In the frame of a CEA/US DOE collaboration, convergent experiments have been done on the Nova laser. Numerical simulations with our 2D Lagrangian code FCI2 led the analysis and correctly reproduced the experimental data. From single mode 2D perturbations, ablation front Rayleigh-Taylor instability growth is computed. Moderate and high convergence ratios are addressed. The shrinking of the wavelength plays a prominent role for small convergence ratio and weakly nonlinear hydrodynamics

Cherfils, C

Galmiche, D

Glendinning, S G

Laffite, S

Remington, B A

Wallace, R J

Cherfils, C.

Galmiche, D.

Glendinning, S. G.

Laffite, S.

Remington, B. A.

Wallace, R. J.

UNT Digital Library

UCRL-JC- 135438 PREPRINT Numerical Analysis of Shperically Convergent Rayleigh-Taylor Experiments on the Nova Laser D. Galmiche, C. Cherfils, S. G. Glendinning, S. Laffite, B. A. Remington, A. Richard, R. J. Wallace This paper was prepared for submittal to the First International Conference on Inertial Fusion Sciences and Applications Bordeaux, France September 12-17, 1999 August 23,1999 This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the . DISCLAIMER This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes. 0-0019254238945 P.04 Numerical analysis of spherically convergent Rayleigh-Taylor experiments on the Nova laser D. Galmiche’, C. Cherfils’, S.G. Glendinningz, S. Laffitel, B.A. Remington 2, A. Richardl, R. J. Wallace2 1 CEA-DIF, BP 12,9 1680 Bruytres le Chbtel, France * LLNL, P.O. Box 808, Livermore, CA 94551, USA Abstract In the frame of a CEA/US DOE collaboration, convergent experiments have been done on [be Nova laser. Numerical simulations with our 2D Lagrangian code FCI2 led the analysis and correctly reproduced the experimental data. From single mode 2D perturbations, ablation front Rayleigh-Taylor instability growth is computed. Moderate and high convergence ratios are addressed. The shrinking of the wavelength plays a prominent role for small convergence ratio and weakly nonlinear hydrodynamics. 1. Introduction Radiarion driven experiments have been conducted on the Nova laser at the Lawrence Livermore National Laboratory in order to study the effect of convergence on the linear and weakly nonlinear growth phase of the Rayleigh-Taylor (RT) instability at the ablation front [I, 21, We report here rhe numerical analyses of two set of spherical experiments, corresponding to moderate and high convergence ratios. 2. Moderate convergence implosion Experiments in moderate spherically convergent geometry have led to a good agreement between the simulations and the experimental data [2J. The convergence ratio, defined as the rario of the initial external radius ot the capsule to the ablation front radius, reaches a value of 2 A during the implosion process. 2.1 Experimental configuration or Fd- CItal x-ray rldmk cunCn(=~ps) II Flgurt 1 : Schematic of the experimenfal geometry. The Nova experimental configuration is shown in figti~re I. Eight of the ten Nova beams enter the hohlraum in a 2.2 ns shaped pulse (“PS26”) and convert to x-rays. Total input energy is about 20 kJ. A  standard Au “scale-l” hohlraum is considered (2.75 m m  long by 1.6 m m  diameter) ; the capsule, 530 pm outer diameter. 42 pm CH(l .?%Ge) wall thickness with no fill presure, is mounted on ~a hole in rhe wall of the hohlraum with half the sphere interior. The interior hemisphere has had a 70 pm wavelength, 2 pm amplitude, 2D single mode axisymmetric sinusoidal perturbation imposed on it. Moderate convergence ratio close to 2 is obtained. 12-l4:+1999 13: 1’3 DE SET 0-0019254233945 P.@E; Two beams are used to irradiate a rhodium disk to create an x-ray backlighting source, and a fast x-ray framing camera images the sphere. Time sequences of raw images are shown in reference [ I]. 2.2 Numerical investigation Simulating the experimental x-ray radiographs waS a multistep process.The average drive temperature is obrained via a view factor code. It peaks at 200 eV and is in good agreement with Dante measurements. Then we used the 2D radiation hydrodynamics code FCE to simulate the capsule implosion and the subsequent pcrrmbation development due to the RT instability, Check of the gross hydrodynamics is realized by numerically, reproducing rhe experimental wavelength time- evolution. Finally, we used a post-processor code to simulate radiographs, which are Fourier analyzed in the same way as the experimental images. Measured and simulated growth facrors in oprical depth (GF,) are plotted in figure 2, both for the fundamental mode and its second harmonic. The accordance is fairly satisfactory. At the same time, the spatial growth factor GF: localized at the ablation front, departs from purely linear regime (ie, exponential growth), but shows no evidence of saturation (seefigure 2). “1 1 b) HARMONk 7 8 ,0.2 5, . a ) FUNDAMENTAL 43 26. -0.15kj 2 4- .s E g z4- w -0.1 g 33. 2 5 z _ 5 2- z2- % f- 01.. 1.“” I 0 0.5 1 1.5 2 2.P 01 0 ‘Time (ns) Time (ns) Figure 2 : Meurured (dors) and simuluted (Ihick curves) RT growth facrnr are planed. re.rpecliveLv in a) I I and b), for rhe fundamenral and irs second harmonic. l%in curves represenr the spatial growrh factoj r at the ablarion fion~ exrracred from FCI2 simulation. The apparent saturation for GFT results from the combined effect of the decompression, the change in the opacity coefficient, the finite instrument spatial resolution and two additional effects due 10 the convergent geometry, which are the time dependent decrease of the instrument modulation transfert function as the wavelength decreases, and the deviation of the spikes from the diagnostic line of sight. 2.3 Comparison between planar and convergent cases Identical experiments were conducted using 50 pm thick planar foils of CH(2%Br) in place of the hemispheres. It appears that the convergent case grows more quickly and enters in the nonlinear regime sooner, but direct comparisons of the planar and convergent case are difficult as shock breakout on the rear side and acceleration phase of the ablation front don’t occur at the same time. From the simulations, we consider rhe evolution of the perturbation amplitudes versus 6, where s is the disrance accelerated. This quantity is directly exrracted from the FC12 simulations, as the distance traveled by the ablation front since [he time when the acceleration stage begins. To rake into account the reduction of the wavelength 1 during rhe compression, we plotted the growth rate versus d--- ~0.. We observe infigure 3 that it gives rougly the same result for the planar and the convergent case. Hence, we conclude that for small convergence ratios and weakly nonlinear hydrodynamics, dominant effect of convergence is simply the shrinking of the wavelength. H O-0819254236945 P.W6 Figure 3 : Simuhted growth rare versus G, where s is the distance accelerated. for the planar (thin line) and rhe spherical (thick line) cases. Classical RI growth rate and linearity rhreshold for the capsule (when the perturb&on amlpitude equals 10% of the wavelength) are in dashed lines. 3. High convergence implosion More recent experiments have addressed convergence ratios up to 4, by considering larger capsules and larger hohlraum. TO avoid a  too important decrease of the drive temperature, [he experiments used a ratio of the capsule radius to the hohlraum radius equal to 0.33. This relative high value for this rado led to a  signifrcarive capsule pressure distorsion. Present numerical analysis investigates the observed experimental distorsions obrained by S.G. Glendinning [Communication at the 29 Monterey, 19991. th Anomalous Absorption Conference, 3.1 Experimental configuration The experimental configuration is very similar to the one described in $2.1. W e  dealt wirh a  longer pulse : a  4.5 ns shaped pulse (“PS35”). The experiments have been performed considering a  “scale-1.5” hohlraum (3.40 m m  long by 2.4 m m  diameter) : the capsule, 800 pm outer diameter, 42 pm CH( 1.3%Ge) wall thickness, is located in the center of the hohlraum. One hemisphere had a 2D single mode axisymmetric Legendrc polynomial perturbation (mode 24 or 32) with a  0.5 /.&I amplitude imposed on it. 3.2 Investigation of the implosion symmetry Numerical analysis is realized step by step in the way developped in 92.2. As the same laser energy enters a  larger hohlraum in a  longer pulse, the drive temperature is significantly lower and peaks at 130 eV. A 2D simulation of the whole geometry, gold hohlraum and unperturbed capsule, is performed with the FCT2 code. From the simuiation of radiographs, we perform a Legendre analysis of the external spatial contour of the capsule, and make a comparison between numerical and experimental data. Numerical simulations are not yet completed, but up to now the agreement on the radius as a  function of time  is correct (seefigure 4) ; in time  shift should be introduced for the experimental data in order to take into account the shot-to-shot drive variations. Experimental data exhibit large fluctuations for P2 and P4 distorsions but general trend is in accordance. Late rime  simulations are going on. 5oo r--------l 400 -2 3 300 I I I I 1  I 1  ’ .J 012345678 lTme (ns) Figure 4  : Time evolurion of [he ourer radius obrained by unalysis of rhe capsule radiograph in the experiments (dors) and in [he FCl2 simularion (plain line). os~~~-A ’ ’ ’ 150 200 250 300 Disrance moved (bm) Figure 5 : Evolution of rhe cupsule rhickness versus the accelerared dirtauce in the expen’ments (dots) and in the FCIZ simulation (plain line). Ft 0-001925423s945 F.07 The thickening of the capsule versus time extracted from experimental radiographs exhibits an unsteady evolution, and specifically a fast evolution when the capsule radius becomes smaller than half the initial radius. This should induce an increase of convergence effects. Although our simulations arc not finished, we have plotted a numerical thickness obtained by taking me E-WHM of the denser part of the simulated radiographs. It is compared against experimental data in figure 5, and plotted versus the distance moved by the external dense radius (close to the ablation front) in order to avoid temporal shift due to laser history variations. The accordance between experimental and numerical data is a good way to check that the simulations arc relevant. We apply an analytic view factor model developped by S. Laffite [Unpublished CEA Report and Communication at the APS Plasma, Seattle, 19991. It provides the illumination pattern for a cylindrical hohlraum geometry. The flux asymrnerries at the hohlraum wall or at the capsule surface is decomposed into Legendre polynomials PI. The polynomials Pz, Pq, Pb,Pg are quantified, while odd orders are zero as asymmetry about the hohlraum midplane is considered. The flux asymmetries at the hohlraum wall or at the capsule surface is decomposed into Legendre polynomials PI. The polynomials PzY P4, P6, Ps are quantified, while odd orders are zero as asymmetry about the hohlraum rnidphme is considered. This model includes laser beams pointing via the widths of the illumination rings, the effects of hohlraum walI motion, the time- varying wall albedo. The results of the model, and specially the time-dependent asymmetries 0 1 2 3 4 5 6 7 of the incident flux on the capsule P2/Po and Time (ns) P4/Pe, compare notably well with the 2D Figure 6 : Time dependence uf Pz/Po and FCE2 simulations (seejigure 6) ; at iate times, P4/P0 incident flux assymerry on [he capsule the nominal incident flux gets small. cutculared by the ana[yric model (solid liner) and by FC12 simulutions (dashed lines). 3. Conclusions and prospects Experiments have been done on the Nova laser to investigate the effects of convergence on Rayleigh-Taylor growth. Reasonable agreement is found between the simulated and measured data. For a moderate convergence ratio case, close to 2, the dominant effect of convergence can be expressed by the shrinking of the wavelength. For high convergence ratio, up to 4, numerical analysis is not yet completed ; experimental data seem to indicate that convergence effects are important when the radius becomes smaller that half its initial value, but it has to be confirmed by numerical simulations. When the distorsions of symmetry will have been fully analyzed and understood. perturbation growth will be addressed. REXXXENCES 111 S.G. Glendinning er al., Hydrodynamic instability experiments on rhc Nova lyscr, in : G. Jourdan, L. Houas (Eds.), Proceedings of the sfh tntcmstional Workshop on the Physics of ComprcssibJe Turbulent Mixing IWPCTM 97. Marseille. France. 1997, pp. 173-178. [2] C. Chcrfils e!~ al.. Numerical investigation of convcrgenc Rayleigh-Taylor experiments on IJK Nova laser, in ; G. Jourdan. L. Houas (Eds.), Proceedings of r.hc 6* Inremational Workshop on the Physics of Compressible Turbulent Mixing 1WPCTM Y7, Marseille, France, 1997, pp. 1 16- 121. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. 

Numerical Analysis of Spherically Convergent Rayleigh-Taylor Experiments on the Nova Laser

Numerical analysis of spherically convergent Rayleigh-Taylor experiments on the Nova laser

Numerical analysis of spherically convergent Rayleigh-Taylor experiments on the Nova laser

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