Eddy currents in a gradient coil, modelled as circular loops of strips

Abstract

The z-coil of an MRI-scanner is modelled as a set of circular loops of strips, or rings. Due to induction, eddy currents occur which lead to the so-called edge-effect. The edge-effect depends on the applied frequency and the distances between the strips, and affects the impedances. The current distribution in the rings is determined and from that the total resistance and self-inductance of each ring separately, all as far as possible by analytical means. From the Maxwell equations, an integral equation for the current distribution in the strips is derived. The Galerkin method is applied, using global basis functions, to solve this integral equation. It turns out that Legendre polynomials as basis functions are an appropriate choice. They provoke an analytical expression for the integrals with a singular kernel function, and bring about a fast convergence; only a very restricted number of Legendre polynomials is needed.