Analytic solutions to dynamic equations of plasma armature railguns

General governing nonlinear differential equations pertaining to the dynamic behavior of a plasma armature electromagnetic railgun are derived. Three different cases are then considered, and the corresponding governing equations are solved exactly by means of a set of nonlinear transformations. The cases correspond to no ablation, continuous ablation, and partial ablation for which an ablation threshold velocity plays a fundamental role. It is concluded that in order to achieve very high projectile velocities the projectile should be injected into the railgun at velocities higher than the ablation threshold velocity. Thus the ablation can be completely alleviated and the ensuing turbulent drag can be significantly diminished. It is shown that under these conditions projectiles can typically be accelerated up to 30 km/s or more while without hypervelocity injection, for the same railgun and typical operating conditions, the maximum projectile velocity could be severely limited