The electromagnetic response of superconducting tapes exposed to transport currents and/or applied magnetic fields is the key issue for electric power application of superconducting tapes. In this article, theoretical expressions on the current distributions, magnetic-field distributions, and ac losses of superconducting tapes are presented. Those expressions are derived on the basis of Bean's critical state model, and the thickness/width ratio of the superconducting layers is regarded as an infinitesimal. The analytical expressions for assembled conductors using superconducting tapes (i.e., stacks, coplanar arrays, and polygonally arranged tapes) are also presented.
Theories on the summation of randomly directed individual pinning forces to estimate the pinning force density are described based on the historical understanding of the pinning phenomena. The statistical theory clarified that the non-zero pinning force density is closely associated with the hysteresis nature of the pinning loss. The result of the dynamic theory was found to reduce to that of the statistical theory in the static limit, indicating the ergodic nature of random systems. However, the two theories failed to explain the experimental result that the threshold value of elementary pinning force to bring about non-zero pinning force density does not actually exist. Larkin and Ovchinnikov showed that the statistical summation theory assuming the long-range order of flux line lattice is not correct because of the finite pinning correlation length. However, since the pinning force density is quite simply estimated using the concept of collective pinning in the Larkin-Ovchinnikov theory, more exact theoretical estimation was needed. Next, the coherent potential approximation theory was proposed based on the mean field theory for random systems. In this theory it was shown that the threshold pinning force is not zero but always smaller than the elementary pinning force. Thus, the threshold problem was actually resolved and it was shown that the pinning loss is of a hysteresis nature even for very weak pinning centers. Observed pinning force density is compared with the predictions of the Larkin-Ovchinnikov theory and the coherent potential approximation theory.