Modeling of Critical Current Density of Bulk High $T_c$ Superconductors

Magnetic field dependence of critical current density $(J_{c})$ of $ErBa_2Cu_3O_y$ thick film "Er-123" and melt textured $GdBa_2Cu_3O_y$ bulk "Gd-123" at liquid nitrogen temperature is reported. Gd-123 exhibits a usual peak effect at magnetic fields around 2 T, while $J_{c}$ of the Er-123 thick film continuously decreases with increasing field. The model of thermally activated flux motion was adopted to fit the critical current density of both Gd-123 and Er-123 materials. It was found that the critical current density of both types of the high $T_{c}$ materials could be modeled by the model of thermally activated flux motion utilizing a combination of two functions; one increasing and another one decreasing with field.