Effects of line tying on resistive tearing instability in slab geometry

The effects of line tying on resistive tearing instability in slab geometry are studied within the framework of reduced magnetohydrodynamics [B. B. Kadomtsev and O. P. Pogutse, Sov. Phys. JETP 38, 283 (1974); H. R. Strauss, Phys. Fluids 19, 134 (1976)]. It is found that line tying has a stabilizing effect. The tearing mode is stabilized when the system length L is shorter than a critical length L_c, which is independent of the resistivity η. When L is not too much longer than L_c, the growth rate γ is proportional to η. When L is sufficiently long, the tearing mode scaling γ∼ η^3/5 is recovered. The transition from γ∼η to γ∼ η^3/5 occurs at a transition length Lt ∼ η^-2/5.