Optical spectroscopy diagnostics of a helium surface wave sustained discharge .2. Modelling and evaluation of experimental data

A theoretical model for the kinetics of the processes for production and destruction of atom excited states in microwave discharges sustained in helium gas at reduced pressures by surface wave propagation is developed. The excited state population densities and the line intensities at the axis of the discharge are obtained from the stationary Boltzmann equation and the set of the rate balance equations for the n less than or equal to 4 excited states solved in a semi-analytical-semi-numerical manner. The numerical evaluation of the results accounts for the experimental conditions investigated in part I of the study. The comparison of the theoretical results with the experimental data (part I) for the population densities of the 2(1)P, 2(3)P, 4(1)S and 4(3)S excited states allows one to deduce the values of the mean electron energy and the electron density at the axis of the discharge. By these means, the two parts of the study complete a procedure for determination of these two plasma parameters in discharges sustained by propagating surface waves. This procedure for plasma diagnostics is extended to obtaining the radial and axial profiles of the electron density. The measured radial and axial distribution of the 504.7 nm line emitted intensity and radial distribution (through line absorption) of the 2(1)P and 2(3)P population densities (part I) are used. The axial density distribution obtained from completing the optical spectroscopy measurements with the theoretical model is in good agreement with that evaluated from radial decay measurements of the surface wave electric field intensity.