Resistive instabilities in a flowing plasma: I. Inviscid case

The properties of resistive instabilities developing in equilibrium configurations in which flows are present are studied. The linearized magnetohydrodynamics (MHD) equations are solved numerically, taking into account the effects of resistivity, adopting equilibria with magnetic and velocity fields in the ( y-z) plane, and varying the x direction with two different scale lengths. The results show that the stability properties of the system are strongly influenced by the profile of the velocity field considered. The static tearing mode is recovered in the limit of small amplitude of the velocity with respect to the Alfvén velocity and/or small values of the ratio between magnetic and velocity scale lengths. In the opposite limit we obtain a purely ideal behavior in which the Kelvin–Helmholtz instability appears to be modified by the presence of a shear magnetic field. In between those limits the effect of the velocity is to change the dependence of the growth rate on the relevant parameters and to distort the spatial profile of the perturbations with respect to the static case.