Eddy currents in a transverse MRI gradient coil

A transverse gradient coil (x- or y-coil) of an MRI-scanner is modeled as a network of curved circular strips placed at the surface of a cylinder. The current in this network is driven by a time-harmonic source current. The low frequency applied allows for an electro-quasi-static approach. The strips are thin and the current is assumed to be uniformly distributed in the thickness direction. For the current distribution in the width direction of the strips, an integral equation is derived. Its logarithmically singular kernel represents inductive effects related to the occurrence of eddy currents. For curved circular strips of width much smaller than the radius of the cylinder one may locally replace the curved circular strip by a tangent plane circular strip. This plane geometry preserves the main characteristics of the transverse current distribution through the strips. The current distribution depends strongly on the in-plane curvature of the strips. The Petrov–Galerkin method, using Legendre polynomials, is applied to solve the integral equation and shows fast convergence. Explicit results are presented for two examples: a set of 1 strip and one of 10 strips. The results show that the current distributions are concentrated near the inner edges and that resulting edge-effects, both local and global, are non-symmetric. This behavior is more apparent for higher frequencies and larger in-plane curvatures. Results have been verified by comparison with finite-element results