# 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, 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.

- Authors:

- Center for Multiscale Plasma Dynamics, University of Maryland, College Park, Maryland 20742-3511 (United States)
- Princeton Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543 (United States)

- Publication Date:

- OSTI Identifier:
- 21532075

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 17; Journal Issue: 12; Other Information: DOI: 10.1063/1.3514141; (c) 2010 American Institute of Physics

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUILIBRIUM; MAGNETOHYDRODYNAMICS; PLASMA; TURBULENCE; FLUID MECHANICS; HYDRODYNAMICS; MECHANICS

### Citation Formats

```
Zhu Jianzhou, and Hammett, Gregory W.
```*Gyrokinetic statistical absolute equilibrium and turbulence*. United States: N. p., 2010.
Web. doi:10.1063/1.3514141.

```
Zhu Jianzhou, & Hammett, Gregory W.
```*Gyrokinetic statistical absolute equilibrium and turbulence*. United States. doi:10.1063/1.3514141.

```
Zhu Jianzhou, and Hammett, Gregory W. Wed .
"Gyrokinetic statistical absolute equilibrium and turbulence". United States. doi:10.1063/1.3514141.
```

```
@article{osti_21532075,
```

title = {Gyrokinetic statistical absolute equilibrium and turbulence},

author = {Zhu Jianzhou and Hammett, Gregory W.},

abstractNote = {A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, 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.},

doi = {10.1063/1.3514141},

journal = {Physics of Plasmas},

number = 12,

volume = 17,

place = {United States},

year = {Wed Dec 15 00:00:00 EST 2010},

month = {Wed Dec 15 00:00:00 EST 2010}

}