Behavior of Superconducting Coil Subjected to Steady Local Heating within the Windings

Abstract

The steady-state heat conduction equation in a nonisotropic solid is solved for the relationship between local heat imput, the size of the heated region and the Joule heating in the resultant normal region. The results are used to derive the steady terminal voltage-current characteristics of a superconducting coil with heat generation within the windings. These terminal characteristics exhibit both a positive as well as a negative slope of the voltage versus current curve. A map of the expected behavior of a current carrying superconducting coil with heat generation in the windings shows that the coil can do one of three things: (1) remain fully superconducting; (2) operate in a stable manner with a nonpropagating normal region; (3) go fully normal (quench). The analytical results are compared with measurements taken with a noninductive and an inductive coil. The measured terminal characteristics as well as over-all coil behavior agreed well with the result derived analytically.