Nonlinear adiabatic electron plasma waves. II. Applications

TL;DR

This paper applies a general theory to address key issues in nonlinear electron plasma waves, including wave modeling, wave breaking limits, envelope evolution, and transverse effects, advancing understanding of plasma wave dynamics.

Contribution

It derives new bounds on wave breaking, analyzes stationary solutions, and models wave evolution and transverse effects in nonlinear plasma waves.

Findings

Derived an upper bound for wave breaking limit based on $k\lambda_D$

Validated the relevance of Bernstein-Greene-Kruskal modes for slow wave variations

Modeled the growth of transverse wavenumbers due to wavefront bowing

Abstract

In this article, we use the general theory derived in the companion paper [M. Tacu and D. B\'enisti, 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.