Spatially dependent global quantities associated with 2-D and 3-D magnetic vector potential formulations for foil winding modeling

A method is developed to take foil winding inductors into account in the frame of the magnetic vector potential magnetodynamic formulation, in 2-D and 3-D. The definition of the foil voltage as a continuous unidirectional spatially dependent global quantity enables to express the elementary foil circuit relations, relating currents and voltages. A convenient form of these circuit relations is developed and its continuous extension is shown to weakly define the constraints on currents peculiar to foil windings, i.e., allowing skin effect in the direction of the height of the foils while maintaining a constant current in each elementary foil.