Extracting dynamic resistance from a pulsed power switch with a least squares approach

Pulsed power gas switches operate under extreme conditions holding off voltages at millions of volts and greater, conducting currents at 100´s of kiloamps, and can reliably trigger with less than 10ns of jitter at optimal operating conditions. However as Martin and Braginskii had noted the impedance of these switches is dynamic and a function of many parameters such as gas pressure, current, and the number of channels. In systems such as Protogen or Ursa Minor many gas switches are utilized to enable optimal performance and pulse shaping. A challenge with either system is that, if the switches are tightly coupled and one switch triggers early, then the fields on the second switch change dramatically and can move the second switch into a new operating regime that will result in a different dynamic resistance. This paper presents a least squares approach to extracting the Martin and Braginskii switch resistance with field dependent carrier recombination from measured data.