Two-fluid tearing mode instability in cylindrical geometry

Atsushi Ito,Jesús J Ramos

doi:10.1063/1.4986116

Abstract

This paper investigates the linear stability of a force-free equilibrium in a plasma cylinder of finite aspect ratio, against the two-fluid resistive tearing mode. An analytic dispersion relation is derived by extending to cylindrical geometry the slab geometry boundary layer theory applicable to two-fluid tearing modes for high beta and general ion skin depths [E. Ahedo and J. J. Ramos, Plasma Phys. Controlled Fusion 51, 055018 (2009)]. The cylindrical dispersion relation shows the dependence of the mode growth rate and real frequency on the ion skin depth, through different regimes that range from the single-fluid MHD limit to the electron MHD limit. It also shows that the non-zero real frequency of the mode arises due to the combination of two-fluid and cylindrical effects. A numerical solution of the complete set of normal-mode equations that resolves the fine-scale singular layer is carried out, for a wide range of resistivity and ion skin depth values. The numerically obtained eigenvalues agree very well with the analytic dispersion relation and the agreement improves the smaller the resistivity and the larger the ion skin depth are. Comparison between the numerical eigenfunctions and the inner solutions of the boundary layer theory shows that the eigenfunctions develop imaginary parts within the resonant layer, also due to the combination of two-fluid and cylindrical effects.

Highlights

The resistive tearing instability has been studied extensively as one of the physical mechanisms that drive magnetic reconnection, an important effect that is crucial to many space and laboratory plasma phenomena
Equation (60) shows that the real frequency appears due to the combination of the two-fluid and cylindrical effects
Using singular perturbation boundary layer techniques, we have derived analytically a two-fluid tearing mode dispersion relation for force-free equilibria in a plasma cylinder of finite aspect ratio. This dispersion relation shows the variation of the growth rate and the real frequency of the mode with the ion skin depth and includes previous theories as special limits

Summary

INTRODUCTION

The resistive tearing instability has been studied extensively as one of the physical mechanisms that drive magnetic reconnection, an important effect that is crucial to many space and laboratory plasma phenomena. [7] derived an analytic dispersion relation for two-flulid tearing modes in slab geometry, for a force-free equilibrium with constant density and temperature, allowing for general values of the ion skin depths and the plasma beta. The goal of this work is to investigate the effects of two-fluid physics and cylindrical geometry on the linear resistive tearing mode, neglecting finite-Larmor-radius, electron inertia and equilibrium pressure gradient effects. To this end, we consider the following system of resistive, cold-ion, Hall-MHD equations:. All the other components of the perturbation can be eliminated algebraically in favor of these three and, without further approximations, the resulting normal-mode system for (B1r , ξ, Q)

F B1r en0 rk 2 0 η

SUMMARY AND DISCUSSION