Analysis of Eddy Currents in a Gradient Coil

Abstract

To model the z-coil of an MRI-scanner, a set of circular loops of strips is shown in {[}4] to be a good approximation. This ring model yields a current distribution that only depends on the axial direction. In order to take the dependence of the tangential direction into account, we introduce rectangular pieces of copper (called islands) in between the rings. In this paper the current distribution in a set of rings and islands, driven by an external applied source current is investigated. The source, and all excited fields, are time harmonic, and the frequency is low enough to allow for a quasi-static approximation. Due to induction eddy currents occur which form the so-called edge-effect. The edge-effect depends on the applied frequency and the distances between the strips, and causes higher impedances. 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. Using Legendre polynomials for the axial direction turns out to be an appropriate choice. It provides a fast convergence, so only a very small number of Legendre polynomials is needed.