闫锐 University of Rochester

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 ~1 mm A hot spot is created in the dense core and reaction starts Laser heating pellet surface rocket liftoff of ablator -> inward shock wave • The National Ignition Facility (NIF) is aimingto 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 A shock ignition pulse1 1. R. Betti et al.,Phys. Rev. Lett., 98, 155001 (2007)

4. The two-plasmon-decay (TPD) instability is a laser-plasma-interaction (LPI) process in underdense plasma Plasma wave 1 • The matching condition • k0=k1+k2 • ω0=ωp1+ωp2 • Since ωp1,ωp2 are close to ωpe, TPD can only take place at n~1/4 ncr. Laser Plasma wave 2 *Simon et al., Phys. Fluids 26, 3107 (1983)

5. Two-plasmon decay (TPD) is a potential danger for direct drive ICF • 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.

6. Outline • Linear regime • Quasi-steady state

7. y laser 0 x 0 Long-time-scale PIC simulations with OSIRIS1 have been performed for a range of parameters • Plane wave and Gaussian beams are used with the peak intensity range: 6e14-2e15W/cm2 • 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. Simulation configuration for OMEGA parameters 1, R. A. Fonseca, L. O. Silva, F. S. Tsung et al., Lect Notes Comput Sc 2331, 342 (2002)

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/cm2 Mi/me=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 PIC A similar spectrum to the PIC simulations was observed in the fluid simulations Fluid

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 eπΛ . • The convective gain isn’t sensitive to k┴. This explains the broad spectrum in PIC simulations Amplification ~ exp[πΛ] 1, M. N. Rosenbluth, R. B. White, and C. S. Liu, Phys. Rev. Lett., 31, 1190 (1973)

14. The high k┴ modes are energetically important in both linear and non-linear stages in the large-L PIC simulation Initial noise level X100 • 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

15. The convective modes are relatively more important in higher η cases E1 E1 I=1e15 W/cm2 ,L=150μm, T=2keV η=3 I=8e14 W/cm2 ,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 Net particle energy flux I= Energy flux/Laser flux t (ps) 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

18. Most hot electrons are produced in the nonlinear stage quasi-steady state saturation linear Electron >50keV distribution in px-py space Py(mec) L=150μm Te=3keV I=6X1014W/cm2 Px(mec) Px(mec)

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

20. Electrons trapped in a plasma wave Phase velocity e- e- 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 Electron distribution • Only the electrons with velocities close to Vph can be coupled by the plasma wave • These electrons are located at the tail of distribution function and the amount is small f v

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.) forward ¼ critical surface e-(>50keV) phase space

23. Ion density fluctuations are driven by plasma waves propagating to lower density regions Density fluctuation • 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. δn (nc) t (ps) Vg=0.013c Ex energy t (ps) <Ex2> (A. U.) n0 (nc)

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 = n0(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. PIC Fluid

26. *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

29. Summary • 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 Te 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