Two-fluid tearing mode instability in cylindrical geometry

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.