pr] is the magnetic scalar potential of the primary magnetic field.

Den, "A new method using Biot-Savart law to derive magnetic scalar potential notation," Journal of Chongqing Institute of Civil Engineering and Architecture, Vol.

NPx1] are the magnetic scalar potentials required on the boundary, and [[phi].

0] is the field due to source currents and can be easily computed by Biot-Savart-Laplace relation, and [phi] is reduced

magnetic scalar potential.

With these solutions, the magnetic scalar potential expression in each region can be expressed in a Fourier series.

According to (39) and (40), the magnetic scalar potential distributions at both the inner and outer air-gaps can be calculated as shown in Figure 5 in which the effects due to PMs on the high-speed and low-speed movers are determined separately.

and, in an analogous manner, for the expansion of the magnetic scalar potential in (50), we can write

In this paper, though, we provide a more general definition for the discrete electric and magnetic scalar potentials because the normal component of the current expanded with the div-TO basis functions is not confined in the facets arising from the discretization.

A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing

magnetic scalar potentials and eddy currents.