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5.2. VIBRATIONAL ENERGY CREATION AND EXCHANGE 5.2 Vibrational energy creation and exchange In contrast to dissociation from the (dissociative) electronically excited states which is a one step process, dissociation due to vibrational excitation is a multi-step process re- quiring energy accumulation by several processes and energy exchange between many molecules. The vibrational energy should be created initially by low energy electrons. Broadly speaking, in non thermal discharges with electron temperatures in the range of 1- 3 eV, electrons excite molecules to the first few vibrational quanta (e.g 0 −→ 1, 1 −→ 2 . Here each number represents vibrational quantum number of the ground electronic state). The rate coefficients for electronic excitation of vibrational quanta can be calcu- lated by solving the Boltzmann equation as discussed in chapter 4 and in order to solve Boltzmann equation energy dependent excitation cross-sections are required as input. Reliable set of cross-sections describing excitation of lower quanta from the ground state are available for many molecules, however the same cannot be said about multi-quanta transitions (e.g 0 −→ 3 ); similarly cross-sections for excitation from higher vibrational states to even higher vibrational states (e.g 3 −→ 5 ) are not easily available. The im- portance of multi-quanta excitations vary depending on the gas. For example, in N2 they are considered insignificant [207], while in H2, they play important role even having higher rates when compared with excitation from the ground state [208]. To calculate the cross-sections of these excitations a semi-empirical formula is suggested in [36] σ(m,n)=σ01(ε+Em −En)(exp(−α(n−m))) (5.1) 1 + βm Here σ01 is the cross-section of exciting the first level from the ground state as a function of electron energy ε; Em and En are the energies of vibration levels m and n; α and β are constants that depend on the gas. Equation 5.1 has been used to calculate the electronic excitation of higher vibrational states in CO2 [64]. Thus calculated cross-sections – for excitation of molecules in asymmetric mode – have been compared with cross-sections reported by Hake et al [209], however, these differ significantly with those measured by Allan [178]. Also, Itikawa who reviewed the cross-sections in CO2 from a variety of sources also does not recommend Hake et al. Therefore, further investigations into vibrational excitation when concentration of vibrationally excited molecules becomes significant is warranted. For our calculations however, we use only one multi-quanta transition along asymmetric stretch that has been different when compared with those recommended by Itikawa (see section 5.7.2). Thus created vibrationally excited molecules exchange the energy deposited from electrons between themselves in collisions, with some losing energy and while some 112PDF Image | Understanding CO2 containing non-equilibrium plasmas
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