Effect of Two-Fluid Equilibrium Flow on Tearing Linear Stability

Tearing modes have been studied extensively. Much attention has been devoted to two-fluid effects (i.e.~on the effect of distinguishing ion and electron dynamics) on their behavior. However, the effect of equilibrium flow on tearing stability, in particular when the equilibrium is described with a two-fluid model, has not been examined in detail. In two-fluid equilibrium ions and electrons are frozen into different surfaces: a flow surface for ions and the magnetic surface for (massless) electrons. Thus in toroidal systems plasma poloidal flow is not aligned with magnetic surfaces and there is a $\theta$-dependent component of the velocity $v_\psi \sim \sin \theta$ normal to the magnetic surfaces. Using a slab model we highlight the differences introduced to the standard tearing mode problem by the presence of a finite $v_\psi$. In particular, it is found that a single-mode analysis is not possible, even if all the effects of toroidicity other than $v_\psi$ are neglected. Moreover, a finite $v_\psi$ introduces a higher-order derivative for the perturbed velocity than in the single-fluid version of the problem. We report on our progress in building a solution for the slab model problem including a sinusoidal component of the equilibrium velocity normal to the magnetic surfaces.