Magnetic flux penetration into high-temperature superconductors in the vortex liquid state under the blow-up conditions

The problem of magnetic field penetration into a type-II high-temperature superconductor that is in the weakly pinned vortex-liquid phase is considered. A magnetic field on the superconductor boundary rises with time in the blow-up regime. A model hydrodynamic equation describing the magnetic induction distribution in the vortex-liquid phase for thermomagnetic motion of the flux is derived. Analytical expressions for the depth and rate of magnetic field penetration into the superconductor are found. It is demonstrated that these quantities depend on parameters of the problem: index of power n in the boundary regime characterizing the penetration rate of vortices into the superconducting half-space and a parameter describing the effect of random pinning forces and thermal fluctuations on the magnetic flux distribution.