A General Method for Calculating the External Magnetic Field from a Cylindrical Magnetic Source using Toroidal Functions

An alternative method is developed to compute the magnetic field from a circular cylindrical magnetic source. Specifically, a Fourier series expansion whose coefficients are toroidal functions is introduced which yields an alternative to the more familiar spherical harmonic solution or the Elliptic integral solution. This alternate formulation coupled with a method called charge simulation allows one to compute the external magnetic field from an arbitrary magnetic source in terms of a toroidal expansion. This expansion is valid on any finite hypothetical external observation cylinder. In other words, the magnetic scalar potential or the magnetic field intensity is computed on a exterior cylinder which encloses the magnetic source. This method can be used to accurately compute the far field where a finite element formulation is known to be inaccurate