Nonlinear adiabatic electron plasma waves. II. Applications

Abstract

In this article, we use the general theory derived in the companion paper [M. Tacu and D. Bénisti, Phys. Plasmas (2021)] in order to address several long-standing issues regarding nonlinear electron plasma waves (EPW's). First, we discuss the relevance, and practical usefulness, of stationary solutions to the Vlasov-Poisson system, the so-called Bernstein-Greene-Kruskal modes, to model slowly varying waves. Second, we derive an upper bound for the wave breaking limit of an EPW growing in an initially Maxwellian plasma. Moreover, we show a simple dependence of this limit as a function of $k{\lambda }_D$, $k$ being the wavenumber and ${\lambda }_D$ the Debye length. Third, we explicitly derive the envelope equation ruling the evolution of a slowly growing plasma wave, up to an amplitude close to the wave breaking limit. Fourth, we estimate the growth of the transverse wavenumbers resulting from wavefront bowing by solving the nonlinear, nonstationary, ray tracing equations for the EPW, together with a simple model for stimulated Raman scattering.

References in corpus (5)

• Anisotropic heating and magnetic field generation due to Raman scattering in laser-plasma interactions
• 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
• Nonlocal adiabatic theory. I. The action distribution function
• Nonlinear adiabatic electron plasma waves. I. General theory and nonlinear frequency shift
• 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

Cited by in corpus (1)

• Nonlinear adiabatic electron plasma waves. I. General theory and nonlinear frequency shift