Boundary-Integral method for calculating poloidal axisymmetric AC magnetic fields

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.