Fluid model for ions and electrons in the low and intermediate pressure regimes

Transport models of bounded plasma are traditionally classified into three pressure ranges: the low- (respectively high-)pressure regimes, characterized by an ion-neutral mean free path larger (respectively much smaller) than the size of the discharge, and the intermediate-pressure regime (between the previous two). In the latter, the edge-to-center density ratio (or h-factor) is usually modeled using a heuristic variable mobility that matches asymptotically the low-pressure and high-pressure regimes. In this work, we derive a transport model from the Boltzmann equation by integrating the collision operator while taking into account the drift between ions and neutrals and considering the general collisional cross sections (both elastic and charge exchange). We compare fluid simulations using this kinetically derived term versus the heuristic one, showing a discrepancy in the h-factor for collisional plasma in the intermediate pressure, especially at low-ion temperature. In the second part of this work, we will discuss closures of the electron fluid equations with high-order moments in order to represent efficiently non-Maxwellian distributions, while minimizing the number of moments to consider (and so the number of equations to solve), and computing the collision terms in an efficient and accurate manner.