Three-Dimensional Studies of the Effect of Residual Kinetic Energy on Yield Degradation

Transcription

1 Threeimensional Studies of the Effect of Residual Kinetic Energy on Yield Degradation Kinetic energy density for single-mode, = 1, m = 6 1. YOC model = (1 RKE) to ( Jm / ) z (nm) Core YOC K. M. Woo University of Rochester Laboratory for Laser Energetics x (nm) RKE 59th Annual Meeting of the American Physical Society Division of Plasma Physics Milwaukee, WI 3 7 October 17 1

2 Summary A hot-spot model indicates that the yield degradation caused by low- and mid-mode nonuniformities is a strong function of the residual kinetic energy A synthetic single-mode database ranging from low mode (, = 1) to mid mode (, = 1) was built using the 3 hydrocode DEC3D* applied to the deceleration phase of inertial confinement fusion (ICF) implosions It is shown that the yield-over-clean (YOC) is strongly correlated to residual kinetic energy (RKE) at bang time The simulation results are also confirmed by a simple analytical hot-spot model TC13778 *K. M. Woo et al., Threeimensional Studies of the Effect of Residual Kinetic Energy on Yield Degradation, to be submitted to Physics of Plasmas.

3 Collaborators R. Betti, A Bose, D. Patel, and V. Gopalaswamy University of Rochester Laboratory for Laser Energetics 3

4 A synthetic single-mode database was built using DEC3D to study yield degradation caused by Rayleigh Taylor instabilities (RTI) in the deceleration phase Simulation method Shot 7768 Shot radiation hydrodynamic deceleration-phase code DEC3D Laser power (TW) LILAC t, u, P, T e 1 3 Time (ns) Initial profiles from LILAC Mass density (g/cm 3 ) 6 4 Initial radialvelocity perturbations do r 4 8 Radius (nm) 1 do r = Do/o is chosen appropriately to degrade the yield 1-keV T e contour surface for single-mode, = 1, m = 6 at stagnation TC

5 The synthetic database includes 3 simulations using different velocity perturbations with spherical-harmonic single modes from, = 1 to, = 1 1-keV T e contour surface at stagnation Initial velocity perturbation Y m, = = 1 Y m, = = 3 Y m, = = 5 Y m, = = 7 Y m, = = 9 Y m, = = 1 1 A shape function to spread out the perturbation over space Y m, = = Y m, = = 4 Y m, = = 6 Y m, = = 8 Y m, = = 1 Y m, = = 1 3- D r,,, t = o1 - D D o i { rt, + f r Ym ^ h ^ h o o ^ h ^i{, h r r, Y, m = = 4 Y m, = = 6 3 Y m, = = 8 4 Y m, = = 1 5 Y, m = = 1 6 do r PPM* Riemann solver HYPRE thermal diffusion Resolution = (r i z zones) TC1378 * PPM: piecewise parabolic method 5

6 A simple 3 hot-spot model is derived using energy conservation and an adiabatic condition, and neglecting the heat flux flowing into the cold bubbles Three-dimensional hot-spot model Neutron yield: Y - n vo Vx Shell Yield-over-clean: T V3 x3 1 T1 V1 1 n YOC - : n D = G = G: x D o b Adiabatic implosion: Burn volume o b o b P V53 / = P V53 / P 5 / 3 3 P = d n 1 1 and V 3 / 3 3 V = d n 1 1 Energy conservation: stag HS max stag = KE KE tot tot stag SH TC

7 Energy conservation and adiabatic condition are used to derive the YOC dependence in the residual kinetic energy Definitions t Q= Q 3 Q 1- D and RKE = shell 3 _ t stag 3 i shell 1 _ t stag 1 max KEtot KE KE i 3 HS 1 HS - 1 RKE Pt = ^1 RKEh, Vt = ^1 RKEh 5 / 3 / 1. Mode 1 YOC model P V M. = t 4 t3 t xt. 1 RKE 55 M ^ h t xt HS HS HS BW HS BW P 3 P 1 HS HS 1..8 V 3 V 1 HS HS Using 1 scaling for the mass ablation rate (next slide) RKE TC1378 7

8 For low modes, a 1 scaling of the mass ablation rate is used to derive the 3 hot-spot mass One-dimensional approximations for mass ablation rate* and hot-spot surface area R MHS x - mo S + T R + _ P V M i V 5 / 5 / 13 / abl HS HS HS HS HS HS 1. model Mt = Pt Vt xt 57 / 17/ 1 7 / HS HS HS BW T 5 / HS R.9 Scaling for 3 hot-spot mass Mt = Pt Vt xt = ( 1 RKE) xt 57 / 17 / 1 7 HS HS HS BW / 47 / 7 BW / M t HS Pt Vt xt / 17 HS HS / 1 7 BW / TC13783 * C. D. Zhou and R. Betti, Phys. Plasmas 15, 177 (8); 16, 7995(E) (9). 8

9 The YOC is a strong function of the residual kinetic energy Yield degradation driven by pure hydrodynamics 55 YOC. 1 RKE M ^ h t xt. HS BW Kinetic energy density for single-mode, = 1, m = to ( Jm / ) Yield degradation includes the mass ablation effect Mt. ^1 RKEh xt HS 47 / 7 / BW z (nm) Core / 44. BW YOC. ^1 RKEh xt. ^1 RKEh Neglect/slowly varying x (nm) TC13784 *A. L. Kritcher, et al., Phys. Plasma, 1, 478 (14). 9

10 The RKE model provides a reasonable approximation for the YOC for low to mid modes and provides an upper bound for the YOC for mid modes 1. Legendre modes, = 1 to 7 1. Legendre modes, > 7.8 (1 RKE) 4.4 (1 RKE) (1 RKE) 4.4 (1 RKE) 5.5 YOC.6 YOC Heat flows into cold bubbles RKE 1 RKE The results are consistent with HYDRA simulations by Kritcher et al.* TC13813 *A. L. Kritcher, et al., Phys. Plasma, 1, 478 (14). 1

11 Summary/Conclusions A hot-spot model indicates that the yield degradation caused by low- and mid-mode nonuniformities is a strong function of the residual kinetic energy A synthetic single-mode database ranging from low mode (, = 1) to mid mode (, = 1) was built using the 3 hydrocode DEC3D* applied to the deceleration phase of inertial confinement fusion (ICF) implosions It is shown that the yield-over-clean (YOC) is strongly correlated to residual kinetic energy (RKE) at bang time The simulation results are also confirmed by a simple analytical hot-spot model TC13778 *K. M. Woo et al., Threeimensional Studies of the Effect of Residual Kinetic Energy on Yield Degradation, to be submitted to Physics of Plasmas. 11