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

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.