# 3D magnetization currents, magnetization loop, and saturation field in superconducting rectangular prisms

## TL;DR

This paper systematically analyzes 3D magnetization currents in rectangular superconducting prisms using numerical modeling, providing new insights into current paths, saturation fields, and practical analytical fits for various aspect ratios.

## Contribution

It introduces a high-degree variational numerical model for magnetization currents in rectangular prisms and offers a practical analytical fit for different aspect ratios.

## Key findings

- Magnetization currents exhibit 3D bending below saturation.
- The saturation magnetic field is characterized with a new relevant definition.
- Current paths are non-rectangular and show flux cutting effects.

## Abstract

Bulk superconductors are used in both many applications and material characterization experiments, being the bulk shape of rectangular prism very frequent. However the magnetization currents are still mostly unknown for this kind of three dimensional (3D) shape, specially below the saturation magnetic field. Knowledge of the magnetization currents in this kind of samples is needed to interpret the measurements and the development of bulk materials for applications. This article presents a systematic analysis of the magnetization currents in prisms of square base and several thicknesses. We make this study by numerical modeling using a variational principle that enables high number of degrees of freedom. We also compute the magnetization loops and the saturation magnetic field, using a definition that is more relevant for thin prisms than previous ones. The article presents a practical analytical fit for any aspect ratio. For applied fields below the saturation field, the current paths are not rectangular, presenting 3D bending. The thickness-average results are consistent with previous modeling and measurements for thin films. The 3D bending of the current lines indicates that there could be flux cutting effects in rectangular prisms. The component of the critical current density in the applied field direction may play a role, being the magnetization currents in a bulk and a stack of tapes not identical.