The free energy balance equation applied to gyrokinetic instabilities, the effect of the charge flux constraint, and application to simplified kinetic models

TL;DR

This paper derives a generalized free energy balance equation for gyrokinetic instabilities, incorporating electromagnetic sources and charge flux constraints, to better understand and predict plasma behavior in simplified models.

Contribution

It introduces a new formulation of the free energy balance including electromagnetic effects and charge flux constraints, enhancing the analysis of gyrokinetic instabilities.

Findings

The free energy balance alone cannot determine eigenfrequencies.

Charge flux constraints can suppress instabilities predicted by free energy considerations.

Application to simplified models illustrates the practical utility of the theoretical framework.

Abstract

The free energy balance equation for gyrokinetic fluctuations is derived and applied to instabilities. An additional term due to electromagnetic sources is included. This can provide a simpler way to compute the free energy balance in practical applications, and is also conceptually clarifying. The free energy balance, by itself, is not sufficient to determine an eigenfrequency. The preceding results are derived in general geometry. The charge flux constraint in gyrokinetics can provide a necessary additional relation, and the combination of these two can be equivalent to a dispersion relation. The charge flux constraint can prevent the appearance of an unstable eigenmode even though the free energy balance would allow strongly growing fluctuations. The application of these concepts to simplified kinetic models in simplified geometry is also indicated.