Gyrokinetic statistical absolute equilibrium and turbulence

TL;DR

This paper applies the concept of absolute equilibrium from inviscid systems to gyrokinetic plasma turbulence, revealing inverse energy cascade features and universal equilibrium shapes, with implications for understanding plasma phenomena like zonal flows.

Contribution

It introduces a statistical equilibrium framework for gyrokinetic turbulence, including negative temperature states and universal shapes, extending classical turbulence theories to plasma systems.

Findings

Negative temperature states indicate inverse energy cascade.

Universal equilibrium shape in 3D gyrokinetics with one conserved quantity.

Comparison with classical models like Charney-Hasegawa-Mima.

Abstract

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity $v$ with $N$ grid points (where $N+1$ quantities are conserved, corresponding to an energy invariant and $N$ entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.