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 I in a perpendicular magnetic field ${\mathit{H}}_{\mathit{a}}$. Constant critical current density ${\mathit{j}}_{\mathit{c}}$ 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 ${\mathit{H}}_{\mathit{a}}$ and I; the initial deviation from a linear magnetic moment is cubic in ${\mathit{H}}_{\mathit{a}}$; 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 ${\mathit{H}}_{\mathit{a}}$ or I is reversed, j falls below ${\mathit{j}}_{\mathit{c}}$ 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.