1. Growth, Saturation, and Energetic Electron Generation in Two-Plasmon Decay Instabilities in Direct-Drive Inertial Confinement Fusion 直接驱动惯性约束聚变中的双等离子体波衰变的增长，饱 和，和热电子的产生 闫锐 University of Rochester

2. Inertial Confinement Fusion (ICF) aims to make fusion a clean and unlimited energy source Laser heating pellet surfacerocket liftoff of ablator -> inward shock wave A hot spot is created in the dense core and reaction starts ~1 mm The National Ignition Facility (NIF) is aiming to achieve ignition within this year

3. Current ICF schemes 1-step –Direct-drive compression –Indirect-drive compression Multi-step –Fast ignition -Channeling (underdense) and/or hole boring (overdense) -Cone –Shock ignition http://www.lle.rochester.edu 1. R. Betti et al.,Phys. Rev. Lett., 98, 155001 (2007) A shock ignition pulse 1

4. The two-plasmon-decay (TPD) instability is a laser- plasma-interaction (LPI) process in underdense plasma The matching condition –k 0 =k 1 +k 2 –ω 0 =ω p1 +ω p2 Since ω p1,ω p2 are close to ω pe, TPD can only take place at n~1/4 n cr. Laser Plasma wave 1 Plasma wave 2 *Simon et al., Phys. Fluids 26, 3107 (1983)

5. Effective compression of ICF targets requires fuel shells in low adiabatic states during implosion. Energetic (hot) electrons generated from laser- plasma interactions can preheat the shell and degrade the implosion The two-plasmon decay instability is a significant concern as a hot electron source. Two-plasmon decay (TPD) is a potential danger for direct drive ICF

6. Linear regime Quasi-steady state Outline

7. Long-time-scale PIC simulations with OSIRIS 1 have been performed for a range of parameters laser x y 0 0 Plane wave and Gaussian beams are used with the peak intensity range: 6e14-2e15W/cm 2 The simulation box is transversely periodic and thermal bath is applied at longitudinal boundaries. Diagnostics on the thermal-bath boundaries record the energy loss through the boundaries and the distribution of electrons having reached the boundaries. 1, R. A. Fonseca, L. O. Silva, F. S. Tsung et al., Lect Notes Comput Sc 2331, 342 (2002) Simulation configuration for OMEGA parameters

8. A linear fluid code has been developed to study the linear regime of TPD The fluid code solves the linear equations:

9. Linear regime –Threshold –Growth rate –Convective gain L=150μm, T=2keV, I=1e15 W/cm 2 M i /m e =3410 (OMEGA relevant parameters)

10. A broad spectrum of plasma waves is observed in PIC simulations The reduction of the PIC growth rate in the low k ┴ region is due to pump depletion. The spatial location where the high k ┴ modes grow is in agreement with the homogeneous theory. 1, A. Simon, R. W. Short, E. A. Williams, and T. Dewandre, Phys.Fluids, 26, 3107 (1983) 2, B. B. Afeyan, E. A. Williams, Phys. Plasmas 4, 3827 (1997)

11. Fluid simulations are used to determine the nature of those high k ┴ modes A similar spectrum to the PIC simulations was observed in the fluid simulations Fluid PIC

12. High k ┴ modes can be identified as convective modes by fluid simulations Absolute modes can grow exponentially without limit in a linear system. Convective modes can only grow exponentially at early time and then saturate (separate).

13. The convective gains observed in the fluid simulations are in agreement with the three-wave theory results The TPD equations can be cast into the standard 3-wave form. 1 The order and trend of convective modes’ amplification can be estimated by e πΛ. The convective gain isn’t sensitive to k ┴. This explains the broad spectrum in PIC simulations 1, M. N. Rosenbluth, R. B. White, and C. S. Liu, Phys. Rev. Lett., 31, 1190 (1973) Amplification ~ exp[πΛ]

14. The high k ┴ modes are energetically important in both linear and non-linear stages in the large-L PIC simulation The linear growth of TPD is interrupted by ion density fluctuations The convective modes are saturated before reaching the convective gain because the initial noise has only been amplified by ~30 in amplitude Initial noise level X100

15. The convective modes are relatively more important in higher η cases E1 I=1e15 W/cm 2,L=150μm, T=2keV η=3 I=8e14 W/cm 2,L=150μm, T=3keV η=1.6

16. Quasi-steady state –Energetic electron generation –Collision and speckle effects

17. Net particle energy flux reaches a quasi-steady state after ~5ps In the quasi-steady state, –Absorbed laser energy is balanced by the energy flux exiting the box –The particle and field energies in the simulation box are essentially constant t (ps) Net particle energy flux Energy flux/Laser flux

18. Most hot electrons are produced in the nonlinear stage L=150μm Te=3keV I=6X10 14 W/cm 2 Electron >50keV distribution in px-py space linear saturation quasi-steady state P y (m e c) P x (m e c)

19. The net energy flux exiting the right boundary includes significant contribution from the hot electrons Energy flux/Laser flux Normalized instant net e- energy flux at t=9.9ps Electron Energy

20. Electrons trapped in a plasma wave e-e- e-e- Phase velocity Electrons could be trapped in a plasma wave if their velocities are close to the phase velocity

21. It is difficult to accelerate thermal electrons in a high- phase-velocity plasma wave Only the electrons with velocities close to V ph can be coupled by the plasma wave These electrons are located at the tail of distribution function and the amount is small f v Electron distribution

22. The hot electrons are generated through staged acceleration initiated by new TPD modes with low phase velocity in the nonlinear stage Ex in kx-x space (A. U.) e-(>50keV) phase space forward ¼ critical surface

23. Ion density fluctuations are driven by plasma waves propagating to lower density regions The region of ion density fluctuations is spreading at the group velocity of plasma waves with the largest k. Ion fluctuations at the low density region can induce new TPD modes locally. Vg=0.013c n 0 (n c ) t (ps) Ex energy (A. U.) t (ps) Density fluctuation δn (n c )

24. Fluid simulations are performed to study the new modes in the nonlinear stage The fluid code solves the linear TPD equations The density fluctuation is modeled by a static n = n 0 (x) + δn

25. Fluid simulations produce modes similar to PIC simulations The background density profile is read from OSIRIS simulation results The spectrum obtained in the fluid simulation is similar to that from the PIC simulation The differences in the relative amplitudes may be due to e- acceleration. Fluid PIC

26. I14maxT(keV)/Ti (keV) Lη*η*Total Abs.Hot (>50kev) electrons 33/1.51500.6~0 63/1.51501.242%17% 83/1.51501.452%24% 6 (collisional)3/1.51501.233%5.5% *Simon et al., Phys. Fluids 26, 3107 (1983)

27. Electron-ion collision significantly reduces hot electron production in PIC simulations Using high-Z materials as the ablator can increase the e-i collision and reduce the hot e- production

28. Laser speckle can also reduce the hot electron generation In experiments, polarization smoothing changes laser polarization even within a single speckle, which can reduce the region for electron acceleration Simulation with a narrow beam has shown a reduced hot electron generation I14maxT(keV)/ Ti(keV) Lη*η*Total Abs. Hot (>50kev) electron s 63/1.51501.242%17% 8 (W=4μm)3/1.51501.422%5%

29. Broad spectra of plasma waves are observed in PIC and fluid simulations –The high- k ┴ modes are identified as convective modes by fluid simulations. They can become energetically dominant and cause pump depletion in high η cases –A convective gain formula retaining the dependence on T e and k ┴ is obtained In PIC simulations, significant laser absorption and hot electron generation occur in the nonlinear stage –Generation of hot electrons is correlated with new TPD modes correlated with ion density fluctuations in the lower density region in the nonlinear stage –Hot electrons are accelerated from the low density region to the high density region through a staged process –Both collision and speckle can reduce the hot electron generation Summary