A revised comprehensive approach for determining the H2 and D2 rovibrational population from the Fulcher-α emission in low temperature plasmas

The emission of the Fulcher- α d 3 Π u → a 3 Σ g + 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 X 1 Σ g + state considering the typically observed hockey-stick population. The projection into the d 3 Π u state is performed via vibrationally resolved electron impact excitation cross sections and radiative decay into the a 3 Σ g + 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 H 2 and D 2 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.