Understanding the scaling of electron kinetics in the transition from collisional to collisionless conditions in microscale gas discharges

Abstract

When gas discharge and plasma devices shrink to the microscale, the electrode distance in the device approaches the mean free path of electrons and they experience few collisions. As microscale gas discharge and plasma devices become more prevalent, the behavior of discharges at these collisionless and near-collisionless conditions need to be understood. In conditions where the characteristic length d is much greater than the mean free path λ (i.e., macroscopic conditions), electron energy distributions (EEDs) and rate coefficients scale with the reduced electric field E/p. However, when d is comparable with or much lower than λ, this E/p scaling breaks. In this work, particle-in-cell/Monte Carlo collision simulations are used to explore the behavior of the EED and subsequent reaction rate coefficients in microscale field emission-driven Townsend discharges for both an atomic (argon) and a molecular (hydrogen) gas. To understand the behavior, a pseudo-analytical model is developed for the spatially integrated EED and rate coefficients in the collisional to collisionless transition regime based on the weighted sum of a fully collisional, two-temperature Maxwellian EED and the ballistic EED. The theory helps clarify the relative contribution of ballistic electrons in these extreme conditions and can be used to more accurately predict when macroscopic E/p scaling fails at the microscale.