Tradeoff between Efficiency and Melting for a High-Performance   Electromagnetic Rail Gun
  We estimate the temperature distribution in the rails of an electromagnetic rail gun (EMG) due to the confinement of the current in a narrow surface layer resulting from the skin effect. In order to obtain analytic results, we assume a simple geometry for the rails, an electromagnetic skin effect boundary edge that propagates with the accelerating armature, and a current carrying channel controlled by magnetic field diffusion into the rails. We compute the temperature distribution in the rails at the time that the armature leaves the rails. For the range of exit velocities, from 1500 m/s to 5000 m/s, we find the highest temperatures are near the gun breech. After a single gun firing, the temperature reaches the melting temperature of the metal rails in a layer of finite thickness near the surface of the rails, for rails made of copper or tantalum. We plot the thickness of the melt layer as a function of position along the rails. In all cases, the thickness of the melt layer increases with gun velocity, making damage to the gun rails more likely at higher velocity. We also calculate the efficiency of the EMG as a function of gun velocity and find that the efficiency increases with increasing velocity, but only if the length of the gun is sufficiently long. The thickness of the melted layer also decreases with increasing rail length. Therefore, there is a tradeoff: for rails of sufficient length, the gun efficiency increases with increasing velocity but the melted layer thickness in the rails also increases. 
William C. McCorkle, Thomas B. Bahder