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

Abstract

This paper addresses the linear and nonlinear three-dimensional propagation of an electron wave in a collisionless plasma that may be inhomogeneous, nonstationary, anisotropic and even weakly magnetized. The wave amplitude, together with any hydrodynamic quantity characterizing the plasma (density, temperature,...) are supposed to vary very little within one wavelength or one wave period. Hence, the geometrical optics limit is assumed, and the wave propagation is described by a first order differential equation. This equation explicitly accounts for three-dimensional effects, plasma inhomogeneity, Landau damping, and the collisionless dissipation and electron acceleration due to trapping. It is derived by mixing results obtained from a direct resolution of the Vlasov-Poisson system and from a variational formalism involving a nonlocal Lagrangian density. In a one-dimensional situation, abrupt transitions are predicted in the coefficients of the wave equation. They occur when the state of the electron plasma wave changes, from a linear wave to a wave with trapped electrons. In a three dimensional geometry, the transitions are smoother, especially as regards the nonlinear Landau damping rate, for which a very simple effective and accurate analytic expression is provided.

References in corpus (9)

• Landau damping
• Self-consistent Langmuir waves in resonantly driven thermal plasmas
• Directed transport in a spatially periodic potential under periodic non-biased forcing
• Adiabatic nonlinear waves with trapped particles: I. General formalism
• Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Variable Velocity Resolution Grids and High-Order Time-Splitting
• Adiabatic nonlinear waves with trapped particles: III. Wave dynamics
• The various manifestations of collisionless dissipation in wave propagation
• Global change in action due to trapping, how to derive it whatever the rate of variation of the dynamics
• On the nature of kinetic electrostatic electron nonlinear (KEEN) waves

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• Nonlinear adiabatic electron plasma waves. II. Applications
• 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
• Multiphase nonlinear electron plasma waves
• Phase mixing importance for both Landau instability and damping