Energetic bounds on gyrokinetic instabilities. Part II. Modes of optimal growth

TL;DR

This paper introduces optimal growth modes in electromagnetic gyrokinetics, providing a new way to bound and analyze energy growth in plasma instabilities with efficient computation and clear physical interpretation.

Contribution

It develops a framework for modes of optimal growth in gyrokinetic equations, offering tight bounds on instability growth rates and simplifying energy flow analysis.

Findings

Optimal modes arise from free energy balance and decompose energy flows.

Optimal growth rates provide rigorous upper bounds on nonlinear and linear growth.

Closed-form solutions for growth rates in asymptotic limits are derived.

Abstract

We introduce modes of instantaneous optimal growth of free energy for the fully electromagnetic gyrokinetic equations. We demonstrate how these "optimal modes" arise naturally from the free energy balance equation, allowing its convenient decomposition, and yielding a simple picture of energy flows. Optimal modes have a number of other favorable features, such as their low-dimensionality, efficiency of computation, and the fact that their growth rates provide a rigorous and "tight" upper bound on both the nonlinear growth rate of energy, and the linear growth rate of traditional gyrokinetic (normal mode) instabilities. We provide simple closed form solutions for the optimal growth rates in a number of asymptotic limits, and compare these with our previous bounds.