Theory of flux cutting and flux transport at the critical current of a type-II superconducting cylindrical wire

TL;DR

This paper develops a comprehensive critical-state theory for type-II superconductors that includes flux cutting and flux transport, explaining magnetic and current distributions at critical current and their dependence on vortex dynamics.

Contribution

It extends the elliptic critical-state model to incorporate flux cutting and flux transport, providing a detailed vortex dynamics framework based on nonlinear resistivities.

Findings

Flux cutting efficiency affects internal magnetic flux and magnetic moment.

Critical current depends on vortex stability under combined flux cutting and transport.

Model explains the relationship between flux cutting and depinning currents.

Abstract

I introduce a critical-state theory incorporating both flux cutting and flux transport to calculate the magnetic-field and current-density distributions inside a type-II superconducting cylinder at its critical current in a longitudinal applied magnetic field. The theory is an extension of the elliptic critical-state model introduced by Romero-Salazar and Perez-Rodriguez. The vortex dynamics depend in detail upon two nonlinear effective resistivities for flux cutting (\rho_\parallel) and flux flow (\rho_\perp), and their ratio r = \rho_\parallel/\rho_\perp. When r < 1, the low relative efficiency of flux cutting in reducing the magnitude of the internal magnetic-flux density leads to a paramagnetic longitudinal magnetic moment. As a model for understanding the experimentally observed interrelationship between the critical currents for flux cutting and depinning, I calculate the forces on a helical vortex arc stretched between two pinning centers when the vortex is subjected to a current density of arbitrary angle \phi. Simultaneous initiation of flux cutting and flux transport occurs at the critical current density J_c(\phi) that makes the vortex arc unstable.