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

Abstract

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 u → a 3 + 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 + g ) and assuming population via the Franck-Condon principle, the upper Fulcher state vibrational distribution can be derived theoretically with T vib as parameter. Comparison with experimentally derived upper-state population gives the corresponding T vib of the ground state. The Franck-Condon factors for the d 3 u ← X 1 + g and d 3 u → a 3 + 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.

Chapter 4: Power and particle control

“…Upgrade show that populations in the molecular vibrational levels required for MAR are only a few percent of the total molecular density [264,265] and that molecular influxes can be comparable to atomic fluxes [266]. The level of MAR in detached plasmas has been inferred to be in the range 10-50% [257,267] of the overall recombination rate, similar to the modelling done by Reiter [259].…”

Diagnostics of Recombining Plasmas in Divertor Simulator MAP-II

“…The Fulcher-band spectroscopy has been employed for the indirect determination of the gas temperature of technical plasmas [42]. In the mid-90s, Fantz applied this method to microwave discharge plasmas [43] and then to the divertor region of the ASDEX-U Tokamak [44], which received considerable attention because of its importance in the study of the vibrational distribution of the molecular hydrogen in the divertor/edge plasmas. Because it is known that the intensities of the P and R branches in the ro-vibronic Fulcher transitions do not follow the Hönl-London branching ratio (i.e., "irregular" intensity ratio), whereas the Q branch exhibits a "regular" intensity ratio [45], the Q branch spectra have been used in the analysis.…”

“…The ro-vibronic structure of for the diagonal band can be well described by the Franck-Condon factor q v′v″ [43] and the Hönl-London factor for the P, Q or R branch, namely, . (8) Note that .…”

From cold to fusion plasmas: spectroscopy, molecular dynamics and kinetic considerations

“…Typical electron density values in divertor region, n e ≈ 10 14 cm −3 , are considerably higher than in technical plasmas and the theoretical model must describe the interplay of different elementary processes, thus considering the different vibrational pumping/de-activation mechanisms of excited electronic states. Attempts in this direction are reported in literature [26], improving the collisional radiative model by Sawada&Fujumoto [27] for hydrogen molecules and atoms. Results [26] clearly indicate that while at low electron densities the pumping mechanism of the excited emitting state is dominated by the forbidden electron-impact induced excitation of the ground state, increasing n e (> 10 12 cm −3 ) the excitation is governed by transitions involving metastable excited states (a 3 Σ + g , c 3 Π u ), with intermediate regimes where both mechanisms are important in populating the emitting state [28].…”