The various manifestations of collisionless dissipation in wave propagation

TL;DR

This paper explores how collisionless dissipation manifests in wave propagation within plasmas, revealing nonlinear effects on wave amplitude, group velocity, and energy distribution in one and multiple dimensions.

Contribution

It demonstrates the nonlinear and nonlocal effects of collisionless dissipation on wave packet dynamics, including amplitude dependence of group velocity and multidimensional defocusing.

Findings

Wave packets experience nonlinear modifications to group velocity.

Electrons are globally accelerated, affecting wave energy and shape.

Weakly nonlinear regime shows a defocusing effect due to collisionless damping.

Abstract

The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet is Landau damped, so that in the reference frame moving at the group velocity, the wave amplitude decays exponentially with time. In the nonlinear regime, once phase mixing has occurred and when the electron motion is nearly adiabatic, the damping rate is strongly reduced compared to the Landau one, so that the wave amplitude remains nearly constant along the characteristics. Yet, we show here that the electrons are still globally accelerated by the wave packet, and, in one dimension, this leads to a non local amplitude dependence of the group velocity. As a result, a freely propagating wave packet would shrink, and, therefore, so would its total energy. In more than one dimension, not only does the magnitude of the group velocity nonlinearly vary, but also its direction. In the weakly nonlinear regime, when the collisionless damping rate is still significant compared to its linear value, this leads to an effective defocussing effect which we quantify, and which we compare to the self-focussing induced by wave front bowing.