Spectroscopic diagnostics of the vibrational population in the ground state of H2 and D2 molecules

A diagnostic method has been evaluated for measuring the relative vibrational ground-state population of molecular hydrogen and deuterium. It is based on the analysis of the diagonal Fulcher bands (d(3)Pi(u) --> a(3)Sigma(g)(+)) and the Franck-Condon principle of excitation. The validity of the underlying assumptions was verified by experiments in microwave discharges and the method is recommended for application in divertor plasmas in controlled fusion experiments. By attributing a vibrational temperature T-vib to the ground-state electronic level (X(1)Sigma(g)(+)) and assuming population via the Franck-Condon principle, the upper Fulcher state vibrational distribution can be derived theoretically with Tvib as parameter. Comparison with experimentally derived upper-state population gives the corresponding Tvib Of the ground state. The Franck-Condon factors for the d(3)Pi(u) <--X(1)Sigma(g)(+) and d(3)Pi(u) --> a(3)Sigma(g)(+) transitions have been calculated for both hydrogen and deuterium from molecular constants using the FCFRKR code. The method has been applied to low pressure H-2/He and D-2/He microwave plasmas, showing good agreement of experimentally and theoretically derived upper Fulcher state vibrational distributions. The vibrational temperatures range from 3200 K to 6800 K for H-2 and 2600 K to 4000 K for D-2. depending on molecular density, pressure and electron temperature, but indicating nearly the same vibrational population for H-2 and D-2 for comparable plasma conditions.