Momentum equation for arc-driven rail guns

Abstract

In several models of arc-driven rail guns, the rails are assumed to be infinitely high to simplify the calculation of the electromagnetic fields which appear in the momentum equation for the arc. This assumption leads to overestimates of the arc pressures and accelerations by approximately a factor of 2 for typical rail-gun geometries. In this paper, we develop a simple method for modifying the momentum equation to account for the effect of finite-height rails on the performance of the rail gun and the properties of the arc. The modification is based on an integration of the Lorentz force across the arc cross section at each axial location in the arc. Application of this technique suggests that, for typical rail-gun geometries and moderately long arcs, the momentum equation appropriate for infinite-height rails can be retained provided that the magnetic pressure term in the equation is scaled by a factor which depends on the effective inductance of the gun. The analysis also indicates that the magnetic pressure gradient actually changes sign near the arc/projectile boundary because of the magnetic fields associated with the arc current.