Dynamic resistance in a slab-like superconductor with J_c(B) dependence

The dynamic resistance in a slab-like superconductor is calculated, taking into account a field-dependent critical current density. In superconductors carrying DC transport current in an AC external magnetic field, the dynamic resistance causes a transport loss which depends on the amplitude and frequency of this field as well as on the transport current. This resistance is calculated analytically in a critical-state model applied to a superconducting slab in a parallel field. The field has a general periodic time dependence and for the superconductor a relation between critical current and momentary magnetic field as in the Kim model is assumed. The dynamic resistance appears only at field amplitudes larger than the so-called threshold field, which depends on the transport current. The model predictions are compared with experimental results obtained with a Bi-2223/Ag tape at liquid-nitrogen temperature. At small field amplitude and at low transport current, the derived model predicts the observed dependence of dynamic resistance on field amplitude, field frequency and transport current. For a larger field amplitude and simultaneous high transport current, the resistance is found to be larger than the model predicts. This is probably due to the not completely slab-like geometry and/or to a different field dependence of the critical current density in a high AC field.