Magnetic flux shock waves and hydrodynamic dendritic instability in type-II superconducting film

In recent experiments, trapped magnetic flux is initially generated by abrupt laser heating of a strip of a type-II superconducting film subjected to a weak magnetic filed. We study herein the non-equilibrium penetration of a magnetic flux into the Meissner state area. A sharp shock wave (SW) front of the magnetic induction is formed due to the singularity of the resistivity at the transition from the mixed to the normal state. In vicinity of the front, superconductivity is suppressed by strong screening currents. The magnetic shock wave front and the temperature profile are moving with a constant velocity determined by the joule heat produced by the electric current in the normal domain at the flux front and the film thickness. It is shown that tangential instability is responsible for a crush of the straight front. For a sufficiently small heat diffusion constant, an ultra-fast dendrite-shaped magnetic flux structure is predicted, while for large thermal diffusion constant the shock wave front is found to be stable.