Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

Abstract

A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation theorem is derived. This kinetic fluctuation-dissipation theorem reduces to the standard "fluid" one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation theorem for the perturbations of the distribution function is derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.

20 pages, 4 figures

References in corpus (5)

• Gyrokinetic turbulence: a nonlinear route to dissipation through phase space
• Fast collisionless reconnection and electron heating in strongly magnetized plasmas
• Intermittency and the passive nature of the magnitude of the magnetic field
• Landau Damping in a Turbulent Setting
• Irreversible energy flow in forced Vlasov dynamics

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