Optical spectroscopy diagnostics of a helium surface wave sustained discharge. II: modelling and evaluation of experimental data

Abstract

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 ≤ 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.

Travelling-wave-sustained discharges

“…7. The values of the gas temperature T g = 700 K for p = 0.3 Torr and T g = 1000 K for p = 1 Torr taken are in accordance with data from spectroscopy diagnostics of the discharge [115,126,133,137] and with its kinetic modelling [113].…”

“…The radiative 2 1 P-1 1 S transition also taken into account involves the effective probability (the corresponding rate coefficient is denoted by A eff 40 ), with the usual concept of escape factors. Such a kinetics of population of the excited states is similar to those in [115,139,291].…”

“…Stemming from the gas-discharge part of the models of TWSDs this relation is valid independently of the type of the high-frequency discharge. Started [104] even before the development of fluid plasma models of SWSDs, the modelling of diffusion-controlled discharges within the kinetic plasma theory has been carried out in parallel, moreover very actively [14,15,[77][78][79][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119]. For discharges in a diffusion-controlled regime, the approaches to the radial plasma density inhomogeneity and the ambipolar field related to it, as well as the problem of locality/nonlocality in the formation of the electron energy distribution, are crucial points in the modelling.…”

“…In fact, regarding this, the spectroscopy diagnostics appeared as very suitable method for studying TWSDs. A lot of data have been accumulated [4,5,115,126,[133][134][135][136][137][138][139][140][141] for gas temperature T g , spatial distribution of spectral line intensities I L (r) and excited-state population densities N k (r) in SWSDs by applying optics spectroscopy techniques. The further extension of these methods has been towards results for plasma parameters (plasma density and electron temperature) which involves, however, kinetic models of the discharges.…”

“…The values of the gas temperatures T g Ar and T g He in pure Ar and He discharges, necessary for calculating T g , are according to experimental data [42,115,126,133,139] for the same p-value. The results in Table 1 show that the elastic electron-neutral collision frequency varies very little.…”