Coil shape design using the quasi-Newton algorithm

The problem to find the shape of the coil to obtain the required magnetic field in a given area is studied. It is assumed that the coil has cylindrical symmetry, and that the current density in the coil is fixed. Two cases of the shape of the target area are considered. When the target area is located on the coil axis, the problem can be simplified by using analytical formula for the magnetic field. In a general case when the target area is located outside the coil axis numerical integration is used to compute magnetic field in the target area. The quasi-Newton method is used to solve the resulting nonlinear optimization problem. It is shown that this optimization method works properly in both cases. Several design examples are presented.