Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence

TL;DR

This paper develops a scaling theory for electrostatic turbulence in magnetized plasmas, highlighting how nonlinear advection and phase mixing interact to confine free energy in low velocity moments, resulting in fluid-like turbulence behavior.

Contribution

It introduces a nonlinear theory accounting for phase mixing and plasma echo effects, showing free energy remains in low velocity moments, contrasting with linear Landau damping predictions.

Findings

Free energy stays in low velocity moments, avoiding divergence at low collisionality.

Long-wavelength perturbations do not produce collisional heating in the nonlinear regime.

The turbulence exhibits a fluid-like cascade with a critical balance between linear and nonlinear timescales.

Abstract

A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g., ITG turbulence) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating ExB flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. It is found that it is possible to construct a consistent theory in which very little free energy leaks into high velocity moments of the distribution function, rendering the turbulent cascade in the energetically relevant part of the wave-number space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also in contrast with the linear problem, in which it occurs at the finite rate equal to the Landau-damping rate). The ability of the free energy to stay in the low velocity moments of the distribution function is facilitated by the "anti-phase-mixing" effect, whose presence in the nonlinear system is due to the stochastic version of the plasma echo (the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wave-number space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins its competition with nonlinear advection is governed by the "critical balance" between linear and nonlinear timescales (which for high Hermite moments splits into two thresholds, one demarcating the wave-number region where phase mixing predominates, the other where plasma echo does).