A method to determine analytically the coil arrangement for a required magnetic field is studied, when the scalar potential of the magnetic field is given. The design process is as follows : a current potential or a stream function i is calculated at first on an adequate surface on which currents flow, and, as next stage, the current potential I is approximated with linear segments along grad (I), in order to convert the surface current to lumped coils, where the current potential I is defined as I=φ
1-φ
2 and φ
2 is the potuatial outside the surface and satisfies the boundary condition on the surface with φ
1.
The scalar potential φ due to the current potential I on the surface S is written as ψ=μ
0/4π∫I grad (1/r) ds.
For thick coil, a number ofsurface must be taken into account, on which current potentials are defined.
The examples are shown for cylindrical-, SPherical-, prolate spheroidal- and troidal co-ordinate.
View full abstract