Understanding Velocity Limits In Plasma Armature Rail Guns

Experiments have shown that rail guns operating with plasma armatures exhibit a velocity limitation. This paper starts with the fundamental equation for momentum conservation in a plasma and develops a simple model for analysis of the motion of the projectile. A preliminary extension to and analysis of physical systems is also provided. The most important consequence of this formulation is that, based on electric forces only, a velocity limit is, in fact, the proper operation of a plasma armature rail gun. The limit is a result of the back-emf as the plasma pushes itself through the magnetic field within the bore; similar to the operation of a MHD generator. Ideally, the maximum velocity can be determined from the electric field between the rails divided by the magnetic field, at the location of the plasma; U
_max
= E/B. With the proper power conditioning methods to cause B to decline faster than E as the projectile moves to the end of the barrel, the muzzle velocity can be increased.