Hysteretic internal fields and critical currents in polycrystalline superconductors

The transport critical current Jc in a polycrystalline superconductor is a hysteretic function of applied magnetic field H0 due to flux trapping by grains. This effect has been observed by several groups and attempts have been made to calculate the intergranular field Hi as a function of the applied H0 in terms of an effective geometrical demagnetization factor D. In general a first-principles calculation of D is very difficult, and furthermore, D is not constant but is itself a hysteretic function of H0 . We develop a self-consistent scheme to extract the D and Hi directly from the Jc(H0) data itself. Our model exploits the fact that there are two field ranges for which the demagnetizing field is a simple function of H0 . At low virgin fields, in the Meissner state, the susceptibility xv'21/4p is well defined, leading to a multiplicative correction: Hi5H0 /(1 1D4pxv). For fields that have returned from high values, a complete critical state is established and M is well defined—although xv is unknown. This leads to an additive correction: Hi5H0 2D4pM for the total field. By matching Jc data in increasing and decreasing fields that satisfy these special cases, it is possible to extract the relevant parameters of the problem without detailed knowledge of the demagnetization geometry. We use this model to analyze data measured on sintered YBa2Cu3O7 superconductive rods. © 1998 American Institute of Physics. @S0021-8979~98!03824-9#