Eddy currents in a gradient coil, modeled by rings and patches

The gradient coils of an MRI-scanner can be modeled by a surface current on a cylinder. A good approximation of the surface current in the z-coil is obtained from a set of rings and patches on the cylinder. In this paper, an integral equation is derived for the current distribution. To solve this integral equation, the Galerkin method is applied, using global expansion functions. We show that Legendre polynomials are an appropriate choice for the expansion functions. They provide fast convergence. So, only a restricted number of Legendre polynomials is needed. Moreover, an analytical solution is derived, which results in efficient simulations.