1. FSC Laser Channeling and Hole-Boring for Fast Ignition C. Ren, G. Li, and R. Yan University of Rochester J. Tonge, and W. B. Mori UCLA FSC Meeting August 4, 2010, Livermore, CA 1

2. FSC The hole-boring scheme may ultimately solve the e- divergence problem Channeling in underdense plasmas is important to the hole- boring scheme of fast ignition Our research in the past year focused on laser SF and hosing in 2D and 3D Channeling/hole-boring to the compressed shell can ultimately solve the e- divergence problem 2

3. FSC Channeling/hole-boring reduces ignition energy required in fast ignition channeling/hole-boring pulse ignition pulse Ignition pulse needs to be placed close to the shell to overcome the e- divergence problem The ignition pulse can also lose energy in underdense plasmas of the FI targets –P/P c ~10 6 P(PW) n/n c >>1 –Pre-plasma also exist inside the cone Key questions –Can laser create a straight channel (hosing?) –What is the channeling speed? –What is the optimum intensity for the channeling pulse Density- and intensity-scalings 3

4. FSC Previous full-scale 2D simulations with OSIRIS showed laser hosing and channel bifurcation/self-correction Can the existing theory describe the observed hosing phenomena? –Why are the observed wavelengths much longer than those of the predicted fastest-growth modes? –Why does hosing grow much slower in 3D than in 2D? Li et al., PRL 2008 4 Laser channeling in mm scale plasmas is a highly nonlinear and dynamic process

5. FSC 3D simulations have also shown the same nonlinear and dynamic phenomena 3D simulations [up to 540  m  (90  m) 2 plasma, 17 billion particles] 16 32 48 y (μm) 0.0 -0.2 -0.4 -0.6 -0.8 Charge density (ec -2 ω p 2 ) 16 32 48 z (μm) Laser hosing/channel bending & branching/self-correction seen in 3D but at slower growth The eventual channel cross section is round 5

6. FSC Hosing is observed in 3D only with sufficiently long plasmas because channeling is faster in 3D 6 L x =180  mL x =540  m

7. FSC The average residual density in 3d is smaller Phasespace Time t=3.0ps 3D 2D 3D simulations show a larger channeling speed than in 2D Channel front position(μm) 3D2D Time(ps) v c-3d =0.24c v c-2d =0.13c V 3D =2 V 2D due to stronger laser self- focusing and easier channeling in 3D 7

8. FSC The stonger 3D ponderomotive force allows the channel to be formed faster F p is larger in 3D than in 2D due to self-focusing 3D: 2D: F p3d /F p2d = w 0 /w f ~ 2 y(μm) For the same laser ponderomotive force F p ~a 2 /w, the channel is deeper in 3D than in 2D 0 16 32 48 64 80 0.35 0.30 0.25 0.20 0.15 vt=1kev ni 0 =0.3n cr w 0 =90 a 0 =2.7 t=0.84ps n i /n cr 3D 2D 8

9. FSC Hosing in laser channeling is in the long wavelength regime Non-dispersive hosing theory (Shvets’94,Sprangle’94,Duda’99) Dispersive theory (Duda’00) Hosing growth rate for a 0 =2.68, n e =0.2n cr, W 0 =90 c/ω 0 Observed modes in PIC 9

10. FSC Hole-Boring Can Ultimately Solve the e- Divergence Problem in FI Ignition with a 20° e-beam at the cone tip requires 43-kJ beam energy (Solodov ‘08) Larger-divergence would suppress magnetic collimation and raise the required energy many times This makes the HB-scheme competitive –HB to the shell surface Density Profile of a FI Target (Betti) (a) Divergence of laser-generated e- (Ren et al., PoP’06) cone tip 10

11. FSC Lower Intensity Beam Saves Energy but Takes Longer to HB The hole boring velocity is (Kruer et al. ’75) V HB has been verified by many 2D PIC simulations for n≤100n c (Wilks et al. ’92,…) T HB ~L(n/I) 1/2 and E HB ~LW 2 (In) 1/2 Funneling of laser by the channel is important to reduce E HB. Reflection front Light Plasma I/c nv·Mv Ren et al. AAC’03 11

12. FSC <200 kJ Is Required to HB to Shell Surface 1  m-Laser FWHM=17  m, assuming no reflection and I 1/2 -scaling 12 0.1~1.0n cr 1.0n cr ~4302n cr 4302n cr ~44413n cr Sum I=10 20 W/cm 2 T hb (ps)44203362609 E hb (kJ)1465.5117196 Need to study -V hb in high density (simulation and exp.) - Shell preheating during HB

13. FSC The hole-boring FI scheme is still competitive compared to the coned-target scheme Channeling in underdense plasmas is important to both HB and cone-target schemes –Laser SF and hosing in 2D and 3D – Channeling/hole-boring to the compressed shell can ultimately solve the divergence problem Based on the simple formula of V HB, 200 kJ of laser energy is needed to channel/HB to the compressed shell of a 300- kJ target in 600 ps 13