Field distributions of arbitrary-shaped magnetic domains calculated by two-dimensional discrete Fourier series

A two-dimensional discrete Fourier series method has been used to calculate the field distributions of arbitrary cylindrical-shaped magnetic domain arrays. In the present method there is generated a scalar magnetostatic potential φ(r), in discrete Fourier series form, which is related to the specified distribution of magnetic dipole densities by Poisson's equation. The magnetic field strength is then derived from the gradient of the scalar magnetostatic potential, using the orthogonal properties of Fourier series to determine the unknown coefficients. A program has been prepared and numerical results are presented. Calculated results comparewell with known results for a specific lattice of magnetic bubble domains, a 24 μm × 41.57 μm hexagonal array.