Finite conductivity and the interface filamentation instability in railgun arcs

We use a first order perturbation expansion of the MHD equations to study the filamentation instability on the plasma-vacuum interface of plasma arcs accelerated by magnetic fields. We model the arc in the same way as Decker, including the effects of finite conductivity σ, but consider perturbations with wave vector k parallel to the magnetic field B. A fourth order mode equation is derived and solved numerically. We find complicated unstable modes, 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 we have explored.