On solving connexity problems within modeling massive conductors

This paper deals with the three‐dimensional modeling of massive conductors carrying a total imposed current and involving multiply connected regions. Both stationary motion and time harmonic eddy current problems are considered. The aim of the modeling is to determine the current distribution and the eddy current’s effects inside the conductor, as well as to calculate the Lorentz force acting on a conducting region. The choice of a suitable formulation based on solving the current vector potential T and the magnetic scalar potential φ is argued, then various methods for the restoration of the Ampere law in the multiply connected regions are presented. Two methods for calculating an auxiliary vector potential T₀ are applied in order to calculate the force acting on the armature of a railgun and the repulsion between the electrodes of a vacuum circuit breaker, then the results are compared.