An analytical formulation of the copper load solid to plasma transition problem when driven by a pulse forming network

We consider the problem of simulating the thermodynamic and electrical processes involved in a solid to vapor-plasma transition of a copper wire of known dimensions when driven by a Pulse Forming Network (PFN). Assuming uniform cylindrical geometry of the wire, we formulate integral equations linking the decay in PFN voltage to the increase in energy (thermal and kinetic) of the copper molecules and hence arrive at analytical expressions for the time taken at each phase transition. We then show that for the transitional liquid-vapor and subsequent phases, accurate resistance modeling requires a differential element formulation. We develop differential equations describing the energy balance and present numerical solutions for these phases. Thence, we present voltage and current studies across the continuous time varying resistance represented by the copper load. Finally, in order to verify the rough order of magnitude of these calculations, we capture images from PFN experiments conducted at the Indian Institute of Science (IISc), and utilize the Planckian locus to arrive at the copper temperature in the images. We use a probabilistic argument to motivate phase matching with these images, and show that the estimated temperatures at the boiling and vapor-plasma phases are very close to experimentally observed values.