Simulation of Voltage and Current Waveforms During Nanosecond Pulsed Capacitive Discharges via Electrically Coupled Plasma Fluid Model and Lossless Transmission Line

A framework for the simulation of voltage and current waveforms during nanosecond pulsed capacitive discharges via electrically coupled plasma fluid model and lossless transmission line is presented. It consists of a transmission line model based on the theory of Riemann invariants for hyperbolic laws, a zero-dimensional two-temperature plasma reactor with detailed non-equilibrium air plasma chemistry and attending load circuit model, and a novel numerical method that enables accurate coupling of ordinary differential equations that describe voltage and current at the load of arbitrary complexity to zero- and multi-dimensional plasma simulators. The framework is demonstrated for nanosecond pulsed discharges and shown to enable the simulation of realistic voltage waveforms and energy coupling to the plasma without any user-defined input beyond circuit parameters. Simulations show that a Gaussian pulse of sufficient duration is required for the plasma channel to become conductive. For such configurations, as the current increases abruptly, the voltage on the load drops, bringing the plasma discharge to a conclusion. Consequently, we find that energy transfer to the plasma occurs as electrons are cooling, yet increasing in density to a maximum before the density decreases slowly due to ion-electron recombination. A parametric study shows that, for a given pulse energy, Gaussian pulses of longer duration lead to a higher fraction of energy being transferred to the plasma due to higher electron densities and associated currents. While demonstrated for a zero-dimensional reactor for clarity, the extension to multi-dimensional plasma solvers is straightforward.