Simple analysis of off-axis solenoid fields using the scalar magnetostatic potential: application to a Zeeman-slower for cold atoms

TL;DR

This paper presents a simple method to calculate off-axis magnetic fields of finite solenoids using scalar potential, applicable to designing devices like Zeeman slowers for cold atoms, without complex integrations.

Contribution

The authors introduce a straightforward approach to determine off-axis fields of finite solenoids using only axial field data, simplifying calculations in magnetostatics.

Findings

Method accurately predicts off-axis fields without integration.

Applicable to designing magnetic devices for cold atom experiments.

Educational examples demonstrate practical use of the approach.

Abstract

In a region free of currents, magnetostatics can be described by the Laplace equation of a scalar magnetic potential, and one can apply the same methods commonly used in electrostatics. Here we show how to calculate the general vector field inside a real (finite) solenoid, using only the magnitude of the field along the symmetry axis. Our method does not require integration or knowledge of the current distribution, and is presented through practical examples, including a non-uniform finite solenoid used to produce cold atomic beams via laser cooling. These examples allow educators to discuss the non-trivial calculation of fields off-axis using concepts familiar to most students, while offering the opportunity to introduce important advancements of current modern research.