Landau Damping in a Turbulent Setting

TL;DR

This paper investigates Landau damping in kinetic turbulence by analyzing the response of a plasma to a stationary random source, revealing that the effective damping rate can vary significantly from the classical Landau damping rate and even become negligible.

Contribution

It introduces a novel analysis of Landau damping under turbulent conditions, showing how resonant particle interactions influence the effective damping rate and phase-locking effects.

Findings

Effective damping rate can differ from classical Landau damping in magnitude and sign.

Phase-locking of density and current can suppress damping, addressing energy paradoxes.

Resonant interactions dominate the asymptotic response in turbulent plasma.

Abstract

To address the problem of Landau damping in kinetic turbulence, the forcing of the linearized Vlasov equation by a stationary random source is considered. It is found that the time-asymptotic density response is dominated by resonant particle interactions that are synchronized with the source. The energy consumption of this response is calculated, implying an effective damping rate, which is the main result of this paper. Evaluating several cases, it is found that the effective damping rate can differ from the Landau damping rate in magnitude and also, remarkably, in sign. A limit is demonstrated in which the density and current become phase-locked, which causes the effective damping to be negligible; this potentially resolves an energy paradox that arises in the application of critical balance to a kinetic turbulence cascade.