Adiabatic Wave-Particle Interaction Revisited

TL;DR

This paper revisits the dynamics of electrons in electrostatic waves, demonstrating that an adiabatic invariant persists for most particles despite complex trapping behavior, enabling long-term distribution predictions.

Contribution

It introduces a refined analysis of wave-particle interactions showing the persistence of adiabatic invariants during trapping, with implications for nonlinear wave frequency shifts.

Findings

Adiabatic invariant remains valid for most particles during trapping.

Disordering occurs near X-points but does not invalidate the invariant.

Potential application to nonlinear frequency shift analysis.

Abstract

In this paper we calculate and visualize the dynamics of an ensemble of electrons trapping in an electrostatic wave of slowly increasing amplitude, illustrating that, despite disordering of particles in angle during the trapping transition as they pass close to X-points, there is still an adiabatic invariant for the great majority of particles that allows the long-time distribution function to be predicted. Possible application of this approach to recent work on the nonlinear frequency shift of a driven wave is briefly discussed.