  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.
