Quasilinear theory for inhomogeneous plasma

TL;DR

This paper develops a comprehensive quasilinear theory for inhomogeneous plasma turbulence, incorporating relativistic, electromagnetic, and gravitational effects, and deriving a positive-definite diffusion operator and a general fluctuation spectrum.

Contribution

It introduces a generalized quasilinear framework that handles inhomogeneous turbulence with off-shell waves and unifies various physical effects in plasma interactions.

Findings

Derivation of a positive-semidefinite local diffusion coefficient.

Formulation of a collision operator conserving particles, momentum, and energy.

Extension of QLT to relativistic, electromagnetic, and gravitational plasma interactions.

Abstract

This paper presents quasilinear theory (QLT) for classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic, and gravitational effects are subsumed. A Fokker--Planck equation for the dressed 'oscillation-center' distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields, and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu--Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum, and energy, and it also satisfies the H-theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave--plasma system. The action of nonresonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-center QLT of electrostatic turbulence (1973, Phys. Fluids 16, 1102) is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.