Collisionless Kinetic Theory of Oblique Tearing Instabilities

TL;DR

This paper develops a kinetic theory for collisionless oblique tearing modes in a Harris equilibrium, revealing that density-gradient-driven diamagnetic drift stabilizes these modes, which previous theories overestimated in growth rate.

Contribution

It introduces a new dispersion relation accounting for drift stabilization effects in 3D oblique tearing instabilities, improving upon conventional analytic theories.

Findings

Oblique modes are stabilized by density-gradient-driven diamagnetic drift.

The derived dispersion relation accurately captures the stabilization effect.

A simple analytic stability criterion is proposed.

Abstract

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for a Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle ($\theta$) with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes ($\theta \neq 0$). We find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. A simple analytic estimate for the stability criterion is provided.