Electric railgun 3D modeling: computation of eddy currents and Lorentz force

In order to arrive at a three dimensional computer simulation of the electric arc, the electric railgun has been adopted as a simple model. The projectile representing the arc is a solid conductor moving between two parallel electrodes supplied by direct current. To accurately describe the problem, a three dimensional formulation that takes into account the eddy currents and the velocity, is required. Within the finite element method, a formulation based on a current vector potential is adopted because it enforces the conservation of the current which is here the origin of the force acting on the projectile. The results show the influence of the velocity on the eddy currents as well as on the Lorentz force. Eddy currents are mostly located in the rails near the contact. While in the magnetostatic case, the Lorentz force acting on the projectile is in good agreement with hand calculations of the loop effect, the current density is strongly affected by the velocity of the projectile.