Two-Fluid Effects on Linear Tearing Mode Stability

In a two-fluid model, equilibrium rotation is tied to “flow surfaces” that are close to, but distinct from, magnetic surfaces. These flow surfaces produce a small but nonzero radial velocity. This is expected to create qualitative modifications in the behavior of modes localized on magnetic surfaces such as tearing modes. We report progress on an exploratory investigation of linear tearing mode behavior when equilibrium poloidal rotation is included in a two-fluid model. Using slab geometry, we were able to show that the layer equation for the fundamental mode must include new terms that depend on the third derivative of the mode sidebands. The direct solution of the coupled system of equations has proven extremely challenging. For this reason, an approximate solution using asymptotic matching is currently underway. Working in Fourier space allows all equations to combine into one. The boundary layer thickness is not as trivially determined as in the single-mode case but can be calculated efficiently by constructing a "Kruskal-Newton diagram", a tool underutilized in the current literature. Preliminary results have indicated that solutions may take the form of exotic special functions which have different asymptotic properties than in the single fluid case. With these tools, we are progressing towards quantifying changes in tearing mode stability in the presence of two-fluid equilibrium flow.