Eddy currents in MRI gradient coils configured by rings and patches

In this paper the current distribution in a set of parallel rings and patches, called islands, positioned at the surface of a cylinder, is investigated. The current is driven by an external applied source current. The islands are rectangular pieces of copper (patches) placed in parallel between the rings. The eddy currents in the islands induce currents in the rings that vary in the tangential direction. From the quasi-static Maxwell equations, an integral equation for the current distribution in the strips is derived. The Galerkin method, using global basis functions, is applied to solve this integral equation. It shows fast convergence. The global basis functions are built up of Legendre polynomials in axial direction and 2p-periodic trigonometric functions in tangential direction. The Legendre polynomials efficiently cope with the singularity of the kernel function of the integral equa- tion. Explicit numerical results are shown for three configurations. Besides the current distributions, the resistance and self-inductance of the three systems of rings and islands are computed. The resulting tool can be used in the design of realistic gradient coils. Keywords: MRI-scanning, Eddy currents, Patches, Legendre polynomials, Gradient coils