Vibrational kinetics of non-equilibrium CO$_{\mathrm{2}}$ plasma discharge in low-excitation regime

The main purpose of this work is to understand in detail the vibrational energy exchanges in non-equilibrium CO$_{\mathrm{2}}$ plasmas. To that end, we develop a kinetic model that couples the electron Boltzmann equations to the rate balance equations describing the time evolution of various individual vibrational levels of CO$_{\mathrm{2}}$(X 1$\Sigma +)$. We have investigated a low excitation regime, where $\nu _{\mathrm{2}}^{\mathrm{max\thinspace }}=$ 5, $\nu _{\mathrm{3}}^{\mathrm{max\thinspace }}=$ 5 and $\nu _{\mathrm{1}}^{\mathrm{ma\thinspace x}}=$ 2, resulting in 72 vibrationally excited levels. Validation of the model was done by comparing the time-dependent densities of the aforementioned states with measurements obtained by time-resolved in situ FTIR spectroscopy in a pulsed CO$_{\mathrm{2}}$ dc discharge (at p $=$ 5 Torr, I $=$ 50 mA) and its afterglow. The calculated maintenance electric field during the pulse and the time-dependent populations are in excellent agreement with the measured values. Work is in progress to extend the study to the higher vibrational excitation.