Three-dimensional eddy-current calculation using loop variables to represent magnetic vector potential in conducting regions

A method for the calculation of fully three-dimensional electromagnetic fields is presented. The continuous field problem is modelled by a network representation. Solution of the field is performed in terms of a scalar magnetic potential in nonconducting regions. In conductors the curl v curl A equation is solved by a loop variable method for the magnetic vector potential alone. No scalar is required in conducting regions. As in previous network methods, the new method is derived in terms of a minimum independent set of discrete variables, so that the field solution is unique. The uniqueness of the curl v curl A equation has always provoked discussion, and so this is examined in detail. It is shown how nonuniqueness is manifested in the discrete linear simultaneous equations. The methods commonly used for ensuring uniqueness are also examined, and it is shown that, with a clear understanding of the conditions required for uniqueness, it is always possible to guarantee a unique solution, as in the network methods. The new method has the advantage over the existing network methods in that it only requires a single field subdivision. It is also very simple to use and it should give accurate results, because, in the absence of a scalar in the conducting region, there is no cancellation problem.