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5.3. VIBRATIONAL DISTRIBUTIONS dominant. By equating the gain and loss of molecules by VV process to zero, a distribu- tion of the form E xeE2 f(E)=Bexp(−T +Tω) (5.2) v0 can be obtained. In equation 5.2, B is normalization factor and the effective vibrational temperature can be defined as 1 = ∂lnf(E) (5.3) Tv ∂E E→0 Equation 5.2 describes the vibrational distributions very well for lower vibrational quanta in many non thermal plasmas. In figure 5.1, Treanor distributions calculated at different translational temperatures for a given vibrational temperature (0.3 eV) is plotted. For comparison, Boltzamnn distribution at the same temperature is also plotted. The Treanor distribution and Boltzmann distribution predict the same numbers for lower quantum numbers but deviate for higher quanta, and the difference increases when the difference between the gas temperature and vibrational temperature is higher. It implies that after certain critical energy, the probability of populating upper levels increases if VV trans- fer is the dominant process. In fact, the increased Treanor effect of over-populating the higher quanta with increasing difference between vibrational and translational temperat- ures is exploited in gas dynamic lasers [213] and has been attributed as the reason for increased dissociation in CO2 supersonic expansions [214]. Treanor distributions have been measured in symmetric modes [215] and in asymmetric mode [216] in CO2 plasmas using high resolution tunable diode absorption spectroscopy, in lower quanta for which VT relaxation is not important. However, Treanor distribution predicts unrealistic distri- butions for higher quanta; this problem has been solved by including VT relaxation for higher levels [210], radiative losses [217] or dissociation and VT losses combined with dissociation [212, 218]. The basis of most of these works is that the rate coefficients calculated according to SSH theory [219] which predicts high rate coefficients for VV relaxation for lower quantum numbers and lower VT relaxation for lower quantum num- bers and an increased rate coefficients of VT relaxation from higher quantum numbers. The effect of dissociation from highly excited vibrational states can be calculated from vibrational distributions and has been dealt in detail in diatomic gases like H2 and N2 [212, 220, 221]. In these works dissociation is considered as populating a pseudo vibrational level whose energy is equal to dissociation energy. A similar approach is taken in this work where the population of very highly excited molecules is taken as equal to the amount of CO produced from CO2 (see section 5.9.3). Alternatively, the method developed by Treanor et al can be modified to describe dissociation rates, by 114PDF Image | Understanding CO2 containing non-equilibrium plasmas
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