The anisotropic redistribution of free energy for gyrokinetic plasma turbulence in a Z-pinch

TL;DR

This paper investigates how free energy redistributes anisotropically across scales in gyrokinetic plasma turbulence within a Z-pinch, revealing complex energy transfer patterns influenced by zonal flows and anisotropy.

Contribution

It introduces a novel angular density approach to analyze anisotropic free energy flux in gyrokinetic turbulence, highlighting the impact of zonal flows on energy redistribution.

Findings

Energy flux exhibits both positive and negative angular sections, indicating complex cascade behavior.

Zonal flows cause highly anisotropic free energy redistribution.

The study provides a new framework for understanding sub-grid scale modeling in plasma turbulence.

Abstract

For a Z-pinch geometry, we report on the nonlinear redistribution of free energy across scales perpendicular to the magnetic guide field, for a turbulent plasma described in the framework of gyrokinetics. The analysis is performed using a local flux-surface approximation, in a regime dominated by electrostatic fluctuations driven by the entropy mode, with both ion and electron species being treated kinetically. To explore the anisotropic nature of the free energy redistribution caused by the emergence of zonal flows, we use a polar coordinate representation for the field-perpendicular directions and define an angular density for the scale flux. Positive values for the classically defined (angle integrated) scale flux, which denote a direct energy cascade, are shown to be also composed of negative angular sections, a fact that impacts our understanding of the backscatter of energy and the way in which it enters the modeling of sub-grid scales for turbulence. A definition for the flux of free energy across each perpendicular direction is introduced as well, which shows that the redistribution of energy in the presence of zonal flows is highly anisotropic.