A multi-term, multi-harmonic Boltzmann equation model for kinetic behavior in intense microwave and terahertz excited low temperature plasmas

A multi-term (MT), multi-harmonic (MH) decomposition of the Boltzmann equation (BE) is developed to describe electron kinetic behavior in microwave and THz excited low temperature plasmas. In the decomposition of the BE, velocity distribution functions retain an arbitrary time dependence enabling the prediction of electron kinetic behavior from an arbitrary initial condition to a steady-state periodic solution. By exploiting the time-periodic nature of the electron swarm, the MTMH-BE model is not restricted to numerically resolving the electric field cycle. The MTMH-BE model is validated via the Reid ramp model gas and the ionization model gas of Lucas and Salee. Following successful validation, the MTMH-BE model is utilized to elucidate the basic electron kinetic behavior in air at atmospheric pressure. Namely, the error associated with the effective field approximation (EFA) is explored, where it is demonstrated that for atmospheric pressure air, given a microwave frequency of 1 GHz, the EFA may result in more than a factor of two errors in the time-averaged ionization rate. In the second part of this study, the MTMH-BE model is demonstrated as a basic modeling tool for low temperature plasmas. First, the MTMH-BE model is utilized to calculate electron heating profiles from a cold initial condition. The MTMH-BE model is demonstrated to be in excellent agreement with strictly time-dependent kinetic models, including a time-dependent MTBE model and a Monte Carlo collision model. To highlight the advantage of this work, the MTMH-BE model is used to predict the formative delay time of 95 GHz high power microwave induced breakdown. In this example, the numerical time step utilized in the MTMH-BE model is approximately six orders of magnitude larger than is possible using a strictly time-dependent MT-BE model. Overall, the MTMH-BE model presents a powerful pathway to modeling temporal kinetic behavior in microwave and THz excited low temperature plasmas.