Surface Coil Winding Profile for Obtaining a Uniform Magnetic Field inside a Spheroidal Body

TL;DR

This paper derives exact surface coil winding profiles for prolate and oblate spheroids to generate uniform magnetic fields inside, improving design methods for applications like MRI.

Contribution

It provides corrected and reorganized derivations of surface coil winding profiles for spheroids, enhancing the accuracy of magnetic field uniformity.

Findings

Derived exact winding profiles for spheroids

Corrected previous derivations in literature

Facilitates uniform magnetic field generation in spheroidal bodies

Abstract

Uniform magnetic field generation is one of the key issues in many physical applications; such as magnetic resonance imaging, magnetic probs etc. There are many ways to obtain highly homogeneous fields. For instance, ellipsoidal bodies - and in special, spheroids - naturally maintain uniform magnetic field inside their bodies, without any need for shimming. Thanks to their rotational symmetry in addition, spheroids are easier to produce and handle, and therefore deserve more emphasis. However, creating a uniform magnetic field inside a spheroid is only possible via maintaining certain current profiles on its surface. In this paper we have derived exact surface coil winding profiles for both prolate and oblate spheroids by reorganizing state of the art derivations in the literature and correcting them whenever necessary.