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

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 Ha. Constant critical current density jc 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 Ha and I; the initial deviation from a linear magnetic moment is cubic in Ha; 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 Ha or I is reversed, j falls below jc 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.

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