A Z-gradient coil on spheroidal geometry

A well-defined analytical magnetic field pattern is of merit in various fields of technological applications, especially in magnetic resonance imaging (MRI). Since the field inherently depends on the geometrical form of its generator, it is essential to put forth a convenient current coil structure to obtain a specific field pattern. This article is about the mathematical formulation, design, and production of a special spheroidal coil generating a magnetic field that linearly changes along its solenoidal axis. We proved that a specifically designed air coil helically wound on a spheroid, induces a perfectly linear field gradient. We also showed that the characteristic field pattern does not suffer from any changes in the geometrical size of the coil.