Two-Dimensional Model of Supersonic Expansion Argon Plasma in Micro Hollow Cathode Discharge: A Comparison of Maxwellian and Non-Maxwellian EEDFs

The electron energy distribution function (EEDF) is the essential foundation of the accuracy of the plasma fluid model. The two-term Boltzmann (TB) equation solver has been widely used to retrieve plasma EEDF and transport properties as the input for plasma fluid modeling. However, the calculation pressure of the model with TB solver increases in comparison with Maxwellian EEDF in each step, especially in the plasma with the nonuniform electric field and gas pressure. This article aims to examine the influence of assumption on the EEDF on the relation between the plasma electron density and the electron temperature for supersonic expansion plasmas. A 2-D plasma fluid model is coupled with TB equations and Maxwellian equations, respectively. We find that the difference between the two EEDFs shows a clear difference in the cathode-dielectric-anode (CDA) area and a negligible difference in the supersonic expansion area. The error of electron density of the TB solver reached 30% compared with Maxwellian in the CDA area, while the temperature reached 3%. The difference between Argon ions and excited particles reaches 30% and 70%, respectively. In addition, the Maxwellian assumption leads to higher electron densities and ahead peak points for electrons, nonelectrically neutral in the expansion area, and lagging peak points for excited argon particles compared to using the non-Maxwellian EEDF. The deviation of electrons from a Maxwellian distribution in the CDA area, isentropic area, and lower density area is different. Inside the higher electron density area, also with high pressure, the EEDF is close to Druyvesteyn while far in the lower electron density area. These findings indicate that the Maxwellian assumption is capable of capturing the main physicochemical features of micro hollow cathode discharge with pulsed planar discharge nozzle (MHCD-PPDN) plasma in the expansion area, but it can lead to large calculation errors at the quantitative level at the CDA area. As for the interesting investigation for expansion region, such as MHCD-PPDN, Maxwellian EEDF could be used to decrease calculation pressure.