Consideration on appearance and disappearance of energy in superconductors during change in external magnetic field

When flux lines are displaced in a superconductor upon an increase in external magnetic field, the energy penetrating the superconductor is larger than the increase in magnetic energy. In some cases, the energy coming out of a superconductor is larger than the decrease in magnetic energy when the magnetic field is decreased, indicating the appearance of energy. These differences between the penetrating energy and the change in magnetic energy can be explained as a work done by the driving force against the pinning force that determines the magnetic flux distribution in the superconductor. The disappeared energy is dissipated or absorbed as an increase in the pinning energy. This indicates that the Maxwell theory is comprehensive also for electromagnetic phenomena in superconductors. The displacement of flux lines is also examined for the force-free state established in a current-carrying superconductor in a parallel magnetic field. A similar difference in energy suggests the existence of a generalized driving force, i.e., a driving torque, since the Lorentz force is zero in this state. This clearly shows that the flux cutting event cannot be realized, since it is based on the magnetic interaction and the penetrating energy cannot be absorbed.

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