The effect of the metal phase state on the growth of thermal instabilities in an electrically exploding conductor

Abstract

The thermal instabilities developing in electrically exploding conductors were analyzed using the methods of linear stability analysis. The analysis was performed for three regions of the phase diagram that represent a liquid, a two-phase mixture, and a metastable superheated liquid. It has been shown that for both a conventional and a metastable liquid there exist a certain minimum wavelength such that at shorter wavelengths, the instabilities are stabilized by heat conduction. For long wavelengths, the instantaneous growth rates of the instabilities are determined by the temperature derivative of the metal resistivity, whereas for short wavelength, they are determined by the derivative of the resistivity with respect to the material density and the time derivative of the temperature. For a two-phase mixture and a metastable liquid, the growth rates of short-wavelength instabilities may be more than two orders of magnitude greater in amplitude than the maximum growth rates for a conventional liquid.