Assessment of common approximations in low-temperature plasma modelling using MC simulations

Understanding the fundamental processes in low-temperature plasmas (LTPs) is crucial for optimizing the configuration for a specific application. However, LTPs are highly complex, hosting multiple species at different temperatures and far from equilibrium. Consequently, modelling requires several approximations, often concerning the electron kinetics and their coupling with heavy species, the central theme of this study. We particularly highlight nanosecond pulsed discharges (NPDs), which induce strong non-equilibrium via short pulses of high reduced electric fields (E/N). To evaluate the impact of different approximations, we consider an accurate Monte Carlo (MC) formulation as the golden standard, implemented in LoKI-MC.

Electron kinetics is often addressed by expanding the electron Boltzmann equation (EBE) over the velocity space under the two-term approximation. We demonstrate that this approximation breaks down at high E/N due to increased anisotropy, a known issue that should be emphasized. Moreover, most EBE solvers assume isotropic scattering for all collision types. We underline that this assumption is not always correct and can significantly impact the accuracy of the results, using rotational collisions in H₂O vapor as an example.

Space and time dependencies of electron kinetics are usually described under one of two assumptions: the local-field approximation (LFA), which equates the solution of electron kinetics to the steady-state calculation with the local and instantaneous E/N; or the local-energy approximation (LEA), which includes an equation for the local mean energy. Here, we focus on time-locality to assess the impact of the LFA and LEA on the modelling of NPDs. Our analysis of electron relaxation in various gases and pressures reveals that LEA significantly outperforms LFA, and should be preferred when a fully kinetic description is unavailable. Lastly, we illustrate how electron energy relaxation after ns pulses differs when collisions between charged particles are included, a commonly overlooked aspect.