Autowave dynamics of the magnetic flux in nonideal type-II superconductors with different current-voltage characteristics

An analysis was performed of the processes of penetration of a macroscopic electromagnetic field into superconducting media with different current-voltage characteristics induced by a variable external magnetic field or by carrier transport. It has been shown that even if a finite electrical voltage arises in the superconductor before the critical current is reached, the magnetic flux, as in the critical state model, penetrates into the superconductor at a finite rate as a characteristic electromagnetic wave. At its front, a special condition is fulfilled; namely, a smooth transition to the nonperturbed value of the strength of the electric field induced by an external perturbation. Formulas are given for the calculation of the penetration rate of the electromagnetic field into a superconductor. For corroboration of the formulated relationships, the study was compared with corresponding numerical calculations.