Scalar finite element solution of magnetic fields in axisymmetric boundaries

Many magnetic field problems involve axisymmetric boundary shapes, but excitations of an essentially arbitrary nonsymmetric nature. Often the current-carrying coils or conductors occupy a space sufficiently small to be considered as thin sheets or filaments. In such cases the magnetic field may be formulated in terms of a scalar potential, with inhomogeneous boundary conditions that account for the presence of current sheets. Any asymmetry of these boundary values can be accommodated by expanding the boundary condition contribution to the field equations as a series and solving term by term. The inhomogeneous boundary conditions which thus appear are of a binary nature, i.e., they express relationships between potentials at distinct points. Such conditions are readily included in a finite element model. The techniques for so doing are developed in detail, and a practical example of their application is given by way of illustration.