Abstract
Current density, magnetic field, penetrated magnetic flux, and magnetic moment are calculated analytically for a thin strip of a type-II superconductor carrying a transport current I in a perpendicular magnetic field . Constant critical current density is assumed. The exact solutions reveal interesting features of this often realized perpendicular geometry that qualitatively differs from the widely used Bean critical state model: At the penetrating flux front the field and current profiles have vertical slopes; the initial penetration depth and penetrated flux are quadratic in and I; the initial deviation from a linear magnetic moment is cubic in ; the hysteresis losses are proportional to the fourth power of a small ac amplitude; the current density j is finite over the entire width of the strip even when flux has only partly penetrated; in thin films, as soon as the direction of the temporal change of or I is reversed, j falls below everywhere, thus stopping flux creep effectively; the Lorentz force can drive the vortices ‘‘uphill’’ against the flux-density gradient. These analytical results are at variance with the critical-state model for longitudinal geometry and explain numerous experiments in a natural way without the assumption of a surface barrier.
- Received 6 July 1993
DOI:https://doi.org/10.1103/PhysRevB.48.12893
©1993 American Physical Society