Thermal instability during an electrical wire explosion

The development of thermal instabilities during an electrical wire explosion is analyzed in the present work based on the methods of small perturbation theory. For two cases, with and without allowance for motion, the dispersion equations are derived that describe a relationship between the instantaneous buildup increment and the axial wave vector component. It is demonstrated that the thermal instabilities are always formed during electrical explosion, irrespective of the explosion mode. There are three destabilizing factors leading to the development of the thermal instabilities: a temperature rise, an increase in the specific resistance with increasing temperature, and an increase in the specific resistance with decreasing density. The critical value of current density below which the sausage instabilities grow faster than the thermal ones and above which, on the contrary, the thermal instabilities are dominant can be found for each metal.