2D collisional-radiative model for non-uniform argon plasmas: with or without 'escape factor'

Collisional-radiative models for excited rare-gas atoms in low-temperature plasmas are a widely investigated topic. When these plasmas are optically thick, an 'escape factor' is introduced into the models to account for the reabsorption of photons (so-called radiation trapping process). This factor is usually obtained assuming a uniform density profile of the excited species; however, such an assumption is often not satisfied in a bounded plasma. This article reports for the first time a self-consistent collisional-radiative model without using an ad hoc 'escape factor' for excited Ar atoms in the 2p states (in Paschen's notation). Rather, the rate balance equations-i.e. the radiation transfer equations-of the 2p states are numerically solved to yield the actual density profiles. The predictions of this self-consistent model and a model based on the escape factor concept are compared with spatially-resolved emission measurements in a low-pressure inductive Ar plasma. The self-consistent model agrees well with the experiment but the 'escape factor' model shows considerable deviations. By the comparative analysis the limitations and shortcomings of the escape factor concept as adopted in a significant number of works are revealed.