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 sigma , 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.<
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