page 1+422003 hedp class inroductory lecture what is radiation hydrodynamics? the science of systems...

2003 HEDP Class Inroductory Lecture +42

What is radiation hydrodynamics?

• The science of systems in which radiation affects the dynamics of the matter

• There are two radiation-hydrodynamic regimes

– Radiative-flux regime, where radiative energy transport is essential (above ~ 30 eV)

– Radiative-pressure regime, where thermal radiation pressure is dominant (above ~ 1 keV)

• Today’s experiments are in the radiative-flux regime

• Two rad-hydro phenomena: Marshak waves and radiative shocks


Radiation waves develop when thermal radiation diffuses into a medium

• They require that the medium be many radiation-mean-free-paths thick (“optically thick”), and so usually involve high-Z materials

• Marshak waves: the penetration of radiation from a constant temperature boundary into an optically thick medium.

• Features for simple cases – Depth– Shape constant in time

(“self-similar” structure)

• These features remain approx. true in more complex cases

€

depth∝ time

From Drake, High-Energy-Density Physics, Springer (2006)


Hohlraums rely on Marshak waves to create thermal environments at millions of degrees

• Put energy inside a high-Z enclosure

• The vacuum radiation field stays in equilibrium with the resulting hot surface

• One gets high temperatures because the Marshak wave moves slowly, penetrating few microns

Credit LLNL

Laser spots seen through thin-walled hohlraum.

Hohlraum with experiment attached on bottom



Shock waves become radiative when

• Radiative energy flux exceeds incoming material energy flux

• Where post-shock temperature is

• Giving a dimensionless threshold

Material Xe Xe CH

Density 0.01 g/cc 10-5 g/cc 0.01 g/cc

Threshold velocity 60 km/s 10 km/s 200 km/s

€

RTs =2(γ −1)

(γ +1)2us

2

€

σTs4 > ρous

3 /2

€

Q =2σ

R4

us5

ρo

>(γ +1)8

16(γ −1)4~ 5,000

downstreamUpstreampreheated


The other key dimensionless parameter for steady radiative shocks is “optical depth”

Downstreamshockedregion

Upstream preheated region

Optically thin

Optically thin

Optically thick

Optically thick

“LTE” shocksSome astro

Some experiments & astroLarger density ratios

Much astroAny experiments?

Reighard Fleury

Blast waves in gasses(photon starved upstream)

Keiter Herrmann

Z dynamic

Recent French workBouquet, Michaut,

& collabs

SN blast wave

Perhaps some shock-clump interactions


Geometry of optically thin (upstream) radiative shocks

Density

Temperature

Upstream o,To,po

Here we ignore ion-electron decoupling, which occurs on a more-localized scale at the density jump

Initial post-shock state i,Ti,pi

Downstream final state f,Tf,pf

Cooling layer


The local fluid energy balance provides a solvable system for steady shocks

• Energy equation

• Assumptions:

1D, use , the momentum & continuity eqs.,

• Result

• Where the radiation model is a transport model not a diffusion model, with

€

∇• u ε +u2

2

⎛

⎝ ⎜

⎞

⎠ ⎟+ pu

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥= −∇• FR

€

ε =p / γ −1( )

€

ous3

2

∂

∂z

−2γ

γ −1( )

ρo

ρ

⎛

⎝ ⎜

⎞

⎠ ⎟+

γ +1( )γ −1( )

ρo

ρ

⎛

⎝ ⎜

⎞

⎠ ⎟

2 ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥= −

∂FR

∂z= 4πκ B− JR( )

€

B =σT 4

π

€

JR =σTf

4

π


Cooling layers are optically thin

T-4/3 0 (approx. Xe conditions) = 4/3 here, so o = 1 mg/cc

Our experiments are in this regime but denser and faster


Density (ratio to

Preshock)

downstreamAn example for the thick-thin caseof our experiments


Amy Reighard is leading experiments to study such shocks for her Ph.D. thesis research

• Laser drive beams launch Be piston into xenon gas

• Piston drives a planar shock

• Radiography detects dense xenon

• Gold grid provides spatial fiducial

• Parameters– 1015 W/cm2 – 0.35 µm light– 1 ns pulse – 600 µm tube dia.


In 1D simulations with HYADES, the shocked layer grows thicker at nearly constant density

40 µm Be diskAt several times~ 140 km/s

Simulation by Amy Reighard


Data from Omega show a dense and apparently uniform layer of shocked xenon

• 20 µm Be drive disk

• Data at 14.6 ns

• Grid cells are 63 µm squares


New phenomena become dominant in relativistic HEDP

• We will discuss – Relativistic electron motion in laser beams – Electron acceleration – Ion acceleration – Some other phenomena

• “Relativistic” laser beams– Quiver momentum

– Lorentz factor

– Todd Ditmire will introduce you to this technology– Bill Kruer will explain the interaction physics

€

ao =pe

mc=

ILλ μ2

1.37 ×1018 W μ 2 /cm2

€

r = 1+ao2


Electrons in a light wave oscillate and drift

• The force equation is

• For an electron in a light wave one can show

• For small laser irradiance the motion is a drifting figure 8 with

• At very high laser irradiance the oscillations become extremely anharmonic and the motion is mainly along z with

€

dp

dt= −eE−

e

cv ×B

€

pz =px

2

2mec

€

px ∝ cos ωt( ) and pz ∝ cos2 ωt( )

€

vx = c2

γ r

and vz = c 1−2

γ r

px

pz

Enam Chowdhury,Ph.D. Thesis


To experience acceleration on a wake, go wakeboarding or surfing

• A wakeboarder can surf the wake on a boat… gaining momentum

http://www.nickandjulz.com/pro/photos/wake/


To accelerate lots of electrons, take them surfing too

• Electrons can surf the wake on a pressure pulse in a plasma

• The pressure pulse can be produced by one or more laser beams or by an electron bunch. This is wakefield acceleration.

– Eric Esarey will introduce you to the alphabet soup of detailed approaches

Credit: LBL OASIS Group

Laser pulse

Electrons

Plasma Wake

Hogan et al., PRL 2005

SLAC beam

AcceleratedAcceleratedelectronselectrons


To accelerate ions, repel them

• If you remove the electrons somehow, the remaining ions will push each other apart

• How to remove the electrons:

• Thermally– Hot electrons leave a surface plasma much faster than the ions do– This produces “sheath acceleration”

– The electron “temperature” and the sheath potential increase with ao

– The maximum ion energy is ~ 20 Z ao MeV

–

• Ponderomotively, which means from the laser light pressure– “Coulomb explosions” occur when a group of ions blows apart– For a sphere

€

Emax ~ 40Z 2 ni

1018 cm−3

ro10μm

⎛

⎝ ⎜

⎞

⎠ ⎟

2

MeV


One can create lots of new phenomena with relativistic lasers

• Transmit light through high-density plasma

• Drill holes in dense plasma

• Make lots of electron-positron pairs

• Cause nuclear reactions

• Create GigaGauss magnetic fields

• And many more

• You will see some of these this week


Part Two: The Toys

• Hardware– J X B guns

– Z pinch

– High-energy lasers

– Ultrafast lasers

– Beams

• Codes– Eulerian

– Lagrangian

– PIC

– Hybrids


Marcus Knudson is a gunslinger with ICE in his veins

• He will show you what one can learn by shooting “bullets” at targets to create shocks and learn from what they do

– These bullets are called “flyer plates” – One gun is the electric pulse generator of the “Z machine” at Sandia

J

B

J X B

• The trick is to drive a current on one surface of a thin conducting material These bullets are called “flyer plates”

• One can launch flyer plates this way with velocities above 20 km/s

• By arranging the currents to create gentle compression, one can do Isentropic Compression Experiments (ICE)


Chris Deeney is a chef

• Much of his career has been cooking samples using “Z pinches”

• Today’s biggest x-ray barbecue is the Z machine at Sandia, when

run as a Z pinch (> 2 MJ of x-rays)

• Z pinches exploit the attraction between parallel currents

Cylindrical wire array Implosion Stagnation

Inward J X B force Inward acceleration

Shock heating &Radiative cooling


The action is at the center of a large though compact structure


Bill Kruer and Todd Ditmire are space rangers

• They spend their time zapping things with lasers

and analyzing what happens when you do

• High energy lasers amplify the light energy across a large area then compress the beam(s) in space to create high energy density

amplify protect

Smooth(spatial filter)

amplify

vacuum

irradiate


High-Energy lasers: big facilities; small targets


Today’s workhorse in the US is Omega

Target chamber at Omega laser


The National Ignition Facility will provide much more energy

• > 1 MJ on target • 192 beams

• LMJ in France will be on the same scale

18-wheeler cab and trailer


Ultrafast lasers compress pulses in time as well as space• Amplify a long pulse over a large area

• Compress it to a small volume in time and space

• A “lambda-cubed” laser has a spot one wavelength in diameter and a pulse one cycle long

• Grating pairs to stretch and compress the laser pulses in time


Accelerators produce high-energy-density beams

• Table from NAS report


All the toys are worthless without good diagnostics

• David Meyerhofer will discuss diagnostics


Now we turn to computer codes

• These toys are essential to

• Evaluating long-term applications

• Designing present-day experiments

• Interpreting aspects of experiments that can’t be measured

• Connecting HEDP experiments with other systems, for example in astrophysics

• There are many approaches; all have strengths and weaknesses


Eulerian codes calculate in a fixed geometric space

• The computational zones are defined in an Eulerian space

• Strengths– Adaptive grids are straightforward– Can follow swirling motions

• Weaknesses – Trouble following material boundaries – Large diffusion – Must start with very large box – Resolving shock waves can be hard

Credit Kifonidis et al.


Lagrangian codes track the motion of mass

• Features– Fixed mass in each zone

– Zone boundaries can move

• Strengths – Keeps materials separate

– Follows shocks well

– Complex physics models straightforward

• Weaknesses– Material cannot swirl– Not readily adaptive

Simulation by Laurent Boireau


Various modern codes combine both Lagrangian and Eulerian features

•CALE (LLNL, Omar Hurricane) •RAGE (LANL, Bernie Wilde)

Diverging Instability Experiment Supersonic Jet Experiment


Particle In Cell (PIC) codes track particles or superparticles

• Simulate motion of actual or representative particles with correct mechanical equations

• Evolve electromagnetic fields based on Maxwell’s equations using particle properties

• Strengths– Exact simulation

• Weaknesses– Limited space and time – Collisions are approximate

• Chuang Ren will discuss PIC codes Friday

Collisionless shock driven by ultrafast laser

Credit: Louis Silva


Part 3: The applications

• Inertial fusion

• Experimental Astrophysics

• Accelerators


These cool toys were developed for inertial confinement fusion (ICF) research


ICF is exciting but also a tough challenge

• Take a mm-scale cryogenic capsule filled with DT • Implode it

– At 300 km/s using giant lasers or Z pinches

– So gently that the fuel stays frozen

– Without letting instabilities rip it apart

– Possible ignite it with a relativistic laser

• Get an energy gain of > 100 from the fusion burn

• Applications – Defense

– Power generation


In ICF one first compresses the fuel using an ablatively driven implosion

• This is necessary to avoid blowing up the lab

Fuel layer is first compressed by shocks.

Then the shell is accelerated inward by high-pressure, low-density corona.

Stagnation creates a central hot spot surrounded by cold dense fuel

An ablatively driven implosion

ICF fusion Capsule


After compression, one has to make the ICF fuel burn by fusion

• Two approaches

This is the traditional approach

Riccardo Betti will tell you about it

Design the central hot spot so it ignites the fuel

Let the central hot spot be much smaller and rapidly ignite the compressed fuel

Options: lasers, particles, slugs

This is called fast ignition

Max Tabak will tell you about it.Rick Freeman will discuss particle transport, also essential.


Some of us are using these new tools to create experimental astrophysics

• New tools enable new science, and create new sciences

e.g., Hubble diagram

Spectroscopy enabled

and created astrophysics Astronomy: the human eye and brain

• High Energy Density facilities are new tools ….. Dmitri Ryutov will describe some of the astrophysical applications


Others are using these tools to create the next generation of particle accelerators

• Eric Esarey will discuss this

Credit:


In you want a better foundation in HEDP

• Come next summer to the second offering of

Foundations of High Energy Density Physics

• A thorough introduction to the foundations of this subject

• Taught by one lecturer (me) to provide a continuous discussion with common notation based on a book

• A two week course

• The 28 students last year were strongly enthused – Otherwise I would not be doing this again!

– Contact [email protected]


High-energy-density physics is exciting!

page 1+422003 hedp class inroductory lecture what is radiation hydrodynamics? the science of systems...

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