A legendre polynomial BEM for axisymmetric coil systems including Iron

The scalar potential of any system of axisymmetric conductors can be expressed as a Legendre polynomial expansion, and this provides an efficient and convenient method for computing the field variables. A method is presented for augmenting the expansion coefficients to include the effects of iron of constant permeability on the system. The approach is based on the boundary element method (BEM). As well as giving physical insight into the effects of the iron, the use of the coefficients circumvents the problem of expensive field retrieval. Numerical accuracy is assessed by considering two geometries for which an exact solution is known.