It seems to be believed that the critical current density is the essential factor which determines the pinning loss as described by the critical state model. However, this is not ture: the pinning loss is the essential factor which determines the critical current density in the dynamic pinning theory. The pinning loss of power is defined as an additional viscous loss of power due to the velocity fluctuation of the fluxons caused by pinning interactions. It is shown that the high velocity due to the unstable flux motion, which occurs when the fluxon drops in and jumps out of the pinning potential well, brings about the pinning loss power density that depends only on the pinning force density. This suggests that the flux motion is nearly reversible with extremely-low-loss power density deviating from the prediction of the critical state model if the flux motion is restricted within pinning potential wells. Such phenomenon is actually observed in multifilamentary wires with very-finr superconducting filaments thinner than the pinning correlation length.
The transport properties for in-field heat-treated monocore and multicore Bi2Sr2CaCu2O8 (Bi2212) tapes and multicore Bi2212 round wires were measured in detail. We found that the in-field heat-treatment enhances not only the critical current density Jc but also the n-value for all samples used in this study. These enhancements for the monocore tapes were more remarkable, compared in those of the multicore tapes and wires. Therefore the in-field heat-treatment is more effective for the Bi2212 tapes with a large core size. Microstructure observation shows that the grain size of the monocore tapes decreases as the result of in-field heat treatment. The analysis based on the percolation model related to the local Jc distribution suggests that the in-field heat-treatment increases the m-value, which determines the shape of the local Jc distribution and is related to the n-values. The two Jc distribution model can explain that the increases in n- and m-values are due to the decreases in the aspect ratio of the grains during in-field heat treatment.