Prolate harmonics and axisymmetric conductor systems

A new method is described for calculating magnetostatic field variables of axisymmetric conductor systems, by expanding them as a series of prolate spheroidal harmonics. The authors include, as a special case, the standard spherical harmonic method of M.W. Garrett (1951, 1961). The comparative advantages and disadvantages of the prolate harmonic method and the spherical harmonic method are examined. A simple measure of convergence is derived for the prolate spheroidal harmonic method and confirmed for a conductor of rectangular cross section. The limitations of the prolate harmonic method are discussed