Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection and electron heating in low-beta plasmas

TL;DR

This paper introduces a simplified yet physically comprehensive fluid-kinetic model for low-frequency magnetic reconnection and electron heating in low-beta plasmas, capturing key dynamics and energy conversion processes.

Contribution

It presents a minimal, rigorous gyrokinetic-based model that includes collisions, electron kinetics, and magnetic topology changes, suitable for both collisional and collisionless regimes.

Findings

The model recovers all relevant linear waves and tearing instability regimes.

A numerical method using Hermite representation efficiently simulates velocity space dynamics.

Electron heating remains finite as collisionality approaches zero due to velocity space scale formation.

Abstract

A minimal model for magnetic reconnection and, generally, low-frequency dynamics in low-beta plasmas is proposed. The model combines analytical and computational simplicity with physical realizability: it is a rigorous limit of gyrokinetics for plasma beta of order the electron-ion mass ratio. The model contains collisions and can be used both in the collisional and collisionless reconnection regimes. It includes gyrokinetic ions (not assumed cold) and allows for the topological rearrangement of the magnetic field lines by either resistivity or electron inertia, whichever predominates. The two-fluid dynamics are coupled to electron kinetics --- electrons are not assumed isothermal and are described by a reduced drift-kinetic equation. The model therefore allows for irreversibility and conversion of magnetic energy into electron heat via parallel phase mixing in velocity space. An analysis of the exchanges between various forms of free energy and its conversion into electron heat is provided. It is shown how all relevant linear waves and regimes of the tearing instability (collisionless, semicollisional and fully resistive) are recovered in various limits of our model. An efficient way to simulate our equations numerically is proposed, via the Hermite representation of the velocity space. It is shown that small scales in velocity space will form, giving rise to a shallow Hermite-space spectrum, whence it is inferred that, for steady-state or sufficiently slow dynamics, the electron heating rate will remain finite in the limit of vanishing collisionality.