Non-local radiation transport via coupling constants for the radially inhomogeneous Hg–Ar positive column

A model is presented for the radially inhomogeneous Hg-Ar positive column discharge with properties similar to the standard fluorescent lamp. The model combines the electron excitation reactions and radiation trapping to self-consistently solve the spatially dependent species rate equations. Collision rates are evaluated from the electron distribution function determined from the inhomogeneous Boltzmann equation with the gradient term. Radiation processes are evaluated through frequency dependent cell-to-cell coupling constants. This general radiation transport method accounts for non-local photo-pumping, line overlap within the isotopic structure of the Hg resonance lines, and an emission line profile subject to partial frequency redistribution. The coupling constants agree with a more computationally intensive Monte Carlo code. The emission line profile provides an effective decay rate for the 185 nm line, which follows trends in measurements. In contrast, the use of a uniform constant escape factor for radiation trapping leads to centrally constricted profiles for the Hg excited states. Model results for the mean electron energy, distribution function and density distribution of Hg triplet levels are found to agree with existing spatially resolved data. Predicted and measured broad profiles for the Hg triplet levels are attributed to photo-pumping of the outer plasma regions by inner ones.