Type-II-superconductor strip with current in a perpendicular magnetic field.

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 [ital I] in a perpendicular magnetic field [ital H][sub [ital a]]. Constant critical current density [ital j][sub [ital c]] is assumed. The exact solutions reveal interesting features of this often realized [ital 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 [ital quadratic] in [ital H][sub [ital a]] and [ital I]; the initial deviation from a linear magnetic moment is [ital cubic] in [ital H][sub [ital a]]; the hysteresis losses are proportional to the [ital fourth] power of a small ac amplitude; the current density [ital j] is [ital 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 [ital H][sub [ital a]] or [ital I] is reversed, [ital j] falls below [ital j][sub [ital c]] [ital everywhere], thus stopping flux creep effectively; the Lorentz force can drive the vortices uphill'' againstmore » 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.« less