Arc dynamics in the rail gun

A one-dimenslonal model is discussed which is suitable for analyzing the properties of the plasma in an arc-driven rail gun. It is pointed out that a set of twelve coupled equations can be derived, the solution of which yields the electromagnetic fields associated with the arc as well as its fluid-dynamical characteristics. The calculations are then applied to analyze the arc in a recent experiment by Rashleigh and Marshall. From a limiting-case analytic solution of the governing equations, some approximate scaling laws can be derived which determine how the arc characteristics vary with gun dimensions, projectile mass, arc mass, and accelerating current. The accuracy of the scaling relations is discussed by comparing results predicted by them for various arcs with results predicted by the more general, numerical solutions of the governing equations.