Two-fluid tearing instability in force-free magnetic configuration

In general, the linear two-fluid tearing instabilities are driven by shear Alfven (SA), compressional Alfven (CA), and slow magnetoacoustic (MA) modes modified on short scales by two-fluid effects. Previous two-fluid theories were devoted to either the hot plasma case where coupling of the SA and the MA waves dominates, or to the cold plasma limit, β=0, where the instability is driven by the SA and the CA waves. Taking into account plasma compressibility and the Hall term, we derive general tearing equations that cover the two limiting cases and the transition between them. In particular, in the hot plasma case, equations are derived that depend on the factor β/(1+β) and span the validity of resistive to electron MHD. The important effect of resistive diffusion of the 'out-of-plane' component of the magnetic field perturbation Bparallel(1) is also included. Two new solutions where this effect dominates are obtained within the scope of the hot plasma model. Whistler scaling γ∝Δ'2 is found for the collisionless tearing mode instead of the kinetic Alfven scaling γ∝Δ' at small Δ'. Previous calculations for coupling with the MA waves at large Δ' did not take the diffusion of Bparallel(1) into account. The joint effect of these factors is presented in the work