Higher-order moment model for modeling the ion dynamics in low and intermediate pressures discharges*

In a weakly-collisional low-temperature plasma, the velocity distribution function (VDF) of the ions and electrons can be highly non-Maxwellian. In this regime, fluid models do not reproduce properly the plasma behaviour since they do not capture kinetic effects. We therefore aim at developing a model based on the moment method, that improves the accuracy of regular fluid models by capturing a more general (non-Maxwellian) VDF while still being computationally more efficient than PIC simulations. The development of such a model is not straightforward and several closures and methods can be found in the literature, with their own advantages and drawbacks. We investigate here some of the most common moment-closures and we propose some modified closures that are better-suited to fit the VDF observed in our plasma regime.

The models are then implemented in a 1D fluid simulation and the results compared with a 1D PIC simulation. The test case chosen is a 1D bounded plasma of a noble gas with one species of singly charged ions. An important feature of this work is the fidelity to capture the collisional exchanges with the gas (for both elastic and charge exchange) within the moment hierarchy