Comparison of magnetic field uniformities for discretized and finite-sized standard $\cos\theta$, solenoidal, and spherical coils

TL;DR

This paper compares the magnetic field uniformities of discretized, finite-sized $ ext{cos} heta$, solenoidal, and spherical coils, revealing that spherical coils can achieve required uniformities with smaller volumes.

Contribution

It provides a comparative analysis of standard coil types, highlighting the efficiency of spherical coils in achieving uniform magnetic fields with minimal size.

Findings

Spherical coils can require significantly less volume than $ ext{cos} heta$ and solenoidal coils for the same uniformity or gradient.

The study offers insights into coil design choices for experiments needing precise magnetic field control.

Discretized and finite-sized coil performance varies notably among standard types.

Abstract

A significant challenge for experiments requiring a highly uniform magnetic field concerns the identification and design of a discretized and finite-sized magnetic field coil of minimal size. In this work we compare calculations of the magnetic field uniformities and field gradients for three different standard (i.e., non-optimized) types of coils: $\cos\theta$, solenoidal, and spherical coils. For an experiment with a particular requirement on either the field uniformity or the field gradient, we show that the volume required by a spherical coil form which satisfies these requirements can be significantly less than the volumes required by $\cos\theta$ and solenoidal coil forms.