Upper bounds on gyrokinetic instabilities

TL;DR

This paper derives rigorous upper bounds on the growth rates of gyrokinetic instabilities in magnetized plasmas, unifying previous results and applying to both linear and nonlinear regimes across various conditions.

Contribution

It introduces a general framework for bounding gyrokinetic instability growth rates, encompassing electrostatic and electromagnetic cases, regardless of particle species, collisions, or magnetic geometry.

Findings

Bounds apply to both electrostatic and electromagnetic instabilities.

Results unify previous special-case findings.

Bounds limit nonlinear free energy growth.

Abstract

A family of rigorous upper bounds on the growth rate of local gyrokinetic instabilities in magnetized plasmas is derived from the evolution equation for the Helmholtz free energy. These bounds hold for both electrostatic and electromagnetic instabilities, regardless of the number of particle species, their collision frequency, and the geometry of the magnetic field. A large number of results that have earlier been derived in special cases and observed in numerical simulations are thus brought into a unifying framework. These bounds apply not only to linear instabilities but also imply an upper limit to the nonlinear growth of the free energy.