Envelope modulations of kinetic plasma waves: A general framework

TL;DR

This paper develops a comprehensive framework for understanding envelope modulations in plasma turbulence under strong magnetic fields, linking dielectric functions to wave evolution and deriving a nonlinear Schrödinger equation for specific plasma phenomena.

Contribution

It introduces a general theoretical framework connecting plasma dielectric functions with envelope modulations, applicable to gyrokinetic plasma turbulence analysis.

Findings

Derived a nonlinear Schrödinger equation for plasma wave evolution.

Unified description of small-scale fluctuations and large-scale flows.

Demonstrated the framework with gyrokinetic zonal flow and drift wave analysis.

Abstract

The general framework of envelope modulations for plasma turbulence in the presence of strong magnetic fields is discussed. It is shown that the problem can be formulated using a functional which is equivalent to the plasma dielectric function for monochromatic waves. Therefore expanding around its linear wave solutions, one can describe the weakly nonlinear evolution of waves. The resulting "quasi-linear" dielectric tensor, can describe the evolution of small scale fluctuations advected and modulated by background flows and corrugations, as well as the evolution of the large scale flows driven by small scales. As a concrete example of the framework, gyrokinetic evolution of zonal flows and drift waves is considered and the resulting nonlinear Schr\"odinger equation is derived.