Skin and heating effects of railgun current

The authors present a calculation in a simplified geometry for the current distribution in the rails of a railgun, taking into account the motion of the armature and the time variation of the current. Closed-form, asymptotic results for the current density are obtained for arbitrary time-dependent currents and velocities, in the limit in which the length scale k₀^-1 is small, where k₀=(μσν), σ is the electrical conductivity of the rails, and ν is the speed of the armature. Because of eddy-current effects the rail current may reverse in portions of the rails when the total current decreases. The current is used as a source of Joule heating to find the temperature distribution in the rails. The heat diffusivity is negligible. Numerical results concerning melting are given