Abstract
The emission of the Fulcher- transition is well-known for providing access to the rovibrational population of the hydrogen molecule in low temperature plasmas by means of optical emission spectroscopy. A revised comprehensive approach is developed for the evaluation that omits several simplifying assumptions, which are often made. The rovibrational distribution is directly calculated in the state considering the typically observed hockey-stick population. The projection into the d 3Π u state is performed via vibrationally resolved electron impact excitation cross sections and radiative decay into the is considered via vibrationally resolved transition probabilities. The obtained steady-state population is fitted to the experimentally measured one via varying the population parameters in the electronic ground state. The impact of this evaluation routine compared to the simplified ones is demonstrated both for H2 and D2 at two experiments: a standard CW low-power laboratory ICP and the pulsed high-power negative ion source plasma of the Linac4 accelerator at CERN. This assessment demonstrates that especially the simplification of measuring only the first five rotational emission lines (i.e. neglecting the rotational hockey-stick distribution) can affect the evaluation results significantly. In the application example, this leads to an overestimation of the gas temperature up to a factor of nine and to an underestimation of the determined intensity of the full Fulcher-α transition (required for applying collisional radiative models) up to a factor of three.
Highlights
The rotational and vibrational excitation of the hydrogen molecule is of high relevance for understanding plasma chemistry and kinetics in low temperature discharges
The projection into the d3Πu state is performed via vibrationally resolved electron impact excitation cross sections and radiative decay into the a3Σ+g is considered via vibrationally resolved transition probabilities
Afterwards, the comprehensive approach is outlined both for H2 and D2: concerning the rotational distribution, it relies on calculating the full rovibrational distribution directly in the ground state and transferring it to the d3Πu state via vibrationally resolved electron impact excitation cross sections
Summary
Chemistry and kinetics in low temperature discharges. A change in the rovibrational distribution can significantly affect several molecular reaction rates. The focus is put on the determination of the intensity of the whole Fulcher-α emission (defined as wavelengthintegrated spectral radiance [m−3s−1]) which can be derived from the excited state population This quantity is required for the evaluation of the plasma emission via collisional radiative (CR) models of the H2 or D2 molecule as such models are typically not rovibrationally resolved and only the whole electronic state is considered (see for example [15] and references therein). Afterwards, the comprehensive approach is outlined both for H2 and D2: concerning the rotational distribution, it relies on calculating the full rovibrational distribution directly in the ground state and transferring it to the d3Πu state via vibrationally resolved electron impact excitation cross sections. In the last section of the paper, the comprehensive and the simplified approaches are compared for OES measurements both of H2 and D2 discharges carried out at two different experimental setups: a typical low pressure low temperature CW ICP and the pulsed highpower negative ion source plasma of the Linac accelerator at CERN
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