Four-dimensional equations for the study of electromagnetic plasma turbulence in a drift kinetic limit

TL;DR

This paper derives a four-dimensional kinetic model for electromagnetic plasma turbulence in a magnetized plasma, capturing the transition between fluid and gyrokinetic regimes with a focus on finite-Larmor-radius effects.

Contribution

It introduces a novel four-dimensional kinetic equation set based on gyrokinetic equations, employing Laguerre and Hermite decompositions to model electromagnetic turbulence.

Findings

Model conserves free energy.

Applicable to plasma scales around $k_ot ho_i oughly 1$.

Enables analysis of fluid-kinetic transition and velocity-space effects.

Abstract

For a magnetised plasma in a straight magnetic guide field, we derive a set of four-dimensional kinetic equations, which can capture electromagnetic turbulence in the drift kinetic limit. To do so, we start from the gyrokinetic equations, employ a Laguerre decomposition in the perpendicular velocity direction, retain only the dominant gyroaverage contributions and only the first two Laguerre moments that source the electromagnetic fluctuations. The model conserves free energy, and can describe electromagnetic turbulence for a plasma at the transition between fluid and gyrokinetic regimes ($k_\perp \rho_i\approx 1$ range of scales), as dominant finite-Larmor-radius (FLR) effects are considered. In addition to the three dimensions in positions space, we retain the parallel velocity dependence, which we describe via a Hermite representation. Employing this system, but without any other physics based assumptions for the plasma species that can bias results, will allow us to investigate how fluid effects transition into the kinetic range, and analyse the interplay between spatial and velocity space mixing for electromagnetic plasma turbulence.