Electromagnetics close beyond the critical state: thermodynamic prospect

TL;DR

This paper develops a thermodynamic theory for the electromagnetic behavior of type-II superconductors near and beyond the critical state, incorporating vortex dynamics and anisotropic effects.

Contribution

It introduces a thermodynamic framework based on free energy and entropy production to describe superconductor responses, including transient and steady states, with a numerical implementation.

Findings

Critical states can be obtained as diffusive final profiles under external conditions.

The model accounts for vortex dynamics and anisotropic critical currents.

Numerical results include voltage generation and magnetic relaxation in superconductors.

Abstract

A theory for the electromagnetic response of type-II superconductors close beyond the critical state is presented. Our formulation relies on general physical principles applied to the superconductor as a thermodynamic system. Equilibrium critical states, externally driven steady solutions, and transient relaxation are altogether described in terms of free energy and entropy production. This approach allows a consistent macroscopic statement that incorporates the intricate vortex dynamic effects, revealed in non-idealized experimental configurations. Magnetically anisotropic critical currents and flux stirring resistivities are straightforwardly included in three dimensional scenarios. Starting from a variational form of our postulate, a numerical implementation for practical configurations is shown. In particular, several results are provided for the infinite strip geometry: voltage generation in multicomponent experiments, and magnetic relaxation towards the critical state under applied field and transport current. Explicitly, we show that for a given set of external conditions, the well established critical states may be utterly obtained as diffusive final profiles.