Analytical model for the dynamic resistivity of electrically-exploded conductors

A detailed model for the dynamic resistivity of an exploding conductor presents many difficulties. An electrically-exploded conductor undergoes significant hydrodynamic expansion as it is heated. Resistivity is a function of both the temperature and density of a conductor and realistic models for resistivity over the range of parameter space experienced by an exploding conductor are quite complex. See for example, the model of Lee and More (1984). Calculation of the hydrodynamic expansion of the conductor during and subsequent to the explosion is likewise dependent on detailed knowledge of the equation of state for the conductor in a range where few experimental data exist. A further complication is the strong magnetic field which couples the hydrodynamic expansion to the currents flowing in the expanding material. In spite of the difficulties, progress is being made on detailed modeling of fuses and exploding conductors (Lidemuth and co-workers, 1985). A simpler approach has proved to be quite useful for modeling the electrical behavior of exploding bridgewire and slapper detonators and for modeling the explosionss of large conductors exploded with large capacitor banks. In the work described here, a simple, empirical model was developed which can be expressed as a closed-form algebraic expression involving four parameters. This model has been used in a computer code which will calculate the burst times and burst currents for up to 15 conductors exploded in series in a capacitor-discharge circuit