UCLA Simulations of Stimulated Raman Scattering in One and Two Dimensions B. J. Winjum 1*, F. S. Tsung 1, W. B. Mori 1,2, A. B. Langdon 3 1 Dept. Physics & Astronomy, University of California Los Angeles 2 Dept. Electrical Engineering, University of California Los Angeles 3 Lawrence Livermore National Laboratory UCLA Work supported by DOE NNSA. Simulations performed on the Dawson Cluster under support of NSF.

UCLA Goals and Motivation Understand the physics of laser-plasma interactions that could affect NIF, specifically indirect drive –Laser-plasma instabilities can reduce the amount of energy coupling to the hohlraum wall and impact implosion symmetry –Backscattering is a direct loss of energy driving the implosion, as well as a source of hot electrons which can preheat the target Understand the kinetic behavior of SRS for weak pumps –Saturation levels of reflectivity and hot electron production –Multiple scattering e.g. backscatter of backscatter –Multi-dimensional effects and density gradients *Multiple scatter: A. B. Langdon and D. E. Hinkel, Phys. Rev. Lett. 89, (2002) and D. E. Hinkel et al., Phys. Plasmas 11, 1128, (2004)

UCLA SRS Saturation Considerations Several arguments have been made for SRS saturation mechanisms –Nonlinear frequency shift* (Vu etal. PRL 2001) –Trapped particle instability** (Brunner and Valeo PRL 2004) –Resonant coupling with beam acoustic modes (Lin etal. submitted) All rely on trapped particle effects and/or modification of the electron distribution function To what extent do we see: –Modification of the electron distribution function? –Trapped particle effects? –Beam acoustic modes? –Something else like wavebreaking? What are additional multi-dimensional considerations? –Finite width pulse vs. laser plane wave –Side scattering and its modification of the electron distribution function *G.J. Morales and T.M. O’Neil, Phys. Rev. Lett., 28, 417 (1972) **W.L. Kruer, J.M. Dawson, and R.N. Sudan, Phys. Rev. Lett., 23, 838 (1969)

UCLA Validation Against Experiment Montgomery performed an experiment to test SRS in a single laser hot spot* –Using a 2  laser (527 nm), SRS reflectivity was measured as a function of laser intensity OSIRIS simulations show approximately the same results –Cut-off in reflectivity at ~1x10 15 W/cm 2 –Average reflectivity levels off between 1-10% => 1D OSIRIS sims can capture the essential physics * D.S. Montgomery, etal., Phys. Plasmas 9, 5, p (2002) *

UCLA 1D Simulation Parameters RPIC* Comparison –Simulation length = 100  m –T e = 1.5 keV, T i = 0.1 keV and fixed –n e0 /n cr = 0.1 –(k D = 0.26 for BSRS) – laser =  m, I 0_laser = 5.6  W/cm 2 –8192/16384 cells, 128/256 particles / cell Experimental Comparison –Simulation domain L = 100  m –T e = 0.7 keV, fixed ions –n e0 /n cr = –(k D = 0.34 for BSRS) – laser =  m, I 0_laser = 1  W/cm 2 –8192 cells, 256 particles / cell Density Gradient –Exactly like RPIC comparison, only n e0 /n cr = 0.10 to 0.11 over the simulation length (100  m) *RPIC from H.X.Vu etal., Phys. Rev. Lett. 86, 4306 (2001)

UCLA OSIRIS and RPIC (same input*) RPIC OSIRIS Reflectivity (%/100) Time (1/  0 /100) Reflectivity Distribution function  Flattening of the distribution function is still seen  Narrow Langmuir wave  Reflectivity hits a high level, but tapers off part-way through the simulation Time-averaged longitudinal k p1 (m e c) *128 particles per cell, 8192 cells

UCLA Scattering in OSIRIS (256 ppc, cells) Raman backscatter at k ~1.5 LDI evident at k ~1.4 in field and k ~2.9 in ion density Rescatter of the Raman backscatter at k ~0.7 LDI of rescatter at k ~0.6 in field and k ~1.3 in ion density Time vs. k of longitudinal field Time vs. k of ion density

UCLA Reflectivity The correspondence between major spike recurrence is fairly good. Time 100 on top plot corresponds to ~3.1 on bottom plot, with 500 corresponding to 15.8 Reflectivity levels reach higher values for OSIRIS than RPIC, with one peak reaching a value > 100% OSIRIS reflectivity tapers off after 400, corresponding to the time when rescatter takes over Reflectivity (%/100) Time (1/  0 /100) OSIRIS Reflectivity

UCLA Convection - fixed ion case Plots of longitudinal E-field Clearly seen are: –Group velocities of relevant waves –Convective behavior –Recurrence patterns –Rescattering Recurrence occurs after the plasma waves have convected and plasma returns to a quiescent state

UCLA Convection - mobile ion case Plots of longitudinal E-field Again see convection LDI (which would not show up in the fixed ion case) Convection pictures are available on my computer for better color resolution

UCLA Fixed vs. mobile flattening Fixed ions: flattening at the phase velocity of the backscattered SRS plasma wave Mobile ions: flattening at the phase velocity of the backscattered SRS plasma wave, as well as the plasma wave from LDI Energetic chatter at higher velocities in fixed ion case due to rescatter Fixed ions Mobile ions

UCLA Trapped Particle Instability? Growth of k’s close to backscatter k~1.5 Frequency behavior similar to TPI TPI is conceptually simple - differences are to be expected –e.g., stronger damping on higher k side was not included in the model Something similar appears to be occurring in simulations k vs time, longitudinal E-field  vs k, longitudinal E-field * *W.L. Kruer, J.M. Dawson, and R.N. Sudan, Phys. Rev. Lett., 23, 838 (1969)

UCLA Wavebreaking? E-field initially shows peaks around eE/mc  0 = 0.010, whereas Coffey* wavebreaking limit = Exact limit? –These are nonlinear waves, with modified distribution functions –Wavebreaking arguments usually made with simplified waterbag model –At stronger v osc, agreement with Coffey limit gets better Recurrence occurs after the plasma waves have broken and convected away *Coffey, T.P., Phys. Fluids, 14, 1402 (1971)

UCLA Experimental Comparison - longitudinal E-field Forward SRS (  ~ 0.2, k ~ 0.2) Backward SRS (0.2, 1.7) Along with dynamical behavior to lower (than  ~ 0.2) frequencies Recurrence again occurs after convection Longitudinal E-field behavior movie available for viewing

UCLA Experimental Comparison - electron phase space Initial trapped particle region due to SRS –Early in time –During another recurrence undergoing less coherent evolution Additional slowly travelling structures -- very coherent as they convect through the simulation domain movie available for viewing

UCLA Density Gradient k (longitudinal) vs. time The rescatter shows significant shift in k. Convecting plasma waves clearly evidenced by k-shifts, as well as the plot of time vs. position of the E-field If  ~ constant, then k changes as the density changes –  p variation along the gradient Strong rescattering recurrence at a localized region would give same initial k Raman backscatter Backscatter of Raman backscatter

UCLA 2D Simulation Parameters Finite width pulse vs. plane wave –Simulation domain L = 100  m x 10.5  m –T e = 1.5 keV, fixed ions –n e0 /n cr = 0.1 – laser =  m –I 0_laser = 5.6  W/cm 2 –Plane-wave and finite pulse width simulations Laser spot size w0 = 2.4  m ( ~6 laser ) –8192 x 512 cells –64 particles / cell Experimental Comparison in 2D –Simulation domain L = 100  m x 10.5  m –T e = 0.7 keV, fixed ions –n e0 /n cr = – laser =  m –I 0_laser = 1  W/cm 2 –8192 x 512 cells –64 particles / cell

UCLA 2D - Finite Width vs. Plane Wave Plane Wave FFT of parallel E-field, k~1.5 for BSRS 1D-ish behavior of the finite laser pulse width –Constant k x over the k y ’s (transverse in the plane) Stronger neighboring k’s of SRS in planewave case Finite Width

UCLA 2D - Finite Width vs. Plane Wave Plane Wave p2 -- transverse momentum (in plane of simulation) p1 -- parallel momentum to direction of laser propagation Flattening due to SRS purely in the parallel direction Appears more strongly for plane wave case –Drive is stronger all across the simulated domain, rather than a localized drive in the finite width case Finite Width Electron phasespace

UCLA 2D - Experimental Comparison FFT reveals very bursty behavior Presence of forward side-scattering (k x ~0.5) FFT’s of Parallel E-field During a BSRS scattering peak Slightly later, in the process of saturating

UCLA 2D - Experimental Comparison Similarly to the 1D case,dynamical behavior at lower frequencies occurs in addition to the forward and backward scattering Flattening of the distribution function is strong in the parallel direction In addition, there is flattening at a higher velocity –Due to forward side-scattering  vs k, parallel E-field on a line through the center of the laser’s width Electron phase space

UCLA Conclusions Comparison with experiment shows reasonable agreement –Closer examination reveals low frequency behavior and appearance of slowly moving trapped particle vortices In simulating SRS we see convection, particle trapping, and a range of nonlinearities –Recurrence is due to convection –Saturation is due to multiple effects including wavebreaking Convection and it’s effect on shifting k is seen in a density gradient 2D simulations reveal differences between finite width laser vs. plane wave, as well as trapping by forward scattering at a definite angle