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In this paper, we address the theoretical resolution of the Vlasov-Gausssystem from the linear regime to the strongly nonlinear one, when significanttrapping has occurred. The electric field is that of a sinusoidal electronplasma wave (EPW) which is assumed to grow from the noise level, and to keepgrowing at least up to the amplitude when linear theory in no longer valid(while the wave evolution in the nonlinear regime may be arbitrary). The ionsare considered as a neutralizing fluid, while the electron response to the waveis derived by matching two different techniques. We make use of a perturbationanalysis similar to that introduced to prove the Kolmogorov-Arnold- Mosertheorem, up to amplitudes large enough for neo-adiabatic results to be valid.Our theory is applied to the growth and saturation of the beam-plasmainstability, and to the three-dimensional propagation of a driven EPW in anon-uniform and non-stationary plasma. For the latter example, we lay a specialemphasis on nonlinear collisionless dissipation. We provide an explicittheoretical expression for the nonlinear Landau-like damping rate which, insome instances, is amenable to a simple analytic formula. We also insist on theirreversible evolution of the electron distribution function, which is nonlocalin the wave amplitude and phase velocity. This makes trapping an effectivemeans of dissipation for the electrostatic energy, and also makes the wavedispersion relation nonlocal. Our theory is generalized to allow for stimulatedRaman scattering, which we address up to saturation by accounting for plasmainhomogeneity and non-stationarity, nonlinear kinetic effects, and interspecklecoupling.

plasma physics and controlled fusion

Self-consistent theory for the linear and nonlinear propagation of a  sinusoidal electron plasma wave. Application to stimulated Raman scattering  in a non-uniform and non-stationary plasma