Magnetic hysteresis of the critical current density in ceramic superconductors modelled as two-dimensional series-parallel Josephson junction array within the intragranular flux-trapping model

A model which takes into account a two-dimensional series-parallel array of Josephson junctions and the magnetic flux trapped in the grains, has been employed to obtain a better agreement between theory and experimental data than in the case of a classical single parallel Josephson junctions array for HTC ceramics. It was found that the theoretical J(B-a) dependences both series-parallel and parallel array Josephson junctions in increasing applied magnetic field (virgin curve) are very similar, but there is an sizable difference in decreasing applied magnetic field (returning curve). The normalized critical current density J(c)(B-a)/J(c)(0) of a series-parallel array is smaller than in a parallel array. This effect is interpreted in terms of a proper hysteretic behavior of the series parallel array of Josephson junctions just when the intragranular flux-trapping model is considered.