Energetic bounds on gyrokinetic instabilities. Part III. Generalized free energy

TL;DR

This paper extends gyrokinetic free energy theory to include resonance effects, reducing growth bounds and enabling more accurate stability analysis, with potential applications in stellarator optimization.

Contribution

It introduces a generalized free energy framework that captures resonance effects and improves bounds on growth rates in gyrokinetic systems.

Findings

Resonance effects are incorporated into the generalized free energy.

Growth bounds are significantly reduced with the new theory.

The approach allows efficient computation of optimal growth rates.

Abstract

Free energy, widely used as a measure of turbulence intensity in weakly collisional plasmas, has been recently found to be a suitable basis to describe both linear and nonlinear growth in a wide class gyrokinetic systems. The simplicity afforded by this approach is accompanied by some drawbacks, notably the lack of any explicit treatment of wave-particle effects, which makes the theory unable to describe things like stability thresholds or dependence on the geometry of the background magnetic field. As a step toward overcoming these limitations, we propose an extension of the theory based on a generalization of free energy. With this it is demonstrated that resonance effects are recovered, and the bounds on growth are significantly reduced. The simplicity and efficient computation of the associated "optimal" growth rates makes the theory potentially applicable to stellarator optimization.