Boundary-Integral method for calculating poloidal axisymmetric AC magnetic fields

Abstract

This paper presents a boundary-integral equation (BIE) method for the calculation of poloidal axisymmetric magnetic fields applicable in a wide range of ac frequencies. The method is based on the vector potential formulation, and it uses the Green's functions of Laplace and Helmholtz equations for the exterior and interior of conductors, respectively. The paper focuses on a calculation of axisymmetric Green's function for the Helmholtz equation which is both simpler and more accurate than previous approaches. We use three different techniques for calculation of Green's function, depending on the parameter range. For low and high ac frequencies, we use a power series expansion in terms of elliptical integrals and an asymptotic series in terms of modified Bessel functions of second kind, respectively. For the intermediate frequency range, we use Gauss-Chebyshev-Lobatto quadratures. We verify the accuracy of the method by comparing its results with the analytical solution for a sphere in a uniform external ac field. We illustrate the application of the method by analyzing a composite model inductor containing an external secondary circuit.