Gyrokinetic statistical absolute equilibrium and turbulence

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.

Physics of Plasmas in press

References in corpus (10)

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Cited by in corpus (10)

• Purely helical absolute equilibria and chirality of (magneto)fluid turbulence
• Energy transfer and dual cascade in kinetic magnetized plasma turbulence
• On the structure and statistical theory of turbulence of extended magnetohydrodynamics
• Dynamics of partially thermalized solutions of the Burgers equation
• Local gyrokinetic simulations of tokamaks with non-uniform magnetic shear
• The effect of background flow shear on gyrokinetic turbulence in the cold ion limit
• Compressible helical turbulence: Fastened-structure geometry and statistics
• Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales
• Zonal Flows and Turbulence in Fluids and Plasmas
• Freely decaying turbulence in two-dimensional electrostatic gyrokinetics