Sensors measure magnetic field components, and the measured fields are used to calculate and estimated transverse position of a longitudinal electric current flowing as an electric discharge across a discharge gap. Based on the estimated position, and according to a selected transverse trajectory or distribution of the estimated discharge position, magnetic fields are applied transversely across the discharge gap so as to control or alter the estimated discharge position. Inventive apparatus and methods can be employed, inter alia, during operation of a vacuum arc furnace.