Some exact solutions for electrothermal breakdown

Exact solutions for electrothermal breakdown have been given by H.J. Wintle (1981) for the case of a DC voltage between plane parallel thermally conducting electrodes. Wintle´s solutions require specific functional dependence on temperature for both electrical and thermal conductivities, and he gives three pairs of suitable functions. In the present work, one of Wintle´s models is chosen to extend the exact solutions to coaxial cylinders and concentric spheres. The boundary conditions used are either a thermally insulating inner electrode and a thermally conducting outer electrode, or both electrodes thermally conducting. For a thermally insulating center electrode, and an electrode radius ratio of 5, the field distorts to an almost constant value for a voltage that is 90% of critical; for a voltage that is 99% of critical, the field at the outer electrode is 10 times the value of the field at the inner electrode