Investigation of the normal zone along a layer of thermally insulated superconductors

During the transition of a superconducting winding, most of the dissipated power heats the conductors causing the propagation of the normal zone. Some part of the dissipated power is also transferred into the surrounding insulation. Due to the weak thermal conductivity of the insulating material, a certain amount of time is required for this heat to diffuse. The propagation front thus carries with it a wake of thermal diffusion, which raises the question of how much insulator should be taken into account in calculating the propagation velocity. Postulating the existence of such a velocity, we derive a model for the thermal behavior of an insulated layer of composite multifilament superconductors during the transition phase. The two-way Laplace transform is used to solve the equations for temperature diffusion/propagation in the conducting and insulating media. This yields an implicit equation for propagation velocity, which is then written in a dimensionless form. We next investigate two limiting cases, deriving in each case a simplified formula for propagation velocity. Last, we complete the analytical solution of our problem by computing the originals of the temperature profiles