A Model of Laser Imprinting. V. N. Goncharov, S. Skupsky, R. P. J. Town, J. A. Delettrez, D. D. Meyerhofer, T. R. Boehly, and O.V.

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1 A Model of Laser Imprinting V. N. Goncharov, S. Skupsky, R. P. J. Town, J. A. Delettrez, D. D. Meyerhofer, T. R. Boehly, and O.V. Gotchev Laboratory for Laser Energetics, U. of Rochester The control of laser imprint is of crucial importance for the successful implosion of direct-drive inertial confinement fusion targets. Irradiation nonuniformities generate, or imprint, modulations in the ablation pressure that seed the Rayleigh Taylor (RT) and Bell Plesset (BP) instabilities, which in turn degrade the symmetry of the implosion and reduce the target performance. To gain physical insight, an analytical model of imprint has been developed. The model takes into account the dynamics of the conduction zone, mass ablation, and the SSD smoothing scheme. The important parameters that characterize laser imprint are found to be the time scale for plasma atmosphere formation, the ablation velocity, and the density-gradient scale length. The first determines the smoothing rate due to thermal transport in the conduction zone, and the last two characterize the dynamic overpressure stabilization described in Ref. [1]. The model has been validated by comparisons to detailed multidimensional hydrocode simulations using a range of ablator materials, perturbation wavelengths, and pulse shapes. The model has been found to be in good agreement with a series of planar-foil imprint experiments performed on the OMEGA laser system at the University of Rochester s Laboratory for Laser Energetics. Imprint s effect on NIF and NIF-scaled OMEGA cryogenic targets has been studied. It is has been shown that such targets will remain intact during the implosion when the laser is smoothed with 1 THz 2-D SSD. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC03-92SF19460, the University of Rochester, and the New York State Energy Research and Development Authority. [1] V. N. Goncharov, Phys. Rev. Lett. 82, 2091 (1999).

2 A Model of Laser Imprinting V. N. Goncharov University of Rochester Laboratory for Laser Energetics 41st Annual Meeting of the Americal Physical Society Division of Plasma Physics Seattle, WA November 1999

3 Collaborators S. Skupsky, P. W. McKenty, R. P. J. Town, T. R. Boehly, D. D. Meyerhofer, and O. V. Gotchev University of Rochester Laboratory for Laser Energetics

4 Summary An analytical model is developed to gain physical insight of the laser imprint Laser nonuniformities imprint surface modulations that degrade the symmetry of implosion. An analytical model has been developed to determine the physical processes contributing to imprint. Hydrodynamic flow is the main imprinting mechanism. Thermal smooting and the dynamic overpressure are the main processes reducing the imprint. Laser imprint, with 1-THz SSD beam smoothing, will not significantly degrade cryogenic-target performance. TC5213

5 Outline Laser imprint in direct-drive ICF Processes contributing to laser imprint Processes reducing laser imprint Analytic imprint model comparison with 2-D numerical simulation comparison with imprint experiments Effect of imprint upon NIF ignition targets polymer overcoat SSD beam smoothing target gain TC5227

6 In direct-drive target designs developed at LLE, the fuel isentrope is controlled by the shock preheat Direct-drive, α = 3, NIF ignition target design CH Power (TW) 100 Foot Main drive DT DT gas 1.69 mm mm Time (ns) TC5216

7 Laser imprint degrades target performance Laser t = Surface finish: σ inner = 1.00 µm σ outer = 0.08 µm Gain D gain Maximum compression rms imprint (µm) t At the beginning of the main drive TC5217

8 Processes contributing to imprint Velocity pertubation due to nonuniform shock propagation Acceleration perturbation from the lateral flow in the compressed region TC5218

9 Hydrodynamic flow is the main imprint mechanism: velocity perturbation Shock speed depends of the ablation pressure U s ~ p a U s δu s p a 0 δ pa Shock Laser ṽ ~ δu s ~ 1 2 U s δp a p a 0 U s + δu s p a 0 + δpa Shock front Ablation front p 0 ρ 0 c 0 Pressure Density Sound speed p a ρ c s η dη dt = ṽ ~ U s δp a p a η vel = ṽt ~ δp a p a c s t TC5215

10 Hydrodynamic flow is the main imprint mechanism: acceleration perturbation Rippled shock creates lateral mass flow. p a + p p a y ~ v y Perturbed acceleration ~ a d 2 η dt 2 = ã k δp a ρ η ac k δp a p a c s 2 t 2 Shock front η = η vel + η ac η t t 2 TC kc s t

11 Physical mechanisms reducing imprint Thermal smoothing Dynamic overpressure (rocket effect) ablation-surface oscillation Fire polishing, vorticity convection TC5273

12 Thermal smoothing 1 suppresses acceleration perturbation Ablation front Absorption region δp a p a δp e kx δi I e kd c kd c δp a /p a D c V c t Time (ns) t D η vel >> η ac Laser perturbations decouple from the ablation front when kd c ~1 Decoupling time t D (kv c ) 1 TC K. A. Brueckner and S. Jorna, Rev. Mod. Phys. 46, 325 (1974).

13 Imprint growth is reduced by thermal smoothing After decoupling time t > t D, a ~ = 0. ~ v = v ~ D η ṽ D δi I c s 2 V c Without thermal smoothing With thermal smoothing 1 Ablation front η at ~ 2 t D ~ η v D t kcst TC A. Velikovich et al., Phys. Plasmas 5, 1491 (1998).

14 Late-time imprint growth is stabilized by dynamic overpressure Rate of change of mass Thrust force = MV bl V bl Exhaust velocity V bl + V bl Absorption region η V bl V bl Ablation front Velocity of blowoff plasma Mass ablation rate TC5276 Dynamic overpressure = m V bl mv bl kη

15 Late-time imprint growth is stabilized by the dynamic overpressure F Ablation front ~ v D p d = mv bl kη F = ( p d ) = k 2 mv bl η F = k bl η Effective spring constant k bl Mass-spring system M ~ v D F = Kη Oscillations η TC5277 Spring Ablation front ω = Œ K/M ω = Œ k bl /ρ = kœ V a V bl

16 Imprint amplitude is determined by the decoupling velocity and oscillation frequency Kinetic energy εk Potential energy εp ε k = ρṽ D 2 2 ε p = k bl η 2 2 = ρω 2 η 2 2 Front amplitude η max = 2ε k = ṽd k bl ω Time TC5278 η max δi I c s 2 V c k V a V bl

17 The most damaging modes oscillate during the shock propagation 4 3 Single-mode imprint ORCHID simulations NIF α = 3 target design l = 50 Amplitude (nm) Time (ns) Shock breakout TC5270

18 Imprint model Description of the model Results ablation-surface oscillations imprint amplitude Comparison with simulations Comparison with imprint experiments TC5279

19 The analytic model is based on solution of the sharp boundary model Undriven target ρ 0 Hugoniot relations Shock front ρ 1 Compressed target [ 2 t cs 2 x 2 k 2 ( )] p = 0 Ablation front Blowoff plasma ρ bl Isotherm y x Assumptions ṽ bl y ṽy h = k ηa ( V bl V a ) V a C s << 1 V b1 Cs ~ 1 D c = V c t Model is solved by multiple-scale technique. τ = k c s t T = k V a V bl t ξ = k V a t η a e 2ξ Oscillations are damped by fire polishing and vorticity convection. sint t TC5214

20 The imprint amplitude is determined by the decoupling velocity and oscillation frequency (η max = ~ v D /ω) Comparison of CH and cryo DT ablators, I = W/cm 2 Decoupling velocity ṽ D ~ c s 2 Vc Oscillation frequency ω = k V a V bl 20 V a CH = 1.0 µm ns Va DT = 2.5 µm ns D c (µm) CH DT η DT CH Time (ns) Time (ns) ṽ D DT ṽ D CH 2.5 ηdt max ηmax CH ω DT 2.5 ωch TC5222

21 ORCHID simulations confirm the predictions of the model Front amplitude (µm)/(δi/i) Perturbation wavelength λ = 40 µm DT CH Time (ns) TC5280 ηdt max ηmax CH

22 The imprint amplitude and oscillation period are reduced by increasing laser intensity Scaling η η max sin ωt ~ δi I V c ~ V a V bl c2 s V a V bl V a ~ I c s ~ I 1/3 V a ~ V bl ~ I 1/3 h max ~ I 2/3 T osc ~ I 1/3 Detailed model results cryo DT planar foil thickness = 345 µm flat-top laser pulse η(µm)/(δi/i) I = W/cm 2 I = W/cm 2 I = W/cm TC5223 Time (ns)

23 Simulations confirm that the imprint amplitude and laser oscillation period are reduced by increasing laser intensity I = W/cm 2 η(µm)/(δi/i) W/cm W/cm 2 Cryo DT planar foil Thickness = 345 µm Flat-top laser pulse Time (ns) TC5281 ç max ~ I 1.0 T osc ~ I 0.4

24 Shorter-wavelength nonuniformities have lower imprint amplitudes and shorter oscillation periods Model: η max ~ λ; T osc ~ λ ORCHID simulation: DD, NIF, α = 3, all-dt target design I = W/cm 2 thickness = 345 µm µm η m ~ λ 1.6 ; T osc ~ λ 1.1 η(µm)/(δi/i) µm 20 µm TC Time (ns)

25 The model has been tested against planar-foil imprint experiments performed on the OMEGA laser system* 20-µm-thick CH Two laser pulse shapes; two perturbation wavelengths Nonuniformities were measured using through-foil x-ray radiography. Intensity (10 14 W/cm 2 ) Foot ramp 3 ns, flat Preimposed mode A pre Imprint A imp Time (ns) Imprint is quantified by the mass equivalence. TC5226 A EQ = A imprint A pre A pre t = 0 ( ) * T. R. Boehly et al., CO2.01, this conference.

26 The results of the experiments agree with imprint simulations and predictions of models Mass equivalence (µm)/(δi/i) Foot ramp 3-ns square η60 ramp η60 square η60 square η30 square Experiments 1.7± ±0.6 Simulations Wavelength (µm) TC5271 Higher intensities and shorter perturbation wavelengths imprint less for modes with t D < shock breakout time

27 Application of the model: effect of imprint on direct-drive NIF ignition design Effect of polymer overcoat Effect of SSD Target gain TC5282

28 The thin polymer layer required for target fabrication results in enhanced imprint Rayleigh Taylor instability Pressure DT CH Ablation front Transmitted shock g Rarefaction wave Shock t = t rw Velocity perturbation Ablation front Rarefaction wave g = 0 g > 0 TC5228 Shock

29 Simulations show increased imprint for polymer overcoated targets ORCHID simulation; pertubation wavelength λ = 40 µm g (µm/ns 2 ) p p g peak ~ CH DT ρ CH d CH t ac ~ d CH c s CH t rw Time (ns) Amplitude (µm)/(δi/i) DT + 4 µm CH CH 0.5 DT Time (ns) TC5283 RT growth factor ~ exp( kgät2 ac )~ exp kd CH ( )

30 Without SSD, thermal smoothing and dynamic overpressure do not reduce imprint to the levels required for high-gain implosions NIF direct-drive, α = 3 target design mode spectrum from DPP s and DPR s; no SSD 40 overlapping beams rms imprint (nm) Beginning of main drive pulse Distance (µm) ORCHID simulation and RT modeling with 3-D saturation Mix (imprint only) Shell thickness TC Mode number Time (ns) Temporal beam smoothing is required.

31 SSD reduces time-averaged laser nonuniformity Target plane Phase plate Focus lens TC5220 σ rms ~ t c t σ0 rms rms nonuniformity (%) *S. Skupsky, Phys. Plasmas 6, 2157 (1999) [ ] 1 t * c = νsin( kδ 2) ν: bandwidth δ: speckle size <t>

32 Imprint amplitude can be reduced by applying SSD smoothing technique (continued) ORCHID simulations For constant-intensity foot pulse δi = δi 0 t c t. Example: CH foil, I = W/cm 2 laser pulse, t c = 8 ps δp a /P a No SSD 0.4 SSD, t 0.2 c = 8 ps t 0.0 D Amplitude (µm) No SSD SSD Time (ps) Time (ns) TC5188 η SSD ηno SSD ~ t c t D ( νkδ) 1 ( ) 1 = V c kv c νδ

33 2-D SSD with the bandwidth ~1 THz gives sufficient nonuniformity reduction Mode spectrum at the beginning of main drive ORCHID simulations and RT analytic modeling with 3-D saturation rms imprint (nm) No SSD 1-THz SSD Gain σ inner = 1.00 µm σ outer = 0.08 µm Mode number Bandwidth (THz) TC5285

34 Summary/Conclusions An analytical model is developed to gain physical insight of the laser imprint Laser nonuniformities imprint surface modulations that degrade the symmetry of implosion. An analytical model has been developed to determine the physical processes contributing to imprint. Hydrodynamic flow is the main imprinting mechanism. Thermal smoothing and the dynamic overpressure are the main processes reducing the imprint. Laser imprint, with 1-THz SSD beam smoothing, will not significantly degrade cryogenic target performance. TC5213a