Flux Pinning Characteristics

Chapter 7 covers the summation theories that predict the global pinning force density as a function of the elementary pinning force and number density of pinning centers. First, the statistical theory of Labusch is discussed. This theory predicted that the pinning force density has non-zero value for the elementary pinning force above the threshold value. This condition is identical with the condition of the hysteresis loss, and this theory is consistent with the dynamic theory. However, this theoretical prediction is significantly contradictory to experiments. Although the fundamental threshold problem was resolved by Larkin and Ovchinnikov, who showed that a long-range order does not exist in the flux line lattice, quantitative disagreements are sometimes found between their theory and experiments. In the coherent potential approximation theory the statistical method is used with taking into account the lack of long range order, and the compatibility of the threshold problem and the instability of flux motion is obtained. A detailed comparison is made between the theories and experiments. The saturation phenomenon observed in metallic superconductors at high fields is also introduced. The pinning potential energy important for the analysis of flux creep is also derived.