PHYSICAL REVIEW E 67, 056409 ~2003!

Two-dimensional effects in laser-created plasmas measured with soft-x-ray laser interferometry

J. Filevich, J. J. Rocca, E. Jankowska,* E. C. Hammarsten, K. Kanizay, and M. C. Marconi†

Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, Colorado 80523

S. J. MoonLawrence Livermore National Laboratory, Livermore, California 94551

V. N. ShlyaptsevDepartment of Applied Science, University of California Davis-Livermore, Livermore, California 94551

~Received 13 June 2002; published 29 May 2003!

Soft-x-ray laser interferograms of laser-created plasmas generated at moderate irradiation intensities (131011– 731012 W cm22) with l51.06mm light pulses of;13-ns-FWHM ~full width at half maximum!duration and narrow focus~;30 mm! reveal the unexpected formation of an inverted density profile with adensity minimum on axis and distinct plasma sidelobes. Model simulations show that this strong two-dimensional hydrodynamic behavior is essentially a universal phenomena that is the result of plasma radiationinduced mass ablation and cooling in the areas surrounding the focal spot.

DOI: 10.1103/PhysRevE.67.056409 PACS number~s!: 52.50.Jm, 42.55.Vc, 52.65.Kj, 52.70.La

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The understanding of the dynamics of laser-created pmas is of fundamental and practical interest. The hydronamic motion of plasmas created by laser irradiation of sotargets is conventionally known to result in electron densdistributions with maximum density along the axis of tirradiation beam. However, in plasmas generated with hirradiation intensities the ponderomotive force has beenserved to cause a density depression or cavity in the elecdensity profile. Early interferometry experiments of lascreated plasmas at irradiation intensities of 331014

W cm22 showed a flattening of the interfering fringes in thsubcritical region that, for an axis-symmetric plasma, isdicative of a density depression@1#. Density depressions induced by the ponderomotive force have also been obsein numerous other high-intensity laser experiments, in agment with simulations. Some of the most recent studiesclude the formation of plasma channels and laser-hole boin underdense and overdense plasmas motivated by theignitor concept in inertial confinement fusion@2,3#. Theseexperiments involved laser intensities of 1.731015 and 231017 W cm22, respectively. In addition, for several casinvolving short laser pulses the saturation of the heat flrefraction, or channeling of the laser radiation due to relaistic self-focusing at ultrahigh fluxes are found to be respsible for density suppression@4,5#.

In this paper, we report the observation of a pronoundensity minimum on axis in both line-focus and spot-focplasmas, generated at intensities as low as 1011 W cm22,which cannot be explained by the ponderomotive force,effects of laser radiation refraction, electron heat saturatnor the influence of plasma instabilities. Our case is diffent, yet universal enough to exist in a wide parameter sp

*Permanent address: Dept. of Physics, Wroclaw UniversityTechnology, Poland.

†Permanent address: Dept. of Physics, University of Buenos AArgentina.

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In fact, in retrospective, evidence of these effects mayinferred from published visible laser plasma interferogramapping much smaller electron densities of the order;1018 cm23 @6,7#. However, this kind of two-dimensiona~2D! plasma behavior was neither clearly revealed fromdata nor understood. In our measurements, the 2D effedistinctively uncovered by the use of soft-x-ray laser~SXRL!interferometry, which for the case of the spot-focus plasexperiment allowed us to map the density profile up;1021 cm23, close to the critical density. Simulations shothat plasma radiation and heat conduction enlarge the ation region creating a plasma density profile with large dtinctive sidelobes and a minimum on axis.

SXRL interferometry is a powerful new tool for the diagnostics of dense plasmas, which allows probing of plasdensities and scale lengths larger than those that canprobed with optical lasers. Interferometry measurementsdense large scale plasmas conducted using a laboraSXRL pumped by the Nova laser@8,9# significantly exceededthe density values probed with optical lasers, but were l

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FIG. 1. Schematic representation of the experimental setup.probe beam propagates along the axis of the line focus. The inferometer was positioned;2 m from the exit of the SXRL. Thedetector was placed;7 m from the interferometer.

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FILEVICH et al. PHYSICAL REVIEW E 67, 056409 ~2003!

FIG. 2. Sequence of soft-x-ray interferograms describing the evolution of 1.8-mm-long plasma generated by focusing a 13-nsNd:YAG laser pulse with 0.6 J energy onto a;30-mm-wide line on a copper target. The time delays are measured with respect tbeginning of the laser pulse. The heating laser is incident from the right.

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ited to several shots per day by the low repetition frequeof the pump laser. The results reported herein were obtawith a new soft-x-ray interferometry tool based on a portaSXRL and a Mach-Zehnder interferometer configurationwhich diffraction gratings are used as beam splitters@10#.The high repetition rate of the probe laser allowed uscomplete several series of interferograms of laser-creplasmas that map the entire temporal plasma evolution.

The experimental setup used in the measurementshown in Fig. 1. It comprises al51.06mm Q-switchedNd:YAG ~yttrium aluminum garnet! laser~Quanta Ray GCR-190! used to irradiate the target, the SXRL probe, andsoft-x-ray interferometer. The Ne-like Ar 46.9-nm capilladischarge laser, which has excellent spatial coherence@11#,was described in previous publications@12,13#. SXRL pulses

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with a full width at half maximum~FWHM! duration of;1.2 ns, energies of;0.1 mJ, and beam divergence of;4.5mrad were used in the experiment. The interferometer ugold-coated diffraction gratings as beam splitters@10#, posi-tioned at an incidence angle of 79°. It has the advantagehigh throughput~;6% per arm excluding imaging mirrors!and increased robustness against plasma debris. Elonggold-coated grazing incidence mirrors are used to directbeams towards the second grating, where they are recbined. Spherical mirrors coated with Si-Sc multilayers~nor-mal incidence reflectivity of;40%! @14# were used to imagethe plasma onto a charge coupled device with a microchnel plate~MCP! detector with a magnification of either 51.2or 24.7x. The line focus plasmas were generated by focuthe beam of the Nd:YAG laser~using a 30-cm-

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FIG. 3. Electron density profiles obtained from the interferograms.

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focal-length cylindrical lens and a 10-cm-focal-lengspherical lens! onto a polished electrolytic copper targplaced in the zero-order arm of the interferometer. A systof pinholes was used to reduce the strong plasma semission collected by the detector. The detector’s MCP wgated to further reduce the background radiation producethe plasma self-emission. The firing of the SXRL was sychronized with respect to the Nd:YAG laser using a commmaster clock and appropriate delays. However, since theter in the firing of the SXRL was significant nearly 100 shoper series were required to map the entire plasma evoluwith ;1 ns resolution. The fringe visibility of the interferograms obtained without the plasma present exceedsacross the entire 4003500mm2 field of view.

Figure 2 shows a series of interferograms that depictevolution of a line focus plasma created at an irradiatintensity of 0.931011 W cm22 by focusing 0.63 J—13-nsFWHM duration laser pulses into a;30-mm-wide line 1.8mm in length. These interferograms were obtained withmagnification of 24.73. Figure 3 shows the correspondindensity maps obtained from the fringe shifts assumingplasma is uniform along the probe beam axis. The earinterferograms~see the 3-ns frame! show an expandingplasma with a density distribution that presents a maximon axis. However, as time evolves and the pump laser in

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sity increases, the plasma density profile acquires a concshape with a density minimum on axis, which is alreaclearly developed at 6 ns after the initiation of the currepulse, and that becomes more pronounced in the subseqseveral nanoseconds. The asymmetry observed in somthe interferograms is due to a slight misalignment of ttarget. At times after termination of the Nd:YAG laser pulsthe decreasing degree of ionization of the plasma causesnificant absorption of the probe beam by photoionizatioMeasurements were conducted to verify that the obserdensity profile is not a consequence of the intensity profilethe pump laser. It should be noticed that due to the lascale length of the plasma and large density gradientsultraviolet laser probe~e.g., fourth harmonic of Nd:YAG at266 nm! would be very strongly refracted.

To understand this unusual electron density profile,conducted simulations with the hydrodynamic codeLASNEX

@15#. The severe distortion of the plasma motion inferrfrom our SXRL interferograms can be well described only2D simulations. Both single-dimension~1D! and 2D model-ing rule out the possibility that the ponderomotive formight be the primary cause of the observed plasma behaas it is known to take place for larger fluxes@1# or with longwavelength laser irradiation@16#. The computed evolution othe plasma density profile is shown in Fig. 4. The result

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FILEVICH et al. PHYSICAL REVIEW E 67, 056409 ~2003!

FIG. 4. ~Color! Simulated electron density~line contours! and temperature~filled contour! profiles of the line-focus plasma of Fig.computed usingLASNEX. The heating laser is incident from the right. The calculations were done for a 1011 W/cm2, 13-ns-FWHM laserpulse.

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physical picture consists of a relatively high temperat~;36 eV! central region surrounded by a lower temperat~;10 eV! plasma on either side. The on-axis density disbution and velocity fit well with the results of both 1D cylindrical expansion and 2D simulations of a laser-irradiaplasma. Instead, the sidelobes are entirely 2D formationsated outside the laser-irradiated target region by the builof new cold material resulting mainly from extreme ultravilet ~XUV ! plasma radiation induced evaporation. In additio2D simulations show that radiation cooling contributessubstantially lowering the temperature of the sidelobes.lobes have slower axial expansion (,13106 cm s21) ascompared to the hotter central plasma region (53106 cm s21). After several nanoseconds the pressure bances in the lateral direction within a distance of;100 mmfrom the axis, as dictated by the sound’s spe

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(;106 cm s21) and plasma lifetime (;1028 s), henceforming a density depression on axis and lobes in the coareas. To illustrate that the sidelobes are mainly causedoutside spot ablation, we conducted simulations in whichconstrained the target ablation outside the area illuminaby the laser, while maintaining otherwise identical physiThe result in Fig. 5~right! shows that in this case the expasion is almost classical and presents significantly smadensity inhomogeneities. Furthermore, an additional simution shows that if all radiation effects are excluded the epansion becomes classical and the sidelobes disappeawhich case the temperature in the conical expansion doesdrop as dramatically along the surface.

Our modeling shows that this 2D density behavior issentially a universal effect. It includes the case of larger fospots, but in this case it is not as pronounced. Some ind

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TWO-DIMENSIONAL EFFECTS IN LASER-CREATED . . . PHYSICAL REVIEW E67, 056409 ~2003!

FIG. 5. ~Color! Simulated density~line contours! and electron temperature~filled contour! profiles for the 12-ns-line-focus plasma~left!,and with the motion of the ablated material from the target outside the spot constrained~right!. Otherwise the conditions for the twosimulations are identical. The heating laser is incident from the top. Both figures are calculated at the peak of the 1011 W/cm2, 13-ns-FWHMlaser pulse.

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tions to this effect can be found in the experimentBol’shov et al. @6#. Due to the fact that dense plasmas avery efficient sources of XUV radiation even at low plasmtemperatures, this kind of plasma behavior should be seemany experiments. However, because it takes a relatilong time ;4–10 ns for the off-spot material to evaporaand the colder plasma to expand, this effect was not prously clearly identified in shorter pulse experiments. Tlonger pulse duration in the present experimental situaallows the establishment of the pressure balance, suchthe hotter central plasma corresponds to a lower density

A similar but even more pronounced density depresswas observed in plasmas generated at increased irradiintensity by focusing the Nd:YAG laser onto a spot,30 mmin diameter, using a 15-cm-focal-length aspheric lens. Incase the irradiation intensity was 731012 W cm22 and theplasma was imaged with 51x magnification. A series ofterferograms were obtained for plasmas generated by efiring the laser onto a new target spot or after firing sevelaser shots in the same target location. In all cases, weserved the formation of similar density lobes and depressHowever, the plasmas produced after multiple laser shotthe same target location are observed to develop largersity sidelobes at larger distances from the target. This resfrom the fact that these plasmas emanate from the crcreated by the previous shots, which constrains its latexpansion and guides the plasmas motion into the direcnormal to the target. In this case the amount of plasma gerated is substantially increased by the larger ablation caby the higher temperature, the contact of plasma withcrater’s wall and the increased XUV emission efficiencyhigher densities. The modeling shows that despite almtwo orders of magnitude larger laser fluxes than in the pvious case, the plasma transport coefficients continue to

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classical and the ponderomotive force is still negligibly smto have any effect on the plasma profile. Figure 6 showsinterferogram corresponding to a second shot in the satarget location obtained near the time of peak laser intentogether with the corresponding electron density distribtions resulting from Abel inversion. The formation of pronounced density peaks off-axis is again seen. In the regmapped by the interferograms the electron density isserved to increase as a function of time, reaching at the tof maximum laser intensity a value of 931020 cm23 ~whichamounts to about 90% of the critical density for thel51.06-mm pump laser! at 27mm from the target. As in thecase of the line-focus plasma, the experimental study oseemingly typical laser-created plasma discloses a situathat cannot be well described by 1D hydrodynamic simu

FIG. 6. Measured soft-x-ray interferogram and correspondelectron density profile for a spot focus plasma. The plasmagenerated focusing a 13-ns-FWHM pulse of 0.63 J energy int30-mm-diameter spot. The interferogram was acquired at a tnear the peak intensity of the heating laser pulse.

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FILEVICH et al. PHYSICAL REVIEW E 67, 056409 ~2003!

tions, though again 1D codes are found to reproduce qutatively well the central region of the plasma expansion.

In conclusion, we have observed 2D hydrodynamicfects of large magnitude in laser-created plasmas generat relatively low irradiation intensities leading to the formtion of concave electron density profiles. Simulations shthat the buildup of cold mass outside the focal spot, cobined with pressure balance results in the formation ofobserved density depression. The results constitute the donstration of the use of table-top SXRL interferometry in tstudy of complex high density plasma phenomena. TSXRL interferometry with compact table-top lasers is potioned to become an important high-resolution diagnosnot only to measure density profiles in high density plasm

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but also for the development and validation of hydrodynamcodes and plasma theory.

The authors would like to thank G. B. Zimmerman, D.Eder~LLNL !, N. G. Kovalsky, A. E. Stepanov~TRINITI !, A.Ya. Faenov~VNIIFTRI !, and Yu. A. Zakharenkov for valu-able discussions. This work was supported by U.S. Depment of Energy Grant No. DE-FG03-98DP00208 and byNational Science Foundation. Part of this work was pformed under the auspices of the U.S. Department of Eneby the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48. Walso gratefully acknowledge the support of the W. M. KeFoundation.

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