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For a more accurate load analysis of the Homopolar Inductor Alternator (HIA), a magnetic vector potential analysis must be used which considers the nonlinearities of the iron and the actual current density fields. A nonlinear quasi-Poissonian partial differential equation, subject to the appropriate boundary conditions, is defined to solve for the vector potential in the middle cross section of the alternator. The partial differential equation and boundary conditions are transformed into a set of partial difference equations which are solved numerically by a successive line-overrelaxation method. The magnetic induction, flux distribution and volt-ampere characteristic are obtained for a 95 KVA, 208/115 V, 3400 Hz experimental alternator.