Reduced Molecular Plasma Kinetics with Non-Boltzmann Vibrational Distribution

Vibrational kinetics can strongly affect energy transfer, chemical kinetics, and discharge behavior in molecular plasmas, but resolving all internal states is often impractical for reactor-scale simulation. Compact, physics-based vibrational closures are particularly needed when complete state-to-state (StS) data are limited. Starting from a detailed ${\mathrm{H}}_2$ StS plasma-kinetics framework coupled to an electron-Boltzmann calculation, this work develops a reduced vibrational-kinetics formulation. The ${\mathrm{H}}_2$ vibrational ladder is reduced to two non-Boltzmann groups that evolve their population and internal energy. State-resolved reaction rates and associated energy-exchange terms are projected onto the groups for subsequent tabulation in reactor-scale plasma models. StS-informed samples of the reduced-model are propagated for pulsed RF ${\mathrm{H}}_2$ plasmas across a scan of pulse-averaged absorbed power and compared with the corresponding StS simulations. Predictions from the sampled models reproduce the bulk plasma response, including electron density, atomic-H density, and ${\mathrm{H}}_3^{+}$ density. Discrepancies in ${\mathrm{H}}^{-}$ production and the upper-energy-group vibrational temperature persist across the sampled reductions. This indicates a limitation of the present VDF reconstruction rather than the nominal parameter choice. Tail-sensitive processes therefore require a more accurate representation of the vibrational distribution.