A conduction model for subnanosecond breakdown gas switch

In our previous work, an ideal model is used to describe the dynamic closing plasma channel for a subnanosecond gas switch. The plasma channel current is assumed to be on the surface of a uniform cylinder. Several authors' studies show that the channel conductivity and radius vary dynamically. This variation results in dynamic impedance of the channel, and corresponding current and voltage that vary with time across the gap. All of the above parameters are hard to measure directly because of the small geometry and the high gap voltage and current on a subnanosecond time scale. Therefore, we have to develop a mathematical model to study the switch properties and compare it with experimental result. In this paper, a Braginskii conduction model is used to describe the nonlinear dynamic plasma channel. When a breakdown happens, the plasma channel electrical conductivity remains almost constant, if we assume that the hydrodynamic cooling associated with expansion, together with radiative cooling, is sufficient to keep the temperature of the conducting channel constant. Therefore, the relationship between plasma channel current 7 and channel radius a is determined by the following formula: a ²∝ ∫ I ^2/3 dt (1) The Braginskii model is simulated by Pspice, and then a switch is driven by the channel current generated by this model. Because the impedance of the switch is different from the Transmission line, the reflected current from the switch, in turn, affects the development of the channel current and radius. An iteration method is used to find the final stable solution of the channel current. In every iteration step, the current drive the switch is simulated by the Finite Element Method in Time Domain (FETD). After that, the channel impedance, the voltage and current across the gap are also studied based on the simulated channel current.