Nonlinear kinetic modeling of stimulated Raman scattering in a multidimensional geometry

Abstract

In this paper, we derive coupled envelope equations modeling the growth of stimulated Raman scattering (SRS) in a multi-dimensional geometry and accounting for nonlinear kinetic effects. In particular, our envelope equations allow for the nonlinear reduction of the Landau damping rate, whose decrease with the plasma wave amplitude depends on the rate of side-loss. Account is also made of the variations in the extent of the plasma wave packet entailed by the collisionless dissipation due to trapping. The dephasing between the electron plasma wave (EPW) and the laser drive, as well as the self-focussing of the plasma wave, both induced by the EPW nonlinear frequency shift, are also included in our envelope equations. These equations are solved in a multi-dimensional geometry using our code dubbed BRAMA, whose predictions regarding the evolution of Raman reflectivity as a function of the laser intensity are compared against previously published particle in cell results, thus illustrating the ability of BRAMA simulations to provide the correct laser threshold intensity for SRS as well as the right order of magnitude of Raman reflectivity above threshold. V C 2012 American Institute of Physics. [http://dx.

Probabilistic approach to nonlinear wave-particle resonant interaction

“…Thus, we can write ∆h = 2εv 2 φ u Q θ , Var(∆h) = 2εv 2 φ uVar(Q) (17) where u and Q are evaluated at z = z R . We calculate analytical changes of energy due to scattering (17) and numerical changes.…”

“…Assuming that the wave spectrum is wide enough and the wave intensity is sufficiently low, one can model the wave-particle resonant interactions using quasi-linear theory [4][5][6][7] generalized for systems with inhomogeneous magnetic field and background plasma [8,9]. However, various recent spacecraft observations in the near-Earth plasma environment [10][11][12][13][14], laboratory experiments [15,16], and inertial confinement fusion simulations and experiments [17][18][19] have demonstrated that the applicability of quasi-linear theory is often questionable, because electrons happen to interact with coherent waves sufficiently intense to significantly influence electron motion over long time intervals. There are two main effects of such nonlinear wave-particle interactions: particle trapping by the waves (phase trapping) and particle scattering (phase bunching) with nonzero average change of particle energy [20][21][22].…”

Envelope equation for the linear and nonlinear propagation of an electron plasma wave, including the effects of Landau damping, trapping, plasma inhomogeneity, and the change in the state of wave

“…To cite a few examples, the EPW may by subjected to secondary instabilities leading to the growth of sidebands [42][43][44], so that, except in some special instances [45,46], the total electrostatic field, E(x, t, ψ), is no longer a slowlyvarying function of x and t (at fixed ψ). Moreover, due to the amplitude dependence of the wave frequency, the wave front may bend so as to make the EPW self-focus [28,38], which, again, renders the assumption of a slowly-varying amplitude no longer valid. In the situation, observed both numerically and experimentally [38,48], when wavefront bowing is followed by the growth of sidebands, the phase modulation due to the transverse variations of the wave amplitude is negligible compared to that due to the space dependence of the nonlinear frequency shift.…”

“…The 3-D version of this code was used in Ref. [28] to predict when the EPW would self-focus and, again, saturate SRS, with predictions on Raman reflectivity comparing even better with experiment [50] than those from PIC codes [38].…”

“…(29), one would find that the EPW might self-focus during its propagation, as shown in Refs. [28,38] Furthermore, as discussed in Paragraph III A, if the wave phase velocity increases, the electron kinetic energy of the trapped electrons also increases, at the expense of the EPW, whose amplitude should decrease as shown numerically in Ref. [31].…”