A fully ro-vibrationally resolved corona model for the molecular hydrogen Fulcher-α system

Abstract

A ro-vibrationally resolved corona model for the molecular hydrogen Fulcher-$\alpha$ transition based on the Yacora solver is introduced. The model couples 1365 ro-vibrational levels of the $X^1{\Sigma }_g^{+}$, $d^3{\Pi }_u$ and $a^3{\Sigma }_g^{+}$ states via electron impact excitation from the ground state into the $d^3{\Pi }_u$ state and subsequent spontaneous emission into the $a^3{\Sigma }_g^{+}$ state. For the process of electron impact excitation a set of 45260 fully ro-vibrationally resolved cross sections calculated with the molecular convergent close-coupling (MCCC) method in the adiabatic-nuclei formulation is applied. The MCCC cross sections are compared with results of a scaling method used in other works, demonstrating the need for dedicated ro-vibrationally resolved cross sections. By post-processing the model output, entire Fulcher spectra can be simulated. These spectra are benchmarked with measurements from an inductively coupled plasma discharge at a pressure between 1.1–10$$Pa and a RF power of 700$$W. The model results agree very well with the experiment both in relative shape and in absolute value. A non-ro-vibrationally resolved, purely electronically resolved collisional radiative model for molecular hydrogen (including further states and reaction channels) is applied to investigate the validity of the corona approximation for the benchmark plasmas and the relevance of possible process extensions of the corona model. Furthermore, the influence of collisional quenching, autoionization and predissociation is discussed.