Vibrational Population Distribution and Conversion Efficiency

sion Efficiency

Figure 5.14 shows several contour plots of the low lying vibrational lev- els for a positive (cathode-directed) streamer discharge at standard tempera- ture and pressure. The first four degenerate symmetric stretch levels which

Figure 5.14: Contour plots of the low lying vibrationally excited CO2levels (in m-3)

in a cathode-directed streamer.

include the resonant bending levels are denoted as CO2a d where CO2va is the

(0, 1, 0) level, CO2vb is the sum of the (0, 2, 0) + (1, 0, 0) states, CO2vc is the

sum of the (0, 3, 0) + (1, 1, 0) states, and CO_2vd is the sum of the (0, 4, 0) + (1, 2, 0) + (2, 0 ,0) states. The first four asymmetric stretch levels indicated by numbers (1-4) are also plotted in Fig. 5.14. The first four symmetric levels (a-d) have vibrational excitation energies of 0.08, 0.17, 0.25, and 0.33 eV, and the first four asymmetric levels have vibrational energies 0.29, 0.58, 0.86, and 1.14 eV.

During a single streamer discharge, the symmetric mode is preferen- tially populated with the highest density occurring in the first symmetric vi-

brational level. In addition, only the first three excited states of the asym- metric stretch vibrational mode are populated by the streamer discharge. The peak densities for all vibrational levels in both modes are observed near the electrode tip which is characterized by high electron densities, and low (1-3 eV) plasma temperatures.

In the streamer head, where electron temperatures are high (_{⇠ 10 eV),} the vibrational populations are at a minimum. Therefore, the streamer tail is the most efficient region for populating the low lying vibrational levels. However, due to the transient nature of the streamer discharge and low density of vibrational states, a multitude of streamers is necessary to have successful vibrational pumping of the low lying vibrational states.

The asymmetric stretch vibrational temperature is estimated from the population of the low lying vibrational levels. Assuming a Boltzmann distri- bution of the excited states, the vibrational temperature (Tv) is determined

from the density ratio of the first two asymmetric vibrational levels, given by Eq. 5.6 where N1 (0, 00, 1) and N2 (0, 00, 2).

Tv =

Ev

kBln(N_N2₁)

(5.6)

where the density of the vibrational states are given by Ni, and Ev is the vibra-

tional energy of the asymmetric stretch mode. The vibrational temperature is estimated to be_{⇠ 4900 K.}

are two orders of magnitude lower than those of the vibrationally excited states of CO2, while molecular oxygen is three orders of magnitude lower.

Additionally, the O2 distribution is localized with peak densities in the region

furthest from the streamer head. This indicates that the region near the electrode is a recombination zone, while the streamer head is responsible for ionizing and dissociation reactions.

Therefore, the primary mechanism for CO and O formation in the streamer is due to direct electron impact dissociation in the head (refer to Fig. 5.10), e + CO_{2! CO + O + e. This results in a low overall conversion} of CO2, _NNCO

CO2 = 0.01 %. To increase the conversion rate for streamer dis-

charges, the population of the low lying vibrational levels must be increased so that vibrational ladder climbing is possible, CO_2v1+ CO_2v1! CO2v2+ CO2.

Vibrational ladder climbing is not possible for single streamer discharges, as indicated by Fig. 5.14, but the presence of several streamers in a DBD reactor will be able to populate the low lying vibrational levels and increase the total conversion.

5.4

Afterglow

A streamer discharge is a fast transient ionization wave lasting approx- imately 1-3 ns. At these time scales only electrons are capable of responding, therefore the primary reaction kinetics in a streamer are attributed to electron impact excitations. The relaxation processes in a streamer occur in the after- glow at timescales of the order microseconds. To simulate at these timescales

Figure 5.15: Contour plots of the CO, O and O2 densities (in m-3) for cathode-

directed streamer.

using a plasma fluid model is not feasible, so a 0D model was formulated by neglecting the spatial terms in the plasma fluid model equations. The 0D model is used to investigate the afterglow of the streamer discharge, and the relaxation of the vibrational population distribution, Fig. 5.14.

To simulate the afterglow in the 0D model an external power source is needed which replicates the energy deposited by a streamer discharge. The external power term for the zero dimensional model is determined from the 2D plasma fluid model by measuring the temporal evolution of the electron Joule heating at a fixed spatial location. The resulting pulse profile is fitted and used as the input power for the 0D model. The 0D models is run for 1 atm. and 300 K.

Figure 5.16: A 0D simulation of the afterglow of a streamer discharge showing the population of the first five asymmetric vibrational levels of CO2 (in m-3). The top

solid line corresponds to the first asymmetric vibrational level, and bottom solid line corresponds to the fifth vibrational level.

The resulting power pulse is a Gaussian profile with a FWHM of 0.1 ns and a peak power density of 5x1012_Jm-3_{. In the first few nanoseconds after the}

applied power pulse the electron temperature relaxes to the background gas temperature, while the electron density decreases by an order of magnitude in the first microsecond. Therefore, the afterglow is governed by the chemical kinetics of the bulk excited species, and electron impact reactions which were dominant in the streamer excitation phase play a minimal role.

Figure 5.16 shows the vibrational relaxation of the first five asymmetric stretch levels of CO2. The first two vibrational levels are populated within

the first 3 ns due to electron impact collisions during the streamer discharge phase, after which they exhibit monotonic decay. The higher vibrational levels (CO_2v3-5) reach their peak density in the first 3 microseconds of the afterglow. Furthermore, as the vibrational quantum number increases the density of the state decreases, and the peak density is shifted further in time.

The monotonic decay (refer to Fig. 5.17) of the first two vibrational levels and shift of the peak density of higher vibrational levels in time is ex- plained by the vibrational ladder climbing mechanism, given by Eq. 5.7

CO_2v1+ CO_{2v1 ! CO2v2}+ CO₂ CO_2v2+ CO_{2v2 ! CO2v3}+ CO_2v1 CO2v3+ CO2v3 ! CO2v4+ CO2v2

. . .

(5.7)

for single quantum vibrational exchange. The first two vibrational levels CO2v1

and CO_2v2 are populated directly by the streamer discharge, while the pop- ulation of subsequent vibrational levels (vj) depends upon the density of the

adjacent lower vibrational level (vj 1) and the collision frequency. Hence, as

seen in Fig 5.17, as the first two vibrational populations are depopulated their energy is transfered to higher vibrational levels resulting in an increase of the adjacent upper vibrational level.

Though a single streamer does populate the low lying vibrational levels, there isn’t sufficient density of the first level for the high lying vibrational states to be populated through VV relaxation. Additionally, there is no re-

Figure 5.17: A 0D simulation of the afterglow of a streamer discharge showing the population of the first four asymmetric vibrational levels of CO2 (in m-3), showing

population of the low lying levels from electron impact reactions. Therefore, multiple streamers are necessary to pump higher vibrational states.