Kinetic description of non-Boltzmann OH rotational distribution in nonequilibrium stationary plasmas

We present a model that describes the departure from equilibrium of the OH(A) rotational level distribution in collisional plasmas. In this model, the OH(A) rotational state densities are governed by a rate equation including: (i) a balanced rotational energy transfer process with the buffer gas species; (ii) unbalanced exothermic reactions, which pump rotationally excited states into the system. Based on the prior assumptions, we formally derive a model function describing the non-Boltzmann distribution. This function depends on five parameters, each of which has a physical meaning. The temperature is given as one of the model function parameters, which can be readily identified with the translational temperature of the buffer gas. The validity of the model was tested by means of the least-squares fitting of data found in literature. Based on this analysis we propose the formation processes of rotationally excited OH(A) in several discharge conditions.

Figure 1

Density distribution function $N\left(E\right)$ for each of the four cases listed in Table 1. The prescribed parameters are $E_0=4.5\mathrm{eV}$, $T=1.0\mathrm{eV}$, $\sigma =0.6$, $N_0=1000.0$, and ${\kappa }_0/k_0=50$. The equivalent Boltzmann distribution is also shown.

Figure 2

Fitting curve of the OH(A) Boltzmann plot obtained from the optical emission spectroscopy of a discharge in water vapor bubble with air present as an impurity [30]. The data was extracted from the work of Bruggeman et al. [30].

Figure 3

Fitting curve of the OH(A) Boltzmann plot obtained from the optical emission spectroscopy of a $\mathrm{He}+0.1\%{\mathrm{N}}_2$ discharge produced at a current of 25 mA and voltage of 0.9 kV [31]. The data was extracted from the work of Bruggeman et al. [31].

Figure 4

Fitting curve of the OH(A) Boltzmann plot obtained from the optical emission spectroscopy of a He discharge at 25 torr [3]. The data was extracted from the work of Bruggeman et al. [3].

Figure 5

Fitting curve of the OH(A) Boltzmann plot obtained from the optical emission spectroscopy of a ${\mathrm{O}}_2$ discharge at 760 torr ($\circ$) and 25 torr ($\blacksquare$) [3]. The data was extracted from the work of Bruggeman et al. [3].

Figure 6

Fitting curve of the OH(A) Boltzmann plot obtained from the optical emission spectroscopy of a dielectric barrier discharge (DBD) in water-argon interface at atmospheric pressure [14]. The data was extracted from the work of Voráč et al. [14].