1. 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

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

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

4. ρ sh P hs r hs r sh (1) M.D.Rosen and J.D.Lindl (1984) UCRL-50021-83 α adiabat at stagnation E L laser energy Non-isobaric fuel assembly and Rosen Model (1) P sh ρ hs Non-isobaric parameter Rosen model shows the low threshold and high gain possibility of a non-isobaric configuration G E L (MJ)

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

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

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

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

9. All DT target performances 211 µm 833 µm DT ice DT gas One sector simulation Ray tracing with focal spot shape ncnc One ray absorbed totally at critical density Same performances Adiabat (α)≈ 1.0 IFAR 0.75 Ri ≈ 30 Imploded mass M imp (mg)≈ 0.27 Implosion velocity :V imp (km/s)≈ 290 Peak density ρ peak (g/cm 3 )≈ 650 Peak areal density ρR peak (g/cm 2 )≈ 1.4 Total absorption design is independant of the ablator composition and simpliflies the analysis. * Ref : Atzeni et al. POP (2007, 2008) HiPER target * Fusion + rad E L =180 kJ Abs = 70 % E L =105 kJ Abs = 100 %

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

11. Spike duration effect on target thermonuclear energy TT RT Spike power time shape t Ps Rise time RT = 200 ps 5003001940 4002001832 3001001724 250501620 Spike absorbed energy and power Es, Ps Thermonuclear energy E TN FWHM (ps)  T (ps) E TN (MJ) Es (kJ) Standard Target thermonuclear energy vary about 15 % and spike energy about 50 % Ps/2 Spike duration: FWHM = 2 RT +  T Simulation with  T between 50-300 ps with same rise time (RT) The ignition mainly depends on the spike power and not on the spike energy tsts

12. Implosion velocity and spike power requirement Laser absorbed power for compression E abs = 105 kJ; P max = 26 TW V imp =290 km/s E abs = 80 kJ; P max = 15 TW V imp =225 km/s Spike threshold: 60 TW Spike absorbed power required for ignition: P s 500 ps FWHM Ps t 500 ps FWHM Ps Spike threshold: 140 TW Ps ≈ 80 TW : 250 ps Ps ≈ 200 TW : 200 ps Low shell implosion velocity requires high power ignition spike, i.e., High intensity spike t V imp = 290 km/s : P sabs = 80 TW : P laser = 160 TW (Hyp: 50 % absorption) V imp = 225 km/s : P sabs = 200 TW : P laser = 400 TW (Hyp: 50 % absorption) Ignition Window

13. Homothetic targets study Compression Energy (kJ)2585180312600 h0.50.811,21.5 Target mass (mg)0.070.280,591,02.0 Threshold absorbed Spike power (TW) 60  R (g/cm 2 ) 0.791.181.341.601.86 Thermonuclear energy (MJ)18173880 = 290 km/s = 3.5x10 14 W/cm² = 650 g/cc =1.2 522 µm 814 µm 1044 µm 1250 µm 1570 µm For all targets Spike power required for ignition is the same for all targets Reference h scaling factor Ignition condition Guderley model Ablation pressure Spike scaling have low h dependence

14. 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  ) peak power ignite HiPER 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