The radial line slot antenna plasma source is a high-density microwave plasma source comprising a high electron temperature source region within the plasma skin depth from a coupling window and low electron temperature diffusion region far from the window. The plasma is typically comprised of inert gases like argon and mixtures of halogen or fluorocarbon gases for etching. Following the experimental study of Tian et al. [J. Vac. Sci. Technol. A 24, 1421 (2006)], a two-dimensional computational model is used to describe the essential features of the source. A high density argon plasma is described using the quasi-neutral approximation and coupled to a frequency-domain electromagnetic wave solver to describe the plasma-microwave interactions in the source. The plasma is described using a multispecies plasma chemistry mechanism developed specifically for microwave excitation conditions. The plasma is nonlocal by nature with locations of peak power deposition and peak plasma density being very different. The spatial distribution of microwave power coupling depends on whether the plasma is under- or over-dense and is described well by the model. The model predicts the experimentally observed low-order diffusion mode radial plasma profiles. The trends of spatial profiles of electron density and electron temperature over a wide range of power and pressure conditions compare well with experimental results.