Initial Behavior of an Exploding Wire

Abstract

The nonlinear circuit equations describing the initial phase of an exploding wire are considered. It is shown that the solution for any arbitrary variation of the wire resistance with the internal energy satisfying certain smoothness requirements can be represented by a single integral curve in the resistance—charge plane. Maclaurin series expansions of the current function and the logarithm of the resistance function for the case of linear variation of the wire resistance with the internal energy are presented in powers of the elapsed time after switch-on. The coefficients which appear in these expansions are obtained exactly and recurrently, using the basic circuit equations and the initial conditions during switch-on. The present results are compared with the approximate expressions described by F.D. Bennett.