# Superconductor strip in a closed magnetic environment: exact analytic representation of the critical state

## TL;DR

This paper derives an exact analytical model for the critical state of a superconductor strip within a high-permeability magnetic cavity, revealing flux penetration reduction in small cavities and enabling analysis of various geometries.

## Contribution

It provides the first exact analytic solution for a superconductor strip in a magnetic cavity, allowing for precise current and flux distribution analysis.

## Key findings

- Flux penetration is significantly reduced in small cavities.
- The model enables analysis of different cavity geometries via conformal mapping.
- Exact current profiles can be obtained for various configurations.

## Abstract

An exact analytic representation of the critical state of a current-carrying type-II superconductor strip located inside a cylindrical magnetic cavity of high permeability is derived. The obtained results show that, when the cavity radius is small, penetration of magnetic flux fronts is strongly reduced as compared to the situation in an isolated strip. From our generic representation it is possible to establish current profiles in closed cavities of various other geometries too by means of conformal mapping of the basic configuration addressed.