Self-consistent state-to-state kinetic modeling of CO2 cold plasmas: insights on the role of electronically excited states

This study focus on the role of electronically excited states in the kinetics of CO 2 cold non-equilibrium plasma discharges by means of a state-to-state OD kinetic model based on the simultaneous and self-consistent solution of the electron Boltzmann equation and the master equations describing the vibrationally and electronically excited state kinetics and the plasma composition. A new CO 2 dissociation model based on the use of the Biagi electron impact excitation cross sections, considered as fully dissociative, of several CO 2 electronic excited states, in the energy range from 6.5 eV and 25 eV, is tested and compared with the results obtained by using the Phelps database in typical glow discharge and microwave discharge conditions. Moreover, a refinement of the kinetics of the CO(a 3 Π) excited state is proposed by including new production and loss terms and the effect of the change of its time evolution density on the eedf, the electron temperature, the CO 2 and CO vibrational distribution functions, electron impact and vibrational induced dissociation rates is investigated. Finally, the contribution of the CO(a 3 Π) state to CO 2 dissociation is examined in terms of production and recombination (or back-reaction) processes both in microwave and glow discharge conditions.


Introduction
In the last decades, the increased emission of greenhouse gas (mainly carbon dioxide) and the decreasing reserves of traditional energy sources has renewed the interest in CO2 conversion by cold non-equilibrium plasmas as a valid alternative to conventional route to increase the energy efficiency of CO2 conversion.Plasma discharges provide a favorable environment for activating the CO2 gas by electron impact excitation (vibrational and electronic), increasing CO2 reactive channels at relatively low gas temperature.Among the complex reactions involved in the conversion chain, the CO2 dissociation is a key process affecting the overall efficiency.Beside the direct electron impact mechanism, CO2 dissociation can occur also by selectively pumping energy into the lowest vibrational levels through electron-vibrational (eV) collisions, followed by vibrational-vibrational (VV) processes, which populate the upper vibrational levels inducing dissociation from these levels.This vibrational induced dissociation process has a maximum threshold energy of 5.5 eV, lower than the threshold of 7.0 eV by electron impact, increasing the energy efficiency of the CO2 dissociation.For this reason, a strong interest in the scientific community has been channeled towards the investigation of the conditions in which vibrational excitation can be maximized in non-equilibrium plasma discharges for a more energy efficient CO2 dissociation [1].
CO2 plasmas are important also for aerospace applications, such as the study of spacecraft entry in Mars and Venus atmosphere [13] or oxygen production on Mars for in-situ resource utilization in future space exploration missions [14].The use of nonequilibriun plasma for CO2 dissociation is also important for biomedical applications.As an example, a helium plasma jet with a 1% CO2 admixture was used to produce small amounts of CO in safe conditions for the treatment of various human health diseases thanks to its anti-inflammatory, vasodilator, anti-apoptotic and anti-proliferative effects [15].
The understanding of the chemistry of non-equilibrium reactive plasmas is a challenging problem and needs the implementation of advanced plasma kinetic modeling.The most refined kinetic simulation description is provided by the State-To-State (STS) approach [16][17] in which the population density of each excited state of atoms and molecules is followed by taking into account the relevant involved collisional processes.This approach becomes essential when the chemistry is dependent on the high lying vibrational or electronic excited states.The corresponding time dependent balance equations involve the rate coefficients of each considered reaction.The rate coefficients of heavy particle collisions are in general gas-temperature dependent and are often described by using Arrhenius rate taken from the literature.The rate coefficients of electron impact processes are calculated from the energy-dependent cross sections and the electron energy distribution function (eedf), which can be obtained by solving the electron Boltzman equation.The electrons have a key role in CO2 dissociation in non-equilibrium plasma discharges.They can directly dissociate CO2 molecules and transfer part of the discharge energy to atoms and molecules by means of inelastic collisions, exciting vibrationally and electronically states, and initiate the climbing of the vibrational ladder up to molecular dissociation.Excited states, in turn, give energy back to the electrons by superelastic collisions, affecting the eedf shape, by creating characteristic peaks [18], and, as a consequence, the calculation of the corresponding electron impact rates.The described scenario confirms the strong coupling between the electron and heavy particle kinetics, showing the importance of using an approach in which the STS master equations describing the vibrational and electronic excited state kinetics of heavy particles are solved simultaneously and self-consistently with the electron Boltzmann equation [1].
In this contribution, we present the results obtained by using an advanced 0D self-consistent STS kinetic model for the description of CO2 reactive plasma mixture in non-equilibrium plasma discharge and post-discharge conditions [19].The model provides a complete characterization of the plasma mixture calculating the temporal evolution of chemical species densities, the vibrational distribution functions (vdf) of the molecules, the electronic excited state densities and the eedf in discharge and post-discharge conditions characterized by different conditions of pressure and gas temperature, power density and/or reduced electric field and residence time in the discharge.A brief description of the model will be presented in section 2. A special attention will be addressed to the investigation of the role of electronic excited states in the kinetics.For the CO2 system, the Phelps database provides two electronic excited state excitation cross sections corresponding to threshold 7 eV and 10.5 eV.However, other CO2 electronic excited states have been identified by means of absorption spectroscopy and electronic structure calculations [20][21] with corresponding electron impact excitation cross sections (see section 3).The availability in the LxCat [22] of a new database of electronic excitation cross sections for CO2, i.e. the Biagi dataset [23][24], have prompted toward the testing of a new dissociation model via electronic excitation in which these cross sections are accounted as fully dissociative (see section 4).A focus on the first electronic excited state of CO molecules, i.e.CO(a 3 Π) at 6 eV is performed in section 5, with a refinement of its kinetics by including new production and loss processes.This electronic state affects the vibrational kinetics of CO ground state molecules by means of the quenching process CO(a 3 Π) + CO → CO(v = 27) + CO [25] with a pumping of vibrational quanta in the CO vdf, giving also a contribution to CO2 dissociation/recombination (see section 6).Conclusions and perspectives are presented in section 7. Finally, the Appendix reports some aspects connected to the possible inclusion of new CO2 electronic excited states as not dissociative ones and the availability of rate coefficients needed for the building up of appropriate kinetic equations for such states is analyzed.

Brief description of the kinetic model
The plasma mixture considered is characterized by the following species, i.e.CO2, CO, O2, C, O, CO 2 + , CO + , O 2 , C + , O + , e -.For the CO2 system, the pure asymmetric mode levels of the kind (0, 0, v) up to the dissociation limit of 5.5 eV (21 levels) and few low lying symmetric and bending levels, i.e.
(010) and the first three Fermi levels, are accounted.The corresponding vibrational kinetics is described by including several intramode vibrational-vibrational (VV), intermode vibrationalvibrational (VV'), vibrational-translational (VT) and electron-impact vibrational excitation (eV) processes.The corresponding VV, VV' and VT rate coefficients have been derived following the approach used in [26][27], i.e. by applying Schwartz-Slawsky-Herzfeld (SSH) scaling laws [28], starting from available theoretical and/or experimental rate coefficients involving low lying vibrational levels.One electronic excited state of CO2 at 10.5 eV is also included (metastable state).
A detailed vibrational and electronic excited state kinetics is also considered for the main CO2 dissociation products, i.e. the CO and O2 systems, taking into account, respectively, 80 and 34 vibrational levels and several electronic excited states with their related quenching and radiative processes [29][30][31].The electron Boltzmann equation calculates the eedf taking into account the effects of the electric field of the discharge and of the relevant collision processes occurring such as elastic electron-molecule, electron-atom and electron-electron collisions, inelastic and superelastic (vibrational and electronic) and electron-induced chemical reactions, such as ionization and dissociation with their corresponding reverse processes.The electron impact cross sections entering in the electron Boltzmann equation are taken from available database such as LXCat [22] and PHYS4ENTRY [32], which, unfortunately, do not provide all the needed vibrational-state resolved cross sections.Scaling laws, such as Fridman's one for eV [33] or simple threshold shifting for ionization and dissociation cross sections, are used to account for missing cross sections.CO2 dissociation occurs via two different mechanisms: 1) direct electron impact (DEM) e + CO 2 (00v) → e + CO + O 2) pure vibrational (PVM and PVMO, respectively) The electron impact dissociation from ground state (000) is described by the 7 eV Phelps cross section, while dissociation from asymmetric vibrational excited levels by the same cross section with a threshold shifting according to the vibrational energy.The PVM and PVMO rate coefficients from ground were taken from literature [26][27], while for higher vibrational levels, the Fridman-Macheret  model is used [33].More detailed information on the model and the list of the included kinetic processes can be found in [19].Some model validation with results already present in literature were performed.In particular, the O2-O kinetics was validated by comparison with the modelling and the experimental results of Annusova et al. [34] in low pressure O2 plasma discharges (P=10 mtorr-80 mtorr, Tgas=620 K -900 K) finding a good agreement for the O2 vdf, confirming the presence of a declining plateau in the range 3<v<20, generated by the three body O atom recombination, i.e.O + O + O → O 2 (v) + O [35].
The model was also able to analyse the plasma conditions experimentally investigated by Groen at el. [6] on CO2 activation in MW discharges at high translational gas temperature (3500 K< Tgas < 5500 K) [36].By comparing the kinetic results with the corresponding thermodynamic ones, it was showed that the major components of the mixture, i.e.CO and O, could be described by the thermodynamic approach, while the other minor components presented large deviations from equilibrium.A qualitative agreement was found between experimental and theoretical values for the electron density, the E/N values and the electron temperature in both diffuse and contracted plasmas.
Recently, the model was applied to the description of glow discharge conditions at low pressure (P=5 torr), discharge current I=50 mA and residence time td=5 ms [37] and its results compared to the modelling and experimental results by Grofulovic et al. [38] and Klarenaar et al. [3], respectively.A good agreement was found for the low-lying CO2 vibrational population densities and vibrational temperatures time evolution with comparable electron densities, stationary eedf and stationary reduced electric field values.
The model has been used also to investigate the conditions for the activation of vibrational-induced dissociation of CO2 in cold non-equilibrium plasma discharges [39].These conditions are linked to the achievement of a sufficiently high non-equilibrium plateau in the CO2 vdf due to the combining effect of eV and VV collisions, overpopulating higher vibrational levels and promoting dissociation.A satisfactory agreement of our simulation results with the Kotov's criterion [40] for vibrationalinduced dissociation is found, confirming that the conditions for the onset of vibrational activation of the CO2 dissociation process occurs for , where Q is the power density and N0 the initial CO2 number density and is a threshold value which depend on the gas temperature and can be calculated from a semi-empirical balance equation for the vibrational energy by means of numerical simulations [40].

CO2 electronic excited states
Electronic excited states of CO2 have been studied both experimentally and theoretically.Several electron impact experiments with incident energy from threshold up to 100 eV [41][42] and optical absorption experiments have been devoted to study low-lying electronic states of CO2 [43][44].Moreover, many ab-initio calculations of its electronic structure, several assuming a linear geometry only, have been performed using different methods with various levels of approximation [45][46][47][48][49][50][51][52].At the moment, as also stated by Itikawa [20], there is no definite consensus about the assignment of the excited electronic-state energies of CO2.Unfortunately, differently from the electronic ground state which has a linear equilibrium geometry, many of the excited states are supposed to have a bent structure and their spectroscopic investigations are difficult since bent states show only weak features in the absorption spectra.As a general agreement, in the energy region between 7 and 10 eV, seven electronic states are assumed to lie ( ), while above 10 eV, the excitation spectrum is composed of several Rydberg series and Rathenau progressions [53][54].Itikawa [20] and Deschamps et al. [21] provides a review of the electronic excited state energies measured or calculated by different authors (see Table 7 in [20] and Table I in [21]).These energies are listed in Table 1.Deschamps reports the vertical excitation energies of CO2 electronic excited states calculated by Winter et al. [45], England et al. [46], Spielfiedel et al. [47][48], Buenker et al. [49] and Nakatsuji et al. [50].Itikawa reports also the spectroscopic results of photoabsorption studies performed by Rabalais et al. [55] and Chan et al. [56] and the excitation energy employed in the crosssection calculation by Lee et al. [51].
The calculations of Nakatsuji et al. [50] are based on symmetry-adapted cluster (SAC) method with CI (SAC-CI) study.Nakatsuji et al. assumed a linear geometry, giving information about the possibility of bent geometry of some excited states by looking to the molecular orbital characteristics.The bent structure of the excited states of CO2, instead, was theoretically investigated by Spielfiedel et al. [47][48] and by Buenker at al. [49].Finally, we have added also the energies calculated by Mulligan [52] by LCAO-MO SCF method (linear combination of atomic orbitals molecular orbitals with the Roothaan's self-consistent field method).
Lee [51] (1999) Kawahara [58] (2008) The available electron impact excitation cross sections for the listed CO2 electronic excited states are reported in Table 2 and in Fig. 1.In particular, Mu-Tao and McKoy [57], by using a distorted-wave method, calculated the cross sections for the excitation of eight states for the energy range 25-60 eV.
Unfortunately, this energy range is far from the threshold energies and cannot adequately describe the process.More recently, Lee et al. [51] have provided more energy extended cross sections (up to the threshold energies) for only five excited states by using a close-coupling method.Excitation cross sections for the   +  and    states have been derived by Kawahara et al. [58] by means of crossbeam experiments [59].These cross sections were also compared to integral cross sections calculated by using the BE f-scaling approach [60], generally used for electron impact excitation of dipoleallowed electronic states, finding a good agreement.Recently, data from Biagi's Magboltz code [23] were added to the LXCat database (Biagi-v7.1)[24].
The Biagi database contains several cross sections for the excitation of electronic excited states, which are assumed to be involved in dissociation (fully dissociative).These electronic excited state cross sections are derived mainly from the analysis of photoabsorption in CO2 [61].This technique gives cross sections for levels that are coupled with the ground electronic state through dipole excitation.For non-dipole allowed transitions, called triplet excitations, the related cross sections are optimized in Magboltz [23] to reproduce the measured Townsend ionization coefficient [62].The electronic excited state cross sections included in the Biagi database are the following and a selection of them is reported in Fig. 2  The highest excitation cross sections from the Biagi database reported in Fig. 2 are lower than 10 -20 cm 2 and of the same order of magnitude, near the threshold, of the 7 eV (dissociation) and 10.5 eV (electronic excitation) cross sections of the Phelps database.

CO2 electron impact dissociation model via electronic excitation
Particular attention in literature has been devoted to the identification of the CO2 electron impact dissociation cross section [63][64][65], which is assumed to be implicitly included among the available electronic excitation cross sections.In general, the 7 eV excitation cross section from Phelps [66][67] with products () + (  1 ) is widely used in literature and seems to give reasonable CO2 dissociation rates compatible with experiments in various conditions [63,65].The Phelps database provides also an electronic excitation cross section at 10.5 eV.This state, in general, is considered as a metastable state even though other authors [68] consider the possible dissociation via this state with products ( 3 Π) + (  3 ).
Another possibility tested in literature [69] is the experimental dissociation cross section of Cosby [70], with an energy threshold of 12.5 eV, which provided lower electron impact dissociation rates respect to Phelps.Recently, Morillo-Candas et al. [64] showed that a better comparison with experimental CO2 dissociation rates is obtained by using the Polak and Slovensky cross section [71] for E/N in the range 45-105 Td.However, they still suggest the use of the 7 eV Phelps cross section for the calculation of the eedf through the Boltzmann equation to maintain the coherence and the consistency of the electron impact cross section dataset obtained by swarm analysis procedures.For E/N values larger that 90 Td, Babaeva et al. [72] suggested again the use of the Phelps dissociation cross sections, in particular the 10.5 eV one, in corona and dielectric-barrier discharges.
The availability of new electronic excited cross sections of the Biagi database which can be assumed as dissociative ones provides another possible model for describing electron impact CO2 dissociation.
For this reason, we would like to test this new dissociation model and to compare the corresponding simulation results with the results obtained by the dissociation model linked to the Phelps database.
The comparison has been made firstly in glow discharge conditions, in which CO2 dissociation occurs essentially by electron impact and the CO2 is characterized by low vibrational excitation, and then in MW discharge conditions in which vibrational excitation becomes more important for CO2 dissociation.
In the dissociation model connected with the Biagi database, we take into account electron impact dissociation as occurring via all the electronic excitation cross sections present in the database, leading to CO and O formation in the ground states.On the other hand, in the dissociation model associated to the Phelps database, the 7 eV electronic excitation cross section is considered as dissociative one, while the one at 10.5 eV is accounted for as an electronic excitation cross section (which becomes a metastable state in a optically thick plasma conditions).Moreover, the electron impact dissociation from vibrational excited levels is also accounted only in the Phelps case by considering the same 7 eV dissociation cross section with a threshold shifting according to the vibrational energy.The glow discharge conditions chosen are the same as those reported by Grofulovich et al. [73] and by Klarenaar et al. [3] and already investigated in [37] (P=5 torr, Tgas experimental time dependent profile, dt=5 ms, Pd=1 Wcm -3 ).Fig. 3 shows the time evolution of species number densities and dissociation rates in these glow discharge conditions in the two dissociation models.The use of the Biagi dataset does not change global number densities both in discharge and post-discharge, showing comparable results with the Phelps database (Fig. 3 a).Calculated dissociation rates are nearly the same in discharge conditions, while some differences are registered for DEM and PVM rates especially in post-discharge conditions due to differences in the eedf time evolution.Stationary eedf in discharge (t=5 ms) and its time evolution in the post-discharge is shown in Fig. 4. The eedf calculated with the Biagi dataset has lower populated high energy tails due to the presence in the database of high threshold energies dissociation cross sections by electronic excitation.Moreover, the eedf does not present the characteristic peaks at energies 10.5 eV and multiple of that as in the case of Phelps database which are due to the superelastic electronic collisions involving the electronic excited state CO 2 (10.5 eV), i.e. the processes of the kind e(nΔε) + CO 2 (10.5 eV) → e[(n + 1)Δε] + CO 2 (4) with n=0, 1, 2, etc and with Δε = 10.5 eV.Some superelastic electronic peaks around 10 eV (and multiple) appears in the Biagi database case (see Fig. 4 b) at stationary conditions due to electronic excited states of O atoms (O( 3 S 0 ), O( 5 S 0 )).Such differences in the eedf and in the calculated dissociation rates in the post-discharge, however, do not influence global CO2 density since the low electron density and electron temperature conditions make dissociation practically absent in the post-discharge.Fig. 5 Time evolution of the species number densities and dissociation rates in MW discharge conditions (P=20 torr, Tgas=300 K, dt=50 ms, Pd=80 W/cm -3 ) calculated with the dissociation model connected to the Phelps database (full lines) and to the Biagi database (dotted lines).
Fig. 5, instead, shows the time evolution of the species densities and dissociation rates in MW discharge conditions characterized by P=20 torr, Tgas=300 K, dt=50 ms, Pd=80 Wcm -3 , in the two dissociation models.Globally, the species densities behavior is similar even if a slightly decrease of CO2 dissociation is predicted when the dissociation model linked to the Biagi database is used.This is essentially due to the lack in the Biagi dissociation model of electron impact dissociation processes from CO2 vibrationally excited states (see eq. ( 1)) which, in this case, differently from the glow discharge case, have a more important impact in the global dissociation of CO2 due to a higher CO2 vibrational excitation.The corresponding CO2 vdf in the case of Phelps has slightly underpopulated upper energy tail due to the account of these processes and the corresponding PVM rates are lower respect to the Biagi case (see Fig. 5 b).The inclusion of higher threshold energy dissociation cross section in the Biagi database underpopulates the eedf at higher energies respect to the Phelps model (see Fig. 6 a) reducing the importance of electron impact dissociation processes with predicted lower DEM rates in the Biagi case as it can be seen in Fig. 6 b.
These results show that, in conditions characterized by low vibrational excitation and in which electron impact dissociation dominates the kinetics as glow discharges, the Biagi database provide same CO2 dissociation rates as Phelps ones.This is the result of the compatibility of the two different datasets which have been built up by using swarm analysis procedure.However, in conditions in which vibrational excitation becomes important, lower CO2 conversion rate are obtained with the dissociation model connected to the Biagi dataset since only dissociation from electronic excited states is accounted for without modeling electron dissociation from vibrational excited states (see eq. ( 1)).Further studies of this particular aspect are necessary, since an integration of the proposed model connected with the Biagi dataset should be performed to take into account also the latter processes.

A focus on 𝐶𝑂(𝑎 3 Π) kinetics
The first electronic excited state of the CO molecule, i.e. ( 3 Π), is a metastable state at 6 eV with a radiative lifetime ~ 2.6  [74][75].Beside affecting the eedf through superelastic collisions, according to Porshnev [25], it affects also the corresponding CO ground state vdf by means of the following quenching and vibrational-electronic (VE) transitions ( > 27) +  → ( 3 Π) + The quenching process in eq. ( 5) creates a well-defined peak at v=27, as shown in [29][30][31], progressively rounded off by VV and VT collisions.Moreover, the ( 3 Π) state is involved in chemical reactions, which contribute to CO2 dissociation/recombination.Recently, its role on the CO2 dissociation mechanisms was investigated in DC glow discharge conditions characterized by pressure from 0.4 to 5 Torr [76][77][78][79] and also by Cenian et al. [80] in similar working conditions.They showed that the (a 3 Π), depending on the CO and O2 density, can either enhance the dissociation of CO2 or stimulates the reconversion back to CO2.Actually, the energy of this state (6 eV) is enough to dissociate CO2 and O2 molecules with rate coefficients close to the gas kinetic collision frequencies.In particular, in [76][77], it is shown that, for gas mixtures with large amount of CO2 but low CO density, the reaction CO(a 3 Π) + CO 2 → 2CO + O contributes to enhance the dissociation.On the contrary, if the concentrations of CO and O2 are larger, the processes CO(a 3 Π) + O 2 → CO 2 + O and CO(a 3 Π) + CO → CO 2 + C are prevailing and leads to the CO2 reconversion [79][80][81].Thus, the (a 3 Π) appears to be a key species in CO2 plasma dynamics and its kinetics needs further investigation with a more detailed kinetic description.Unfortunately, its direct measurement is very challenging and has been done only in very diluted gas mixture for CO2 laser study [82].
5.1 New and old kinetic scheme for ( 3 Π) The kinetics of the (  ) was already studied in [29][30][31] by taking into account the processes listed in Table 3.An important improvement of the (  ) kinetics is proposed by including also new processes of production and loss.The new kinetic scheme is shown in Table 4.As new production processes, we have added the dissociative excitation of CO2 by electron impact (>11.5 eV) (process 7), with the cross section measured by Wells et al. [90] by means of time-of-flight spectra and the dissociative recombination of   + ion (process 8), whose rate was suggested by [89], according also to measurements performed in the downstream of a MW plasma by [91][92].The new loss processes are quenching processes to the ground state in collisions with O2 (processes 9-10) and reactive quenching by collisions with O2 leading to dissociation into CO2 + O (process 11), quenching to the ground state in collisions with CO2 (processes 12-13), quenching to the ground state in collisions with O (process 14) and reactive quenching by collisions with CO with dissociation into C + CO2 (process 15). 2 CO(a 3 Π) + CO → CO(X, v = 27) + CO 10 -10 cm 3 s -1 0.984 [25] 3 CO(X, v > 27) + CO → CO(a 3 Π) + CO 10 -13 cm 3 s -1 [84][85] CO(a′ 3 Σ + ) → CO(a 3 Π) + hν 1 The new kinetic scheme was tested in the MW discharge condition characterized by Tgas=300 K, P=20 Torr, Pd=80 Wcm -3 , td=50 ms.The following figures show what happens when, for the CO(a 3 Π) kinetics, we use the old kinetic scheme (old), the old kinetic scheme with the adding of only the quenching processes 9-15 in Table 4 (old + only quenching) and finally the complete new kinetic scheme (new), with the addition also of the new production terms 7-8.Fig. 7 shows the time evolution of the CO(a 3 Π) density in the three different kinetic schemes (old, old+only quenching, new) and of the rates (cm -3 s -1 ) of the new processes added to the CO(a 3 Π) kinetics.
It is clear that by adding to the old kinetic scheme only the quenching processes (old + only quenching), the CO(a 3 Π) state is globally less populated, while the insertion also of the new production terms, i.e. processes 7-8 in Table 4 (new), increases the CO(a 3 Π) population essentially in the initial temporal range up to 10 -4 sec.In the microsecond time range, instead, the CO(a 3 Π) population density, is equal to that one predicted by adding only the quenching processes.By looking to the time evolution of the rates in Fig. 7 b, it can be deduced that the new production and quenching terms act in different temporal ranges.The CO(a 3 Π) population kinetics is dominated by the dissociative recombination process up to 10 -5 sec, due to its high rate coefficient, and by the quenching by CO2 due to the high CO2 concentration.After that, up to 10 -4 sec, also the dissociative excitation process become important in the production of CO(a 3 Π) state due to the increase of its corresponding rate coefficient in time.For t>10 -4 s up to the end of the pulse (t=50 ms), quenching processes dominate the CO(a 3 Π) kinetics, with an order of importance correlated to the concentration of the colliding partner, i.e the kinetic is dominated by the quenching by CO2 for 10 -4 s<t< 5 10 -3 , and by the quenching by CO and O, for 5 10 -3 s< t< 50 ms.In the post-discharge, production rates strongly decrease due to the decrease of the electron density, as well as the quenching rates.The use of the new CO(a 3 Π) kinetic scheme in the MW test case has some effects in the global kinetic of CO2 reactive plasma but only in the temporal range up to 10 -4 sec, i.e. in the range in which the production of CO(a 3 Π) is increased by the dissociative excitation and dissociative recombination processes.In the microsecond range, the global kinetic remains more or less the same.Here the list of the changes: 1) Eedf, electron temperature and CO2 and CO electron impact dissociation rates (DEM rates) The higher CO(a 3 Π) number density up to 10 -4 s in the new kinetic scheme (see Fig. 8 a) pumps the eedf towards higher energies respect to the old case by means of the superelastic electronic process involving the CO(a 3 Π), i.e. e(nΔε) + CO(a 3 Π) ⟶ e((n + 1)Δε) + CO(0) with n=0, 1, 2, etc and Δε = 6 , increasing the electron temperature (see Fig. 8 b) and also CO2 and CO electron impact dissociation (DEM) rates (see Fig. 8 c) up to 10 -4 s.
2) CO2 vdf and CO2 vibrational-induced dissociation rates (PVM) The change in the eedf indirectly affects also the CO2 vdf by means of eV collisions: the overpopulation of the eedf at higher energies, in the new kinetic scheme and up to 10 -4 sec, pumps more energy to the vibrational energy levels in the higher-energy range, increasing the corresponding vdf tails and promoting CO2 dissociation from upper levels.This is confirmed by looking to Fig. 9 which shows the CO2 vdf in the two kinetic schemes during the discharge (Fig. 9 a) and the time evolution of CO2 vibrational-induced dissociation rates of the processes in eq.
(2) (PVM) and (3) (PVMO).The low-energy part of the CO2 vdf is not affected by the change of the kinetic scheme and as a consequence no effect on the CO2 vibrational temperature is observed.
3) CO vdf, CO vibrational temperature and CO vibrational-induced dissociation rates For the CO system, in addition to the indirect effect through eV processes (see previous point 2), also a direct effect on the CO vdf is present.The CO vdf is affected by the quenching process 2 (see Table 3 and 4) which induces a transfer of energy from CO(a 3 Π) to the vibrational v=27 level, creating a well distinct peak in the CO vdf.Fig. 10 shows the comparison of the CO vdf in discharge conditions in the two kinetic schemes.The greatest differences occur again up to 10 -4 s with the formation of higher peaks at v=27 in the new kinetic scheme respect to the old one.An increase of the CO vibrational temperature of nearly 500 K up to 10 -4 s is also registered together with an increase of the CO vibrational induced dissociation rates of the processes CO + M → C + O + M (PVMCO) and of the Boudouard ones CO(v) + CO(w) → CO 2 (v) + C (Boud) (see Fig. 11) Fig. 10 CO vdf time evolution in the (a) new and (b) old kinetic scheme during the discharge in the MW test case (Tgas=300K, P=20 Torr, Pd=80 Wcm -3 , td=50 ms).4) CO2 dissociation Fig. 12 shows the CO2 and CO number densities time evolution in the new and old kinetic scheme for CO(a 3 Π).As expected, CO production is slightly increased in the new kinetic scheme up to 10 -4 sec.This increase is due to the observed DEM and PVM rate increase (see Fig. 9 c and Fig. 10 b, respectively) in the same time range.In the ms time range, instead, the CO production does not change between the new and the old kinetic scheme because CO2 dissociation is due essentially to vibrational induced dissociation channels and the introduction of the production and quenching processes involving the CO(a 3 Π), CO2 and CO does not affect the composition.

Contribution of the CO(a 3 Π) to CO2 dissociation
The new reactive quenching processes introduced for the CO(a 3 Π) state give also a contribution to production and loss of CO2 molecules.In particular, 1.The quenching of the CO(a 3 Π) state by collisions with CO2 in the ground state, i.e.CO(a 3 Π) + CO 2 → 2CO + O can be seen as another dissociation mechanism for CO2, i.e. induced by the excitation of the ( 3 Π) state.2. The quenching processes of ( 3 Π) by collisions with O2 and CO, i.e. O(a 3 Π) + O 2 → CO 2 + O and CO(a 3 Π) + CO → CO 2 +  can be considered as back-reactions which reform CO2.
Their correspondent rates can be compared to the other CO2 loss and production rates in order to understand their relative importance.The list of all the production and loss processes for the CO2 density accounted in the model is presented in Table 5. Fig. 13 shows the time evolution of the corresponding rates in the MW test case.In the early time range of the discharge, the quenching by CO2 prevails up 10 -5 s due to the initially high CO(a 3 Π) concentration, followed by DEM one up to 2-3 10 -4 s.After that, PVM mechanisms overcome the other ones showing the importance of vibrational excitation induced processes in the ms time range.In particular, a prevalence of the PVMO process on the PVM one occurs due to the higher PVMO rate coefficient and to the increase of O concentration with the CO2 dissociation progress.
In the MW test case, the most important recombination process for CO2 in the ms time range is CO + O 2 → CO 2 + O, while the two ones involving the CO(a 3 Π) state, i.e.CO(a 3 Π) + CO → CO 2 + C and CO(a 3 Π) + O 2 → CO 2 + O, are one and two orders of magnitude lower, respectively.
Fig. 14, instead, shows CO2 production and loss rates in glow discharge conditions (P=5 torr, Tgas experimental time dependent profile, td=5 ms, Pd=1 Wcm -3 ).As it can be seen, in these conditions, CO2 is dissociated essentially by electron impact (DEM) and vibrational induced dissociation (PVM) and the dissociation by quenching of the ( 3 Π) with collisions with CO2 have a minor importance.Note also that PVMO mechanism is orders of magnitude lower than previous mechanisms.The CO2 is instead reformed essentially by means of the quenching process involving the ( 3 Π) by collisions with CO during the discharge and in the post-discharge by recombination of CO and O atoms.

Conclusions and perspectives
In this paper, an in-depth study of the role of electronic excited states in the kinetics of CO2 cold nonequilibrium plasmas was carried out by means of a 0D kinetic model in which the electron Boltzmann equation was solved simultaneously and self-consistently with the state-to-state master equations describing the vibrational states, the electronic excited states and the plasma composition.Beside the 7 eV and 10.5 eV electronic excitation cross sections of the Phelps database, other CO2 electronic excited levels have been identified by experiments and theoretical methods.Recently, new added data from the Biagi's Magboltz code to the Lxcat database have provided a set of several electronic excitation cross sections for CO2 in the energy range from 6.5 eV up to 25 eV.A new dissociation model has been proposed based on the use of the Biagi electronic excitation cross sections as fully dissociative ones and the corresponding simulation results have been compared to the results obtained with the dissociation model connected to the Phelps database in typical glow discharge and MW discharge conditions.In glow discharge conditions, where dissociation occurs essentially by electron impact and low vibrational excitation is present, the results of the two models are comparable due to compatibility of the two cross section databases obtained by swarm analysis procedures.In the MW discharge case, instead, some discrepancies start appearing when vibrational excitation becomes important, showing the need to integrate a model based only on dissociation from electronic excited states with a model that takes into account also electron impact dissociation from vibrational excited states.The inclusion in the kinetics of some CO2 electronic excited states as separate species without considering them as dissociative ones needs the implementation of corresponding kinetic equations.
Unfortunately, the lack of data present in literature concerning quenching and radiative processes of these states prevent at the moment the construction of corresponding accurate kinetic description and further experimentally and/or theoretically investigations on these aspects is still necessary.Due to its important role in the kinetics, a new more accurate kinetic description of the CO(a 3 Π) state is presented and tested in MW discharge conditions.The newly added processes affect mostly the kinetics by increasing the CO(a 3 Π) in the early time of the discharge (up to 10 -4 s) through dissociative excitation and dissociative recombination processes.In the ms time range the CO(a 3 Π) kinetic is dominated by quenching processes with O, CO, CO2 and O2.The results have shown that a change in the time evolution of the CO(a 3 Π) density has a direct effect on the eedf, the electron temperature and the electron impact dissociation rates thanks to the effect of superelastic electronic collisions.A direct effect is also present for the CO vdf, CO vibrational temperature and CO vibrational-induced dissociation rates due to the quenching and VE processes involving the CO(a 3 Π) and the CO ground state.The CO2 vdf and consequently the CO2 vibrational-induced dissociation rates are only indirectly affected by the change of CO(a 3 Π) due to the change in the eedf due to eV processes.
Finally, the contribution of the CO(a 3 Π) state to CO2 dissociation is examined in terms of production and recombination (or back-reaction) processes both in MW and glow discharge conditions.
Future investigation on electronic excited states will be performed in conditions in which dissociation of CO2 via electronic degrees of freedom is assumed to become the dominant mechanism, i.e. at values of the reduced electric field E/N of hundreds of Td as reported in [33].Such conditions are obtained in DBD experiments or, for example, in those experimentally and numerically analyzed by Pokrovskiy et al. [68], in nanosecond capillary discharges ignited in pure carbon dioxide at moderate (10-20 mbar) pressures.The latter ones are characterized by high reduced electric field, high specific deposited energy and high value of dissociation degree and present the so-called phenomenon of fast gas heating (FGH) [96][97], i.e. the high increase of the gas temperature at sub-microsecond timescale due to the high excitation of the electronic excited states during the discharge and their subsequent quenching towards the translational degrees of freedom.For the future, we should take into account the solution of the gas heating equation for the describing also high pressure and high temperature plasmas.Moreover, an improvement of the CO2 vibrational kinetics following the approach of Armenise and Kustova [98][99] which consider the coupling of the three CO2 vibrational modes with the use of possible newly calculated state-to-state vibrational energy transfer rate coefficients [100][101][102] is desirable.Finally, the introduction in the kinetics of He atoms and their processes not only for explaining the results of ref. [15] but also to reproduce the behavior of new mixture types of the kind CO2-N2-He-CO [103] could be interesting.

Appendix: Possible approaches for CO2 electronic excited state kinetics
There are in literature attempts to include some of the CO2 electronic excited states in the kinetic model without considering them as purely dissociative ones.The first difficulty is to understand which electronic excitation cross sections should be considered as already implicitly included in the electron impact dissociation cross sections considered in the electron-impact database used, and which of them, instead, can be added to the set of cross sections without overlapping.The Phelps and Biagi databases are based on swarm data analysis, and their dissociation cross sections could already include some electronic excitation cross sections.Following the consideration made by Polak [71] in the building up of his CO2 dissociation cross section, one could reasonable think that the first seven excitation cross section related to the singlets ( Σ  ) states could be considered as already included in the 7 eV cross section.This approach has been used by Stankovic et al. in [104].They calculated electron impact ionization and electronic state excitation rate coefficients in non-equilibrium CO2 plasma under time-dependent radio-frequency (RF) electric field with the eedf calculated by Monte Carlo (MC) simulations.The MC calculations were performing by including in the CO2 cross section database: 1) the 7 eV excitation cross section taken from the Hake and Phelps database; 2) the two electronic excitation cross sections measured by Kawahara et al. [58] related to the states Σ  + 1 and Π  1 .
The first seven electronic excited states excitation cross sections are assumed already included in the 7 eV cross section.The 10 eV cross section was calculated after subtraction of the summed cross sections for all scattering types they considered in the simulation (elastic scattering, excitation of different vibrational modes, electronic excitation and ionization) from the experimentally measured total cross sections given by Itikawa [20] with an excellent agreement between their calculated transport coefficients and transport parameters measured by other authors.
Another difficulty for the inclusion of electronic excited states in the kinetics is related to the necessity of implementing appropriate kinetic equations for each of them, considering either electron impact excitation and de-excitation or radiative and quenching processes by collisions with the plasma mixture species.Unfortunately, for the CO2 electronic excited states very little information exists about such processes.An attempt in this direction has been performed by Bultel et al. [106]  and for such states they consider the electronic excitation processes under heavy particle impact of the kind CO 2 (X 1 Σ g + ) + CO 2 (X 1 Σ g + ) → CO 2 ( Σ u The correspondent rate coefficient is calculated by applying the following analytical form [107], derived from Park et al. [108], Bhadra and Ghosh [109] and Drawin [110].reporting some Arrhenius coefficients for selected transitions (see Table III in [106]).
It should be noted that the rate coefficients calculated from eq. (A2) depend on the energy thresholds ∆ and vary according to the excitation energy chosen for each electronic excited state (see Table 2).For example, the Arrhenius fit coefficients reported by Bultel et al. [106] describing the first transition Σ (see Table 2).Fig. 6 shows the heavy particle electronic excitation rate coefficients as a function of the temperature for selected allowed and forbidden transitions from ground state calculated by applying eq.(A2) with electronic energies taken from Nakatsuji [50].As it can be seen, these processes are activated at high gas temperature, conditions in which thermal dissociation of CO2 dominates and their importance could be negligible.) + CO 2 (X 1 Σ g + ) calculated from eq. ( A2) from [106][107].

Fig. 3
Fig.3Time evolution of the species number densities and dissociation rates in glow discharge conditions (P=5 torr, Tgas experimental time dependent profile, dt=5 ms, Pd=1 W/cm -3 ) calculated with the dissociation model connected to the Phelps database (full lines) and to the Biagi database (dotted lines).

Fig. 4
Fig. 4 Eedf time evolution in the post-discharge calculated with the dissociation model based on the Phelps database (a) and the Biagi database (b) in glow discharge conditions.

Fig. 11
Fig. 11 Time evolution of the (a) CO vibrational temperature and of the (b) CO dissociation rates by PVMCO, i.e.CO + M → C + O + M and by the Boudouard process, i.e.CO(v) + CO(w) → CO 2 (v) + C, in the new and old kinetic scheme during the discharge of the MW test case (Tgas=300K, P=20 Torr, Pd=80 Wcm -3 , td=50 ms).

Table 2 .
Available electron excitation cross sections from ground state.
Excitation continuum with threshold 12.75 eV 9) Excitation sum of Rydberg states, described by 7 different cross sections with thresholds from 12.901 to 13.68 eV 10) Dipole allowed transitions leading to dissociation, described by 25 different cross sections with threshold from 13.78 to 19.75 eV.11) Dissociative excitation via sum of triplets with a threshold of 25 eV.

Table 3 .
Kinetic processes involving the (a 3 Π) electronic excited state: old kinetic scheme.

Table 4 .
New kinetic scheme for the (  ) electronic excited state

Table 5 .
CO2 production and loss processes included in the kinetics.