Whistler Chorus Amplification in the Magnetosphere: The Nonlinear Free-Electron Laser Model and the Ginzburg-Landau Equation

TL;DR

This paper introduces a nonlinear free-electron laser model for whistler-mode chorus amplification, deriving equations that predict exponential wave growth and amplitude modulations, and connects these phenomena to the Ginzburg-Landau equation for solitary wave analysis.

Contribution

It develops a novel nonlinear model linking whistler-mode chorus amplification to FEL mechanisms and introduces the Ginzburg-Landau equation framework for wave behavior analysis.

Findings

Small seed waves can exponentially grow to hundreds of picoteslas.

The Ginzburg-Landau equation describes chorus wave amplitude and phase.

The model aligns with satellite observations of wave growth.

Abstract

We present a novel nonlinear model for whistler-mode chorus amplification based on the free-electron laser (FEL) mechanism. First, we derive the nonlinear collective variable equations for the whistler-electron interaction. Consistent with in situ satellite observations, these equations predict that a small seed wave can undergo exponential growth, reaching a peak of a few hundred picoteslas after a few milliseconds, followed by millisecond timescale amplitude modulations. Next, we show that when one accounts for multiple wave frequencies and wave spatial variations, the amplitude and phase of the whistler wave can be described by the Ginzburg-Landau equation (GLE), providing a framework for the investigation of solitary wave behavior of chorus modes. These findings enhance our understanding of wave-particle interactions and space weather in the Van Allen radiation belts, deepen the connection between whistler-electron dynamics and FELs, and reveal a novel connection between whistler-mode chorus and the GLE.