On effects of superelectron inertia and flux-quantization in moving deformable superconductors

Abstract

Within the framework of the generalized Galilean relativity, the paper formulates electrodynamic behaviors of moving deformable superconductors at the magneto-quasi-static approximation. It is shown that the well-known Minkowski theory for moving media cannot be simply used to model moving deformable superconductors since the commonly used hypothesis that macroscopic electromagnetic properties of deformable media in instantaneous rest-frames are unaffected by accelerations is not appropriate for superconductors even at low velocity and low acceleration approximation. Different from the Minkowski theory and classical London’s approach, the formulation in the paper takes explicitly into account the effect of inertia of superelectrons in moving deformable superconductors by generalizing the concept of instantaneous rest-frame to include non-inertial frames of reference. With the aid of the new model, formulated to be relativistically consistent within the generalized Galilean relativity, some macroscopic electrodynamic phenomena of moving deformable superconductors are studied. It is shown that superconductors not only exhibit the well-known features of the zero-dc resistance, the Meissner effect, and the macroscopic quantum behavior, but also have a unique feature on their macroscopic electromagnetic response to the non-uniform motion and/or local dynamic deformation of the superconducting media. Effects of moving multiply connected superconductors are studied, the result of which indicates the possible modification of the well-known flux-quantization relation due to the non-uniform motion of the superconducting media. Possible effects of inertia of flux lines in type-II superconductors in the mixed state, operating at microwave frequencies, are also formulated and analyzed quantitatively in comparison with Bean’s critical-state model.