Expansion of the magnetic flux density field in toroidal harmonics

This study investigates the multipolar expansion of the magnetic flux density in toroidal harmonics, with the main purpose of identifying a valid procedure for the calculation of the multipole coefficients. Because of the analytical complexities introduced by the toroidal coordinates system, numerous verifications are necessary to validate the expressions of the magnetic flux density components. The methodology developed for the evaluation of the multipole coefficients is based on fitting procedures. The only requirement for the application of this technique is the knowledge of the magnetic flux density values (or of the scalar potential) in defined points of a toroidal shape surface. Furthermore, a possible numerical strategy is introduced for the acquisition of the magnetic flux density values on the points of the mentioned grid.