Two-Fluid Equilibrium Flow Effects on Linear Tearing Mode Stability

In a two-fluid model of a tokamak plasma, equilibrium rotation is tied to “flow surfaces” that are close to, but distinct from, magnetic surfaces. As a result, the equilibrium plasma velocity acquires a component normal to the magnetic surfaces. This normal flow, which varies poloidally, is expected to qualitatively modify the behavior of magnetic-surface-localized instabilities, such as tearing modes. We present an analytical investigation in the slab approximation of linear tearing mode stability in the presence of two-fluid equilibrium flow. The poloidal periodicity of the normal flow introduces coupling between sideband poloidal harmonics, and the resistive layer equation gains additional terms dependent on the derivatives of these sidebands. In Fourier space, these equations combine into a single differential equation that is analytically intractable without further simplification. By applying standard order of magnitude estimates within the layer, we reduce the problem to a solvable form and derive analytic expressions for the tearing stability index Δ′ in both the constant-flux and internal kink regimes. Preliminary analysis suggests that the equilibrium flow has a stabilizing effect. These analytical findings are validated against numerical simulations. The model is then applied to flow profiles representative of several tokamak confinement geometries.