General formulas for the adiabatic propagation velocity of the normal zone

The influence on the propagation velocity of the normal zone of four phenomena was investigated: (1) the temperature dependence of the specific heat and the thermal conductivity; (2) the current-sharing zone; (3) the electromagnetic diffusion of current through a possible superstabilizer; and (4) the thermal diffusion through a possible insulator. At the beginning, these influences were studied independently of each other. In all cases, after a model of the particular phenomenon was created, the equations of thermal and electromagnetic behavior were solved analytically and the expressions for the propagation velocity obtained. These expressions were then put into nondimensional forms, which have allowed four correction factors to be defined that take into account the influences studied, and depend only on one or two nondimensional parameters. Subsequent studies were made to investigate how to combine these correction factors to obtain general formulas for the velocity, taking into account a part or all of these influences. A review is presented of these formulas, which are of interest for the superconducting windings where the heat transfer to helium can be neglected on the time scale of the quench process.>