Global Model Development Using Least-Squares Weighted Residual Methods

Abstract

A popular paradigm for the study of complex plasma discharges is the global model, which can provide estimates of volume-averaged plasma parameters of interest (number densities, temperatures, viable chemical reaction paths, etc.). Although global models are useful for parameter scoping, they cannot generally provide information on the spatial distribution of these physics processes. In this work, we present a reformulation of the global model equations using numerical methods that approximately capture these spatial dependencies. Plasma quantities are expressed in terms of rational functional representations with undetermined coefficients. Least-squares weighted residual methods are then applied to the ensuing global model equations to determine these coefficients in a way that minimizes various norms (L2, L-inf, etc.). Optimal coefficients corresponding to a given norm can thus be computed for all plasma components, permitting approximate profiles to be constructed.