The influence of opacity on hydrogen excited-state population and applications to low-temperature plasmas

Atomic hydrogen lines and line ratios are being used for diagnostics of technical plasmas in hydrogen or of edge plasmas in fusion research. In the presence of hydrogen molecules, dissociative excitation also contributes to this radiation. The H Lyman lines become optically thick quite easily, which modifies the excited-state population and ionization balance. Line ratios are then a function of electron temperature and density, but also of molecular densities and opacity. To quantify these effects, collisional-radiative population calculations were carried out for the conditions of technical low-pressure plasmas using the most recent hydrogen cross sections and population escape factors. The model for computing opacity is described and results are shown as a function of optical depth. Various spatial emission profiles and spectral line profiles can be included. These results allow the analysis of hydrogen lines from low-temperature plasmas. Measurements are presented, which were carried out in microwave discharges in mixtures of hydrogen or of deuterium and helium. Atom densities and dissociation degrees were determined from absolute Balmer line intensities and from line ratios. The effects of non-Maxwellian electron energy distributions are briefly discussed. The results demonstrate the influence of dissociative excitation and opacity. Taking into account these processes, very consistent results were obtained within the experimental error limits, thus confirming the analysis methods and the rate coefficients used. Dissociation degrees of 0.1-10% were measured depending on pressure and hydrogen concentration. For standard diagnostics, a suitable method can be chosen according to the experimental conditions.