Abstract
We investigate the dynamics of interface between the normal state and the superconducting state when a type-I superconductor is quenched below its critical field Hc. A sharp interface is assumed, in which the magnetic fields obey diffusion equations in the normal part and satisfies the Gibbs-Thomson boundary condition at the interface. In a linear instability analysis, the interface is found to have Mullins-Sekerka instability when the fields are perpendicular to the interface perturbation; while if the interface perturbation is parallel to the magnetic fields, extra stable mechanism due to the bending energy is found. In the absence of surface tension, this problem also have Ivantsov type solutions. We further investigate the effect of temperature and find that in certain parameter regime, the interface can be both isothermal and constant-field contour. Relations to experiments are briefly discussed.