Shock ignition modeling Ribeyre X Schurtz G Lafon

Shock ignition modeling Ribeyre X. , Schurtz G. , Lafon M. , Weber S. , Olazabal-Loumé M. , Breil J. and Galera S. CELIA Collaborator Canaud B. CEA/DIF/DPTA 7 th Direct Drive and Fast Ignition Workshop

Shock ignition principle: How it works ? Typical laser pulse Spike : Converging shock : Ignition of the hot central region Laser Mesh Hot spot Fuel Divergent return shock during the shell stagnation phase

Shock ignition : Stagnation conditions Two steps process Shell stagnation 1 Compression phase Standard quasi-isobaric configuration - Low implosion velocity: Vimp < 300 km/s - Hot spot ignition fails Identical to fast ignition compression 2 Ignition phase With convergent shock Non-isobaric configuration (1) Increased central pressure and temperature ignites a central hot-spot (1) Betti el al : PRL 98 (2007)

Non-isobaric fuel assembly and Rosen Model (1) Phs Non-isobaric parameter ρsh Psh ρhs G rhs rsh α adiabat at stagnation EL laser energy EL (MJ) Rosen model shows the low threshold and high gain possibility of a non-isobaric configuration (1) M. D. Rosen and J. D. Lindl (1984) UCRL-50021 -83

Temperature CHIC 1 D SIMULATIONS Pressure Without Spike Density Quasi-isobaric Configuration Temperature Grad P Pressure With Spike No Fusion Density Non-isobaric Configuration Pressure Temperature Density Grad P With Spike and Fusion Ignition and burn Grad P

Shock convergence model : Spherical NOH problem (1) Converging shock collision in spherical geometry Shock Spike Pressure evolution V t =0 t>0 Accreting shock: Divergent return shock Radius (normalized)

Model : Spherical NOH problem (2) Shock amplification during convergence and collision

Shock ignition pressure evolution: spherical effect • Shock wave pressure amplification during convergence Shock spike convergence Shock collision 300 Gbar CHIC shock pressure Guderley solution Amplification after collision between shock spike and return shock If pressure balance = X 6 700 Mbar Return shock Guderley (1) self-similar spherical solution: The shock pressure follows approximatively the Guderley solution (1) Guderley 1942, Aleksandrova et al. 2003

All DT target performances • Ray tracing with focal spot shape Hi. PER target * • One ray absorbed totally at critical density DT ice 211 µm DT gas nc One sector simulation EL=105 k. J Abs = 100 % EL=180 k. J Abs = 70 % 833 µm * Ref : Atzeni et al. POP (2007, 2008) • Total absorption design is independant of the ablator composition and simpliflies the analysis. • Same performances Fusion + rad Adiabat (α) ≈ 1. 0 IFAR 0. 75 Ri ≈ 30 Imploded mass Mimp (mg) ≈ 0. 27 Implosion velocity : Vimp (km/s) ≈ 290 Peak density ρpeak (g/cm 3) ≈ 650 Peak areal density ρRpeak (g/cm 2) ≈ 1. 4

Shock igniting of Hi. PER target Pabs Robustness study Spike power Shock launching time Launching window Iso-energy t 250 ps confidence interval at 80 TW 180 k. J, 10 ns - 50 TW for compression (3 w) + 70 -100 k. J, ≈ 500 ps – 150 -200 TW for ignitor (3 w) (1) Ribeyre et al. : PPCF (2009) 20 MJ (TN) : Gain ~ 80

Spike duration effect on target thermonuclear energy Spike absorbed energy and power Es, Ps Thermonuclear energy ETN Spike power time shape Ps DT FWHM (ps) Ps/2 RT RT Standard Rise time RT = 200 ps ts t Spike duration: FWHM = 2 RT + DT Simulation with DT between 50 -300 ps with same rise time (RT) DT (ps) ETN (MJ) Es (k. J) 500 300 19 40 400 200 18 32 300 17 24 250 50 16 20 Target thermonuclear energy vary about 15 % and spike energy about 50 % The ignition mainly depends on the spike power and not on the spike energy

Implosion velocity and spike power requirement Laser absorbed power for compression Eabs= 105 k. J; Pmax= 26 TW Vimp=290 km/s Spike absorbed power required for ignition: Ps Ps Ignition Window Ps ≈ 80 TW : 250 ps Spike threshold: 60 TW 500 ps FWHM t Eabs= 80 k. J; Pmax= 15 TW Vimp=225 km/s Ps Spike threshold: 140 TW Ps ≈ 200 TW : 200 ps 500 ps FWHM t Vimp= 290 km/s : Psabs= 80 TW : Plaser = 160 TW (Hyp: 50 % absorption) Vimp= 225 km/s : Psabs= 200 TW : Plaser = 400 TW (Hyp: 50 % absorption) Low shell implosion velocity requires high power ignition spike, i. e. , High intensity spike

Homothetic targets study h scaling factor 1570 µm For all targets Reference = 3. 5 x 1014 W/cm² 1044 µm 814 µm = 290 km/s 522 µm = 650 g/cc =1. 2 Ignition condition Guderley model Ablation pressure Spike scaling have low h dependence 1250 µm Compression Energy (k. J) 25 85 180 312 600 h 0. 5 0. 8 1 1, 2 1. 5 Target mass (mg) 0. 07 0. 28 0, 59 1, 0 2. 0 Threshold absorbed Spike power (TW) 60 60 60 R (g/cm 2) 0. 79 1. 18 1. 34 1. 60 1. 86 Thermonuclear energy (MJ) 1 8 17 38 80 Spike power required for ignition is the same for all targets

Conclusions • Shock convergence amplification follows approximatively the Guderley solution • Rosen model is well adapted to give the gain for shock ignition configuration • Shocks driven by 150 TW (3 w) peak power ignite Hi. PER target proposed by S. Atzeni et al. , with target gains up to 80. In agreement with Rochester work (Betti et al). • Shock timing robustness : 250 ps ignition window. • Ignition: low dependence to spike duration or spike energy • Low target implosion velocity requires high spike intensity • Homothetic targets shows that shock ignition power is constant