Finite conductivity and the interface filamentation instability in railgun arcs

A first-order perturbation expansion of the magnetohydrodynamics (MHD) equations is used to study the filamentation instability on the plasma-vacuum interface of plasma arcs accelerated by magnetic fields. The arc is modeled in the same way as A.M. Decker (1989), including the effects of finite conductivity σ, but considers perturbations with wave vector k parallel to the magnetic field B. A fourth-order mode equation is derived and solved numerically. Complicated unstable modes were found, but largely in a region of very small k, beyond the limit of interest in railguns. This instability is therefore much less disrupting than the interchange instability in the parameter ranges explored