Scalar potential concept for calculating the steady magnetic fields and eddy currents

The concept of scalar potential has been used for magnetic field calculation in the USSR during the last decade. It is based on treating the eddy component of the magnetic field separately and calculating the potential field with the help of the scalar potential, by introducing imaginary magnetic charges. This method has been developed for digital calcula - tions of magnetic fields in various electromagnetic devices, by solving linear and nonlinear partial-differential equations through mathematical simulation. This paper presents the mathematical formulation of the method. It is advantageous to use the scalar potential method for two-dimensional eddy-current calculations because of the possibility to solve the equations just over the conductor surfaces. The general three-dimensional problem can be formulated in different ways. The scalar potential method is also used for the computer-aided analysis of eddy-current problems of conventional and superconducting electric machines.