Global parameter optimization of Mather type plasma focus in the framework of the Gratton-Vargas two-dimensional snowplow model

Abstract: Dense Plasma Focus (DPF) is known to produce highly energetic ions, electrons and plasma environment which can be used for breeding of short-lived isotopes, plasma nanotechnology and other material processing applications. Commercial utilization of DPF in such areas would need a design tool which can be deployed in an automatic search for the best possible device configuration for a given application. The recently revisited [S K H Auluck, Physics of Plasmas 20, 112501 (2013)] Gratton-Vargas (GV) two-dimensional analytical snowplow model of plasma focus provides a numerical formula for dynamic inductance of a Mather type plasma focus fitted to thousands of automated computations, which enables construction of such design tool. This inductance formula is utilized in the present work to explore global optimization, based on first-principles optimality criteria, in a 4-dimensional parameter-subspace of the zero-resistance GV model. The optimization process is shown to reproduce the empirically observed constancy of the drive parameter over 8 decades in capacitor bank energy. The optimized geometry of plasma focus normalized to anode radius is shown to be independent of voltage, while the optimized anode radius is shown to be related to capacitor bank inductance.