in this chapter, and should be noted when

49

50

comparing images whether they are targets of the same type.

Most of the data presented here are from x-ray radiography imaging diagnostics.

Two other primary diagnostics were used over the course of this experimental cam-

paign. The first, fringe shift data from a VISAR diagnostic, will be discussed at the

end of this chapter. The second, spectral data recorded on a UV streak camera, will

be discussed in the Thomson Scattering Experiment, which describes in detail the

experiment designed to measure a Thomson-scattered spectrum.

Uncertainties on positions in x-ray framing camera images include contributions

from metrology measurements and shot day alignment, compounding errors in fabri-

cation. This warrants a separate discussion from that of the discussion of fabrication

tolerances in the previous chapter. The uncertainties in the relative x-ray intensi-

ties are not important here, because the present work makes no attempt to infer

conclusions from the magnitude of the x-ray intensity.

Errors from metrology arise from two sources. The first occurs if the calibration

of the azimuthal position of the metrology system is not correct. In this setup,

the azimuthal position is the position of the target as it rotates around it’s stalk

when mounted in the metrology system. Metrology relies on the definition of angle

measurements that correspond to angular locations in the target chamber. To do

this, the target must first be situated in a known position, from which we can then

define the rest of the locations. The polar coordinate θ was absolutely calibrated

between the two systems, but the azimuthal location φ varied, as the placement of

the target in the target holder varied around the axis of the stalk. For these targets,

we defined φ = 0 to be when the projection of the target axis pointed towards the

front viewer. This was defined by a combination of the ellipse made by the drive

disk, the long axis of which would lie parallel to a horizontal crosshair on the front

51

viewer, and the target body tube, which would lie parallel to a vertical crosshair

on the same viewer. Using this method for repeated positioning of the same target

in metrology, as was done for several targets, the variation in the azimuthal angle

definition was ∆φ = 0.25 degrees.

The second source of error from metrology was from using a set of crosshairs of

finite width to make position measurements. Positions of features which were later

visible on data images were measured relative to the center of the drive disk. This was

done from a view on the metrology system that would be equivalent to the angular

position of the collection diagnostic. These features were measured using a set of

crosshairs that at the highest magnification of the system appeared approximately

25 µm thick. While care was taken to measure the features in the same way, such as

always approaching the measured feature from the same direction until it was just

barely obscured by the crosshairs, this finite width introduces a compounding ± 25

µm error on all position measurements.

Other sources of error arose in the positioning of targets on shot days. After careful

metrology, each target was positioned in shadow in the Omega target chamber. Main

targets were located with some feature at target chamber center, and so were usually

in focus in the two viewers, named XTVS and YTVS. For early experiments, correct

rotational positioning was achieved using a set of circular reticles imposed on the

YTVS screen. The target was rotated until the main tube lined up on the circles.

Imitating this procedure using a 3D CAD program, the estimated accuracy of this

technique was ± 1 degree. For later experiments, an extra wire was attached to the

target for rotational alignment. After correctly aligning the target on the metrology

system, the target was rotated until this alignment wire barely touched the edge of

the gold grid in the YTVS view, and the rotated angle was noted. On shot day,

52

the target was positioned such that the wire touched the grid in the same view,

and then rotated by the measured angle in the opposite sense, so the target was

at the correct angle. Again using a 3D CAD program to imitate this procedure,

the estimated accuracy of this method was ± 0.5 degrees. This method also proved

faster, a significant plus on shot days. After achieving rotational alignment, the

target was positioned in space using reticles on the drive disk and along the target

axis. The estimated accuracy using this method was ± 25 µm.

On all shot days, drive beams were positioned at the beginning of the day and were

left untouched for the day. These beams were precisely positioned by the Omega staff,

and alignment checked using low-powered pulses. The uncertainty on the position

of these beams was very small; much smaller than the uncertainty of the drive disk

position. Backlighter beams were also precisely positioned at the beginning of the

day, but were often moved after a few shots to diagnose a different section of the

experiment. The beam termination point was routinely moved a millimeter down the

target axis using a method referred to at the Omega facility as “blind repointing”.

This repointing process introduced an uncertainty that was approximately 20% of

the distance moved, giving a possible error of the position of the beams of 200 µm

at their new position.

Errors from fabrication, metrology, and target positioning compounded into the

errors reported for measurements in collected data.

4.1 Radiographic Image Processing

Framing cameras were used to image absorption features from the driven shock.

As explained in the Radiation Hydrodynamics chapter, a shock that loses a significant

fraction of it’s energy can be compressed to much higher levels than normal for a

53

non-radiative strong shock. Backlighter energies were chosen for each fill gas to be

highly absorbed by dense features in the gas, and to be transparent to beryllium

and plastic, the other main components of the target. Gold is opaque to very high

energy, and so was used to calibrate the magnification and positions of the image.

In these images, a dark feature across the diameter of the shock tube is radiatively

collapsed shocked gas layer.

Data images are calibrated using information from pre-shot metrology. Raw,

uncalibrated data are shown in Figure 4.1a. In these experiment, the laser pulse

that launches the piston into the gas to drive a shock is intense enough to completely

destroy the target. When target mounts are retrieved after an experiment, all that

usually remains is part of the hypodermic fill tube and plastic hose attached opposite

the drive end of the target. Therefore, careful measurements must be made before

the actual experiment to help interpret the data. Metrology measurements give the

target coordinates of the location of edges of the gold grid mounted on the target (as

discussed in the Experimental Description chapter), as well as the features cut into

the grid at regular intervals. The origin of the target is measured as the center of

the drive disk, which generally aligns very well with the center of the target cylinder.

In the data photos, the beryllium from the drive disk does not appear, as beryllium

is transparent at these backlighter energies. However, the edges of the polyimide

cylinder are visible on all data images. Polyimide is somewhat more absorptive at

these levels, but does not obscure data when looking effectively radially through the

25 µm thick target walls. Only when we approach the target edges in the picture,

where we look almost tangentially through the polyimide, can you see noticeable

absorption. In all calibrated images, the shock moves from left to right.

Data captured with a single-strip framing camera are smoothed to help minimize

54

Figure 4.1: a) Data captured by framing camera. Data from a framing camera are recorded onfilm, then digitized. A wedge file is created to help calibrate scanned exposure levels tox-ray illumination. b) Calibrated image. Pre-shot metrology measures the position offeatures on the target, to give axes in target coordinates. The gold grid shown in imagesprovides not only a vehicle for introducing these features onto a data image, but alsoprovides a reliable way to measure the actual image magnification. c) Data smoothedover a resolution element. Source-limited resolution limits the level at which useful datacan be gathered. By smoothing over a resolution element, we remove small variationsdue to noise from the data image. d) Image with background variations subtractedout. Image is smoothed over a large fraction of the image, so only large scale variationsremain, and then subtracted from the original image.

55

the effect of the noise. Sources of noise on the image include photon statistics and

framing camera induced noise. To make sure no useful data is lost this way, smooth-

ing is done on smaller scales than the level of source-limited resolution, or smearing

from the pinhole source of light. In these experiments using a single strip framing

camera, the pinholes used to backlight the target were 20 µm in diameter on an 80

µm thick substrate. The thickness of the backlighter substrate causes vignetting of

the light through the pinhole, shrinking the effective source size to 14 µm. Source-

limited resolution arises when light from different parts of the source pass through

the same point on the target, then continue on a straight line path onto different

parts of the imaging component of the framing camera, smearing the data from the

image slightly as shown in the diagram in Figure 4.2. In this target geometry, the 14

µm source creates a 210 µm smear on the microchannel plate of the framing camera.

Since the target image is magnified to 20x at the imaging surface, this translates to

resolution elements of 10.5 µm in target coordinates. For the images in question,

10.5 µm is equivalent to 9 pixels. Thus, smoothing over 9 pixels in these images min-

imizes small scale variations from noise without smoothing out resolved data details.

The effect of smoothing over a resolution element in the data is shown next to an

unsmoothed image in Figure 4.1 b and c.

Variations in the level of overall image intensity complicates the data analysis.

Non-uniform illumination could occur due to mispointing of the backlighter target

by more than 2.0 degrees, which would rotate the cone of photons from the pinhole

away from the center of the target and detector. On some images, dark strips occur

near the center of the film, while illumination levels near the edges of the image are

equal, which may result from gain variations in the microchannel plate of the framing

camera. We used a smoothing technique to help remove large scale variations in the

56

Figure 4.2: Diagram of source limited resolution. Smear from photons passing through the samepart of the target but hitting different parts of the detector is calculated using the sizeof the pinhole source and similar triangles. The extent of the smear on the detector isthen divided by the magnification of the image (image distance/object distance) to getthe size of a source-resolution-limited element in target coordinates.

data from both these sources. To remove these variations, the calibrated image was

smoothed over large fractions of the image, 200-300 pixels in all images, which leaves

only features larger than 220-330 µm. In all these images, the only features that

were that large were large-scale intensity variations. That ultra-smoothed image was

then subtracted from the data image, removing some of the effect of the variations.

The result of this process is shown in Figure 4.1d.

4.2 X-ray Radiographic Data

Most of the data collected is in the form of radiographic data of shocked xenon gas,

differing in drive disk thickness, timing, pointing, and type of framing camera. Data

were collected over seven shot days over the course of 3 years. Below, the radiographic

images are organized by collection device and drive disk thickness. A table of the

information for each shot taken, including both successful and unsuccessful shots,

is given in Appendix C. This table includes laser irradiances, specific target details,

57

and failure modes for shots, if known.

4.2.1 Single-strip framing camera data from 40 µm beryllium drive disks

Firstly, let us look at data produced from targets with a 40 µm drive disk, using

a single strip framing camera diagnostic. Shown in Figure 4.3a is an image taken 10

ns after the drive beams turn on. Unfortunately, the dark feature from the collapsed

shock is somewhat compromised by a bright stripe through the data that was too thin

to be effectively removed from the image without possibly smoothing over data. The

source of this bright stripe is high-energy noise from an area backlighter, discussed

in the Dual Radigraphy section. Figure 4.3b was also taken at 10 ns after the drive

beams turn on. Here, the image has better contrast. This shock is tilted slightly

from the target axis, and is about 65 µm thick.

Figure 4.3c is by far the thickest collapsed layer imaged, measuring 150 µm thick.

It is also the latest time recorded in the experiment, taken at 20 ns after the drive

beams turn on. It also shows quite a bit of structure on the front and back sides.

Lineouts in all directions show slight variations in the transmission levels through the

shock, having pockets of slightly higher transmission in the thickest part of the layer.

For reference, Figure 4.4 shows data smoothed over a resolution element versus the

data background smoothed and subtracted. Figure 4.3d was taken at 12 ns after the

drive beams turn on. This image was captured with part of the shock cut off, as the

image was taken too early, and the shock was just entering the field of view of the

camera.

4.2.2 Single-strip framing camera data from 20 µm, beryllium drive disks

Figure 4.5 shows the five data points collected on a single-strip framing camera,

using a 20 µm beryllium drive disk. Over the course of time imaged, 8 ns to 15 ns,

58

(a) (b)

(c) (d)

Figure 4.3: Single-strip framing camera from a shock driven with a 40 µm beryllium disk. a) t =10 ns. b) t = 10ns. c) 20 ns. d) 12 ns.

59

Figure 4.4: Single-strip framing camera from a shock driven with a 40 µm beryllium disk at 20 nsafter drive beams turn on. a) Image smoothed over a resolution element. b) Imagebackground smoothed and subtracted. This piece of data is also displayed in Figure4.3c.

the evolution of the shock does not seem to differ significantly. All shocks imaged

here have an average velocity between 135 and 150 km/sec at the time they are

imaged, as measured from the right side of the collapsed layer. All the images show

a shock that is roughly the same thickness, ranging from 50 µm thick to 95 µm thick,

not necessarily in order of increasing time. Four of the shocks are relatively planar,

while the latest shock, imaged at 15 ns, has a curved structure. All the shocks have

some degree of structure on both the front and rear surfaces of the shock.

60

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61

The most unique shock imaged here, shown in Figure 4.5e, is shown below in

Figure 4.6, to show how the structure emerges when the background is smoothed

and subtracted away. Semi-regular features near the top of the front side of the

shock were especially surprising to see; only one other shock imaged has more regular

features than this.

Figure 4.6: Plot of shock from 20 µm beryllium driver. a) Calibrated data smoothed over a reso-lution element. While the collapsed layer is visible, the contrast in the image is poor,and features in the shock are not clearly defined. b) Image smoothed over 250 µm,subtracted from original image, then once again smoothed over a resolution element.Not only is the collapsed layer more clearly defined, but some structure emerges on theback side of the dense layer, as well as possibly repeating structure near the top of thefront side of the shock, across from features on the backside. For comparison, the largewhite pixels are dead pixels smoothed to a source-limited resolution element, which issmaller than the structure observed.

4.2.3 Single-strip framing camera data from 10 µm beryllium drive disk

Experiments with 10 µm thick beryllium drive disks were fielded on one shot day,

and produced one piece of radiographic data. These data are shown in Figure 4.7,

and were taken 4 ns after the drive beams turned on. This image shows the front of

the shocked layer, and the front of the collapsed layer is shown at 1200 µm from the

initial beryllium disk position. The dark line features cutting diagonally across the

62

Figure 4.7: Single-strip framing camera from a shock driven with a 10 µm beryllium disk. a)Data smoothed over a resolution element. b) Smoothed data was large scale variationssubtracted out, showing more structure on both sides of the collapsed layer.

image are flaws on the film. The average velocity over the first 4 ns is 300 km/sec, the

fastest average shock velocity recorded for these experiments. The collapsed layer is

85 µm thick, measured through the center of the dark feature. It shows a slight tilt

with respect to the target axis. Subtracting out large scale variations on the image

shows some structure on both sides of the collapsed layer, though a flaw in the film

blocks a clear view of the front side of the layer.

4.2.4 Single-strip framing camera data from 80 µm polyimide drive disk

One shot using a polyimide drive disk was successful. On this shot, both single-

strip and four-strip data was collected, so it was also one of the few shots with

successful dual radiography, discussed further below. This piece of single strip data

is shown in Figure 4.8.

63

Figure 4.8: Single-strip framing camera from a shock driven in xenon gas with a 80 µm polyimidedrive disk. This image shows only part of the shock, as the diagnostic was timed tooearly. The shock is just entering the field of view of this diagnostic. The shock is alsoobscured by a bright stripe across the image, which is from interference from anotherdiagnostic. This is described further in the Dual Radiography section.

64

4.2.5 Four-strip framing camera data

The first successful diagnostic fielded in the radiative shock experiments were

four-strip framing cameras. These side-on radiographic images were taken in argon

gas using a tin area backlighter, as described in the previous chapter, using a 50 µm

thick drive disk. These data are shown in Figure 4.9. In this image, and all four-strip

framing camera images, time increases from left to right, and from top to bottom of

the figure. Each strip is delayed from the nominal backlighter timing by an extra

200 ps from the strip before it, and within each strip, each cell is delayed by 60 ps

from the last.

The shock is visible in each cell of this image, but only the cells in the first two

columns have images of the grid, which gives the position of the shock. In addition,

the position of the shock can only be determined if the edge of the grid is in the

image, which was a feature measured in metrology. Only one cell gives a clear image

of a grid edge, and this cell was calibrated to metrology measurements, and shown

in Figure 4.10. A significant difference between this data and the single-strip data

shown above is that the target walls are not visible in this image, nor any signs of

absorption by plasma trailing along the target wall. However, these targets were

built with beryllium shock tubes, as opposed to plastic tubes for later experiments,

which should have lower absorption.

Later, in efforts to do radiography from two directions at two different times,

we obtained our only four-strip data of shocks driven with polyethylene, as well as

an additional piece of data with a beryllium driver. These experiments were done

using 1.1 ATM xenon gas, using a vanadium backlighter source. The plastic driven

four-strip data is shown in Figure 4.13.

Zooming in on one cell, we see this is the thinnest shock image seen to date.

65

Figure 4.9: Raw four-strip framing camera data for a shock in argon at 12 ns, launched with a 50µm beryllium drive disk. This particular image was backlit using x-rays from L-shelltransitions of tin. While grid features are visible, target walls are not, making it difficultto confirm radial position of the shock. On this image, only four frames have any imageof the gold grid, and only one has a grid edge, the position of which was measured inmetrology. Each strip is delayed 200 ps, with time beginning at the upper-left corner.Within each strip, each cell is delayed by 60 ps.

66

Figure 4.10: Blow-up of one cell of four-strip framing camera data from August, 2002, shown inFigure 4.9. This cell is in the second column, first row as measured from the lower leftcorner of the image, at time t = 12.4 ns.

Shown in Figure 4.14 is the cell in row two, column four as measured from the lower

left of the four-strip image. This shock is approximately 45 µm thick, and is slightly

curved.

Four-strip data collected with a 40 µm beryllium driver at 15 ns is shown in Figure

4.15. Timing of this shot was not optimal, as the shock is imaged near the edge of

the frames.

The cell with the most complete image of the shock, in the second row, fourth

cell as measured from the lower left of the image, is shown in Figure 4.16.

4.3 Dual Radiographic Data

On experiments in July, 2003, April, 2004, and February, 2005, targets were fielded

with the intent of doing radiography from two different directions with different

67

Figure 4.11: Raw four-strip framing camera data for a shock in xenon at 18 ns, launched with a 50µm beryllium drive disk. This particular image was backlit with a material more suitedto a shock in argon gas, but shock features are still visible, if not optimal. While gridfeatures are visible, target walls are not, making it difficult to confirm radial positionof the shock. All frames image the shock and the grid.

68

Figure 4.12: Blow-up of one cell of the four-strip framing camera data from December, 2002, shownin Figure 4.11. This cell, in the second column, second row as measured from the lowerleft corner of the image, at time t = 18.4 ns

timings. On these shots, targets were constructed and positioned to use a pinhole

backlighter to image the shock on a single-strip framing camera, then a short time

later use area backlighting to image the shock on a four-strip framing camera. The

delay between these two diagnostics was 3-6 ns, using plas-delayed beams on the

same driver. Radiography directions were almost orthogonal (100 degrees apart),

and both directions were perpendicular to the target axis. A diagram of this target

setup is shown in Figure 4.17.

In this diagnostic scheme, two shots collected single-strip framing camera data,

and four shots collected four-strip framing camera data. Only 2 shots collected

information from both diagnostics on the same shot, and single-strip cameras on

both of these shots were timed earlier than optimal, placing the image of the shock

on the far edge of the image. In these cases, only part of the shock structure is seen.

69

Figure 4.13: Raw four-strip framing camera data for a shock in xenon at 13 ns, launched with a80 µm plastic driver. Unlike previous four-strip framing camera data, one wall of thetube is visible in this image, as is trailing xenon gas along the wall. The other wall isobscured by a grid.

70

Figure 4.14: Blow-up of one cell of the four-strip framing camera data from April, 2004, shown inFigure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadiumsource. This cell, in the fourth column, second row as measured from the lower leftcorner of the image, at time t = 13.4 ns

These data are shown above in the four-strip section, in Figure 4.13 and Figure 4.15,

and in the single-strip section in Figure 4.3d and Figure 4.8.

On many shots in this scheme, high-energy noise generated by the area back-

lighter washed out data collected on the single strip framing camera. This signal

was collected while the gating mechanism on the single-strip framing camera was

closed, bypassing the microchannel plate and exciting the phosphor directly. This

is evident because area outside the active strip on the framing camera shows signal;

area outside the active strip was never opened via the voltage gate, and so collected

no data from x-rays entering the microchannel plate pores. An example of washed-

out single-strip framing camera data is shown in Figure 4.18. Initial investigation

showed no obvious link to higher laser energies on the area backlighter target and the

71

Figure 4.15: Raw four-strip framing camera data for a shock in xenon at 15 ns, launched with a 40µm beryllium driver. One wall of the tube is visible in this image, but the placementof the shock on the image cuts out any possible traces of xenon trailing along the wallof the tube. The other wall is obscured by a grid.

72

Figure 4.16: Blow-up of one cell of the four-strip framing camera data from April, 2004, shown inFigure 4.13. This image uses a plastic driver in xenon gas, backlit with a vanadiumsource. This cell, in the fourth column, second row as measured from the lower leftcorner of the image, at time t = 15.4 ns

presence of the high energy noise. Some correlation was shown between geometry

and the presence of noise. Variations of the positioning and tilt of the area back-

lighter target may have exposed more of the laser-irradiated area of the foil to the

single-strip backlighter, increasing the amount of high-energy noise it detected.

4.4 Odd Radiographic Data

While most data exhibited a thin layer with the normal of the dense layer parallel

to the axis of the cylinder, some data were unusual. Two pieces of data in particular

departed from the norm. The first was a shock launched with a 40 µm beryllium

disk, which was recorded with a single-strip framing camera at 9 ns after drive beams

turned on. Instead of launching a planar shock, this shock launched a shock that

looks like a bubble. The data from this shot are shown in Figure 4.19.

73

Figure 4.17: CAD drawing of dual radiography setup. Pinhole and area backlighters were 80 or 100degrees apart, imaging areas of the tube separated by approximately 1 mm at differenttimes relative to the drive beam pulse.

The first route to explore to try to explain this odd data piece is to make sure that

the target contained xenon gas at the time the shock was launched. If the target were

empty, no planar collapsed shock would form, and the image on the data might be

just the edge of the driven beryllium expanding into the empty cylinder. Even though

beryllium is virtually transparent at these x-ray energies, we may see the edge of the

beryllium due to phase contrast imaging, which may show more features at sharp

edges in density. The gas pressure inside the tube was recorded approximately 10

seconds before the laser beams fired, and showed a pressure of 1.12 ATM at that time.

The camera trained on the voltage transducer measuring the target gas pressure is

turned off during the shot, to prevent damage to the camera from the high voltages

in the target chamber. Within a few seconds after the shot, the camera turns back

on, and it was noted that the pressure recorded by the transducer dropped to zero.

This detail is important because it confirms that we were measuring the pressure in

74

Figure 4.18: Raw single-strip framing camera data, washed out by high-energy noise. Notice signaloutside of the active area of the microchannel plate. The bright strip present in thecenter of this image was present on other pieces of single-strip framing camera datataken in the dual radiography setup. On some pieces of data that were washed out, afaint image of the grid on the target is still visible.

the target, and not in a clogged fill hose.

A second explanation is that either the drive beams or the target was mispointed,

and so the beryllium piston was not launched evenly. If the target were misaligned

significantly, this would be evident from the radiography image. The target would

not be centered on the framing camera strip, or at the very least look different

than subsequent data images taken by the same camera at the same pointing. The

target position looks identical to those images. This was the first shot of the day,

and the lasers were aligned to the proper position that morning. No changes were

made to the laser pointing for the next shots, and those shots resulted in successfully

launched shocks. No other shots resulted in similar looking data images, ruling out

mispointed laser beams. It is possible the target was mispointed, however, metrology

of the target shows no features out of the ordinary.

75

Figure 4.19: Unusual data. This data was recorded 9 ns after the drive beams turned on, and doesnot show the normal thin, dense layer of xenon showed in most data images.

Though the target drive disk backside was inspected for glue after it had been

attached to the body tube, it is conceivable that some glue escaped notice, and

affected the structure of the shock.

The second piece of strange data produced a relatively normal dense collapsed

layer. However, this piece of data was the only collapsed layer which had a signif-

icant tilt with respect to the target walls. This data was produced by launching

a 20 µm thick beryllium disk, and was imaged with a single strip framing camera

8 ns after drive beams turned on, and is shown in Figure 4.20. Dotted lines are

superimposed to show the deviation of the shock normal from the target axis. This

tilt is approximately 10 degrees from the target axis, by far the most of any piece of

shocked data. Also, it seems that less xenon is imaged as trailing close to the target

walls, as it is in most pieces of single strip data.

76

Figure 4.20: Unusual data. This piece of data showed an exaggerated tilt of the collapsed layerfrom the target axis. Dotted lines show the deviation to be about 10 degrees.

A possible explanation for the exaggerated tilt of this shock is that the drive disk

may have not been uniformly illuminated. One drive beam was lost on this shot,

which may have affected the overall uniformity of the beam spot the 10 drive beams

usually make on the beryllium disk. This target may also have been misaligned in

the target chamber. If the center of the tube was not within 100 µm of the center

of the spot created by the drive beams, the beryllium may not have been launched

evenly down the tube. This kind of error could have occurred, for example, if the

center of the tube was off by 50 µm from the center of the drive disk, combined in

the correct sense with a 2 degree mounting error, which could translate to a 35 µm

move of the center of the beam spot, due to the tilted surface, plus the small error

in positioning the drive disk in the reticles.

77

4.5 Fringe Shifts from a Velocity Interferometry System for Any Reflec-tor

The Velocity Interferometry System for Any Reflector (VISAR) diagnostic was

deployed in early experiments, using a slightly modified target design that included

two openings in the side of the target; one covered by a quartz window, the other

covered with a quartz window with a reflective coating on one side, acting as a mirror,

as shown in Figure 4.21. Again, it was hoped that as the electron density increased

as the shock collapsed, the changing optical path for the interferometer beam would

cause fringe shifts.

Figure 4.21: Target for experiments using the VISAR diagnostic. Arms through the radius of thetarget were capped on one end with a quartz window, and on the other with a coatedmirror.

Unfortunately, radiative preheat from the shocked layer very quickly heated and

ionized the gas contained in the target. This ionization was significant enough that

before the drive beams even turned off, the probe beam used in the VISAR system

was significantly attenuated due to collisional absorption. Shown in Figure 4.22, the

fringes from the VISAR diagnostic cease even before the drive lasers turn off. In this

image, time increases to the right.

78

Figure 4.22: Representative piece of VISAR data. Note the fringes from the interferometer ceasebefore the drive beams turn off. Also note late time signal with no fringes, correspond-ing to the passage of the shock through the VISAR path.

79

This does not mean that this diagnostic was completely unsuccessful. While it

didn’t work in the way originally intended, several lessons were learned from the

data. Firstly, we know from these results that the preheat in the unshocked gas is

large enough to cause some level of ionization, causing the collisional absorption of

the green-light VISAR beam. We currently do not have an exact measure of this

level of preheat, but to cause ionization it must be on the order of 10 eV. Secondly,

examining the right side of Figure 4.22 (later in time), one sees a featureless blip in

signal on the interferometer. This blip (labeled thus because of the lack of fringe

data) corresponds to the time when the shock would have passed by the VISAR

window. It is logical then that the data comes from the reflection of the VISAR

probe beam off of the dense shock front.

Figure 4.23: Only VISAR data which showed any fringe shift. The total signal length was approx-imately 2 ns.

Only one piece of data showed any successful fringe shift. A small shift was noticed

on one shot, early in time, well before the shock could have approached the scattering

volume. These data are shown in Figure 4.23. After approximately 2 ns, these

fringes also fall prey to collisional absorption of the probe beam. Calculations from

80

collaborators estimate that this fringe shift would have been caused by a maximum

electron density of 1019 cm−3 . There is no discernible experimental reason why this

shot was successful while all others failed.

CHAPTER V

Radiographic Image Analysis

In the previous chapter, radiographic data from 9 shot days were reviewed. A

summary of all shots, both successful and unsuccessful, is given in Appendix C, Table

3. In the radiographic data, the presence of a dark feature spanning the diameter of

the shock tube was reported as detection of the collapsed shock. Other components of

the target, mainly beryllium and plastic, are transparent at the backlighter energies

used, 5.2 keV for xenon using a vanadium backlighter, and 3.6 keV for argon using

a tin backlighter. Gold is opaque for all backlighter energies used, and provided an

important means of calibrating both position and magnification in the radiographic

images.

From these images, we can discern the shock position, which gives us an average

velocity at the time of measurement. This measure is not an instantaneous veloc-

ity, which has not been measured. We can also measure imaged thickness, though

the caveat remains that this thickness is at best an upper limit due to alignment

considerations.

We cannot easily measure density as a function of transmission. Most of the light

that reaches the detector from the backlighter source is centered around the He-α-like

transition line from the material. Some of the light is from other transitions to the

81

82

Figure 5.1: Darkest radiographic image and horizontal lineouts showing intensity. a) Shot 40706,taken at t = 20 ns with a 40 µm thick drive disk. This piece of data had the lowestrelative intensity measurement taken. b) Horizontal lineout of the the shock. Thelineout is taken over the center 400 µm of the shock, with the x-coordinate given in thefigure. c) Horizontal lineout of the grid. The lineout is taken over 60 µm. The valleys ofthe grid wires in the image are not well resolved, as shown by the lack of a flat featureat the lowest transmission point.

K- and L- shells of the material. But a small fraction of emitted photons are very

energetic; energetic enough to pass directly through the tantalum substrate instead of

only through the pinhole on backlit pinhole images. These same high-energy photons

also pass through the microchannel plate in the framing camera to hit the phosphor

of the framing camera, creating a high-energy background on the image. This should

be relatively uniform across the image, so one might suspect it could be subtracted

out. Experimentally, the contribution to the intensity from high-energy photons

could be measured using the nominal backlighter setup and placing a filter before

the detector of the same material of the backlighter. At a sufficient thickness, this

filter would absorb photons generated from K- and L- shell transitions. However,

this filter should be transparent to the high-energy component, which could then

be recorded on the detector. As a comparison, beryllium filters used to shield the

framing camera from shrapnel was 0.010”, equivalent to 250 µm, and the foil used

to generate the backlighter x-rays was 5 µm. This particular measurement was not

83

made for the data in the previous chapter, as it would have the unfortunate side effect

of blocking important data. However, a high-energy background should be detectable

even where the image was completely opaque, as the photons need not have passed

through the target by way of a pinhole. In the radiography images in the previous

chapter, the dense shock was not completely opaque, as seen in a lineout of one of

the darkest shock images, shown in Figure 5.1. The gold grid in the radiography

images should be opaque, but covers a small surface area, so an average is taken over

a small number of pixels. The wires on the gold grid are only 20 µm thick, covering

only 2 source-limited resolution elements. As you can see from the lineout shown in

Figure 5.1c over 60 µm of the grid, it is not well resolved in this shot. If the grid

were well resolved, the peaks and valleys of the lineout would be flat, which they

are not in this image. Therefore, examination of transmission through the grid wires

does not give a measurement of the high-energy background, either. To measure this

contribution on future shots, a larger piece of highly opaque material could be placed

on the targets, which would provide the necessary measurement without the loss of

any shots for data.

5.1 Shot-to-Shot Variability

Each data image from a single-strip framing camera was taken on a single shot,

which introduces the question of shot-to-shot variability. Though we strived to use

identical laser conditions on each shot, average laser energy varied by up to 20%,

and the orientation of the target changed between shot days to accommodate other

experiments, decreasing the amount of time spent adjusting the laser and increasing

the amount of shot data obtained. Small differences in the targets could also make

a difference. As the University of Michigan team learned more about target fabri-

84

cation, targets were produced with more uniform features, and were produced with

tighter specifications. When we could not control the specifications on a component,

such as for components produced in other facilities, measurements were made in the

laboratory of the deviations from nominal values. The most important example of

this was that the beryllium drive disks were produced with a 10% tolerance on thick-

ness. These thicknesses were measured with micron accuracy using calipers at the

University of Michigan.

Figure 5.2: Two images showing shot to shot variability in the data, taken at 10 ns ± 0.25 ns.Sources of the variability are discussed in the text. a) Shot number 37033, using a 38µm drive disk. b) Shot number 37034, using a 44 µm drive disk.

As an example of the importance of tracking these individual contributions to

shot-to-shot variability, let us examine two pieces of single-strip framing camera

data, taken at 10 ns ± 0.25 ns after the drive beams turned on to illuminate a 40

µm beryllium drive disk. These two pieces of data are shown in Figure 5.2. Part a of

this image is shot 37033, and part b is shot 37034; these data were taken on the same

day, one after the other. The target used for shot 37033 had a 38 µm ± 1 µm drive

disk, while the target used for 37034 had a 44 µm ± 1 µm drive disk. Metrology of

85

these two targets was double-checked for consistency, and is accurate to within the

tolerances discussed in Chapters 3 and 4, as is positioning in the target chamber.

All of these things contribute to shot-to-shot variability. The data is consistent with

the different drive thicknesses measured; the slightly thinner disk used in Figure 5.2a

moved farther than the thicker disk.

5.2 Shock Position as a Function of Time

0.000

500.0

1000

1500

2000

2500

3000

3500

4 6 8 10 12 14 16 18 20

Measured and Simulated Position vs. Time

40 µm position20 µm position40 µm sim position20 µm sim position

Po

sit

ion

(!

m)

Time (ns)

Figure 5.3: Plot of position data from experiments using 20 and 40 µm thick drive disks, and fromsimulations of those experiments using a 1D radiation hydrodynamics code HYADES.The simulations overestimate the shock position for both drive disk thicknesses, seem-ingly from an error in the first few nanoseconds of the experiment. The experimentaldata also hints that at a late times the shock may slow, possibly from the loss of asignificant driving force from the beryllium piston.

86

A plot of shock position versus time shows two important features. Firstly, when

compared with shock positions given by 1-D radiation hydrodynamic simulations, it

shows that experiments are significantly slower than predicted. From the plot shown

in Figure 5.3, it seems that the discrepancy in the prediction comes from early time

interactions, as the simulation curves lie well above the data even at the earliest

measured position . This is discussed further in the Radiation Hydrodynamics Sim-

ulations chapter. Secondly, the plot shows at some late time for both the 20 and 40

µm drive disk, the shock may slow. This transition marks when the rarefaction wave

acting on the driven side of the beryllium moves all the way through the slab, and

begins to rarify the backside of the collapsed gas layer. At this point, the evolution

of the shocked gas will change. In simulations, the shock slows, and collapsed layer

becomes more extended as a rarefaction begins to affect the side of the layer near

the rarefied beryllium.

5.3 Shock Thickness as a Function of Time

As the shock moves through the gas in these experiments, the shocked gas gets

denser as it loses energy to radiation. It continues this density collapse until it is

optically thick, as explained in more detail in the Radiation Hydrodynamics chapter.

As the shock continues through the gas-filled tube, the thickness of the collapsed

layer increases, as the shocked then cooled gas piles on the front of the already

optically thick layer of xenon. This prediction is echoed by radiation hydrodynamic

simulations, discussed in Chapter 7. In Figure 5.4, we plot the measured thicknesses

of collapsed layers from 20 µm and 40 µm thick drivers as points, as well as a

predicted layer thicknesses from simulations as lines.

This effect proves difficult to measure, as the measured thickness of the collapsed

87

20.00

40.00

60.00

80.00

100.0

120.0

140.0

160.0

500 1000 1500 2000 2500 3000 3500

Measured and Simulated Thickness vs. Position

40 µm layer thickness20 µm layer thickness40 µm sim thickness20 µm sim thickness

La

ye

r T

hic

kn

es

s (!

m)

Position (!m)

Figure 5.4: Plot of imaged thickness of dense collapsed xenon as a function of the distance the shockhas traveled. Data are shown as points, with the position error bar from uncertaintyestimates from metrology, and the thickness error bar from uncertainty from the densityat which the collapsed layer “begins”. Though the data shows a general trend towardsthicker shocks as more ground is covered by the shock, this measurement is highlysusceptible to overestimating the thickness of the shock due to slight departures fromperfect side-on imaging. Note that only one data point lies on the simulation curve, andthe rest for both drive disk thicknesses lie well above. This effect is some combination ofimaging a tilted shock and radiation treatment in Hyades, discussed in the next chapter.

88

layer depends greatly on the alignment of the target with respect to the imaging

plane. A target that is imaged perfectly side-on will give the actual thickness of the

collapsed layer, plus some amount of smearing due to the finite length of time that the

shutter is open. Any variation from perfect alignment introduces a projection of the

layer’s width to the measurement. Most of the imaged shocks have a width between

50 and 120 µm. However, the depth of these collapsed layers will be approximately

the target diameter. Because the depth is so big compared to the width of the

shock, the effects of misalignment are great. Tolerances for target construction allow

a ± 2 degree error in mounting angle around the target axis. An additional error

from target mounting angle on the stalk makes the compound error even greater.

In addition to this effect, the shock may be tilted from the target axis. This would

happen if the spot made by the drive beams on the beryllium surface was offset from

the center of the target tube. Evidence of tilted shocks, and therefore some error

in positioning the target, exists on pieces of data shown in Figure 4.20, discussed in

the last chapter. At most, we suspect that the target may be imaged as 5 degrees

away from side-on. A 5 degree misalignment of a 50 µm wide shocked layer can

result in the imaging of a 90 µm wide feature on the film. This is explained further

in the Radiation Hydrodynamics Simulations chapter, in the creation of a simulated

radiograph from 2D simulation data. Structure in the collapsed layer may also cause

the layer to spread more than the 1D predictions suggest.

5.4 Structure in the Cooling Layer

Images from single-strip framing cameras underwent additional image processing

to help compensate for non-uniform illumination. Despite strong efforts to make

sure the area that was imaged was illuminated uniformly by the backlighter, data

89

images often showed dark vertical strips on images, as well as scratches and other

irregular features. In an effort to at least remove large scale variations on the data,

calibrated images were smoothed over large areas (much larger than the collapsed

layer thickness), and then subtracted from data images. This large scale smoothing

left the data, grid, and target wall features intact on the image, but removed any

features which were larger than the smoothed elements. These elements ranged from

100 to 300 µm, depending on the results for an individual image.

(a) (b) (c)

Figure 5.5: Images of shock from shot 39927, t = 14.6 ns launched with a 20 µm beryllium driver. a)Calibrated data smoothed over a resolution element. b) Image smoothed over 200 µm,subtracted from original image, then once again smoothed over a resolution element. c)Image smoothed over 100 µm, subtracted from original image, then once again smoothedover a resolution element. Notice how smoothing over a shorter distance emphasizes thedarkest parts of the shock, showing that the shock image is actually somewhat knotted.

This smoothing revealed formerly obscured structure in some images, and showed

more detail of structure in others. The data from a 20 µm drive disk at 14 ns after

the drive beams turned on proves to benefit greatly from this subtraction technique.

Shown in Figure 5.5, we compare the data smoothed over a resolution element in part

(a) with the same image smoothed over 200 µm, subtracted from the unsmoothed

image, and then smoothed over a resolution element. This piece of data is the most

striking example of structure on the front and back side of the collapsed layer. As

this piece of data was smoothed to different degrees, different features became visible,

90

as is shown by examining Figures 5.5b and c. Regular structure emerges from the

image when the background is smoothed out and subtracted over 200 µm elements,

but knots of denser structure appear when the image is smoothed and subtracted

over smaller elements. The clumps of dark material seem in Figure 5.5c are several

times larger than a source-limited resolution element, with most of the visible clumps

being about 30-40 µm in diameter.

Figure 5.6: Images of shock from shot 38983, t = 15 ns using a 20 µm beryllium driver. a) Cal-ibrated data smoothed over a resolution element. b) Image smoothed over 200 µm,subtracted from the original image, and smoothed over a source-limited resolution ele-ment. Smoothing in this image seems to enhance the contrast between the shock andthe surrounded gas. Structure emerges in the smoothed image, as well, on both thefront and back sides of the image. These structures are larger than a source-limitedresolution element. The white pixel near the top edge of the shock is a dead pixelsmoothed over a resolution element, showing the size comparison.

Smoothing significantly increased the contrast of the image from shot 38983,

shown in Figure 5.6. It also revealed small, clumpy structure on the front side of the

shock, most visible near the top-right of the shocked layer in Figure 5.6b. A white

pixel smeared over a source-limited resolution element confirms that the structures

are a few times larger than a resolution element. Three knots of material are about

30 µm in diameter, and are somewhat regularly spaced.

91

Figure 5.7: Images of shock from shot 39925, t = 4 ns using a 10 µm beryllium driver. a) Calibrateddata smoothed over a resolution element. b) Image smoothed over 200 µm, subtractedfrom the original image, and smoothed over a source-limited resolution element. Inthese images, the light and dark diagonal stripes are scratches on the film. While somestructure emerges in the smoothed image, the front side of the shock is obscured by ascratch.

Some structure is also visible on the only successfully imaged shock driven with

a 10 µm beryllium drive disk, imaged at 4 ns after the drive lasers turned on. This

shock is shown in Figure 5.7. The features are clearer in Figure 5.7b, which was

smoothed over 200 µm and subtracted from the original image. Unfortunately, a

scratch in the film makes it difficult to discern features on the front side of the shock,

but features on the backside that are 30-40 µm long and 20-30 µm wide are visible.

The densest and thickest shock imaged also shows quite a lot of structure, and is

shown again in Figure 5.8. The single-strip image from shot 40706, taken at t = 20

ns, driven with a 40 µm thick drive disk shows features on the front side, back side,

and top side of the shocked layer (near the target wall). On the front side of the

shock, the largest structure feature measures approximately 40 µm in diameter, the

largest feature on the front side of a shock imaged to date. The features on the back

side are also larger than in other images, with a large clump near the center of the

92

Figure 5.8: Images of shock from shot 40706, t = 20 using a 40 µm beryllium driver. a) Calibrateddata smoothed over a resolution element. b) Image smoothed over 200 µm, subtractedfrom the original image, and smoothed over a source-limited resolution element. Thisimage shows quite a bit of structure, and shows the largest features on the front side ofthe shock.

tube on the backside (visible as a dark spot in Figure 5.8b) measuring approximately

50 µm in diameter. The longest finger of dark material not trailing along the edge

of the target measures almost 100 µm in length.

It seems odd that if this structure was caused by an instability that the dramatic

features be always on the backside of the shock. Some of this bias may be explained

by the finite shutter length for the image. The voltage spike that effectively opens

the camera is 200 ps long. For a shock moving 100 km/sec, this leads to a smear

of 20 µm. Most of the structure imaged is on the order of 30-40 µm. On the back

side of the shock, the moving layer would drag out the effect of structure, making

it appear longer and more pronounced. On the front side of the shock, the features

would be obscured by the densest part of the layer as it moved forward during the

open shutter. At these high velocities, this could be a sizable effect. The actual

distribution and cause of this structure is an interesting topic for future graduate

93

student work.

CHAPTER VI

Thomson Scattering Experiment in Argon Gas

The previously described experiment was novel, and is poised to make a significant

contribution to the study of radiation hydrodynamics. It explored a radiative shock

that was faster than those of previous research in denser material, producing sig-

nificant radiative effects. The possible extensions of the experiment may cover new

regimes, especially with the National Ignition Facility at the Lawrence Livermore

National Laboratory. In the meantime, new experiments to measure temperatures

and densities will extend the practical capabilities of existing diagnostics, priming

them for use on the problem of ignition in inertial fusion.

As an effort to begin using existing techniques in the novel setting produced in the

collapsing radiative shock experiment, we performed an experiment using Thomson

scattering techniques on a radiative shock driven in argon.

Thomson scattering is a technique that probes the characteristics of a plasma. A

coherent light source at a certain wavelength is Thomson scattered off of electrons

in a system. The spectrum of the scattered light is affected by the state of the

plasma. This technique can give information about the electron temperature, the

ion temperature, and the density of the probed plasma.

Thomson scattering operates in two distinct regimes, which give information

94

95

about different plasma phenomena. The measure of this is the scattering param-

eter, α, which is proportional to the ratio of the fluctuation wavelength (λ) to the

Debye length (λDe) in the probed plasma;

(6.1) α =1

kλDe

∝ λ

λDe

.

The Debye length of a plasma in cgs units is given by the expression

(6.2) λDe =

√kBTe

4πnee2,

where ne is the electron density of the plasma, Te is the electron temperature, and kB

is the Boltzmann’s constant. When α is large, or the ratio of the probed wavelength

is large compared to a Debye length, Thomson scattering will probe collective wave

effects over many plasma scale lengths. Collective scattering easily probes electrons

in the Debye sphere of ions affected by wave phenomena, such as low-frequency

ion-acoustic waves and higher frequency electron-plasma waves. When α is small,

or when the ratio of the probed wavelength is small compared to a Debye length,

Thomson scattering will probe individual electron effects on scale lengths shorter

than the Debye length.

One can probe the desired effects by correctly choosing the Thomson scattering

probe laser beam wavelength (kts = 2πλts

), compared to the wavelength of the observed

scattered light(ks = 2πλs

), taking into account the direction of observation with respect

to the incident light (θ). For wavelength shifts between the incident and observed

light that are small, the wave-vector probed (k) is

(6.3) k = 2ktssinθ

2.

96

This equation is valid for low-frequency fluctuations, for example from ion-acoustic

fluctuations in the plasma, but not for scattering from higher frequency electron-

plasma waves. The light scattered from these low frequency fluctuations results in

two spectral peaks, scattered from the ion-acoustic waves propagating parallel and

anti-parallel to the probed wave-vector.

In the collective regime, the separation between the measured peaks of the scat-

tered light is proportional to the sound speed of the probed wave in a plasma. For

this experiment, the important wave phenomenon is the ion-acoustic wave, which

has a sound speed of ([46])

(6.4) c2iaw =

ZTekB

mi

(1

1 + (kλDe)+

3Ti

ZTe

).

The separation of the peaks is given by

(6.5) ∆λiaw =2λprobe

2πc(ciawkiaw),

where λprobe is the wavelength of the probe beam and kiaw is the wave-number of the

probed ion acoustic wave. If the ions have a flow velocity relative to the laboratory

frame and parallel to the probed ion acoustic wave, the scattered light peaks will be

shifted from the central wavelength by

(6.6) ∆λflow =2λprobe

2πc(vflow · kiaw),

where vflow is the flow velocity of the probed plasma. The wavelength shift from

the flow can also be derived from the relation between the k-vectors. The probed

97

vector k is equal to the difference between the incoming wave-vector and the vector

of the scattered light, k = ks − ko. For small shifts, ko ≈ ks, so

(6.7) k ≈ 2kosinθ

2= 2

ωo

csin

θ

2.

Given that ω = k · v, this equation is equivalent to a frequency shift,

(6.8) ω =2vωo

csin

θ

2.

Converting to wavelength, ω = 2πλ

, we obtain

(6.9)2π

λ− 2π

λo

=π

λo

2v

csin

θ

2

Rearranging to get the fractional wavelength shift, ∆λλ

,

(6.10)∆λ

λ=

2v

csin

θ

2

In this experiment, the wavelength of the probe beam was 263.3 nm. The Debye

length of a plasma is given by

(6.11) λDe =

(kTe

4πne2

)1/2

= 7.43× 109T 1/2e n−1/2

e nm

for Te in eV and ne in cm−3.

Usually, Thomson scattering is used to probe a uniform or slowly changing plasma.

In this way, the separation and width of the peaks and the intensity of the scattered

light gives the electron and ion temperature, and the electron density of the plasma.

98

If one of these quantities changes over the course of the experiment, it may be

detected on a streak camera by the changing peak width, separation, or intensity as

a function of time.

OmegaDrive

Beams

Scattered light exit hole(towards TIM 2)

Gas fill tubeBe Drive Disk

4! entry hole(towards P9)

Ar gas cell

Figure 6.1: 2D diagram of the target used in the Thomson scattering measurement of the drivenradiative shock. It is very similar to the target discussed for earlier experiments, with anextra arm and inlet and outlet holes for the probe beam and scattered light diagnostic.

The experimental setup was similar to that in the radiative shock experiment

described in Chapter 3, and a diagram showing the main features of the target is

shown in Figure 6.1. Here, a 20 µm thick, 2 mm diameter beryllium disk is mounted

on a 575 µm ID, 625 µm OD polyimide tube. This tube was fitted with a hypodermic

fill tube, attached to a transducer to measure gas pressure just before the laser shot.

In addition to this geometry, another polyimide tube was mounted at a 45 degree

angle to the main polyimide tube axis. The axis of this tube intersects the center of

the main target axis at 3.7 mm from the beryllium drive surface. When the target

is oriented correctly in the laser target chamber, the axis of this tube points towards

the probe beam port through target chamber center. The end of this tube closest to

the probe beam was covered with a 3000 A thick polyimide film, while the opposing

end of the tube was filled with epoxy. At a scattering angle of 100 degrees and

also at an angle of 45 degrees from the main target axis, another hole was drilled

in the target that, when properly oriented, pointed at the scattered light collection

99

diagnostic. This opening was also covered with a 3000 A thick polyimide film. This

assembly was gas tight, and was filled with argon gas at 1.1 ATM, equivalent to

0.001 g/cm3 or 1.5 x 1019 atoms/cm3. Metrology photos of the assembled target are

shown in Figure 6.2.

Figure 6.2: Metrology photos of targets used in Thomson scattering experiments.

A driven shock was produced in the argon gas as in previous experiments, by

focusing 10 laser beams of the Omega laser facility in a 1 mm spot on the beryllium

disk in a 1 ns square pulse. The beam energy was a maximum of 400 J/beam,

resulting in a total drive irradiance of 4.8 x 1014 W/cm2. The beams were smoothed

once again by SSD (Smoothing by Spectral Dispersion) and using Distributed Phase

Plates (DPPs) to produce as uniform a laser spot as possible. The midpoint of the

rising edge of the laser pulse defines t = 0. At t = 13 ns after the start of the drive

beams, 4 backlighter beams fired in a 2 ns square pulse and at a 400 µm spot on a 5

µm thick tin foil. This resulted in a backlighter irradiance of 1.5 x 1014 W/cm2, and

used no beam smoothing. At t = 16 ns after the drive beams fired, a single destroyer

beam with no beam smoothing struck the plastic covering over the scattered light

exit hole. This beam was approximately 400 J in energy in a 1 mm spot, in a 2 ns

square pulse, resulting in an irradiance of 6 x 1012 W/cm2, used to explode the thin

100

covering to allow the scattered light to escape. At t = 19 ns after the drive beams

fired, a frequency-quadrupled (4ω, λ = 263 nm) probe beam was directed to target

chamber center (tcc) at 200 J in a 2 ns square pulse and in a 100 µm spot. This beam

destroyed the thin plastic cover to the entrance hole on the target as it propagated

through the arm tube to scatter from the plasma on the axis of the target.

Let us first check that this experiment does in fact fall into the collective regime.

Both the temperature and the density change throughout the system, so we will

examine certain points of interest. In the unshocked argon gas, the material density

(at 1.1 ATM) is 1.5 × 1019 cm−3. We do not have a good measurement of the

temperature of the unshocked gas, but let us estimate that it is approximately 10

eV, the same as the estimate given in the xenon gas temperatures discussed in the

earlier chapters. This is a good estimate based on VISAR experimental results in

xenon given in Chapter Four, which show that the gas must be at least a few eV and

partially ionized. In this case, the Debye length of the gas would be about 6 nm. The

wavelength of the probe beam scattered from the plasma is 263.3 nm, which gives

a scattering parameter α = 43. As the shock moves through the gas, compressing

and ionizing the material, the Debye length gets slightly shorter. For example, in

the regime near full radiative compression, where the ions reach a compression of

more than 20 times the original density, the gas reaches an average ionization state

Z ∼ 10 − 15, and the maximum electron temperature is 200 eV. Here, the Debye

length is shorter, at 1.9 nm. This gives a scattering parameter α = 138, well into the

collective regime. Farther behind the shock, temperatures drop while compression

remains high, which would result in an even shorter Debye length. Therefore, the

probed plasma is in the collective regime through the entire experiment.

Collected scattered light was observed for approximately 300 ps during the middle

101

Time

Wavelength

Figure 6.3: Streak camera image of collected scattered light data from TS experiment. Early intime, the detector captures light from the destroyer beam blowing off the cover on thetarget that points towards the collection diagnostic, which then fades. A short timelater, the characteristic two-peaked spectrum of collective Thomson-scattering behaviorappears.

of the 2 ns window during which the probe beam was on. Scattered light was collected

with a spectrometer using a 3600 lines/mm grating, giving a dispersion of 0.036

A/pixel. This spectrum was recorded on a UV streak camera, with a sweep window

duration of 5 ns, centered at t = 20 ns after the drive beams turn on, with a time

resolution of 6.0 ps/pixel. The collected spectrum is shown in Figure 6.3. Data

collected showed that emission caused by the destroyer beam to be fading away,

shortly after which classic two-peaked scattered light signal was detected. The onset

of the collection of scattered light from warm plasma happens as the shock front

crosses the scattering volume, both heating and compressing the material. Here,

the ion temperature would have peaked, while the electron temperature would have

been raised only slightly by the shock. The cessation of signal happened more than

a nanosecond before the probe beam itself turned off. This would have happened

102

either as the cooling, collapsing gas became more dense than the reflection density

at that wavelength and angle, or as the signal got refracted away from the detector

as the density increased. The reflection wavelength is

(6.12) nreflection = nc cos2 θ =1.1× 1021

λ2µm

cos2 θ,

where nc is the critical density of the gas, θ is the angle of probe laser incidence, and

λµm is the probe laser wavelength in microns, For a probe wavelength of 0.2633 µm

and an incident laser angle θ = 45 deg, this reflection density is nreflection = 7.9×1021

cm3.

Between the near-instantaneous increase of temperature and density at the shock

front and the high-density cutoff of the signal, the Thomson scattering diagnostic will

probe large gradients in ion temperature, electron temperature, and electron density,

or mass density and average ionization state. This means that the signal detected

will actually be a weighted average of the plasma parameters, where high electron

temperatures will be responsible for most of the signal. If measured quantities are

changing at a rate near or faster than the electron plasma frequency, these changes

may not be resolved on the detector. The electron plasma frequency is

(6.13) fpe =ωpe

2π=

1

2π

√4πnee2

me

.

An estimate of the frequency in this region of changing parameters is possible,

using the initial shock compressed value of the ion density, ni, and an educated guess

of the average charge state of the plasma. The unshocked ion density of the argon

gas is 1.5 × 1019 ions/cm3. Shock relations say that the initial density increase as

a strong shock compresses the system is a factor of 4 to 10, depending on the value

103

of the polytropic index of the gas. Average charge state is a function of electron

temperature, which doesn’t increase until after collisions with shock-heated ions.

We will need to use an average charge state somewhat lower than the average charge

state at the estimated peak of the electron temperature. This happens farther away

from the shock front, and Z = 10 is a good estimate of this value. This results

in an estimate of the electron density just after the shock front of ne = 6 × 1020

electrons/cm3, and gives an electron plasma frequency of 2.2 × 1014 sec−1. At such

a high frequency, smearing of the signal as the electrons cool is not expected.

The flow velocity was measured to high accuracy by examining the shift of both

of the peaks of the scattered light away from λo by Doppler shift. On the Thomson-

scattered spectra, we see a wavelength shift of 1.41 ± 0.1 A, where λo was obtained

from measurements of stray (unscattered) probe beam light recorded on the streak

camera. From this, the measured flow velocity of the shocked plasma is 110 ± 7

km/sec.

The onset of detected signal marks the arrival of the shock at the scattering

volume, and therefore gives a measurement of average shock velocity. Because the

shock reached the scattering volume at 20.1 ± 0.2 ns after the drive beams turned

on, the average velocity over that period of time was 193 ± 5 km/sec. The probe

beam was on before the shock reached the scattering volume, and could scatter off

of the preheated gas ahead of the shock. However, no signal was seen from this lower

temperature, lower electron-density region. It is possible that with a more sensitive

spectrometer, Thomson scattering could be used to measure temperatures in the

upstream, unshocked region, but the spectrometer used did not detect signal on this

experiment.

The separation of the two scattered peaks is proportional to ZTe +3Ti in the limit

104

of a fluid treatment of the plasma. The separation is equal to

(6.14) ∆λ =λ2

probe

πc(kcs),

where λprobe is the wavelength of the probe beam, k is the wavenumber of the probed

ion-acoustic wave, given in Equation 6.3, and cs is the ion-acoustic sound speed,

given in Equation 6.4. Substituting and rearranging into a useful quantity,

(6.15) ZTe + 3Ti =mi

kB

(∆λ

λprobe

c

4 sin θ/2

)1/2

Recall for this experiment that the probe wavelength (λprobe) is 263.3 nm, the scat-

tering angle (θ) is 101 degrees, and the atomic weight of argon is 40 amu.

We measure the separation of the peaks by fitting the lineout of each peak with a

Gaussian curve, and measuring the separation of the maximums of each curve. On

the data shown here, the separation of the peaks is 2.75 ±0.2 A, giving the sum of

ZTe + 3Ti = 4343 ± 750 eV. The main contributor to this sum will be the product

of the electron temperature with the average charge state Z.

We can use fits to the data taking advantage of scattered light form factors from

kinetic plasma theory to get a better idea of individual temperatures. This fluid limit

quantity will help constrain the range of the main contributor to this quantity, ZTe,

as reasonable estimates should fall within the error bars on this directly measured

quantity. Our form fitting calculation explicitly included account of the spectral

resolution of the instrumentation.

Using form factor fits to these peaks should give us a well-constrained estimate

of the ion temperature and the product of the electron temperature and the average

charge state. Comparing different atomic models, which give the average charge state

105

Figure 6.4: Results from atomic models, giving Z and ZTe as a function of Te.

as a function of temperature, it is then possible to estimate the electron temperature

and average charge state individually. This was done using a Saha atomic model,

an average-atom model, and an analytic estimate also based on the Saha atomic

model. Shown in Figure 6.4 are results from these models, giving both Z and ZTe

as a function of Te. A straight line fit through the center of these values provides

the estimates used to give separate results for average charge state and electron

temperature from fits to the scattered light spectrum. The best fits in Figure 6.5a.

Combining information from the fluid separation of the peaks, the data from the

kinetic model fit, and the temperature dependence from the ionization state models,

we can conclude that in the plasma measured, Ti = 300 +200/-85 eV, Te = 250 ±

35 eV, and Z = 13.7 ± 0.5. Due to physical reasons, the ion temperature cannot

be lower than the electron temperature, constraining the lower error bar on the ion

temperature. Fits using the extreme values of the error bars, for comparison, are

shown in Figure 6.5b and c.

106

(a)

(b)

(c)

Figure 6.5: Best fit and error bars to Thomson scattered data. a) Lineout from data (purple) andbest fit to data (black), with Ti = 300 eV, Te = 250 eV, and Z = 13.7, based on averageatom model. b) Lineout (purple, solid) and Te error bars from fluid limit. Dashed lineis Ti = 300 eV, Te = 285 eV, Z = 14.2. Dotted line is Ti = 300 eV, Te = 215 eV,Z = 13.2. These lines obviously lie well outside the lineout of the data. c) Lineout(purple, solid) and Ti error bars from fitting the data. Dashed line is Ti = 500 eV, Te

= 250 eV, and Z = 13.7, while the minimum of the ion temperature is the same as theminimum of the electron temperature. That curve does not lie significantly outside thedata points.

107

Changes to the fit parameters (ZTe and Ti) change the shape of the fit in distinct

ways that provide unique information. As stated above, the separation of the peaks is

proportional to ZTe +3Ti. So, changes to Ti will move the peaks slightly, while small

changes to Te or ZTe will have larger effects on the relative separation of the peaks.

However, changes to the ion temperature also affect the depth of the trough between

the two peaks and broadens or tightens the wings of the spectrum. This effect is

the result of the level of Landau damping, which corresponds to the ratio ZTe/Ti.

These characteristics of the fit can be seen in Figures 6.5 b and c. In Figure 6.5b, the

uncertainty in the separation of the peaks is used to calculate the uncertainty on the

electron temperature and average ionization state, as ZTe is the main contributor

to that quantity. The extreme values of Te and Z are then plotted as a fit to the

data, holding Ti at its best fit value, 300 eV. The fit with these values deviates from

the data, with the peaks being too wide on the upper value (long dashes) and too

narrow on the lower value (short dashes). Since it also affects the value of ZTe/Ti,

the trough between the peaks is too low for the higher value (long dashes), and too

high for the lower value (short dashes), as well as deviating slightly in the fit to the

wings of the data. In Figure 6.5c, we use the deviation of the fit from the trough

between the peaks as an indicator of the ion temperature uncertainty. Keeping Te

and Z at best fit values, we let Ti increase until the trough height was well above

the data level. This variation had some effect on the fit to the wings of the data, but

this effect is much less pronounced.

These results differ from the predictions from 1D radiation hydrodynamic models,

which predict a peak electron temperature of Te = 200 eV, with Ti = 450 eV and Z

= 15.6 at the same position. This indicates that the shock may be initially stronger

than in the simulation, resulting in a higher initial ion temperature that transfers

108

more energy to the electrons in the plasma. The ion temperature prediction is within

the large error bars given on that quantity. The average charge state is dependent

on the model used, which was a Saha model in these simulations.

This measurement of average velocity at 20.1 ns and 3.7 mm from the initial

position of the drive surface marks the latest measurement of position after the

shock is launched. This may be significant, as it raises the question as to how

quickly the shock is decelerating at this point. The driven system depends on the

momentum of the shocked beryllium slab continuing to drive the system forward.

At the probed point, 3.7 mm from the initial drive disk position, assuming all of

the argon is swept up by the shock, the shocked gas mass is 1.05 µg. The beryllium

piston mass inside the tube for a 20 µm thick drive disk is 10.0 µg, so the beryllium

momentum is still significant compared to the momentum in the argon, assuming

they are moving at the same speed. A rarefaction wave on the laser-incident side

spreads out the beryllium plasma, and continues through the beryllium as the shock

loses strength. When the shock has slowed significantly, the rarefaction wave moves

completely through the beryllium slab, and begins to affect the dense, shocked gas.

This may affect the shock speed, increasing the rate of deceleration.

What happens when a shock is no longer driven? If the shock were the only

element of a system, a rarefaction wave would form on the side of the disturbance that

was initially driven, moving at the sound speed of the shocked plasma. Eventually, it

would overtake the shock front, and form a blast wave. In this system, a rarefaction

wave begins to propagate through the beryllium slab as soon as the driving laser

beams turn off. This rarefaction wave proceeds through the beryllium. However,

radiation from the collapsed layer can ablate the backside of the beryllium slab,

causing the material to flow in the opposite direction of the material affected by the

109

rarefaction wave at slightly supersonic speeds. It is only as the shock slows from

the build up of shocked material in the collapsed layer that the rarefaction wave can

proceed through the remaining beryllium, and into the collapsed layer. This will

depend on how strongly the collapsed layer is radiating, and how much material is

involved in the supersonic flow.

CHAPTER VII

Radiation Hydrodynamic Simulations

7.1 One-Dimensional Hyades Simulations

The bulk of the simulation of this experiment was done using the 1-D version

of the radiation hydrodynamics code, Hyades [31]. Hyades is a single-fluid, three-

temperature Lagrangian code. This means the electrons and ions are treated as a

single fluid instead of two separate fluids in the system, but the radiation temper-

ature, electron temperature, and ion temperature are calculated and tracked sepa-

rately. A Lagrangian code has zones that are initially assigned parcels of material,

and the mass remains in the zone for the entire simulation; the zone moves to track

the material as the experiment evolves, becoming more compressed or expanding

as the material changes density. Hyades uses a multigroup, flux-limited diffusion

scheme to account for radiation in the system. Multigroup means that photons are

divided by wavelength into groups, and the appropriate opacities for each group of

energy/wavelength are calculated. Hyades can also run with radiation transport off

or in a greybody mode, where it is assumed that all radiation is at the same “grey”

wavelength and uses a tabular opacity. Flux-limited diffusion means that radiation

transport is approximated as a diffusion mechanism, which is fairly accurate for an

optically thick system, limited by a physically acceptable limit for the amount of flux

110

111

which can propagate. At the extreme, this is the free-streaming limit for photons.

In hydrodynamic codes, the amount of thermal energy conducted by electrons can

become unphysically high. This is because codes use a Spitzer-Harm model for heat

flux, which can overpredict the heat flow in systems with steep temperature gradients.

Here we use an electron heat flux-limiter to reduce the heat flux to physically sensible

levels.

Hyades was used first for proof of principle in the experiment described in previous

chapters, then later as a guide to experiment design. Simulations discussed in this

section were done at a laser irradiance of 4.2 x 1014 W/cm2. This number is 42%

of the highest irradiance ever used on an actual shot, 1.0 x 1015 W/cm2. The lower

irradiance in the simulations are used to account for 2D energy transport effects

in the laser irradiated surfaces, which has been confirmed in other laser-irradiated

hydrodynamic experiments. Subsequent experiments were done at a lower irradiance.

In the section comparing simulation results to experiment results, simulations were

performed at an irradiance of 42% of the lower laser irradiance, 3.36 x 1014 W/cm2.

This is discussed further in Section 7.3.

7.1.1 Production of a radiatively collapsed shock

The first task put to Hyades was to show that a low-Z pusher launched via laser

ablation pressure could produce a shock in a gas that collapsed higher mass density

than would occur through strong shock compression. Recall, a strong shock in an

ideal gas (γ = 5/3) compresses the shocked material by

(7.1)ρf

ρo

=γ + 1

γ − 1= 4.

Processes that increase the internal degrees of freedom of a gas will lower the poly-

112

tropic index, and increase the initial compression seen in a plasma. In simulations

of the experiment, where a 40 µm thick beryllium disk is launched into 6 mg/cm3 of

xenon gas with no radiation transport, we see a shock compression to a maximum

density of 0.06 g/cm3, or by factor of 10 over the initial density. This suggests that

the polytropic index of the material as calculated by the SESAME equation of state

table is γ = 11/9, or 1.22. After the initial shock compression of xenon gas, further

compression occurs when radiation saps energy from the shocked gas, decreasing the

temperature, and correspondingly increasing the density.

Figure 7.1: Two 1D hyades simulations of density. The solid line shows the density profile ofa beryllium-driven shock in xenon using a multigroup treatment of radiation. Thevertical line shows the boundary between these two materials, with the xenon featurebeing the rightmost dense feature. The dashed line shows the same experimental setupin a Hyades run with radiation transport turned off. Again, the vertical line shows theboundary between the driving beryllium plasma and the xenon plasma.

In Figure 7.1, two density profiles at 16 ns from the start of the drive beams

from Hyades runs are plotted. The dashed line is the simulation mentioned above,

113

where 40 µm of beryllium is launched via laser ablation pressure into 6 mg/cm3 of

xenon gas, with the radiation transport in the system turned off. The laser launches

a shock that moves from left to right. The boundary between the xenon and the

beryllium is indicated by a vertical line, here labeled “contact surface”, with the

beryllium to the left of the surface and the xenon to the right. In this simulation,

we see that the beryllium has produced a region of shocked xenon in the simulation

that is approximately 10 times as dense as the initial gas, and spans the extent of

200 µm. In this case, the boundary between the beryllium and xenon has moved

about 1.85 mm from the initial position of the beryllium.

The solid curve in Figure 7.1 is a density profile from an identical simulation to

the one just described, except with a multigroup, diffusive radiative transport model

to treat radiation. This simulation used 90 photon groups with group boundaries at

the atomic transition energies. Most of these groups had an average energy of less

than 10 keV. The maximum density of the xenon feature in this simulation is 0.2

g/cm3, more than 30 times the initial density of the xenon gas. The leading edge of

this xenon feature is in approximately the same place as the leading edge of the xenon

feature in the no-radiation case, but the thickness of the layer is only 80 µm. That is

2.5 times smaller than the thickness of the xenon layer with no radiation transport.

In this simulation, the boundary between the beryllium and the xenon has moved

2.0 mm from the initial beryllium position, 150 µm further than the boundary in the

no-radiation simulation. The significance of this difference will be discussed later in

this chapter.

At the xenon density shown in the multigroup simulation of Figure 7.1, the dense

collapsed layer should be observable via x-ray radiography, and motivated the use of

xenon as the fill gas for these experiments. From Chapters Four and Five, we know

114

0.100

0.010

0.001

500

400

300

200

100

01.80 1.951.901.851.75

Position (mm)

Mass D

en

sit

y (

g/c

m3)

Tem

pera

ture

(eV

)density

ion

temperature

electron

temperature

Figure 7.2: Profile of radiatively collapsed layer in xenon gas. This simulation was done with a20 µm beryllium drive disk in 1.1 ATM of xenon. The solid line is mass density, thedashed line is ion temperature, and the dotted line is electron temperature. The spikein ion temperature marks the position of the shock front.

that the shocked layer is thin and dense, rather than extended with lower density,

confirming that radiation plays a significant role in the dynamics of this shocked

system.

Figure 7.2 shows a profile of mass density (solid line), electron temperature (dotted

line), and ion temperature (dashed line) as a function of position at 10 ns for a shock

in xenon at 10 ns after the drive beams turn on. Compare this, for example, the

the cartoon in Figure 2.1 in Chapter Two. The shock front is marked by a sharp

increase in the ion temperature. Collisions with ions quickly heats electrons, which

radiate energy away. The shocked gas is compressed to high density as the ions and

elecrons cool.

A second question to answer before using precious laser time was how early the

115

0.010

0.100

1.000

massdensity(g/cc)

200 400 6000

1 ns 2 ns

3 ns

Distance (µm)

Figure 7.3: Formation of a collapsed shock in the first few nanoseconds after the drive beams turnon. Note the different peak density of collapsed plasma, which is the rightmost densefeature for each plotted curve.

shock could be imaged. If the shock did not collapse to a high enough density or

produce a thick enough shock, it would not be as obvious on the radiography images.

Early times in the multigroup simulation show the formation of the dense collapsed

layer in xenon using a 40 µm thick drive disk. In Figure 7.3, we see density profiles of

multigroup simulations at 1, 2, and 3 ns after the laser beams turn on. In these curves

we see a large beryllium feature on the left, followed by a burgeoning xenon feature to

the right. Between 1 ns and 2 ns, we see the density of this feature increase. Between

2 and 3 ns, we see that the feature has reached the maximum density, and the feature

becomes thicker. The density of the xenon feature at 3 ns actually decreases a little,

and we see a growing gap between the xenon feature and the bulk of the beryllium.

116

This is indicative of significant radiation from the xenon acting as a pressure source

on the optically thick beryllium, causing a slight separation.

10 ns15 ns

20 ns

0.100

0.010

0.0011.0 1.5 2.0 2.5

massdensity (g/cc)

Distance (mm)

Figure 7.4: Density profiles from multigroup simulation at three times for a shock launched witha 40 µm drive disk. Note that as the shock moves farther, the thickness of the shockincreases, and the maximum density decreases slightly.

As the shock evolves at later time, we see the thickness of the shocked layer

increasing as it moves through the xenon. Shown in Figure 7.4 are three density

profiles from a shock launched with a 40 µm drive disk, shown from left to right

at 10, 15, and 20 ns. The right-most dense feature is compressed xenon, while the

feature to the left on each curve is the dense beryllium pusher. Here, you see that the

maximum density of the shock decreases slightly as the beryllium pusher slows down,

driving a weaker shock. The thickness of the collapsed layer increases significantly

over time, from a thickness of about 40 µm at 10 ns to a thickness of over 100 µm at

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20 ns. A perfect side-on measurement of the collapsed layer via radiography should

observe this difference. However, difficulties with exact side-on observation prevent a

precise measurement of this feature. The measured and simulated shock thicknesses

as a function of time are shown in Chapter Five.

7.1.2 Drive disk thickness variation

Once experiments verified the production of a collapsed shock in the nominal

target configuration, we turned to the possibility of driving faster shocks to produce

more dramatic radiative effects. As discussed in the Radiation Hydrodynamics chap-

ter, when the ratio of radiative flux to energy flux carried by the material gets large

(defined as the quantity Rrad), the system will radiate away energy to bring that ratio

down. To produce more dramatic radiative effects, one would seek to increase this

ratio in the experiment. Using the strong shock relation that tells us that Ti ∝ u2s,

we remind the readers that

(7.2) Rrad =σT 4

ρouscvT∝ u5

s

ρo

.

Shock velocity and initial mass density are both quantities we control in an ex-

periment. To launch a faster shock, we can use the same laser intensity on a thinner

beryllium disk. By using a thinner disk, the shock launched by the laser through the

beryllium takes less time to pass through the whole disk. When all the beryllium

is shocked, the laser pressure is a subsonic disturbance, which accelerates the whole

disk. Since the disk is thinner, there is less material to accelerate, and the laser can

push it to higher velocities. Also, because the shock passed through the material

faster, the laser pulse is subsonic for longer, and therefore accelerates the material

for a greater period of time. These combined effects mean that a thinner drive disk

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can launch a much faster driven shock in the xenon.

Shown in Figure 7.5 are three density profiles from multigroup Hyades simulations

at 10 ns after the drive lasers turn on. These simulations were run with three different

drive disk thicknesses, from left to right, 40, 20, and 10 µm beryllium disks.

There are several things to note when examining this figure. The most obvious

is the difference the drive disk makes on the shock velocity. The thinner the disk,

the farther the shock has propagated in 10 ns. The second is the structure on the

front (right) side of the dense xenon layer. On the profiles for the 40 and 20 µm

disks, the rise in density looks smooth and sharp, all in one continuous step. The 10

µm curve shows more refined structure, where one can see the initial density jump

due to strong shock compression, followed by the further increase in density due to

radiation loss. This structure is actually present on all three curves, but is not well

enough resolved on the first two to notice on this plot.

The third thing to notice is that the beryllium pusher in each case looks very

different. As the beryllium drives the shock from left to right in these simulations,

the beryllium is also expanding to the left now that the pressure source from the

laser is gone. A rarefaction wave is causing some of the material on the left side of

the beryllium (the laser driven side) to expand to the left as the bulk of the material

moves to the right. It is the momentum in the beryllium driving a shock in xenon,

enhanced by supersonic expansion of the beryllium towards the beryllium/xenon

boundary. This supersonic flow is mainly driven by ablation of the beryllium by the

radiation escaping from the collapsed layer. Because the rarefaction wave moves at

the speed of sound, it cannot overtake the region of supersonic flow until the shock

slows due to the effect of mass build up in the collapsed layer. When the shock slows,

the rarefaction can overtake the rest of the beryllium driver, and proceed into the

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collapsed gas layer. In Figure 7.5c, the rarefaction has moved into the xenon gas.

The density profile at maximum density in the layer shows a tilt towards the left, as

the gas begins to expand to the left. This late-time evolution is discussed more in

the next section.

Figure 7.5: Density profiles from three multigroup simulations at the same time, 10 ns after thedrive beams turn on. Each simulation used a different thickness of drive disk, picturedfrom left to right on the plot, 40 µm, 20 µm, and 10 µm.

7.1.3 Late-time effects

At some late time, the evolution of the system should change from that of a col-

lapsed shock driven by a piston to that of an undriven system. As mass builds up

in the shocked xenon layer, the beryllium piston slows by momentum conservation.

This simple picture is complicated by material backflow from the rarefying beryl-

lium plasma, so that the piston does not slow as quickly as a piston would without

backflow of material. This rarefaction wave moves at the speed of sound in the beryl-

lium plasma. At the beryllium/xenon boundary, the beryllium is optically thick to

the radiation from the xenon layer. This radiation source ablates material at that

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boundary, causing it to flow to the right at a speed faster than the sound speed of

the beryllium plasma, creating a lower-density gap between the bulk of the beryllium

and the xenon layer. This is best seen in Figure 7.5a for a 40 µm drive disk. In this

figure, the boundary between the beryllium and the xenon is at the left edge of the

dense xenon feature.

Figure 7.6: a) Density and b) velocity profiles at 6, 12, 18, and 24 ns after the drive lasers turn onfor an experiment using a 20 µm thick beryllium drive disk.

As the shock moves through the xenon gas and the collapsed layer becomes thicker,

momentum conservation slows the piston, and the rarefaction wave can eventually

move through the region of ablated material at the beryllium/xenon boundary. The

wave can then move into the collapsed xenon layer, causing the layer to expand. At

this point, the beryllium plasma is no longer driving the shock in xenon.

A simulation showing this transition is presented in Figure 7.6. In Figure 7.6a, we

show density profiles of a simulation of the experiment driven by a 20 µm thick drive

disk at 6 ns intervals, up to 24 ns. While the xenon feature gets much thicker in time

and slightly less dense, the beryllium expands towards the left of the figure. After

121

about 6 ns, the densest part of the beryllium is less dense than the xenon feature,

and continues to decrease in time at all points in the beryllium. In Figure 7.6b, we

show the velocity profiles at the same times. For the first 18 ns, the deceleration of

the shock is roughly linear, as shown by the dotted line through the peak velocity

through the first three times shown. However, at late time the velocity does not

follow the linear decrease; in fact, it stays moving relatively fast. This may be the

effect of expanding xenon now that the driving force of the beryllium no longer

controls the velocity of the shock in xenon gas. Also note the effect of the rarefaction

wave on the xenon layer at t = 24 ns in Figure 7.6a; the lower density at the left

edge of the layer is due to the rarefaction wave. Free expansion of the xenon to the

left in this figure would be hampered by the presence of the low-density beryllium

plasma in a 1D simulation.

7.2 Two-Dimensional Simulations

Two-dimensional simulations were done of this experiment in xenon gas to ensure

that lateral material and energy losses were not significant. Hyades has a 2D package,

but the strong shear near the walls of this experiment made the version of the code

available at that time unusable. In this geometry, one must let the xenon move along

the polyimide tube walls to contain the experiment. This led to zones along the walls

folding over themselves, or “bowtie-ing”. The presence of these bowties slowed the

code to a crawl. It was possible to pause the code, manually fix the zone boundaries

to untie them, and restart the code, but the bowtie-ing happened so quickly that not

much ground was gained before the code slowed again. Therefore, other codes were

tapped to help explore the 2D simulations of our experiment.

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7.2.1 FCI

FCI-2 is a Lagrangian hydrodynamic code, also using single-fluid, three tem-

perature treatment [11]. It treats radiation via a flux-limited multigroup diffusive

transport model, and uses flux-limited electron-heat transport. In these respects,

it is much like Hyades. However, FCI uses non-local-thermodynamic equilibrium

model, where Hyades uses an average atom local-thermodynamic equilibrium model

to calculate the relevant atomic physics.

Shown in Figure 7.7 is the 2D density profile generated by FCI-2 at 8 ns, using

a 40 µm beryllium driver, showing from the center of the tube to one edge. The

shock is moving from left to right. Here, the color scheme reflects the compression

of the material compared to the initial density of 0.006 g/cm3. This simulation also

shows a thin, collapsed layer of xenon gas at a higher density than predicted by the

1D Hyades simulation. Peak compression of the xenon is 45 times the initial gas

density, while Hyades predicted just over a factor of 30 compression. Here, we also

see a low-density layer in between the dense xenon and the beryllium pusher, again

due to the radiation from the xenon acting as a pressure source. While there is some

curvature in the collapsed layer structure near the polyimide wall of the experiment

tube, most of the front structure away from the walls is not very curved. Also, at

this time, almost all of the xenon that has been shocked is contained in the collapsed

layer; very little has escaped around the beryllium.

Using this 2D simulation, a radiograph can be simulated to check that the simula-

tion results actually reflect the experimental ones. Using the density data from this

simulation, and the opacity of beryllium and xenon at 5.2 keV from the NIST FFast

X-ray Database (online at http://physics.nist.gov/PhysRefData/FFast/Text/cover.html),

transmission levels should be similar to those of a radiograph taken with a vanadium

123

Figure 7.7: Density simulation in two dimensions using the FCI-2 code at 8 ns after the drive beamsturn on. The shock moves from left to right. The leftmost dense feature is the berylliumpusher, separated by a low-density region from the rightmost dense xenon feature. Thecoloring of the graph reflects the density expressed in units of the initial xenon gasdensity. Peak compression of the xenon gas is 45 times over initial density.

backlighter. The cylindrical geometry of the target was taken into account, and noise

and resolution information was taken from actual data. The simulated radiograph

that resulted is shown in Figure 7.8.

From this simulation, we can also futher explore the effects of a slight tilt in the

line-of-sight of the diagnostic. From tilting the line of sight of this radiograph by 5

degrees, the imaged dense layer grew from 50 µm in thickness to over 90 µm in thick-

ness, due to the 600 µm diameter of the polyimide tube containing the experiment.

This dramatic effect shows how much even a small misalignment in the chamber or

error in fabrication can make big differences on the data image.

7.2.2 Zeus

Zeus-2D is a Eulerian code (fixed zone positions), using a single-fluid, two tem-

perature treatment of the material with gray radiation transport. As described in

124

900700 800Distance in Target Coords. ( m)

100

200

80

160

240D

ista

nce

in T

arge

t Coo

rds.

(m

)

(a)

(b)

300

µ

µ

0

9

18

27

36

45

54

63

Thin XeLayer

ρ/ρο

(a)

Figure 7.8: a) FCI-2 density profile at 8ns, shown also in Figure 7.7. b) Simulated radiographfrom data in that 2D density profile. This simulated radiograph shows an image of thecollapsed xenon layer slightly thicker than that shown in the simulation, approximately50 µm thick.

125

his 2005 papers, Leibrandt et al. ([34], [33]) implemented a flux-limited diffusion ra-

diation module, as well as a front-tracking module and a heuristic ionization model.

For simulations of the driven xenon experiment, the code used ideal gas equations

of state and least-squares fits of the SESAME opacities, described in more detail in

this paper. This simulation also used a polystyrene drive disk at 1.05 g/cm3, at a

thickness of 72 µm instead of a beryllium drive disk, However, at this density and

thickness, the areal mass driven is the same as a 40 µm beryllium disk. Zeus-2D

does not have a laser package, so the initial conditions are linearly interpolated from

Hyades at 1 ns, the instant when the lasers turn off. This time is also chosen because

it is unlikely that 2D effects will have made significant impact on the system at this

time.

The assumption of flux-limited diffusion introduces an assumption about the an-

gular dependence of the radiation field. This eliminates the need to treat radiation

discretely over angle, reducing computation time. This assumption is only really

justified in optically thick systems. This paper is one of few to explore the validity of

the flux-limited diffusion approximation in systems that are not inherently optically

thick. By doing a convergence study on grid spacing and time steps in both one-

and two-dimensional simulations, this study shows that the results of a flux-limited

diffusion scheme do converge on the experimental values, but do not capture all the

structure seen in the data.

In one dimension, grid spacing dominates the error in the measurements of early

shocked-layer thickness, while it’s time rate of change depends more on the time

step. As the experiment progresses and the shocked layer becomes thicker, time step

errors take over. In two dimensions, the shock shows a curved structure, with trailing

xenon visible along the walls, between the walls and the shocked drive disk.

126

7.3 Issues Between Simulation and Experiment

As has been documented for 2D simulations, the laser irradiance used in such 1D

simulations must be reduced to give accurate results, because radial heat transport

reduces the ablation pressure in the actual system. The irradiation in the present

experiments is nearly identical to that used in previous work with two-layer, non-

radiative, purely hydrodynamic targets, differing only in these ways: a) the present

experiments use SSD (Smoothing by Spectral Dispersion, see Chapter Three), b)

the present experiments use an irradiance that is 80% of the value used previously,

and c) the present experiments use 20 µm of Be, from which the shock emerges

during the laser pulse, while the previous experiments used 150 µm of polyimide

as a first layer, so that the shock traversed only about half of this layer during the

laser pulse. In the previous work we have extensively compared the results of Hyades

simulations to measurements of the shock and interface positions. We found that

the code reproduced the observations very well using an irradiance that was 42% of

the actual value. This was the value scaled here.

Even after scaling the laser intensity to sensible levels in the 1D simulation, beryl-

lium/xenon interface position data collected over several shots show a large discrep-

ancy between the measured position of the interface and the predicted interface

position from 1D simulations. The uppermost curve in Figure 7.9 is a 1D Hyades

simulation run at the irradiance described above. This curve lies well above the

experimental data, overpredicting the distance the interface has traveled by approx-

imately 25%. The other curves on the plot show the effect of decreasing the laser

irradiance on the interface position. To obtain the observed trajectory of interface

locations, the laser irradiance must be reduced to almost 70% of the nominal value.

127

While this represents a possible avenue for getting the correct interface position, it

is an ad hoc adjustment to match the data that is not supported by our previous

understanding.

Figure 7.9: Data points are experimentally measured positions of the beryllium/xenon interface forexperiments using a 20 µm thick drive disk. The lines represent interface positions insimulations with full laser intensity and scaled laser intensities. The laser intensity mustbe reduced by approximately 25% to match the data.

The discrepancy just described might be a consequence of either the one-dimensional

dynamics of the system or of two-dimensional effects. The potential physical issues

that could create errors in the one-dimensional behavior include the equation of state

of the Be, the effect of radiation in the Be as it is shocked and accelerated, and the

effect of the radiation from the Xe on the Be as the shock evolves. The potential

issues in two dimensions are the lateral flow of energy, presumably reducing the ab-

128

lation pressure during the laser pulse, and the lateral flow of matter after the laser

pulse. We had only a limited ability to learn from two-dimensional simulations.

Simulations using the FCI code, which includes laser absorption and flux-limited,

diffusive electron heat transport [43] exhibited a discrepancy similar to that seen in

the 1D results. Simulations with FCI and with Zeus ([34], [33]) did not produce

significant lateral mass flow. This motivated a more extensive exploration of the

one-dimensional issues, described here.

Because the shock velocity and collapsed layer position in these experiments and

simulations depend on the position of the driven surface, we first undertook to exam-

ine the treatment of the beryllium in the simulations more closely to help explain the

interface position discrepancy. We explored the possibility that errors in the Be equa-

tion of state (EOS) might be important by doing a sequence of simulations varying

γ. While this might fail to capture details associated with changes in compressibil-

ity as different electron shells open up in the material, it should show whether the

behavior of the system is strongly sensitive to the EOS. In addition, for Be shocked

to 50 Mbars it would be quite surprising to find subtle differences relating to the de-

tailed structure of the equation of state. We found that variations in γ produced the

expected increase or decrease of the Be density but led to only small changes in the

interface velocity. This is not surprising as the ablation pressure and mass ablation

rate due to the laser should be weakly affected by changes in compressibility, so that

the main determinants of the velocity are the total impulse from the laser and the

total areal mass of the target.

We proceeded to explore the impact of radiation on the simulated structures.

In simulations done with xenon gas, as shown in Figure 7.10, there is a distinct

difference in the beryllium profile when radiation is turned off, which might or might

129

Figure 7.10: Simulations of laser driven beryllium into 0.006 g/cm3 helium gas. These simulationsare identical to simulations done of the experimental setup described, except using aweakly radiating fluid. Solid lines are simulations with diffusive multigroup radiativetransport, while the dotted lines are simulations with radiation artificially suppressed.Note the marked difference in the density profile of the beryllium at 10 ns between thetwo simulations.

130

not be due entirely to the xenon acting as a radiation source on the beryllium. The

first question to explore then was whether the radiation treatment of the simulation

affected the density profile of the beryllium if such a radiation source were no longer

present. To that end, we performed simulations identical to those described above,

removing xenon gas and replacing it with helium gas at the same mass density,

0.006 g/cm3. Helium gas is not a strong radiation source, and therefore differences

in the beryllium profile would be caused only by radiation in the Be. Shown in

Figure 5 are the results of simulations over 10 ns with beryllium driven into helium

gas, with multigroup radiation transport (solid line) and with radiation artificially

suppressed (dashed line). The dense feature in both of these simulations is the

beryllium. After 10 ns, the beryllium density profile in the radiative simulation

is significantly different than in the non-radiative simulation. While the position

and density of the beryllium/helium interface is approximately the same in the two

simulations, the radiative case shows the beryllium extended farther backwards, at a

peak density that is less than half the peak density in the non-radiative simulation.

Therefore, even in a weakly radiating fluid, the radiation treatment in the simulation

has a significant effect on the beryllium behavior. However, the difference in the

position of the interface between the Be and the He is negligible between these two

cases, so the effect of the radiation within the Be during the laser pulse appears not

to explain the discrepancy we are exploring.

The third issue we explored is the impact of the radiation from the xenon. In

Figure 7.11 we compare simulations using multigroup radiation transport in xenon

gas (solid line) to those in helium gas (dashed line) over 10 ns. At 2.5 ns, the

difference in the beryllium profile between these two simulations is minimal. But as

the radiatively collapsed layer becomes more defined, the differences become more

131

Figure 7.11: Multigroup simulations of a beryllium disk driven into xenon (solid lines) and helium(dashed lines). At 2.5 ns, the difference in the beryllium structure and interface posi-tion between the two simulations is minimal. By 10 ns, the difference in the structureof the beryllium is quite different. At this time, the beryllium/xenon interface hasmoved 250 µm further than the beryllium/helium interface. The beryllium in thexenon simulation at this time also has significantly more material to the right of thedensity peak, suggesting flow of beryllium ablated by the xenon radiation source.

132

dramatic. At 10 ns, the peak density of the beryllium driven into xenon gas is less

than 1/3 that of the peak density of the beryllium driven into helium gas. Much

more beryllium is located to the right of the peak density in the xenon simulation,

suggesting that beryllium ablated by the radiating xenon layer is flowing to the right

in this figure relative to the motion of the peak density of the beryllium. This is

confirmed by examination of Figure 7.6, which shows a region of acceleration to the

right of the beryllium peak at 6 ns. Here, the position of the interface in the xenon

simulation is approximately 250 µm farther to the right than that in the helium

simulation. The interface position at this time in the helium simulation is located

at 1500 µm from the initial position of the drive disk; this interface position at this

time is about 10% farther than the experimentally measured interface position at

10 ns. The profiles to the left of the beryllium density peaks are the same in both

simulations.

7.4 One-Dimensional Simulations in Argon Gas

The bulk of the radiography data displayed in Chapter Four was imaged in xenon

gas, which motivated the focus of this chapter. Some early radiography data and

the Thomson scattering experiments were done with argon as a fill gas. Argon is

less radiative than xenon, so the peak compression of the collapsed layer is slightly

lower in argon than in xenon. Shown below is a simulation of a 20 µm beryllium

disk launched into 1.1 ATM of argon gas (0.001 g/cm3 or 1.5 x 1019 atoms/cm3) at

a simulated laser intensity of 3.36 x 1014 W/cm2, 42% of the laser intensity used in

the experiments.

Figure 7.12 shows density profiles in argon gas at several times. Based on the time

and the position that the Thomson scattered spectrum was collected, this simulation

133

0.100

0.010

0.001

Mas

s D

ensi

ty (

g/c

m3 )

1.0 2.0 3.0 4.0

Position (mm)

5 ns

10 ns15 ns

20 ns

Figure 7.12: Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM(1 mg/cm3).

134

overpredicts the shock position in the same way that the xenon simulations did, by

about 25%. The argon structure here is more extended than the xenon structure.

After an initial density jump and plateau at 28 times the initial mass density, the

argon begins to collapse again, to a final density that is 80 times the initial density.

A small ablation driven gap separates the argon from the bulk of the beryllium, but

it is not as distinct as in the xenon simulations. This is intuitively sensible, assuming

that argon radiates less strongly than xenon. It also seems that the beryllium has

spread out less at late times compared to similar xenon results, which are shown in

Figure 7.6.

densityion

temperature

electrontemperature

0.100

0.010

0.001

Mas

s D

ensi

ty (

g/c

m3 )

300

200

100

0

Temp

erature (eV

)

3.6 3.83.4

Position (mm)

Figure 7.13: Multigroup simulations of a 20 µm beryllium disk driven into argon gas at 1.1 ATM(1 mg/cm3), showing mass density, ion temperature, and electron temperature.

135

Figure 7.13 shows the simulated density (solid), electron temperature (dotted),

and ion temperature (dashed) for a simulation in argon at 16 ns after the drive

beams turn on, using a 20 µm beryllium drive disk. The position of the shock front

at this time is the same as the position as the Thomson scattering volume described

in Chapter Six. The shock front is marked by the spike in the ion temperature. The

ion and electron maximum temperatures are both lower than in xenon, as is the

maximum mass density. However, the final compression is higher, because the initial

gas mass density was lower in argon than in xenon.

Two-dimensional simulations were not done in argon gas. If more experiments

are done in the future to examine the structure of the collapsed layer in argon, this

may be useful for comparison.

7.5 Summary of Simulation Results

Hyades simulations in one dimension provided a useful tool for understanding

and visualization of the important physical quantities. However, the limitations of

the radiation treatment in one dimension prevent this from being a quantitative,

predictive tool. In all the simulations shown, the position of the shock was overshot

by up to 30%. As this experiment evolves, other physical quantities will be measured,

quantifying the errors in the simulations of those quantities..

Detailed radiation treatment, especially in multi-dimensions, is computationally

expensive, and unavailable to the author at the time this thesis was written. However,

as more powerful lasers become available, more of the radiative flux- and pressure-

dominated will be accessible via experiment. It will be essential to have a compu-

tational tool capable of handling the physics of radiation hydrodynamics to model

these experiments to help maximize the efficiency of these experimental campaigns.

CHAPTER VIII

Conclusions and Future Directions

Side-on backlit x-ray radiography was successful both in targets that were area-

backlit and imaged on to a 4-strip framing camera and for targets that were pinhole-

backlit and imaged onto a single-strip framing camera. Using a single-strip framing

camera yielded higher-contrast images than were first obtained with four-strip im-

ages, after experimentation with target design resulted in a viable pinhole-backlighter

target. Further smoothing of backlit pinhole images to minimize source and gain vari-

ation revealed a clumpy structure on some collapsed layers. Attempts to do both

kinds of radiography on the same shot were unsuccessful, as high-energy noise from

the area backlighter contaminated data on the single-strip framing camera, exposing

the phosphor despite the gating mechanism.

VISAR diagnostics show that there is enough preheat of the unshocked material

to partially ionize it, creating an inverse-bremsstrahlung barrier for the green probe

beam from that diagnostic, even though the attempted novel use of the interferometer

to see the changing electron density of the shocked plasma via fringe-shifting was not

successful.

One- and two- dimensional simulations of this radiation hydrodynamic phenomena

aided qualitative understanding of the formation and evolution of the driven system.

136

137

These simulations were very limited in their predictive ability, miscalculating the

shock position in all simulations.

The use of the Thomson scattering diagnostic with a scattering volume within

a driven shock front provided data about the temperature and flow velocity of the

shocked plasma. Fits to the spectra structure determined the ion and electron tem-

perature in the small scattering volume, confirming the temperature calculations of

1D simulations to within the error bars of the measurement.

8.1 Radiative Shocks in Astrophysics

At the 6th International High-Energy-Density Laboratory Astrophysics confer-

ence in March, 2006, John Castor mentioned in his invited talk that it is difficult

to pick an astrophysical system and model a radiative shock experiment after it.

However, he said, if you create a radiative shock in the laboratory, it was almost cer-

tainly possible to find an astrophysical system with the same properties, due solely

to the sheer number of radiative shocks in astrophysics [10]. I did not succeed in

forming quantitative link between this experiment and any astrophysical shock dur-

ing the course of this research. Perhaps a more extensive object search, along with

more quantitative measures of the experimental system, would reveal an appropriate

subject.

However, I did find examples in astrophysics in the same fundamental regime as

the shocks described in the previous chapters. Recall from Chapter Two that we

can establish regimes of radiative shocks according to the optical depth upstream

and downstream from the shock. In the case of the radiative shock experiments

and of the astrophysical shocks discussed below, we explore shocks that are optically

thin in the unshocked material (“upstream”) and optically thick in the shocked

138

material (“downstream”). This similarity in structure allows us to describe the

systems with the same equations. This similarity also means that a code which

can correctly reproduce the experimental radiative shock system, with known initial

conditions, should also correctly describe these astrophysical radiative shocks in the

same regime. The examples that I found are discussed below, where similarities

between the example and the experiment are highlighted.

8.1.1 Shocks Emerging from Supernovae

The life of a large star is ended by a dramatic explosion, known as a core-collapse

supernova, or Type II supernova. Fusion burning at the center of the star generates

heat that provides a pressure source that hydrostatically counters the inward pull

of gravity. Fusion of low-mass elements produces energy, and produces heavier and

heavier elements until iron is produced. Since iron has the highest binding energy per

nucleon, fusion is not energetically favored, and an iron core is produced. This core

is supported by the degeneracy pressure of its electrons, and when the core exceeds

a 1.4 solar masses, this pressure is no longer enough to carry the weight of the star.

The core collapses, and the star implodes.

In consequence of the core collapse of a large star, a powerful shock wave moves

outward and blows the star apart, ejecting most of the stellar material. The process

of shock breakout into the surrounding shell of circumstellar material takes on the

order of a day, measured as the light curve rises to peak luminosity. The luminosity of

the star rises greatly when the shock deposits energy in the optically thin outermost

layers of the star. The deposited energy is radiated away, producing the so-called

“ultraviolet burst.” In this optically thin layer, it is possible for the shock to lose a

significant amount of energy through radiation loss [53].

As described in the Radiation Hydrodynamics chapter, loss of significant amounts

139

of energy via radiation lowers the internal pressure of the shocked material, leading

to increased density response in the form of compression. This compression continues

until the gas has cooled via radiation to its postshock equilibrium temperature.

Simulations from Ensman and Burrows [17] show the formation of a cooling layer

for parameters from the observations of nearby supernova 1987a. These simulations

were done using the 1D code VISPHOT, which is a Lagrangian, two-temperature,

LTE radiation hydrodynamics code. This code solves the co-moving frame frequency-

integrated moment equations of the radiative transfer equation. It does not make

the assumption of isotropic radiation, nor does it require a flux-limited diffusion

scheme for proper treatment of radiation. The model used a 20 solar mass main

sequence star with the outer layers removed to get the correct envelope mass for SN

1987a, which then was given an enhanced helium abundance in the envelope. This

procedure gave a 17.6 solar mass progenitor star, with a radius of 3 ×1012 cm and a

luminosity of 4.4 ×1038 ergs/sec. The optical depth profile for this system is given

in Figure 8.1. This profile was calculated assuming blackbody radiation at effective

temperatures calculated from the bolometric light curve.

Simulations of shock breakout show a spike in ion temperature just behind the

hydrodynamic shock front, followed by a rapid increase in mass density. Even at

large radii, this layer remains physically thin. This is similar to the density and tem-

perature profiles from 1-D simulations of the shock wave, described in the Radiation

Hydrodynamics Simulations chapter, and shown again in Figure 8.2. There, we see

a similar dense region that is thin compared to the distance it travels from where

the shock is launched. We also see a spike in temperature at the shock front (as one

will see at all shock fronts), with rapid cooling behind the shock front. Also in both

cases, the final post-shock temperature is approximately the same temperature as

140

1992ApJ...393..742E

Figure 8.1: Optical depth and mass profiles from 1D simulation of the supernova explosion of 1987aMost of the mass is within the inner 350 zones. Optical depth is calculated from thesurface (zone 500) inward, and 22 zones are at an optical depth less than 1. The risein optical depth in zone 40 marks the location of the shock front. From Ensman andBurrows, 1992.

that of the unshocked material.

In Figure 8.2a, the collapsed layer is almost four magnitudes higher in density than

the unshocked gas, and is extremely thin. These two features from the simulation

suggest an enhancement in the density jump at the shock front from radiative cooling.

If strong shock compression alone was responsible for the enhancement in density,

the polytropic index of the shocked gas would have been approximately γ = 1.0002,

which is a very small value. Also, while all shocks have a spike in ion temperature,

not all shocks have such a fast drop of the ion temperature. Here, both the fast

cooling and thin, dense feature are effects of radiative collapse of the shocked gas.

This process is physically identical to the radiative collapse of the shocked gas in

the experiment presented here. Simulation results from the experiment are shown

in Figure 8.2b for comparison. While the shocks are not identical (with different

initial densities, shock speeds, compositions, and total radiative fluxes), the physics

141

Figure 8.2: Temperature and mass density profiles from (a) Ensman and Burrows, 1992 and (b) 1Dradhydro simulations of driven radiative shock experiment in xenon. While the scalesare different, both the density and temperature profiles are qualitatively similar. Notethe spike in temperature, followed by rapid cooling and a significant increase in thedensity in a thin layer. This similarity will last until the supernova shock moves into aregime where the material behind the shock becomes optically thin, farther away fromthe exploding star.

describing the process is the same. Therefore, any simulation that can correctly

describe the experimental system, which has well known initial conditions, should

be able to describe this type of shock in an astrophysical system, such as SN 1987a.

This would be subject to the ability of the code to treat the different materials and

radiation mechanisms that may be present in the two systems.

8.1.2 Cooling of Stellar Atmospheres

Stationary shocks, ubiquitous in many astrophysical systems, also exist within

the atmosphere surrounding large stars. These shocks in the low-density atmosphere

can cool radiatively. In this scenario, the star will be optically thick downstream

of the shock, while the unshocked low density atmosphere upstream from the shock

will be optically thin to radiation, similar to the experimental scenario explained in

other chapters. Fokin, Massacrier, and Gillet [18] attempt to model the radiative

wake structure in a shocked stellar atmosphere by assessing iron line and continuum

radiative cooling. The treatment presented in this paper is offered as a general

solution for shocks in low-density atmospheres. As an example, the model is applied

142

to shocks in different types of pulsating stars.

As explained in Fokin, 2004, most of the radiation cooling will happen just behind

the shock front in what they call the “radiative wake structure”. This structure is

shown in Figure 8.3. The model of the wake adopted for the study by Fokin et. al

is shown by the solid lines in the figure.

Figure 8.3: Shock structure from computational analysis of a radiative shock in a stellar atmo-sphere. The solid line structure was adopted for analysis of the temperature and densitystructure in the radiative wake. From Fokin et. al, 2004.

Shown in Figure 8.4 are 1D simulation results of the temperature and density

structure behind a radiative shock with a velocity of 50 km/sec in a stellar atmosphere

with an unshocked gas temperature of 5000 K (or 0.43 eV), an initial density of

2 × 10−12 g/cm−3, and an with the initial temperature just behind the shock front

of 10000 K (or 0.86 eV) . Note that the density at the shock front in Figure 8.4

is approximately 4 × 1010 g/cm3, two orders of magnitude higher than the initial

density quoted.

Because the optical depth profile in the system studied by Fokin et al. is similar to

143

∆r [cm]

T10

9

7

8

6

5

T [1000K]

ρ [10-10 g/cm3]

µ [g/mol]

ρ

µ

1.5

1.0

0.5

02.1044.104105106107

Figure 8.4: Temperature, mean molecular weight, and mass density profile of a stationary shock ina stellar atmosphere. The x-axis is the distance from the shock front. The vertical linemarks a change in scale, as quantities change more slowly farther from the shock front.From Fokin et. al, 2004.

that of the experiment described in previous chapters, we can undertake to compare

them a little more closely. Figure 8.4 shows the temperature, mean molecular weight,

and density profile of the shocked system discussed in the reference. Simulations of

typical Population I and Population II type stars show that much of the cooling

comes from iron line radiation, with a non-negligible contribution from continuum

radiation of hydrogen transitions. In an LTE calculation, the authors undertook the

task of performing a detailed calculation of the thermal radiative wake structure.

Figure 8.5 shows the contributions to the cooling of the shocked gas from several

of the main contributors. The solid line in the figure shows the total cooling rate

of the gas. The short dashed line shows the contribution from the Fe I line. The

long dashed line shows the contribution to the cooling rate from the Fe II line. Note

that this line actually heats the system at some distance from the shock front. The

dotted line shows the continuum contribution, from hydrogen series transitions.

We used simulations of the experiment described in the Computational Support

144

Figure 8.5: Effect on cooling rates from different contributions. This log plot gives both heating andcooling of the system, with zero on the y-scale corresponding to no heating or cooling.From Fokin et. al, 2004.

chapter to back out a similar cooling rate profile from thermal radiation from the

shocked xenon, shown in Figure 8.6. The opacity of xenon was taken from fits to the

sesame tables calculated in Leibrandt et al.[33]. The beryllium opacity was taken

from minimum values in the online NIST FFast Database. This shows the cooling

rate is significant in the optically thin transition region just behind the shock. As

the xenon becomes more dense, cooler, and more optically thick, the cooling slows

quickly, and then levels off and some much slower rate. The maximum cooling rate is

more than 3 orders of magnitude higher than this final level. This final downstream

xenon cooling rate is lower than the cooling rate calculated for the unshocked xenon,

which is the material to the right of zero in Figure 8.6. Figure 8.6a is the cooling

profile over the extent of the experiment in xenon, and Figure 8.6b is a close-up of

the cooling layer near the shock front.

As you can see in Figure 8.6, the total cooling rate does not go to zero far away

145

Figure 8.6: Calculated cooling rate from experiment in xenon. Radiation was assumed to be thermalradiation from the cooling layer in the shocked plasma. This plot is in similar units tothe cooling rate of Fokin, with cooling rates reported as negative. a) Cooling profile ofmost of the experiment, including beryllium driver. b) Cooling profile of just xenon,near the shock front.

from the shock, as it does in the astrophysical example, and as shown in Figure

??. However, further examination of the cooling times for this system show that

the smallest cooling rates correspond to cooling times of approximately 50 ns, which

is more than twice the duration of the experiment. At the highest cooling rates

(just behind the shock), the cooling time is approximately 100 picoseconds, which is

reasonable based on simulations of the experiment.

In Fokin et al., the authors placed an emphasis on the incomplete nature of mod-

eling radiative transfer in such a complicated environment. They cited several works

with questionable results due to insufficient modeling of the radiation, and offered

their solution with several caveats. They also state in the text, “we have no way of

directly proving our main hypothesis, i.e. that the region between our “front” and

the viscous shock front is effectively transparent for all iron lines.” While the exper-

iment in the present thesis described does not provide a testbed for measurement

of spectral lines relevant to stellar atmospheres, it does provide a vehicle through

146

which this hypothesis might be tested in the future, using a higher-powered laser

and a relevant gas mixture.

8.2 Applications

In addition to providing a vehicle that may lead over time to further understanding

of certain astrophysical shocks, this experiment has direct relevance to a new type

of directly-driven laser fusion target. This target is called a laser-driven dynamic

hohlraum, or LDDH. This type of target combines the smooth radiation source from

a traditional gold hohlraum, with the more efficient convergent geometry of a tra-

ditional directly-driven fusion fuel capsule. In this geometry, a fusion fuel pellet

is surrounded by a layer of high-Z gas in addition to the normal spherical ablative

and driving layers. Xenon was used in early tests. Lasers irradiate the outer layers,

launching them radially inward. This drives a shock in the gas, which undergoes

radiative collapse. The radiation from this gas, in addition to the centrally converg-

ing material, compresses the central fuel with a smooth radiation source from the

collapsed shock in the gas. This approach combines the major attractions of both

direct and indirect drive into one target. Unfortunately, these assets are combined

into a target that is difficult to make. The compression of the central fuel in a fu-

sion target must be as symmetric as possible to maximize the yield of the fusion

explosion. These gas-filled LDDH must have a fill tube to pump gas into the target,

which then must be attached in a way that keeps the target gas-tight. This requires

a significant amount of glue, creating a large irregularity on the outside of the target

and a spot that cannot be driven by lasers.

147

8.3 Future Directions

This experiment can benefit from being diagnosed in a more quantitative way.

Measurements of the temperature of shocked plasma as well as the warm precursor

would be useful in quantitative comparison of the shock in this experiment to other

radiative shocks, as well as to radiation hydrodynamics codes. In the past year,

initial experiments were performed to do just that, as well as to improve the current

radiography diagnostic.

8.3.1 Flux Measurements

A natural measurement of a system with significant radiation would be a radia-

tion temperature measurement with a flux-collecting diagnostic. Initial experiments

have been designed and executed for experiments utilizing both a soft-x-ray detector

(the DANTE diagnostic), and a soft-UV detector (the Streaked Optical Pyrometer

diagnostic) at the Omega Laser Facility. These experiments should work with either

fill gas used in previous experiments (argon and xenon), but initial experiments used

xenon gas. These diagnostics would measure the effective radiation temperature of

different parts of the experiments by fitting the collected radiation flux to a black-

body curve. The Streaked Optical Pyrometer would probe the unshocked, preheated

material, which VISAR measurements estimate to be at least a few eV. The DANTE

diagnostic would be more sensitive to the soft x-ray emission from the shocked mate-

rial itself, which 1D and 2D simulations predict to be a few hundred eV. This number

is supported by the Thomson-scattering measurements in argon gas. Initial results

were promising for the use of this diagnostic in future experiments.

148

8.3.2 Short-Pulse Backlighters and Ungated Imaging Diagnostics

The experiment that tested the viability of the flux measuring techniques for this

experiment also incorporated advances in radiography techniques. Other experi-

ments done in this research group have successfully used an ungated x-ray collection

diagnostic, with excellent results. Ungated diagnostics have intrinsically less noise

than gated diagnostics, as there are no voltage pulses or microchannel plates to in-

troduce any gain variation. This ungated diagnostic actually uses the length of the

backlighter pulse as the “gating” mechanism to image onto a piece of x-ray film

shielded only with beryllium. This unprotected piece of film is also susceptible to

x-rays generated by the lasers and laser-irradiated sources other than the backlighter.

These other sources may expose the film and lower the contrast on the data image,

and so extreme shielding measures are taken to protect the film from these sources.

A large acrylic shield with gold wedges pointing towards the diagnostic protected

the x-ray film from high-energy photons produced in the driving pulse. The target

design also afforded protection from a laser beam used to blast an opening in the

back end of the target to afford a direct line of sight to the xenon plasma to the

diagnostics described above. A shadowed image of the target in the target chamber

is shown in Figure 8.7.

For slow moving shocks like those in previous successful experiments, backlighter

pulses of the length used for the gated experiment described in previous chapters,

1 ns, are appropriate. However, the radiative shocks move at well over 100 km/sec,

and so an image with a backlighter source lasting 1 ns would smear the image over

100 µm. Therefore, in the most recent experiment, a 100 ps backlighter was used for

the first time. This pulse length is at the lower edge of what is currently possible for

an Omega beam. Initial attempts to use this diagnostic were successful.

149

Figure 8.7: Targets for new generation of radiative shock experiments. Targets are gas tight withview up the back end of the target into cylinder. A large acrylic shield with gold wedgesfacing the diagnostics surrounds the drive surface. a) Three-D CAD image of target.b) Shadowed image of target prototype roughly positioned in the Omega chamber.

It is anticipated that future students will employ these techniques mentioned

above, as well as Thomson scattering, and very likely other diagnostics to develop a

much more detailed understanding of these shocks and their structure.

APPENDICES

150

151

APPENDIX A

“Observation of collapsing radiative shocks in laboratoryexperiments,” [43].

Observation of collapsing radiative shocks in laboratory experimentsA. B. Reighard, R. P. Drake, K. K. Dannenberg, D. J. Kremer, M. Grosskopf,E. C. Harding, and D. R. LeibrandtDepartment of Atmospheric Oceanic and Space Sciences, University of Michigan,Ann Arbor, Michigan 48109

S. G. Glendinning, T. S. Perry, B. A. Remington, and J. GreenoughLawrence Livermore National Laboratory, Livermore, California 94551

J. Knauer and T. BoehlyLaboratory for Laser Energetics, University of Rochester, Rochester, New York 14623

S. BouquetDépartement de Physique Théorique et Appliquée (DPTA), CEA-DIF, BP 12, 91680 Bruyères-le-Châtel,France

L. BoireauDépartement de Physique Théorique et Appliquée (DPTA), CEA-DIF, BP 12, 91680 Bruyères-le-Châtel,France, and LUTH, Observatoire de Paris, Paris, France

M. Koenig and T. VinciLaboratoire pour l’Utilisation des Lasers Intenses, Ecole Polytechnique, 91128 Palaiseau, France

�Received 27 March 2006; accepted 21 June 2006; published online 3 August 2006�

This article reports the observation of the dense, collapsed layer produced by a radiative shock in alaboratory experiment. The experiment uses laser irradiation to accelerate a thin layer ofsolid-density material to above 100 km/s, the first to probe such high velocities in a radiative shock.The layer in turn drives a shock wave through a cylindrical volume of Xe gas �at �6 mg/cm3�.Radiation from the shocked Xe removes enough energy that the shocked layer increases in densityand collapses spatially. This type of system is relevant to a number of astrophysical contexts,providing the potential to observe phenomena of interest to astrophysics and to test astrophysicalcomputer codes. © 2006 American Institute of Physics. �DOI: 10.1063/1.2222294�

I. INTRODUCTION

Radiative shocks are a type of radiative hydrodynamicphenomenon. Shock waves heat the material they passthrough, and first become radiative shocks when the radiativeflux from the hot material becomes energetically significant.Radiative shocks abound in the universe, but their study inthe laboratory is relatively new. Creation of these systemsrequires temperatures of tens of electron volts or more, suf-ficient to create ionized matter in which at minimum radia-tive energy fluxes locally can exceed material energy fluxes.In any radiative shock there is an “optically thin” region�having small optical depth� where radiative effects are large,near the density jump. Here by “optical depth” we refer tothe number of e-foldings of attenuation of thermal radiation.The optical depth of the entire system on each side of thedensity jump corresponding to the shock determines the de-tailed properties of radiative shocks,1,2 including the extentof the region over which radiative effects are large. In ex-periments on radiative shocks, the optical depth, for the ther-mal radiation from the shocked matter, must be adequate toallow significant energy exchange between matter and radia-tion on the time scale of the experiment. There is also inprinciple a regime of very high temperature and very largeoptical depth in which the radiation pressure can exceed thematerial pressure.1 Current experiments cannot reach this re-

gime but can reach the regime of large radiative fluxes justdescribed.

Achieving both high enough temperature and sufficientoptical depth simultaneously requires the use of high-energy-density facilities. Little laboratory data exist on radiativeshocks, as they are difficult to establish under controlled con-ditions. If the region on either side of the shock is “opticallythin” �easily allows the passage of the thermal radiation fromthe shocked matter�, the density of the shocked layer canincrease greatly as it cools by radiating away its energy.3,4

The thickness of the shocked layer correspondingly de-creases, so the shock can be said to collapse. Here we reporta laboratory experiment to observe, for the first time, thecollapsed layer produced by a radiative shock.

Radiation and radiative collapse both play importantroles in astrophysical shock waves. The shock wave emerg-ing from a supernova passes through a regime in which theshocked layer collapses in space because of radiative energylosses.5 Similar dynamics can occur at the accretion shocksproduced during star formation,6–8 and at the reverse shockin a supernova remnant formed from a star with a densestellar wind9 or preexisting dense material as in supernova1987A.10,11 Stratified ionization states form in a radiativeprecursor of a Herbig-Haro object with a radiative coolinglayer.12 There is more generally a radiative cooling zone be-hind most astrophysical shocks. Collapse of an existingshocked layer can occur in some cases, as, e.g., in aging

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152

supernova remnants in which the shocked layer is no longerdriven.13

One can organize the prior laboratory work on radiatingshock waves by the strength of the radiative effects that werepresent, which scale very strongly with shock velocity,us. Experiments discussed by Edwards et al.14 producedus�8 km/s in a cylindrical blast wave, and observed radia-tive cooling effects that resulted from heating of the shockedgas by electron heat conduction. At higher us, experimentscan exceed the threshold15 for the formation of a thermalradiative precursor, in which thermal radiation from matterheated by the shock itself heats the matter ahead of �“up-stream” of� the shock. Radiative precursors have been ob-served in experiments by Bozier et al.,16 Grun et al.,17 Keiteret al.,15 Bouquet et al.,18 Koenig et al.,19,20 and Vinci.21 Theexperiment of Grun et al.17 produced a quasispherical radia-tive blast wave, in which radiation during the shock transi-tion is calculated to play a key role.22

The present experiment is the first in planar geometry toexceed the threshold for radiative collapse by formation of apostshock cooling layer, and to detect the material that hasbeen shocked and cooled. Following the shock, which heatsions primarily, the ions and electrons equilibrate rapidlycompared to the rate of radiative cooling. The resulting, ini-tial postshock electron and ion temperature for a strongshock, Tinit, is4

Tinit =2

�� + 1�2

us2

cv, �1�

in which � is the polytropic index appropriate to the shocktransition and cv is the specific heat at constant volume of thepostshock material, equal to 3�Z+1�kB / �2Amp� for a fullyionized gas. �Here kB is the Boltzmann constant, mp is theproton mass, and Z and A are the average ionization andatomic mass numbers, respectively.� In a material like xenon,cv and � both should include the effects of ionization. Apostshock cooling layer must form when the energy flux dueto thermal radiative losses from the shocked material exceedsthe energy flux entering the shocked material. This naturalnormalization of the fluid energy equation in an opticallythick system gives a threshold for significant radiative cool-ing as Rr�1, where

Rr =�� + 1�

�

4�Tinit4

�0us3 =

64

��� + 1�7

�

cv4

us5

�0, �2�

in which � is the Stefan-Boltzmann constant and �0 is themass density of the unshocked, upstream material. The cor-responding threshold velocity23 in xenon, at 10 mg/cm3, isapproximately 50 km/s. If the optical depth of the regionbehind the shock decreases, decreasing the emissivity of theshocked material, the value of Rr required to see large radia-tive effects increases.

II. EXPERIMENT

We drive a planar, radiative shock through a xenon-filledtarget and observe the structure of the shocked xenon layer.Figure 1 shows a target schematic. The inside diameter �i.d.�of the gas cell was either 600 or 912 �m. We used the fill

tube to evacuate the target and then fill it with xenon. Thexenon pressure was measured for each experiment, and was1.1 �±10% � atm for the cases of interest here correspondingto �0=6 mg/cm3 or to 2.7�1019 atoms/cm3. The drive diskwas either 51 �m of polyimide �±3% and at 1.41 g/cm3�overcoated with 20 �+5/−10� �m of polyvinyl at 1 g/cm3,or 20 �m or 40 �m �±7% � of Be. We focused ten laserbeams of wavelength 0.35 �m onto a 1 mm spot centered onthe �2.5 mm diameter drive disk in a square, 1 ns flat-toppulse, with the midpoint of the rising edge defining timet=0. The total energy was �4000 J. Distributed phase plates�DPPs� created super-Gaussian focal spots of 720 or 820 �mdiameter �full width at half-maximum�, with small-scalestructure which fluctuated via smoothing by spectral disper-sion �SSD�. The resulting laser irradiance was up to1015 W/cm2. The pressure from laser ablation first shockedand then accelerated the drive disk, launching it into thexenon and driving a shock.

X-ray radiography was the principal diagnostic, usingtwo types of x-ray sources called “backlighters.” The laserbeams producing the x rays were of the same wavelength andlaser pulse as given previously, at a nominal energy of450 J /beam, without SSD and usually without DPPs. Someshots included an “area backlighter,” in which such laserbeams were focused to a �1 mm spot on a vanadium foilseveral square millimeters in area and 5 �m thick, to pro-duce K-shell emission at �5.2 keV. This millimeter-sizedsource was placed 4±0.25 mm from the target, and imagedonto a framing camera24 through pinholes. A “backlit pin-hole” was also used on some shots, where the laser beamswere focused to a 400 �m spot on a 5 �m thick V foil,spaced by 100 �m of CH behind an 80 �m thick Ta sub-strate with a 20 �m through hole, covered by 100 �m ofCH. This small x-ray source was located 12±0.1 mm fromthe target, and projected a radiograph of the target onto aframing camera located �229 mm beyond it. Due to vignett-ing, the effective source size for this measurement was�15 �m. A gold grid was placed on the target to calibratethe location and magnification of the image. A velocity in-terferometer system for any reflector �VISAR� diagnostic�see Fig. 1� was also used in some cases.

FIG. 1. Target diagram. In this view the backlighter plate would sit directlybehind target, below the plane.. When the VISAR �velocity interferometersystem for any reflector� diagnostic was used �see the text for reference�,additional arms were added to hold a quartz window and a mirror for theVISAR laser, and shielding was added behind the drive disk and to the leftof the arms to reduce preheating of the gas in the arms. When a pointbacklighter was used, its line of sight was in the same direction as theVISAR line of sight.

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III. EXPERIMENTAL RESULTS

Radiography of the shock in xenon shows clear indica-tions of a thin, dense shock. On a range of experiments, wehave seen dense shocked layers with thicknesses ranging be-tween 45 and 80 �m. In the plane of the radiograph, somelayers were tilted with respect to the target axis by as muchas 10°. We show the thinnest of these layers in Fig. 2, takenat 13.5±0.3 ns, with the region of highest opacity being45 �m thick. One can see the center of the shock �which ismoving to the right� at approximately 1600 �m from theinitial driven surface, with indications of a trailing layer ofdense xenon along the wall of the tube. The velocity aver-aged over the first 13.5 ns is 118 km/s. Figure 3 shows atypical radiograph with a thicker layer, from an experimentwith a 22 �m drive disk and a 10% lower drive irradiance.In this image, the center of the layer has moved 1150 �m in8.0±0.3 ns, where its thickness is 65 �m. The average ve-locity of the shock until this time is �140 km/s.

When the VISAR diagnostic was used,25 fringe patternsfrom the VISAR diagnostic ceased before the drive laser shutoff. We attribute this to collisional absorption in the Xe gas,heated to a few eV by radiative preheat.26 Later, a thin fea-ture appeared, showing no fringes and nonuniform in spaceand duration. We attribute this signal to reflection of the in-terferometer beam from the edge of the shock front. Theshock velocity inferred from this is consistent with that de-termined from the radiographic data.

Even without any input from computer simulations, thedata provide strong evidence that there is a shock that hassignificantly collapsed. Assuming that two-dimensional �2D�lateral flow is small, which is supported by the limited layerof absorbing material along the tube wall in the image andalso by the simulations discussed below, the thickness of thelayer corresponds directly to the amount of compression inthe shock. For the thinnest observed thickness of 45 �m,assuming the line of sight to be exactly side on and given theinstrumental resolution of 10 �m, one concludes that the

data image shows a compression of approximately 35 in thexenon layer. If the line of sight was not exactly side on, thetrue compression would be higher. One-dimensional �1D�and 2D simulations discussed in the following provide fur-ther support of the creation of a radiatively collapsed shock.

IV. SIMULATION RESULTS

One can gain further insight into the impact of radiationon the experiment through simulations. We first discuss theresults of simulations of this system using the 1D, Lagrang-ian, single-fluid-three-temperature code HYADES,27 run usingmultigroup, diffusive radiation transport with 90 photongroups, adjusted to resolve the edges in the xenon opacity atup to 6 keV. The equation of state of xenon was theSESAME table.28 In the regime of this experiment, the poly-tropic index ��� inferred from the table is in the range of1.2–1.3, as is appropriate for an ionizing medium that isdense enough that collisional recombination is dominant.23 Itis worth noting that the effective � of xenon can be signifi-cantly smaller, e.g., in lower-density media in �more or less�coronal equilibrium, which is the case for the experimentswith blast waves in gases.22,29 The xenon was modeled usingan average-atom, local-thermodynamic-equilibrium �LTE�description. One would expect this description and the radia-tion transport model to be qualitatively accurate but not fullypredictive. As has been thoroughly documented through 2Dsimulations,30 the laser irradiance used in such 1D simula-tions must be reduced to give accurate results, because radialheat transport reduces the ablation pressure in the actual sys-tem. Here it was adjusted to the level required to match thebehavior of relevant purely hydrodynamic experiments.

The solid curve in Fig. 4�a� shows the above-mentionedradiative simulation results, whereas the dashed curve showsresults of a simulation in which radiation is artificially sup-pressed. The shock transition is the right-most increase indensity, which is moving to the right into preheated matter.The shocked xenon layer is just to the left of the shock tran-

FIG. 3. �Color online� Radiography image from a point-projection back-lighter, or a “backlit pinhole,” from an experiment with a 20 �m drive diskattached to a polyimide tube of 575 �m i.d., irradiated with SSD at 4.8�1014 W/cm2 onto an 820 �m laser spot, again using a V backlighter. Thesame type of fixed spatial fiducial is present, as are the tube walls. The shockis tilted in the plane of the image, but some evidence of trailing xenon alongthe tube walls is present.

FIG. 2. �Color online� Radiography image from an area backlighter, at13.5 ns, from an experiment with a polyimide drive disk attached to a poly-imide tube of 912 �m i.d., irradiated with SSD at 9.3�1014 W/cm2 onto a720 �m laser spot. The illumination was by x rays from V produced byoverlapping six laser beams. The grid with a fiducial feature establishing anabsolute location is evident in the lower part of the figure. The wall of thetube can be seen near the upper edge.

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sition. In the radiative case one can see the postshock densityincrease due to cooling. This density increase is well re-solved in this Lagrangian calculation, and shows a maximumcompression of a factor of 35 over the initial gas density,compared to a maximum compression of 13 in the radiation-suppressed case. To the left of the contact surface is a more-structured layer of low-Z material. The structure in this layerhas been established during the laser pulse, when there isshock reverberation in the driving material. The radiation hastwo effects. First, it narrows the shocked xenon layer byincreasing its density. This is the primary effect one can de-tect using radiography. Second, it heats the low-Z materialthat is driving the shock and causes the xenon layer to sepa-rate from it. As the xenon layer radiates, radiation-drivenablation creates a distinct, low-density region between thedense driver material and the dense collapsed layer.31 In Fig.4�b� one can see the effects of radiative heating ahead of theshock, of the cooling that accompanies the density increasein the cooling layer, and of the radiative heating and ablationof the beryllium.

We also ran 2D simulations using the code FCI,32,33 aLagrangian, one-fluid, three-temperature code with multi-group diffusive radiation transport, an average atom non-LTE treatment of materials, and flux-limited electron heattransport. Figure 5�a� shows the calculated profile of massdensity at 7 ns for a case with a 600 �m gas cell and an820 �m laser spot. The density in most of the shocked layeris about 45 times the initial density, and there has been verylittle radial flow of mass out of the shocked layer. In the 2Dsimulations, the decrease of temperature ahead of the shockis more rapid than in 1D simulations, as one would expectdue to the inclusion of radial radiation losses. Again, the

low-Z material behind the shock is heated, and has separatedfrom the xenon layer. This separation is clearly seen in Fig.5�a�, but not in radiography, because of the low absorption ofthe diagnostic x rays by low-Z material.

Figure 5�b� is a simulated radiograph based on the den-sity profile shown in Fig. 5�a� and the experimental resolu-tion. The boundary between xenon and beryllium is at theleft edge of the right-most dense feature, whereas the densefeature at the top of the image is the plastic wall. Mass ab-sorption coefficients for beryllium and xenon at 5.4 keVwere taken from the National Institute for Standards andTechnology FFAST database.34 The source-induced broaden-ing is 250 �m at the microchannel plate. Poisson noise esti-mated from representative experimental data is included, andthe image is smoothed based on the instrumental smoothingdetermined from grid edges in data. This assumes also thatthe shock is observed from exactly side-on; if the shock weretilted by 5° from edge-on, a 50 �m thick, 600 �m diameterlayer would appear almost 90 �m thick. Therefore, thismethod of detection gives an upper limit on the actual thick-ness of the layer, and thereby the density of the collapsedmaterial.

V. CONCLUSIONS AND FUTURE DIRECTIONS

The layer of xenon produced by a nonradiative shock,with an effective � of 1.2-1.3, would be from 140 to 220 �mthick at the location seen in Fig. 4, and the observed layer is45 �m. Thus, one might suggest that the density has in-creased another factor of 3–4 in consequence of radiativelosses, reaching a total of �40 times the initial xenon den-sity. The inferred density increase would be reduced to what-ever extent material has left the shocked region by flowing

FIG. 4. �a� Density vs position from two Hyades simulations, at 16 ns, forexperiments at a laser intensity of 1015 W/cm2. The boundaries between thedrive plasma, in this case Be, and the xenon are shown, labeled “contactsurfaces.” The solid line shows the result for multigroup, diffusive radiationtransport, whereas the dashed line shows the result for a nonradiative sys-tem. When radiation is suppressed �dashed line�, a collapsed layer does notform. �b� Density and temperature vs position from the Hyades simulationwith radiation transport at 16 ns. The solid line is mass density, the dashedline is ion temperature, and the dash-dotted line is electron temperature.Note the difference in scales between �a� and �b�.

FIG. 5. �Color online� �a� Density profile at 7 ns, from a 2D simulation ofthe experiment, using the FCI code. The shock is moving to the right. Thecolor bar calibrates the density as a ratio to the initial gas density. �b�Simulated radiograph, using density data from �a�. Poisson noise and apoint-spread function from data are included.

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radially, although the 2D simulations find this to be small.However, this line-of-sight measurement will have a strongtendency to overestimate the thickness of the shocked layer,due to any tilt, curvature, or rippling of the shock front. Aperfectly aligned measurement of the density profile shownin Fig. 3�a�, with the resolution of the pinhole used, wouldproduce a layer from 30 to 40 �m thick. Thus, it appearsreasonable to conclude that we have observed a thin layer ofshocked xenon whose density has been increased signifi-cantly by radiative losses.

Future experiments can work in several worthwhile di-rections. They can examine the structure of the shocked layerin more detail, can assess how it scales with parameters suchas shock velocity and initial gas density, and can attempt todevise diagnostic approaches that can directly measure theproperties of the shocked layer. In addition, by watching thelong-term evolution of the shocked layer, such experimentsmight observe the onset of hydrodynamic instabilities likethose discussed by Vishniac and Ryu.35 Beyond such work,this system could be developed as a radiation source for ex-periments to examine other issues such as radiation transport.

ACKNOWLEDGMENTS

The authors acknowledge the vital contributions of theOmega technical staff, the target fabrication staff atLawrence Livermore National Laboratory, Erika Roesler,Rebecca Gabl, and Peter Susalla, as well as for useful dis-cussions with Dmitri Ryutov and Russell Wallace.

This work is supported by the National Nuclear SecurityAgency under DOE Grant Nos. DE-FG03-99DP00284 andDE-FG03-00SF22021, and by other grants and contracts.

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157

APPENDIX B

“Thomson scatttering from a shock front,” [44].

Thomson scattering from a shock frontA. B. Reighard, R. P. Drake, T. Donajkowski, M. Grosskopf, and K. K. DannenbergDepartment of Atmospheric, Oceanic, and Space Sciences, University of Michigan,Ann Arbor, Michigan 48109

D. Froula, S. Glenzer, J. S. Ross, and J. EdwardsLawrence Livermore National Laboratory, Livermore, California 94551

�Received 8 May 2006; presented on 8 May 2006; accepted 29 May 2006;published online 22 September 2006�

We have obtained a Thomson scattering spectrum in the collective regime by scattering a probebeam from a shock front, in an experiment conducted at the Omega laser at the Laboratory for LaserEnergetics. The probe beam was created by frequency converting a beamline at Omega to a 2 nspulse of 0.263 �m light, focused with a dedicated optical focusing system. The diagnostic systemincluded collecting optics, spectrometer, and streak camera, with a scattering angle of 101°. Thetarget included a primary shock tube, a 20-�m-thick beryllium drive disk, 0.3-�m-thick polyimidewindows mounted on a secondary tube, and a gas fill tube. Detected acoustic waves propagatedparallel to the target axis. Ten laser beams irradiated the beryllium disk with 0.351 �m light at 5�1014 W/cm2 for 1 ns starting at to, driving a strong shock through argon gas at �o=1 mg/cc. The200 J probe beam fired at t=19 ns for 2 ns, and at t=20.1 ns a 0.3 ns signal was detected. Weattribute this signal to scattering from the shocked argon, before the density increased above criticaldue to radiative collapse. © 2006 American Institute of Physics. �DOI: 10.1063/1.2220069�

Thomson scattering measurements use an optical laserwith some initial wavelength and wave number ��o and ko� toelastically scatter from electron density fluctuations with agiven wave vector �k�.1,2 Over the last 40 years, experimentshave used Thomson scattering to extract fundamental plasmaproperties from the scattered frequency spectrum, and it isnow widely used as a diagnostic in fusion research.3–5

Thomson scattering probes individual electrons in thenoncollective regime, when light is scattered from plasmafluctuations �of wave number k� with wavelengths shorterthan a Debye length �k�De�1�. Resonant plasma fluctua-tions in the collective regime, in the form of probed collec-tive ion-acoustic wave features �of wave number kiaw�, areobserved when the probed electrons follow the motion of theions �ZTe /Ti�kiaw�De, where Z is ionization state, Te is elec-tron temperature, and Ti is ion temperature�. In this regimethe electrons move to screen the potential created by ionfluctuations.6 To probe electrons in the collective regime of adriven shock wave in gas, we have applied Thomson-scattering techniques to a radiatively collapsed shock wavein argon gas.

The experiment conducted for this purpose created adriven shock in argon with shock velocity high enough tocause radiative collapse. Thomson-scattered light was thencollected from the shocked gas, and an attempt was made toimage the dense, postshock gas using x-ray radiography. Toaccomplish this, the targets were designed to form a laser-driven piston that drove the shock, and the target body wasstructured to create unobstructed paths for the probe entranceand scattered light exit paths. Beam timing was specified toallow for x-ray radiography of the shock, using an indepen-dently positioned backlighter target. The target for these ex-periments was based on those for driven radiative shock ex-

periments described in Reighard et al.,7,8 and fabricated atthe University of Michigan. A three-dimensional �3D�computer-aided design �CAD� drawing of the experimentalgeometry in the target chamber is shown in Fig. 1.

To create a driven shock that may radiatively collapse, alow-Z, planar disk was launched by laser ablation pressureinto a cylindrical volume filled with argon gas. This disk wasfashioned from beryllium, 20±3 �m thick, 2.0±0.1 mm indiameter. The disk was mounted on a polyimide tube, insidediameter �i.d.� 575 �m, outside diameter �o.d.� 600 �m. Thetarget package was gas tight, and fitted at the back end witha hypodermic tube through which the target was evacuatedof air and filled with argon. The argon pressure was mea-sured for each experiment, and was 1.1 �±10% � atm for thecases of interest here, corresponding to �o=1 mg/cm3 or to2.7�1019 atoms/cm3.

To allow for probe entrance and Thomson-scattered-light-exit holes, another polyimide tube of larger diameterwas fitted over the main target tube, creating an arm at a 45°angle to the shock propagation axis, pointing towards the 4�probe beam location when properly aligned. This polyimidetube was 725 �m i.d., 875 �m o.d., and totaled approxi-mately 3 mm long. This arm served two main purposes.First, it acted as a guide to drill an entrance hole into themain target body, clearing a path to what would be the scat-tering volume on the shock axis. Second, it provided a flatsurface onto which a thin film of polyimide could be affixed,sufficiently far from the target axis that plastic plasma wouldnot mix with argon plasma on the shock axis, providing atleast a 2 mm offset from the center of the main target tube.This thin film was 3000 Å thick, and provided a gas tightbarrier. Design calculations showed that the plastic plasmaproduced in the destruction of this film cleared from the

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probe beam path sufficiently quickly such that it did notinterfere with the propagation of the probe beam. The align-ment of this tube was checked during target metrology toensure a clear path to the shock propagation axis, as this wassensitive to mounting angle and both rotational and transla-tional alignment of the target in the chamber. Another holewas drilled in the main target body that faced the scatteredlight diagnostic when the target was properly positioned inthe target chamber. This opening was approximately 400 �min diameter, drilled through a flat surface fashioned fromepoxy, and was also covered with a 3000-Å-thick polyimidefilm. This provided an unobstructed path for scattered lighttowards the diagnostic when this film was destroyed in theexperiment.

We focused ten laser beams of wavelength 0.35 �m ontoa 1 mm spot centered on the beryllium drive disk in a square,1 ns flat-top pulse, with the midpoint of the rising edge de-fining time t=0. The total energy was �4000 J. Distributedphase plates �DPPs� created super-Gaussian focal spots witha diameter of 820 �m �full width at half maximum�FWHM��, with small-scale structure which fluctuated viasmoothing by spectral dispersion �SSD�. The resulting laserirradiance was up to 1015 W/cm2. The pressure from laserablation first shocked and then accelerated the drive disk,launching it into the argon and driving a shock in the argongas. At 16.0±0.25 ns after the drive beams turned on, asingle destroyer beam with an energy of 400 J and a spotsize of 400 �m fired on the film facing the UV spectrometerdiagnostic in a 2 ns flat-topped pulse with no beam smooth-ing, clearing the path to this diagnostic. At 19.0±0.25 nsafter the drive beams turned on, the probe beam turned on at200 J in a 100 �m spot with no beam smoothing, in a 2 nsflat-topped pulse, which first exploded the film on the armfacing this beam, as described above. This beam was alignedto target chamber center first using a frequency doubledbeam, then confirmed in an alignment shot prior to the ex-periment. The alignment shot used the 4� beam shooting avanadium disk positioned at target chamber center. This shotalso checked the successful propagation of the scattered lightonto the UV spectrometer slit through target chamber center.

The probe beam came from port P9 ��=116.57, =234.0� in the Omega chamber, and was a frequency qua-drupled component of the main beam, at �=0.263 �m. The

probe-beam spot size was 100 �m, and with an energy of200 J. The collection diagnostic was an imaging UV spec-trometer located in the TIM 2 �ten-inch manipulator� port��=79.19, =90.0� of the Omega chamber, with a 250 �mslit. In this geometry, the scattering angle was 101°. Thetarget axis ��=69.6, =241.5� was chosen such that the ion-acoustic waves probed via Thomson scattering were parallelto the shock propagation direction. The scattering volume inthe target was 3.7±0.1 mm from the drive surface of thetarget. The volume was determined by the overlap of the100 �m spot size from the probe beam and the slit from thespectrometer.

The spectrometer used was an f /8.7, 1 m imaging UVspectrometer with a grating with 3600 grooves/mm. Thespectrometer dispersion was calibrated with lines from mer-cury lamp near 0.310 �m, with a standard adjustment tomake the measurement appropriate for the 4� probe beamwavelength of 0.263 �m. The central wavelength, �=0.263,was confirmed by measuring stray 4� light on an experimentin the same week. Spectra were imaged on a streak camera,with a wavelength dispersion of 0.036 Å/pixel in a 5 ns win-dow, with 6 ps/pixel dispersion in time.

In addition to Thomson scattering, we performed x-rayradiography of the target, using an x-ray framing cameraopposite the backlighter target. Point projection radiographyof the shock proved unsuccessful, as an L-shell backlighterproved too dim to effectively image the absorption featuresat that low an irradiance.

A double-peaked scattered-light spectrum was detectedat 20.1±0.25 ns after the drive beams turned on, 1.1 ns afterthe probe beam turned on, about halfway through the dura-tion of the probe beam. The signal lasted 300±12 ps. Thepeaks were Doppler shifted by +1.41±0.2 Å by the plasmavelocity of the gas in the scattering volume, corresponding toa plasma velocity of 110±8 km/sec. The timing of the sig-nal, along with the measured plasma velocity, suggests theprobe beam was scattered off of shocked plasma in the tran-sition region of the radiatively shocked gas in argon, beforethe gas density increased above critical for this geometry.The imaged spectrum is shown in Fig. 2. Further data analy-sis is discussed in Reighard et al.9

The authors would like to thank the University of Michi-gan target fabrication team, including Mark Taylor, ChristineKrauland, Donna Marion, and Douglas Kremer. The authorswould also like to thank the technical staff at the Omegalaser facility. This work is supported by the National Nuclear

FIG. 1. 3D CAD rendering of experimental geometry, with beam directions.Beam timings and properties are discussed in the text. The gas fill tube wasattached to plastic hose through a voltage transducer to measure target gaspressure. In addition, alignment wires used for metrology and rotationalalignment were positioned at two separate places on the target. A dottedcircle outlines the location of the scattering volume on the target axis.

FIG. 2. Imaged spectrum from successful Thomson scattering experiment.Scattered light signal begins at 20.1±0.25 ns after drive beams turn on,about halfway through the 2 ns duration of the probe beam. The Thomsonscattered light duration was 300±12 ps. Timing and velocity measurementswere consistent from scattering within the driven shock transition layer, asthe gas collapses due to radiation loss.

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Glenzer, and C. Rousseaux, Phys. Rev. Lett. 95, 195005 �2005�.4 S. H. Glenzer et al., Phys. Rev. Lett. 82, 97 �1999�.5 S. H. Glenzer et al., Phys. Rev. Lett. 79, 1277 �1997�.6 J. Sheffield Plasma Scattering of Electromagnetic Radiation �Academic,New York, 1975�.

7 A. B. Reighard et al., Proceedings of the Third Inertial Fusion Scienceand Applications, edited by B. A. Hammel, D. D. Meyerhofer, J. Meyer-ter-Vehn, and H. Azechi �American Nuclear Society, Inc., 2004�.

8 A. B. Reighard et al., Phys. Plasmas �to be published�.9 A. B. Reighard et al., Phys. Rev. Lett. �in preparation�.

10E504-3 TS from a shock front Rev. Sci. Instrum. 77, 10E504 �2006�

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160

161

APPENDIX C

Shot data, diagnostics, and metrology tolerances

The purpose of this appendix is to collect all the relevant shot information that

was not suitable to include in the text. Table C.1 gives a summary of the diagnostics

fielded on each shot day. Tables C.2 through C.10 give a list of all shots taken on

each shot day, with relevant laser and target information, as well as a list of the data

collected. Table C.11 gives the metrology tolerances for the targets for each shot

day, and was also listed in Chapter Three. Finally Table C.12 gives the meaning of

all the acronyms used in these tables.

162

163

Tab

leC

.1:

Tab

leof

faci

lity

setu

pat

the

Om

ega

lase

r

faci

lity

for

each

shot

day

.

164

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

Backli

gh

ter

Targ

et

nam

e

Driv

e

dis

k

thic

kn

ess

/

mate

ria

l

Measu

red

driv

e d

isk

thic

kn

ess

(!

m)

Main

driv

er

ad

van

ce

(n

s)

PH

BL

driv

er

dela

y

(n

s)

PH

BL

gate

dela

y

(n

s)

PH

BL

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

PH

BL

targ

et

(J)

PH

BL

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

d

Fail

ure

mo

de

40707

18596

ABR-S

AU

05-

20-4

ABR-T

SA05-

PH

6-V

20 B

e26

-17

-30.6

14.6

3813

4.8

57E+

14

V1344.8

1.3

38E+

14

1.1

61.1

0SSFC

SSFC

N/A

40706

18595

ABR-S

AU

05-

40-3

ABR-T

SA05-

PH

5-V

40 B

e46

-23

-30.6

20.6

3721

4.7

4E+

14

V1325.2

1.3

18E+

14

1.1

89

1.1

3SSFC

SSFC

N/A

40705

18594

ABR-S

AU

05-

20-3

ABR-T

SA05-

PH

4-V

20 B

e26

-19.5

-30.6

17.1

3810

4.8

54E+

14

V1310.8

1.3

04E+

14

1.2

46

1.1

9SSFC

none

possib

le

mis

poin

ting

40703

18593

ABR-S

AU

05-

20-1

ABR-T

SA05-

PH

2-V

20 B

e25

-13

-30.6

10.6

3836

4.8

87E+

14

V1350.8

1.3

44E+

14

1.1

93

1.1

4SSFC

SSFC

N/A

40702

18592

ABR-T

SA05-

20-3

ABR-T

SA05-

PH

8-S

n20 B

e23

-16

-30.6

13.6

3770

4.8

03E+

14

Sn

1020

1.0

15E+

14

1.1

74

1.1

2TS,

SSFC

TS

BL t

oo d

im

40700

18591

ABR-T

SA05-

20-2

ABR-T

SA05-

PH

10-S

n20 B

e24

-16

-30.6

13.6

3784

4.8

2E+

14

Sn

1308

1.3

01E+

14

1.0

84

1.0

3TS,

SSFC

none

mis

poin

ting,

SSFC

mis

tim

ed

Tab

leC

.2:

Sum

mar

yof

allsh

ots

take

non

the

Aug

ust,

2005

shot

day.

See

tabl

eof

acro

nym

sfo

rm

ore

deta

ils.

165

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

BL T

arg

et

nam

e

Driv

e d

isk

thic

kn

ess/

mate

ria

l

Measu

red

driv

e d

isk

thic

kn

ess

(!

m)

Main

driv

er

ad

van

ce

(n

s)

PH

BL

driv

er

dela

y

(n

s)

PH

BL

gate

dela

y

(n

s)

PH

BL

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

PH

BL

targ

et

(J)

PH

BL

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

d

Fail

ure

mo

de

39929

18267

ABR-S

M05-

10-3

ABR-S

M05-

PH

810 Be

11

-90

0.6

9.6

3762

4.7

92E+

14

V1696

2.9

89E+

14

1.1

56

1.1

0SSFC

none

unre

solv

ed

39928

18266

ABR-S

M05-

40-1

ABR-S

M05-

PH

740 B

e47

-20

00.6

20.6

3763

4.7

94E+

14

V1658.4

2.9

23E+

14

1.1

38

1.0

8SSFC

none

unre

solv

ed

39927

18265

ABR-S

M05-

20-2

ABR-S

M05-

PH

420 B

e24

-14

00.6

14.6

3139.2

3.9

99E+

14

V1656.4

2.9

19E+

14

1.1

69

1.1

1SSFC

SSFC

N/A

39925

18264

ABR-S

M05-

10-2

ABR-S

M05-

PH

310 Be

11

-40

0.6

4.6

3109.5

3.9

61E+

14

V1640

2.8

9E+

14

1.1

62

1.1

1SSFC

SSFC

N/A

39924

18263

ABR-S

M05-

20-1

ABR-S

M05-

PH

920 B

e24

-7.5

00.6

8.1

3789

4.8

27E+

14

V1622

2.8

58E+

14

1.1

83

1.1

3SSFC

SSFC

N/A

39922

18262

ABR-S

M05-

40-1

ABR-S

M05-

PH

140 B

e47

-90

0.7

59.7

53842

4.8

94E+

14

V1644.8

2.8

99E+

14

1.3

71.3

0SSFC

SSFC

N/A

Tab

leC

.3:

Sum

mar

yof

allsh

ots

take

non

the

May

,20

05sh

otda

y.Se

eta

ble

ofac

rony

ms

for

mor

ede

tails

.

166

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

BL T

arg

et

nam

e

Driv

e

dis

k

Measu

red

driv

e d

isk

thic

kn

ess

(!

m)

Main

driv

er

ad

van

ce

(n

s)

PH

BL d

riv

er

dela

y (

ns)

PH

BL

gate

dela

y

(n

s)

PH

BL

tota

l

dela

y

(n

s)

Area B

L

driv

er

dela

y

(n

s)

Area B

L

gate

dela

y

(n

s)

Area B

L

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

PH

BL

targ

et

(J)

PH

BL

Irrad

ian

ce

(W

/cm

2)

En

erg

y

on

Area

BL t

arg

et

(J)

Area B

L

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

dFail

ure m

od

e

38983

17696

ABR-S

F05-

20-2

ABR-F

05-

PH

420 B

e25

-15.5

00.2

15.7

N/A

N/A

N/A

3765

4.7

9618E+

14

V1626.8

5.6

012E+

14

N/A

N/A

1.0

88

1.0

4SSFC

SSFC

N/A

38982

17695

ABR-S

F05-

20-1

ABR-F

05-

PH

220 B

e25

-15.5

00.2

15.7

30.2

18.7

3727

4.7

4777E+

14

V1559.2

5.3

684E+

14

2321.4

1.8

25E+

14

1.2

02

1.1

4SSFC/4

SFC

none

nois

e/

mis

poin

ting

38981

17694

D25

ABR-F

05-

PH

320 B

e19

-15.5

00.2

15.7

30.2

18.7

3741

4.7

6561E+

14

V1493.6

5.1

425E+

14

2338.2

1.8

38E+

14

1.0

62

1.0

1SSFC/4

SFC

none

nois

e/

mis

poin

ting

38976

17700

ABR-T

SF05-

20-4

N/A

20 B

e25

-15.5

N/A

N/A

N/A

-30.2

12.7

3757

4.7

8599E+

14

Sn

N/A

N/A

2211.6

1.7

38E+

14

1.0

08

0.9

6TS/4

SFC

none

mis

poin

ting/d

i

m

38975

17699

ABR-T

SF05-

20-2

N/A

20 B

e25

-15.5

N/A

N/A

N/A

-30.2

12.7

3390

4.3

1847E+

14

Sn

N/A

N/A

1840.2

1.4

46E+

14

1.1

68

1.1

1TS/4

SFC

none

mis

poin

ting/d

i

m

Tab

leC

.4:

Sum

mar

yof

allsh

ots

take

non

the

Febr

uary

,20

05sh

otda

y.Se

eta

ble

ofac

rony

ms

for

mor

ede

tails

.

167

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

BL

Targ

et

nam

e

Driv

e

dis

k

Measu

red

driv

e d

isk

thic

kn

ess

(!

m)

Main

driv

er

ad

van

ce

(n

s)

PH

BL

driv

er

dela

y

(n

s)

PH

BL

gate

dela

y

(n

s)

PH

BL

tota

l

dela

y

(n

s)

Area B

L

driv

er

dela

y

(n

s)

Area B

L

gate

dela

y

(n

s)

Area B

L

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

PH

BL

targ

et

(J)

PH

BL

Irrad

ian

ce

(W

/cm

2)

En

erg

y o

n

Area B

L

targ

et

(J)

Area B

L

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

dFail

ure m

od

e

37043

16440

D19

PH

-29

10 Be

9-9

00.2

9.2

30.2

12.2

3748

4.7

75E+

14

V1706.4

2.4

14E+

15

2559.6

4.0

234E+

14

1.1

31.0

8SSFC/4

SFC

none

dual ra

dio

gra

phy

washout/

4SFC

mis

tim

ed

37041

16439

D22

PH

-27

20 B

e24

-12

00.2

12.2

3.5

0.2

15.7

3778

4.8

13E+

14

V1719.6

2.4

33E+

15

2577

4.0

508E+

14

1.1

66

1.1

1SSFC/4

SFC

none

dual ra

dio

gra

phy

washout/

4SFC

mis

tim

ed

37040

16438

D8

PH

-24

40 B

e41

-20

-10.2

19.2

40.2

24.2

3651

4.6

51E+

14

V1731.2

2.4

49E+

15

2546.4

4.0

027E+

14

1.1

21.0

7SSFC/4

SFC

none

dual ra

dio

gra

phy

washout/

4SFC

mis

tim

ed

37039

16445

D23

PH

-17

20 B

e23

-50

0.2

5.2

2.5

0.2

7.7

3763

4.7

94E+

14

V1737.6

2.4

58E+

15

2587.8

4.0

678E+

14

1.3

01

1.2

4SSFC/4

SFC

none

dual ra

dio

gra

phy

washout/

4SFC

mis

tim

ed

37038

16444

D24

PH

-14

20 B

e23

-5.5

00.2

5.7

2.5

0.2

8.2

3700

4.7

13E+

14

V1576

2.2

3E+

15

2350.2

3.6

943E+

14

0.5

95

0.5

7SSFC/4

SFC

none

dual ra

dio

gra

phy

washout/

4SFC

mis

tim

ed

37037

16443

D13

PH

-13

20 B

e24

-60

0.2

6.2

30.2

9.2

3767

4.7

99E+

14

V1638.4

2.3

18E+

15

2350.2

3.6

943E+

14

1.1

69

1.1

1SSFC/4

SFC

none

dual ra

dio

gra

phy

washout/

4SFC

mis

tim

ed

Tab

leC

.5:

Sum

mar

yof

allsh

ots

take

non

the

Aug

ust,

2004

shot

day.

Muc

hof

the

data

onth

issh

otda

yw

ere

vict

imto

dual

radi

ogra

phy

was

hout

(see

Cha

pter

Four

).Se

eta

ble

ofac

rony

ms

for

mor

ede

tails

.

168

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

BL

Targ

et

nam

e

Driv

e

dis

k

Measu

red

driv

e d

isk

thic

kn

ess

(!

m)

Main

driv

er

ad

van

ce

(n

s)

PH

BL

driv

er

dela

y

(n

s)

PH

BL

gate

dela

y

(n

s)

PH

BL

tota

l

dela

y

(n

s)

Area B

L

driv

er

dela

y

(n

s)

Area B

L

gate

dela

y

(n

s)

Area B

L

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y o

n

PH

BL

targ

et

(J)

PH

BL

Irrad

ian

ce

(W

/cm

2)

En

erg

y o

n

Area B

L

targ

et

(J)

Area B

L

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

d

Fail

ure

mo

de

35840

15853

Be-7

PH

-340 B

eN

/M-1

20

0.2

12.2

30.2

-8.8

4269.4

5.4

36E+

14

V1675

2.3

6964E+

15

2687.7

4.2

248E+

14

1.1

56

1.1

0SSFC/4

SFC

4SFC

nois

e

35839

15854

2 m

il 9

PH

-480 P

EN

/M-1

00

0.2

10.2

30.2

-6.8

3788.7

4.8

24E+

14

V1660.5

2.3

4913E+

15

2668.4

4.1

945E+

14

1.0

23

0.9

7SSFC/4

SFC

4SFC

nois

e

35838

15851

Be-5

RAD

BL-

140 B

eN

/M-1

00

0.2

10.2

30.2

-6.8

3822.2

4.8

67E+

14

V1865.3

2.6

3886E+

15

2782.2

4.3

733E+

14

1.1

17

1.0

6SSFC/4

SFC

none

SSFC

mis

tim

ed,

4SFC

mis

poin

ted

Tab

leC

.6:

Sum

mar

yof

alls

hots

take

non

the

Apr

il,20

04sh

otda

y.M

uch

ofth

eda

taon

this

shot

day

wer

evi

ctim

todu

alra

diog

raph

yw

asho

ut(s

eeC

hapt

erFo

ur).

See

tabl

eof

acro

nym

sfo

rm

ore

deta

ils.

169

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

BL

Targ

et

nam

e

Driv

e

dis

k

Measu

red

driv

e d

isk

thic

kn

ess

(!

m)

Main

driv

er

ad

van

ce

(n

s)

PH

BL

driv

er

dela

y

(n

s)

PH

BL

gate

dela

y

(n

s)

PH

BL

tota

l

dela

y

(n

s)

Area B

L

driv

er

dela

y

(n

s)

Area B

L

gate

dela

y

(n

s)

Area B

L

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

PH

BL

targ

et

(J)

PH

BL

Irrad

ian

ce

(W

/cm

2)

En

erg

y

on

Area

BL

targ

et

(J)

Area B

L

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

d

Fail

ure

mo

de

34046

14930

1-m

il-3

PH

13

1 m

il P

EN

/M-1

00

0.2

10.2

30.2

13.2

3730

4.7

5159E+

14

V1609.6

4.8

507E+

14

3147.9

4.9

48E+

14

2.1

38

1.1

3SSFC/4

SFC

none

tim

ing,

poin

ting,

targ

et

constr

uction

34045

14929

2-m

il-2

PH

-15

2 m

il P

EN

/M-1

40

0.2

14.2

40.2

18.2

3843

4.8

9554E+

14

V1766.4

5.3

232E+

14

3137.4

4.9

32E+

14

2.0

91

1.1

0SSFC/4

SFC

none

tim

ing,

poin

ting,

targ

et

constr

uction

34044

14928

1-m

il-6

PH

-18

1 m

il P

EN

/M-5

00.2

5.2

30.2

8.2

3821

4.8

6752E+

14

V1749.6

5.2

726E+

14

3131.1

4.9

22E+

14

2.1

06

1.1

1SSFC/4

SFC

none

tim

ing,

poin

ting,

targ

et

constr

uction

34043

14927

1-m

il-2

PH

-19

1 m

il P

EN

/M-5

00.2

5.2

30.2

8.2

3791

4.8

293E+

14

V1576

4.7

494E+

14

3088.4

4.8

55E+

14

2.1

74

1.1

4SSFC/4

SFC

none

tim

ing,

poin

ting,

targ

et

constr

uction

34042

14926

2-m

il-3

PH

-21

2 m

il P

EN

/M-7

00.2

7.2

40.2

11.2

3753

4.7

8089E+

14

V1616

4.8

7E+

14

3152.8

4.9

56E+

14

2.1

61

1.1

4SSFC/4

SFC

none

tim

ing,

poin

ting,

targ

et

constr

uction

Tab

leC

.7:

Sum

mar

yof

allsh

ots

take

non

the

Nov

embe

r,20

03sh

otda

y.T

his

shot

day

prod

uced

nous

able

data

.Se

eta

ble

ofac

rony

ms

for

mor

ede

tails

.

170

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

BL

Targ

et

nam

e

Driv

e

dis

k

Measu

red

driv

e d

isk

thic

kn

ess

(!

m)

Main

driv

er

ad

van

ce

(n

s)

PH

BL

driv

er

dela

y

(n

s)

PH

BL

gate

dela

y

(n

s)

PH

BL

tota

l

dela

y

(n

s)

Area B

L

driv

er

dela

y

(n

s)

Area B

L

gate

dela

y

(n

s)

Area B

L

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

PH

BL

targ

et

(J)

PH

BL

Irrad

ian

ce

(W

/cm

2)

En

erg

y

on

Area

BL t

arg

et

(J)

Area B

L

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

d

Failu

re

mo

de

32355

14217

W6

none

75 P

EN

/M-9

N/A

N/A

N/A

00.4

-8.6

4833.9

6.1

547E+

14

VN

/AN

/A2766.4

4.3

49E+

14

N/M

N/M

4SFC

none

constr

uction,

poin

ting

32354

14216

P2

none

75 P

EN

/M-1

1N

/AN

/AN

/A0

0.4

-10.6

4945

6.2

962E+

14

VN

/AN

/A2708

4.2

57E+

14

N/M

N/M

4SFC

none

constr

uction,

poin

ting

32352

14215

P1

none

75 P

EN

/M-1

9N

/AN

/AN

/A0

0.4

-18.6

4776.6

6.0

818E+

14

VN

/AN

/A2670.9

4.1

98E+

14

N/M

N/M

4SFC

none

constr

uction,

poin

ting

32347

14214

M4

none

75 P

EN

/M-2

5N

/AN

/AN

/A0

0.4

-24.6

4959

6.3

14E+

14

VN

/AN

/A2707.6

4.2

56E+

14

N/M

N/M

4SFC

none

constr

uction,

poin

ting

32346

12149

W1

none

75 P

EN

/M-2

2N

/AN

/AN

/A0

0.4

-21.6

no d

ata

no d

ata

VN

/AN

/Ano d

ata

no d

ata

N/M

N/M

no d

ata

none

not

know

n

32345

14213

none

BL14

none

none

none

00.9

0.9

N/A

N/A

N/A

N/A

N/A

V1229.3

9.7

82E+

14

N/A

N/A

N/A

N/A

SSFC

none

constr

uction,

poin

ting

32344

14118

BL2

75 P

EN

/M-1

10

0.9

10.1

N/A

N/A

N/A

4715

6.0

033E+

14

V1201.9

9.5

64E+

14

N/A

N/A

N/M

N/M

SSFC

none

constr

uction,

poin

ting

32343

14103

W3

BL1

75 P

EN

/M-1

30

0.9

12.1

N/A

N/A

N/A

4851.9

6.1

776E+

14

V1164.5

9.2

67E+

14

N/A

N/A

1.9

75

0.9

63415

SSFC

none

shra

pnel hit

fram

ing

cam

era

Tab

leC

.8:

Sum

mar

yof

alls

hots

take

non

the

July

,200

3sh

otda

y.T

his

shot

day

prod

uced

nous

able

data

,and

was

the

first

day

that

used

Uni

vers

ity

ofM

ichi

gan.

See

tabl

eof

acro

nym

sfo

rm

ore

deta

ils.

171

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

Driv

e

dis

k

Main

driv

er

ad

van

ce

(n

s)

Area B

L

driv

er

dela

y

(n

s)

Area B

L

gate

dela

y

(n

s)

Area B

L

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

Area

BL

targ

et

(J)

Area B

L

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

d

Failu

re

mo

de

29937

12956

OTEM

EAS-

48

50 B

e0

4.5

0.2

4.7

4426

5.6

354E+

14

Sn

2271.6

3.5

707E+

14

1.6

39

1.0

84SFC/V

ISAR

none

mis

tim

ed/

absorp

tion

29936

12954

OTEM

EAS-

44

50 B

e0

11

0.2

11.2

4065.2

5.1

76E+

14

Sn

2719.2

4.2

743E+

14

1.8

46

1.2

24SFC/V

ISAR

none

mis

tim

ed/

absorp

tion

29935

12955

OTEM

EAS-

47

50 B

e0

4.5

0.2

4.7

4507.9

5.7

396E+

14

Sn

4090.3

6.4

295E+

14

1.5

48

1.0

24SFC/V

ISAR

none

mis

tim

ed/

absorp

tion

29934

12953

OTEM

EAS-

45

50 B

e0

18

0.2

18.2

4263.1

5.4

279E+

14

Sn

2818.9

4.4

31E+

14

1.6

01

1.0

64SFC/V

ISAR

4SFC

absorp

tion

29932

12952

OTEM

EAS-

46

50 B

e0

18

0.2

18.2

4716.3

6.0

05E+

14

Sn

2861.2

4.4

975E+

14

1.6

67

1.1

04SFC/V

ISAR

none

mis

poin

ted/

absorp

tion

Tab

leC

.9:

Sum

mar

yof

allsh

ots

take

non

the

Dec

embe

r,20

02sh

otda

y.T

houg

hth

efil

lga

sw

asxe

non

onth

isda

y,a

tin

back

light

erw

asus

ed.

See

tabl

eof

acro

nym

sfo

rm

ore

deta

ils.

172

Sh

ot

Nu

mb

er

Sh

ot

Req

uest

Fo

rm

RID

Main

Targ

et

nam

e

Driv

e

dis

k

Main

driv

er

ad

van

ce

(n

s)

Area B

L

driv

er

dela

y (

ns)

Area B

L

gate

dela

y

(n

s)

Area B

L

tota

l

dela

y

(n

s)

To

tal

driv

e

en

erg

y

(J)

To

tal

Irrad

ian

ce

(W

/cm

2)

BL

mate

ria

l

En

erg

y

on

Area

BL

targ

et

(J)

Area B

L

Irrad

ian

ce

(W

/cm

2)

Gas f

ill

vo

ltag

e

(V

)

Gas f

ill

pressu

re

(A

TM

)

Prim

ary

Dia

gn

osti

cs

Data

co

llecte

d

Failu

re

mo

de

28388

12322

OTEM

EAS-3

850 B

e0

4.5

0.2

4.7

N/A

N/A

Sn

N/A

N/A

0.9

68

0.6

54SFC/V

ISAR

none

mis

tim

ed/

absorp

tion

28386

12321

OTEM

EAS-4

050 B

e0

4.5

0.2

4.7

N/A

N/A

Sn

N/A

N/A

1.6

42

1.0

94SFC/V

ISAR

none

mis

tim

ed/

absorp

tion

28382

12320

OTEM

EAS-4

150 B

e0

12

0.2

12.2

N/A

N/A

Sn

N/A

N/A

1.6

52

1.1

04SFC/V

ISAR

4SFC

absorp

tion

28380

12253

OTEM

EAS-3

950 B

e0

10

0.2

10.2

N/A

N/A

Sn

N/A

N/A

1.6

14

1.0

84SFC/V

ISAR

VIS

AR

mis

poin

ted

Tab

leC

.10:

Sum

mar

yof

allsh

ots

take

non

the

Aug

ust,

2002

shot

day.

Thi

sw

asth

efir

stsh

otda

yfo

rth

era

diat

ive

gas

expe

rim

ents

.Las

eren

ergy

info

rmat

ion

both

inan

onlin

ear

chiv

ean

dpe

rson

alno

tes

isun

avai

labl

e.Se

eta

ble

ofac

rony

ms

for

mor

ede

tails

.

173

Table C.11: Target feature tolerances as a function of shot day. Items listed as unknown wereeither not measured (if built at U. MI) or had no measured details on the documentaccompanying finished targets (if built at LLNL).

Experiments

TS Thomson Scattering

RadGas Radiative Shock in Gas

SNRT

Supernova Rayleigh-

Taylor

Diagnostics

4SFC

Four Strip Framing

Camera

FXI Framed X-ray Imager

HENEX

NRL High-Energy X-ray

Spectrometer

PFM Pulse-Forming Matrix

SSC X-ray Streak Camera

SSFC

Single Strip Framing

Camera

VISAR

Velocity Interferometer

System for Any

Reflector

XRPHC X-ray Pinhole Camera

XRFC X-ray Framing Camera

Lasers

DPP Distributed Phase Plate

SSD

Smoothing by Spectral

Dispersion

Misc.

N/A

Not available or Not

applicable

N/M Not measured

Table C.12: Acronyms used to describe radiative shock experiments, both in the above tables andin the text.

BIBLIOGRAPHY

174

175

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ABSTRACT

Collapsing Radiative Shock Experiments on the Omega Laser

by

Amy B. Reighard

Chair: R. Paul Drake and Fred C. Adams

Radiative shocks are notoriously difficult to produce in a laboratory setting, due to

the extreme demands of the production of relatively high temperatures over sufficient

extent for radiation and matter to interact. This dissertation describes a fundamental

radiation hydrodynamics experiment, using a low-Z piston to drive a strong shock

through low density gas, creating a driven, radiatively collapsed shock.

Using 10 beams of the 60-beam Omega Laser facility at the University of Rochester,

a low-Z disk is irradiated with an intensity of approximately 5 × 1014 W/cm2 in a

1 ns square pulse over a 1 mm spot size. The laser disturbance first shocks then

accelerates the disk via laser ablation pressure, achieving velocities well over 200

km/sec. This accelerated piston drives a shock into gas, usually xenon. The strong

shock heats the gas to several hundred eV, which then radiates away a significant

amount of energy, leading the shocked plasma to collapse to very high compression.

This experiment is compared to astrophysical systems with similar optical depth

1

profiles. Radiative shocks are common in astrophysical settings, where it is easy to

generate fast shocks in low-density media. This experiment has applications to laser-

driven dynamic hohlraums, which would take advantage of the radiative shock as a

smooth implosion source while still reaping the benefits of a converging geometry.