Wave packet formulation of nonlinear plasma wave kinetics

Abstract

A theory of nonlinear plasma wave propagation is presented which contains, as particular cases, both the nonlinear Schrödinger equation for coherent waves and the kinetic wave equation for weak plasma turbulence. Fluctuations are represented as a superposition of “micro” wave packets, with finite spread but negligible overlap in wavenumber and frequency. For the case of coherent wave propagation a nonlinear Schrödinger equation is derived, generalized over precious versions in that linear Landau damping nonlinear frequency shift, nonlinear damping, and three-dimensional effects are all included, as well as the non-local, non-Markovian interaction characteristic of this equation. In the case of weak plasma turbulence, the kinetic wave equation is generalized to include self-interaction of the micro packets, which, just as in the coherent case, results in non-local, non-Markovian terms, not heretofore considered in weak turbulence formulations.