Spatially resolved TALIF investigation of atomic oxygen in the effluent of a CO2 microwave discharge

A diagnostic setup for one-dimensionally spatially resolved two-photon absorption laser-induced fluorescence (TALIF) detection of ground state oxygen atoms ( 2p43P2,1,0 ) is developed. The goal of this study is to investigate the evolution of temperatures and absolute number densities of oxygen atoms along the effluent of a low-pressure CO2 microwave discharge in order to gain insights into some of the mechanisms governing the post-discharge regime. The plasma source is operated at conditions of 600 W– 1200 W of absorbed power with flow rates of 74 sccm and 370 sccm pure CO2 at pressures between 1.2 mbar and 5 mbar with specific energy inputs up to 111.9 eV/molecule. These operating conditions exhibit high CO2 conversions (up to 90%) at low energy efficiencies (2%–7.4%), due to direct electron impact dissociation driving the conversion process resulting in splitting of CO2 into CO and metastable oxygen atoms. The TALIF measurements yield spatially resolved translational temperatures between 1000 K– 1600 K for most operating conditions and axial positions along the effluent. Reference measurements with xenon 6p′[3/2]2 are used for absolute number density calibration. The resulting axially resolved number density profiles of ground state atomic oxygen increase along the effluent, even at considerable distances of several centimeters from the active discharge, before they reach a maximum between 5×1020 m−3 and 2.2×1021 m−3 depending on the condition, and decrease after that. This behavior indicates the potential significance of quenching of metastable oxygen atoms within the post-discharge regime of the investigated CO2 discharges. The measured spatially resolved number density evolutions are qualitatively consistent with quenching via wall collisions being the dominant deactivation mechanism, underlining the importance of particle-wall interactions.


Introduction
The electrification of chemical processes is garnering increasing importance as renewable energies are filling the gaps left by their less environmentally acceptable predecessors.The field of plasma technology for gas conversion is a very active area of research, which aims to utilize plasma processes to convert different molecules into useful species, for example as a feed stock for other chemical processes.A prominent example is the conversion of CO 2 into CO, a crucial ingredient for the production of synthetic fuels [1,2].
Within the field of plasma CO 2 conversion, especially microwave discharges have been, and continue to be, the focus of extensive research [3][4][5][6][7][8][9][10]. The underlying mechanisms driving the CO 2 conversion can differ widely between different microwave plasma sources.While at higher pressures thermal dissociation appears to be driving the CO 2 conversion [6,11], low-pressure discharges can be used to operate in non-equilibrium regimes and direct dissociation via electron impact can become dominant [12,13].Experimental investigations of the plasma offer valuable insights into specific attributes of the discharges for example temperatures and inner energy distribution of the molecules [13][14][15], electron temperatures and densities [16,17], and concentrations of species of interest [18,19], while sophisticated modeling approaches are developed to breach the gap towards understanding the underlying reaction kinetics [20][21][22][23][24].
Naturally, a lot of this research is focused on the active discharge regime.However, the ability to accurately predict the post-discharge conditions is also essential to fully understand the overall plasma conversion process and ultimately enabling the optimization of any plasma conversion application.This is because the conversion process is not finished before the post-discharge gas has cooled down far enough so that it reaches a stable composition.Until it is complete, the post-discharge kinetics along the effluent of the plasma source will impact the achievable CO retention for example via recombination reactions with oxygen radicals.In two recent studies, Hecimovic et al have for example demonstrated the significance of employing post-discharge cooling in the effluent of an atmospheric pressure microwave discharge in order to prevent back-reactions and retain high CO 2 conversions [7,8].
In this study, an experimental setup is developed allowing for one-dimensionally resolved two-photon absorption laserinduced fluorescence (TALIF) detection of atomic oxygen along the effluent of a low-pressure CO 2 microwave discharge.For the investigated operating conditions of the surfaguide discharge, direct electron impact is expected to be the dominant dissociation mechanism, leading to the formation of CO alongside electronically excited atomic oxygen metastables [25].The employed TALIF scheme is tailored to detection of oxygen atoms in the electronic ground state allowing for quantitative assessment of the evolution of oxygen radicals along the plasma effluent while potentially offering indirect insights into the post-discharge behavior of the metastable oxygen atoms created in the plasma.
TALIF has been successfully applied to the detection of atomic oxygen in CO 2 plasmas in the past [19,26,27].Due to the comparatively low powers of the laser pulses, simultaneous detection of spatially resolved TALIF signals created with a ns-pulsed laser source like the one used in this study can be challenging compared to TALIF approaches using shorter pulses and higher peak powers, e.g. with durations in the fs range [28].However, the lower peak powers of ns pulses help avoid unwanted effects such as saturation that might otherwise complicate the calibration procedure necessary to obtain absolute number densities [29,30].
The investigated plasma source and operating conditions are outlined first alongside the most important parameters before the developed laser diagnostic setup is introduced and characterized in detail.Ultimately, the goal of this study is to measure absolute number densities and translational temperatures of ground state atomic oxygen with one-dimensional spatial resolution along the effluent of the CO 2 plasma in order to gain insights into some of the complex mechanisms governing the post-discharge regime.Uniquely, this study investigates the effluent of a low-pressure CO 2 microwave discharge with very high specific energy inputs that are exceeding typically investiagted or modeled conditions.It is therefore of primary importance to ensure the rigorous nature of the measurements and a significant portion of the article is devoted to the verification of the experimental methodology.

Plasma source
The investigated plasma source is a surface wave microwave discharge (SAIREM Surfaguide).It consists of a magnetron able to supply up to 6 kW of microwave power with a frequency of 2.45 GHz, which is directed through a tapered waveguide to a quartz tube with outer and inner diameters of 20 mm and 17 mm respectively.The plasma is created within the quartz tube.The microwave power supply is equipped with a water-cooled oscillator used to monitor and dissipate the reflected power, which is minimized manually using a three stub tuner.The power values assigned to different operating conditions refer to the difference between the forward power emitted by the magnetron and the reflected power thus representing the absolute power delivered to the system.
The surfaguide setup is detailed in figure 1. CO 2 (purity 3.5, Air Liquide) is fed through two tangential gas inlets into the quartz tube at a constant flow rate for a given condition controlled by a flow controller (Brooks GF40).The discharge originates at the axial position of the quartz tube that intersects with the waveguide.Microwave leakage is minimized by two chimneys that are enveloping the quartz tube in both up-and downstream directions.They are fixed to the waveguide and supplied with pressurized air, which is directed to the surface of the quartz tube within serving as a means of cooling and preventing thermal damage to the tube.The low-pressure conditions are achieved using a vacuum pump (Leybold TRIVAC D8B).The pressure inside of the quartz tube can be precisely monitored and controlled using a pressure gauge (Pfeiffer Vacuum CMR 363) and a precision valve in between the surfaguide setup and the pump.
The plasma source is initially ignited with pure argon, after which CO 2 is introduced and the argon flow is turned off, resulting in a pure CO 2 plasma.A given operating condition of the plasma source is characterized by the parameters volumetric flow rate Γ CO2 , pressure p, and absorbed power P abs .Here, the plasma source is operated with flow rates of 74 sccm and 370 sccm of pure CO 2 within the pressure range 1.2 mbar ⩽ p ⩽ 5 mbar using 600 W as well as 1200 W of absorbed power.It can be operated with pressures up to 100 mbar, however the reduced signal intensities and increased collisional quenching prohibit the quantitative investigation of conditions  beyond 5 mbar of pressure with the TALIF setup.Another important quantity for the characterization of a plasma conversion process is the specific energy input SEI.It is calculated as the ratio of P abs and Γ CO2 , commonly expressed in the unit eV/molecule, and indicates how much energy is available on average for the conversion of each CO 2 molecule entering the reactor.As discussed above, the absorbed power P abs refers to the power delivered to the system as a whole.This means that while the SEI is a useful macroscopic quantity enabling the achievement of similar discharge conditions across different plasma sources, the exact power absorbed by the discharge still depends on the losses of a given reactor setup.
The operating conditions investigated in this study are listed in table 1.The experimental determination of conversion χ and energy efficiency η is discussed in the following section.

Conversion and energy efficiency
Apart from the already mentioned sensors and controllers used to operate the plasma source at reproducible and well defined conditions, another important diagnostic tool is mass spectrometry (MS) specifying CO 2 conversion χ and energy efficiency η.
The MS system is comprised of a spectrometer model QMG 220 M2 Prisma Plus with a cross-beam ion source by Pfeiffer Vacuum.It is equipped with a custom designed multi-stage gas sampling system that enables measurement of gas compositions over a wide pressure range.More details on the MS system developed by Hecimovic et al can be found elsewhere [31].The MS system samples the gas at a significant distance downstream of the plasma discharge in front of the vacuum pump where the gas has significantly cooled down and no more recombination reactions are taking place.This is essential in order to assess the conversion and the energy efficiency of the overall plasma process including the post-discharge regime.The conversion χ is calculated from [31] with the molar flow rate of remaining CO 2 behind the discharge ṅCO2,out and the total molar flow rate ṅtotal,out comprised of contributions from CO 2 , CO, and O 2 measured by the MS system.The energy efficiency η of the conversion process is determined as with the enthalpy of the dissociation reaction ∆H = 2.9 eV/molecule and the specific energy input SEI.The conversions χ and the energy efficiencies η determined for the different operating conditions are listed in table 1.The investigated conditions are characterized by high conversions.However, their large energy demand (see SEI in table 1) results in low energy efficiencies for the conversion process.The effect of pressure variation within the investigated parameter space on the conversions is very small with around 80% conversion for pressures between 1.2 mbar and 5 mbar at constant flow rates and absorbed powers.However, variations of flow rate and absorbed power impact the conversions significantly.Increasing the flow rate by a factor of 5 for constant pressure and absorbed power results in a conversion decrease from 82% to 57% while doubling the power leads to a significant conversion increase from 57% to over 90%.Britun et al [13] have investigated CO 2 conversion in a surfaguide plasma source with similar geometry and operating conditions.The main difference between the two plasma sources is the pulsed operation of the surfaguide used in [13].Regardless, both surfaguide sources appear to show comparable performances with maximum conversions of around 90%.The observed drop in conversion for increasing flow rates at constant pressure and power is reported in [13] as well.This indicates that the performance metrics of CO 2 conversion for the investigated surfaguide setup are typical for this type of source and range of operating conditions.

Length of the plasma
The plasma elongation within the quartz tube differs for different operating conditions.For the majority of investigated conditions apart from the one with the lowest pressure of 1.2 mbar, the plasma does not extend outside of the chimneys.However, since the effluent of the plasma is the object of research of this study, it is important to consider exactly how far downstream from the active discharge any given measurement is obtained.In order to determine the plasma elongations, equally spaced holes with a diameter of 4 mm are made along the axis of the downstream chimney in order to grant optical access.Axial intensity profiles along these optical access ports are recorded with an ICCD camera (Andor iStar).The obtained images are corrected for the background and a linear fit is applied to the intensities recorded at the defined axial positions with the plasma elongation being represented as extrapolation of the linear fits to zero intensity.The downstream distance is defined as distance from the outer wall of the waveguide corresponding to x 0 = 0 as indicated in figure 1.An example of a measurement is presented in figure 2(a).The measurements are repeated using spectral bandpass filters for different atomic oxygen emission lines (777 nm and 844 nm) as well as ND filters to capture the broadband emission of the plasma.Different filters are used as relying on a singular emission component, e.g. the atomic oxygen lines around 777 nm, might not provide a reliable estimate of the plasma dimensions [32].The results are consistent throughout all profiles of different spectral intensities.In addition, the plasma extends out of the chimney for one of the five investigated operating conditions.Therefore, for this condition (600 W, 74 sccm, 1.2 mbar), the plasma elongation is known and can serve as a benchmark.
The resulting plasma elongations are presented in figure 2(b).The blue bars represent the average plasma length measured for each condition.The dashed line represents the length of the chimney.The error bars indicate the standard deviations.Naturally, the measurement uncertainties increase for conditions where further extrapolation is required.However, as indicated by the benchmark, the measured average plasma elongations are a very good approximation even for the most challenging case.The measurements demonstrate that pressure p and absorbed power P abs have a large effect on the length of the discharge in contrast to the flow rate Γ CO2 , towards which the plasma length appears to be insensitive within the investigated parameter space.

TALIF experiment
The diagnostic setup for TALIF measurements of atomic oxygen in the effluent of the discharge has been developed for this study.The laser source is a tunable pulsed dye laser (Sirah Cobra-Stretch) pumped by a frequency doubled Nd:YAG laser (Innolas Spitlight 600) at 20 Hz with pulse durations of around 7 ns.The dye laser is operated with a Pyridine 1 dye solution to create the fundamental beam, which is then frequency tripled.This results in an available tunable wavelength range between 221 nm and 237 nm.For the investigations of this study, the wavelength is tuned around 225 nm.During a given measurement, the laser wavelength is tuned with a spectral resolution of 0.5 pm around the two-photon resonance of the probed atomic oxygen or xenon two-photon transition respectively with the latter serving as a reference species for absolute number density calibration [33,34].
The detection setup for the axially resolved TALIF measurements is depicted in figure 3. The slightly divergent laser beam is directed towards the downstream end of the quartz tube with mirrors and subsequently directed axially through the tube with careful horizontal alignment entering the tube through the downstream optical access window and exiting the tube through another window located upstream of the plasma source.Before entering the quartz tube, the beam is passed through an aperture in order to prevent reflections that might otherwise perturb the measurements from entering the tube.The beam is focused to an axial position of 3 cm downstream of the chimney exit using a plano-convex lens with a focal length of 500 mm.The focus position is kept constant during the experiments.Before entering the quartz tube, the laser beam has a diameter of approximately 5 mm, and it is focused to a diameter of around 300 µm.The laser pulse energy is detected behind the optical access window at the upstream end of the quartz tube using an energy probe (Ophir PE10-C).The energy measurements are corrected for attenuation through the upstream optical access window to determine the laser pulse energies available for TALIF excitation within the quartz tube.Typical laser pulse energies within the quartz tube during the measurements are around 20 µJ.The fluorescence signals are recorded downstream of the discharge using an ICCD camera (Andor iStar) with a 840 nm bandpass filter (10 nm full width at half maximum (FWHM)) positioned in front of the lens of the camera.The distance from the laser beam to the camera lens during the measurements is around 32 cm.The lens is a 35 mm f/2D lens (Nikon) mounted to the camera via an F-mount adapter.The intensifier diameter is smaller than the sensor width, resulting in an active sensor area of 1330 × 512 pixels with a pixel width of 13.5 µm.The camera intensifier's quantum efficiency is <5% in the range of the oxygen and xenon fluorescence wavelengths.Therefore, it is operated at maximum gain.The exposure is gated to a 200 ns window.The laser pulses and the camera acquisition are synchronized with a digital delay generator (Stanford Research Systems DG 645).
The excitation schemes of the utilized two-photon transitions are detailed in figure 4. The ground (2p 4 3 P J ) and excited (3p 3 P J ) states of atomic oxygen are triplets.In the notation schemes, the three total angular momentum quantum numbers J of the respective levels are listed in order of increasing energy.In the TALIF experiment, specifically the 2p 4 3 P 2 level of the atomic oxygen ground state is probed.Different xenon two-photon transitions are available for absolute number density calibration measurements, differing in excitation and fluorescence wavelengths.For example, a commonly used xenon transition with an excitation wavelength especially close to that of atomic oxygen is xenon 7p [3/2] 2 which is excited at 225.5 nm and emits fluorescence at 462 nm, see for example [26,35].For the experimental setup developed here, however, it is crucial that the fluorescence wavelength of both xenon and atomic oxygen are as similar as possible, because the spectral response of the camera intensifier exhibits inconsistent sensitivity profiles over the width of the sensor when comparing 462 nm to 835 nm light.Therefore, the xenon 6p ′ [3/2] 2 transition (see figure 4) is best suited for the detection apparatus at hand.
For each of the investigated conditions, three TALIF measurements are carried out at different radial positions.For the first one, the laser beam is directed along the center axis of the quartz tube and subsequently, two additional measurements are carried out at different radial positions 5.5 mm above and below the center axis respectively.In addition, xenon cold gas (purity 4.8, Air Liquide) measurements at 0.3 mbar for absolute number density calibration are carried out for each position.The center line measurements exhibit higher intensities than the off-center measurements.This is the case for both oxygen as well as xenon measurements and thus is likely caused by additional reflection losses for non-normal angles between fluorescence, quartz tube surface, and detection line of sight.Since both oxygen and xenon measurements are affected equally by the reduced intensity for off-center measurements, the effect does not prohibit calibration.However, it demonstrates that separate xenon measurements for all radial positions are crucial for absolute number density calibration.
The recorded images are accumulated over 300 individual exposures for each wavelength step of a laser scan.The acquisition speed of the camera is slower than the repetition rate of the laser and therefore not every laser shot is registered.This prohibits a shot-to-shot evaluation of the laser pulse energies during the measurements and the average laser pulse energy is recorded instead.Each of the measurements consists of 27 recordings at different laser wavelengths (0.5 pm steps) in order to spectrally resolve the two-photon absorption profiles.The images are background corrected by subtracting images recorded with the laser wavelength tuned away from the absorption lines, thus eliminating any contributions from oxygen/xenon fluorescence from the dark images while still potentially allowing for correction of other influences like light reflections or fluorescence from inclusions in the quartz tube if present.However such contributions are not observed here.
The images are calibrated with regard to their absolute position by recording reference images with a millimeter scale positioned along the quartz tube axis.With this approach, each horizontal pixel position in the images can be converted into an absolute axial position x with x 0 = 0 being defined as the downstream outer wall of the waveguide as indicated in figure 3. Typically, one pixel in the images corresponds to an axial distance of around 0.1 mm.
The fluorescence intensity is collected by integrating over the three central vertical pixels of the fluorescence images along the laser beam incidence.The resulting data set consists of fluorescence intensities for different laser wavelengths and at different axial positions x, corresponding to hundreds of absorption lines along the axis of the quartz tube.An example of such a data set is depicted in figure 5.A Savitzky-Golay filter is applied to the data along the x-direction for each wavelength step separately in order to reduce the pixel-to-pixel noise.This is especially beneficial for the line-shape fitting for the temperature determination discussed in section 3.1.
Atomic oxygen is successfully detected downstream of the axial focus position, while xenon fluorescence is detected along the entire axial range.Moving the focus several centimeters further upstream into the chimney results in a decline in signal-to-noise ratio, but not in an axial shift of the oxygen signals.Similarly, shifting the camera position also has no effect on the absolute position of the signals.This confirms that any absence of oxygen signal at different axial positions is directly linked to the lower detection limit of the setup instead of signal losses due to parasitic effects such as photo-ionization or detection related artefacts.
In section 3.2 the absolute number density calibration method is discussed in detail.The saturation behavior of the TALIF signals at varying laser pulse energies is investigated in section 3.3 and the number density threshold for the onset of detrimental amplified spontaneous emission (ASE) is estimated.Measurements of excited state lifetimes required for absolute number density calibration are presented in section 3.4.

Temperature determination
In order to determine the translational temperatures T of the oxygen atoms in the effluent of the CO 2 plasma, the line shapes of the two-photon absorption lines are systematically analyzed.As discussed above, the 2p 4 3 P 2 level is probed during the experiment resulting in three overlapping absorption lines with excitations to the states 3p 3 P 1,2,0 .To account for this, the profiles fitted to the measurements are composed of three individual spectral lines.The spectral positions of the central wavelengths of these lines are fixed relative to each other based on NIST data for the individual states [36].The relative intensities of the three transitions are fixed as well according to the relative cross sections from Saxon and Eichler (table IX) [37].
The line shapes of the atomic oxygen measurements are found to be best approximated using pure Gaussian profiles, meaning that they are comprised of Gaussian contributions from Doppler broadening and instrumental broadening while pressure related broadening effects like collisional broadening that would result in a Lorentzian contribution to the line shapes, appear to be negligible for the investigated conditions.The fitting parameters for the oxygen line shapes are the width of the Gaussian profiles ∆λ G (half width at half maximum HWHM), the central wavelength of the ∆J : 2 → 2 transition, and a factor for scaling the area-normalized profiles to the measurement data.For all of these parameters, the 95% confidence intervals are determined as well in order to allow for estimation of the uncertainties of the individual fits.Figure 6(a) shows an example of a line shape fit to a measured atomic oxygen profile.During the measurements, hundreds of profiles like this one are recorded simultaneously for different horizontal pixel positions.Figure 6(b) depicts the deviating fits based on the 95% confidence intervals of the fitting parameters.Although the fitted profiles look very similar, the slight discrepancy near the peak of the absorption line has a fairly large influence (±4%) on the width of the fits, which is defined at half maximum of the intensity.
In order to allow for temperature determination from these line shape fits to the oxygen profiles, the instrumental broadening is determined using the xenon cold gas measurements.However, in contrast to the oxygen measurements, the measured xenon profiles are best approximated using a Voigt profile with a slight Lorentzian contribution.The Voigt profiles for the line shape fitting are calculated using the approximations from [38,39] with the additional fitting parameter Lorentzian width ∆λ L .An example of a xenon profile is shown in figure 7(a).The presence of a Lorentzian contribution in the overall line shape is an indication that for xenon at 0.3 mbar, pressure related broadening effects may not be neglected.In order to verify that this is indeed the cause for the Lorentzian contribution to the xenon line shapes, a complementary set of xenon measurements varying the pressure over a large range up to 400 mbar is performed.The resulting average line shape contributions over the observed length of the laser beam are depicted in figure 7(b).The Gaussian contribution to the fits remains almost constant over the entire pressure range while the Lorentzian contribution shows a significant increase towards higher pressures.Similar behavior of the pressure dependent width increase of other xenon twophoton transitions has been reported by Raymond et al [40] and Meindl et al [41].Therefore, the instrumental broadening ∆λ I can be determined from the Gaussian portion of the xenon line shapes by subtracting the Doppler width for xenon at room temperature according to  with the Doppler broadening (HWHM) with the central wavelength λ 0 , the speed of light c, Boltzmann constant k B , translational temperature T, and particle mass m.For the experimental setup of this study, the instrumental broadening is found to be around 0.9 pm (HWHM).With known ∆λ I of the setup and ∆λ G measured for atomic oxygen, the translational temperatures T of the oxygen atoms can be determined.The measured instrumental broadening is relatively close to the linewidth expected from the dye laser specifications, which is in the range of around 0.6 pm (HWHM).The presence of stable xenon isotopes could lead to an overestimation of the instrumental broadening [42].However, the xenon isotope composition is not considered here as the spectral resolution is not sufficient to quantify its impact.

Absolute number density calibration
The axially resolved number densities of atomic oxygen n O in the effluent of the CO 2 discharge can be determined through calibration of the oxygen measurements with xenon as a reference species.This approach results in the relation [33,43,44] n Xe (5) where the subscripts O and Xe refer to the atomic oxygen and xenon two-photon transitions respectively.S is the fluorescence signal integrated over time, excitation wavelength, and fluorescence wavelength.A 2 is the total radiative decay rate of the excited level (see numbering of the states in figure 4).
A 23 is the part of the radiative decay that specifically accounts for the observed fluorescence transition with optical branching ratios A 23,O /A 2,O = 1 and A 23,Xe /A 2,Xe = 0.733 [35,45].Q is the quenching rate, E L is the laser pusle energy, ν is the excitation frequency, η is the detection efficiency, and σ (2) O is the relative two-photon absorption cross section.
The detection setup is used to probe the 2p 4 3 P 2 level of the atomic oxygen ground state.The determined number densities are therefore corrected to reflect the entire ground state 2p 4 3 P 2,1,0 assuming Boltzmann distribution of the levels' populations with the average temperatures determined for each condition, which is close to the statistical weights of the levels due to the elevated temperatures.
Due to the way the TALIF detection setup is designed, integration of the signal over time and fluorescence wavelength occurs during recording.The performed laser scans allow for integration over the excitation wavelength during post-processing.
The detection efficiency η combines influences such as the quantum efficiency of the intensifier and the transmissivity of the bandpass filter, camera lens, and quartz tube.The quantum efficiency of the intensifier exhibits only a negligible amount of deviation over the 10 nm wide spectral difference between oxygen and xenon fluorescence.Similarly, other potential influences on η e.g. from differences in transmissivity of the quartz tube or the camera lens are negligible as well.However, the narrow bandpass filter has a FWHM of 10 nm and therefore its influence is significant.In order to determine the transmissivity for the oxygen (844.6 nm) and the xenon (834.7 nm) fluorescence, the spectral transmission profile of the filter is determined by recording optical emission spectra of an absolutely calibrated Ulbricht sphere with and without the filter placed in front of the collection optics of the spectrometer (Ocean Optics S2000).
In previous TALIF studies, the relative two-photon absorption cross section σ −0.34 × 10 −43 m 4 in a detailed experimental study [46].They conclude that this new value leads to a significantly smaller relative cross section.The relative cross section can be determined with the atomic oxygen cross section of σ (2) O = 1.33 ± 0.4 × 10 −43 m 4 from Bamford et al [47].Considering the propagation of uncertainties of both absolute cross sections, the resulting relative cross section is σ 46  −0.39 which is appreciably smaller than the commonly used cross section of σ (2) Xe /σ (2) O = 1.90 ± 0.38 from Niemi et al [35].The number density results determined here have been acquired using the relative cross section σ 02.The number densities as calculated with equation ( 5) can be easily scaled to a different relative cross section.For example, multiplying the determined number densities with a factor of 1.86 would scale them to the relative cross section σ Other sources of systematic uncertainty are the detection efficiencies η O and η Xe from equation (5) determined by the transmissivity of the bandpass filter.However, this uncertainty is negligible compared to the systematic uncertainty introduced by the relative two-photon absorption cross section.
Besides these systematic uncertainties, the determined number densities are subject to random uncertainties as well.Apart from pixel-to-pixel noise, which is largely elimated during data acquisition and processing, the major source of random uncertainty are energy fluctuations of the dye laser pulses during the measurements.These are accounted for by considering random laser energy variations of ±10% for both laser energies of oxygen and xenon measurements and their uncertainty propagation into the calibration of absolute atomic oxygen number densities via equation ( 5) resulting in random uncertainties of around ±20% for the measured number densities.

TALIF signal intensities
If no saturation effects are present, the TALIF signal should display a squared dependence on the energy of the laser pulses (see equation ( 5)).In order to verify this, TALIF measurements with varying laser pulse energies are conducted with the ICCD detection setup both for xenon as well as during operation with CO 2 plasma.Laser scans are performed as described and the signals are integrated spectrally in order to determine the representative intensities.This results in a dataset containing several different intensities at different laser pulse energies for each axial pixel position in the images.A slope is fit to the data for each pixel position in a double-logarithmic scale to verify the exponential dependence of the TALIF signal intensity as a function of laser pulse energy.In this analysis scheme, a perfect quadratic dependence would thus translate to a slope of 2. Figure 8(a) shows such a fit to the data for one pixel position of a measurement conducted with the plasma source operating at 5 mbar with 370 sccm CO 2 and P abs = 600 W. The highest two laser energies are excluded from the slope fit since the onset of saturation can be observed quite clearly.Figure 8(b) shows the results of the slope fits for the different axial pixel positions of the camera sensor along the length of the TALIF signal in the effluent of the CO 2 plasma as well as the resulting average slope of 1.9.These measurements have been repeated for the high power CO 2 plasma condition with P abs = 1200 W (average slope = 1.99) and xenon cold gas at a pressure of 0.3 mbar (average slope = 1.92).With these values being so close to the optimum of 2, it can be concluded that the condition of quadratic dependence of the TALIF signal intensity on the laser pulse energy is satisfied for laser energies below 25 µJ at the measurement positions.It should be noted that the operation window in terms of laser energies is quite narrow for the ICCD used here as minimum laser energies of around 7 µJ have to be used for successful TALIF detection.Furthermore, it is necessary to operate the system close to the saturation regime in order to achieve the best signal-to-noise ratios possible, especially in view of the off-center measurements where the signal yields are even smaller.Therefore, knowing the laser energy of the saturation onset is crucial for obtaining the best possible results for the 1D-resolved measurements.
At sufficiently high number densities, ASE has to be considered as another potential source of error for the measurements as, if strong enough, it might eventually lead to a significant deviation of the linear dependency of the TALIF signal on the ground state number density.ASE has not been observed in the present study, however, the number density threshold above which it could become significant for the diagnostic setup can be estimated.Tserepi et al derive an approximate expression for experimental conditions just below the threshold of ASE onset of the form [48] with n 1 and n 2 as number densities of the ground and excited state respectively, the two-photon absorption cross section σ (2) , the Einstein coefficient of emission A 23 , and the areaspecific photon flux Φ of the laser.The approximation is derived from a kinetic model developed and experimentally verified by Huang and Gordon [49].The number density n 2 is the determining parameter for the onset of ASE, however, the approximation shows that it is related to the ground state number density n 1 , and the laser pulse energy and beam diameter of a given TALIF excitation setup as indicated by Φ.For their setup, Tserepi et al found a threshold number density for the onset of ASE of n 1,thr = 2.5 × 10 20 m −3 for a photon flux of Φ = 3 × 10 25 cm −2 s −1 [48].It should be noted that the impact of ASE increases rather slowly beyond the threshold number density and does not necessarily result in immediate large errors or outright loss of TALIF signal.Tserepi et al report a 10% reduction of the TALIF signal at n 1 = 2 n 1,thr and a 30% reduction at n 1 = 3 n 1,thr [48].The photon flux for the present experimental setup is estimated conservatively for a beam diameter of 300 µm at the focus region for maximum laser pulse energies of 24.9 µJ to Φ = 6.68 × 10 24 cm −2 s −1 , which results in a threshold number density of n 1,thr = 5 × 10 21 m −3 for ASE onset in the focus region.For the investigated conditions, the measured number densities are significantly lower than this threshold (see section 4.2), especially considering that in this context n 1 refers to the number density of the probed 2p 4 3 P 2 level with a statistical weight of 0.56 and not the entire ground state 2p 4 3 P 2,1,0 population.

Measurement of lifetimes/decay rates
The quenching rates, accounting for loss of fluorescence signal due to collisional quenching, depend on parameters like pressure and temperature as well as available collision partners in a given gas composition.Therefore, both quantities, the radiative lifetimes τ 0 = 1 A2 as well as the effective lifetime reduced by quenching τ = 1 A2+Q are determined experimentally.For experimental determination of the decay rates, a photomultiplier tube (Hamamatsu R955) is used in conjunction with an oscilloscope (Teledyne LeCroy Wavesurfer 4054HD) in order to detect the time-dependent fluorescence signals at different pressures.The detection setup for measurements of decay rates / lifetimes is detailed in figure 9.
The measurements are carried out at laser wavelengths close to the respective oxygen and xenon two-photon resonances and each measurement is averaged over 100 laser pulses in order to reduce random noise.Within the investigated parameter space the decay rates are observed to be constant within the limits of accuracy of the measurements for different axial positions and operating conditions of the plasma source.The decay rates, or inverse lifetimes, are determined by applying an exponential decay fit to the detected pulses. Figure 10 shows an example of a lifetime measurement of atomic oxygen in the effluent of the CO 2 plasma at 2 mbar.The small afterpulse starting at ∆t = 100 ns in figure 10 is likely an artifact caused by ionization of residual gas inside the PMT, which is not uncommon for detectors like the one used here [50,51].
It is necessary to account for the laser pulse duration in order to determine the correct decay rates, because the  presence of the laser is counteracting the decay of the excited states while it is active.This is often done by determining the laser pulse duration seperately, potentially even with a different detector, and then accounting for the determined laser pulse duration in the lifetime fitting.However, this approach potentially neglects the rise and fall time of the sensor used for the lifetime measurement (in this case a PMT).Here, the laser pulse duration is accounted for by recording fluorescence waveforms at significantly higher pressures (>60 mbar).At these conditions, the collisional quenching becomes so dominant that the fluorescence is only present during the laser pulse and the detected decay rates behave independently of the pressure.This approach not only accounts directly for the laser pulse duration itself, but also the resulting fluorescence signal and the sensor response to it.
Figures 11(a) and (b) show the measured decay rates for the excited atomic oxygen and xenon states respectively.The radiative lifetimes τ 0 are determined by extrapolation of the linear fits to zero pressure.The error bars represent the standard deviation over 10 measurements.The uncertainties grow larger as the decay rates increase, because the duration of the fluorescence after the laser pulse decreases and the part of the pulse waveform that is suitable for fitting a decay rate (see figure 10) becomes shorter.The uncertainties for τ 0 from the linear fits are determined with Moffat's approach for systematic uncertainty analysis [52].
Table 2 gives an overview on τ 0 as reported by other experimental studies in the past.The presented list is not exhaustive, but serves to illustrate the spread of reported radiative lifetimes by diffferent authors.The measured lifetimes for both O 3p 3 P J and Xe 6p ′ [3/2] 2 are in good agreement with values reported in other studies.For Xe 6p ′ [3/2] 2 , the lifetime agrees especially well with the values reported by Niemi et al [35] and Alekseev and Setser [53].The lifetime measured for O 3p 3 P J is slightly smaller than other reported values, though it is very close to the one recommended by NIST [36].

Results
Figure 12 depicts a detailed overview of the TALIF experiment illustrating the most important dimensions.The operating conditions are defined by the CO 2 flow rate Γ CO2 , the absorbed microwave power P abs , and the pressure p (see table 1).Different conditions result in different downstream plasma extensions as investigated in section 2.2.The red and blue lines in figure 12 indicate the profiles of n O and T obtained via TALIF measurements.Such profiles are determined for the three radial positions indicated in the figure for each of the investigated operating conditions.

Temperatures
The translational temperatures of the oxygen atoms measured at different axial positions the effluent of various CO 2 discharges are plotted in figures 13(a)-(e) for radial center line position y 0 = 0.It should be noted that the oxygen atoms are detected at different axial distances from the plasma for the various conditions.However, there is significant overlap between the distance ranges from the plasma for all investigated conditions.The method of determining the uncertainties has been discussed in section 3.1.The uncertainties tend to increase towards the upstream and downstream ends of the signals due to decreasing signal-to-noise ratios at weak TALIF intensities.As mentioned before, the measurements at other radial positions y 1 = 5.5 mm and y 2 = −5.5 mm suffer from decreased signal yields.This causes significantly larger uncertainties in the temperature determination for these radial positions, thus limiting the capability of useful comparison between different radial positions.Therefore, the radial off-center measurements have been omitted from the plots.
The measured temperatures are for the most part relatively stable over the observed distance ranges from the plasma with absolute values between 1000 K and 1400 K for most axial positions of the low power (600 W) conditions (figures 13(a)-(d)).These gas temperatures are slightly higher than those determined by Britun et al [13], between 700 K and 1100 K, in the active discharge zone of comparable surfaguide conditions with pulsed operation (800 W average power, 1.3 mbar-6 mbar) and an actively oil-cooled quartz tube.Britun et al found these discharge conditions to be characterized by a strong non-equilibrium with preferential vibrational exciation [13].An increase in gas temperature from the active discharge into the post-discharge regime is expected due to vibrationaltranslational relaxation following the strong non-equilibrium with significantly higher vibrational temperatures of these discharge conditions [13].The generally high SEI values (up to 111.9 eV/molecule) employed in the present investigation can be expected to further contribute to the non-equilibrium nature of the discharge [58].
A weak pressure dependence of the temperatures is observed.The comparison of figures 13(a)-(c) indicates that increasing the pressure of the discharge leads to slightly lower translational temperatures in the effluent.With increasing pressure, the gas velocity can be expected to decrease for a constant volumetric flow rate as a result of the pressure dependent nature of the gas density and the conservation of the mass flow rate through the discharge.Hence, it takes longer for the gas to reach a certain axial distance downstream of the discharge at higher pressures.This effect is intensified, because the axial distance from the plasma, at which the oxygen atoms are detected, increases for higher pressures.
An increase in absorbed power from 600 W to 1200 W results in a significant temperature increase, for example from around 1000 K at 600 W (figure 13(d)) to 1600 K at 1200 W (figure 13(e)) at a distance of 130 mm from the plasma.The gas flow rate does not appear to have an appreciable impact on the post-discharge temperatures (figures 13(c) and (d)).
Some of the measured temperature profiles exhibit specific trends along the axial direction in the effluent of the plasma.At higher pressures (5 mbar), the temperatures of the oxygen atoms show a continuous decrease as the atoms move further away from the discharge (figures 13(c) and (d)).The most obvious trend is visible in the high power case (1200 W, figure 13(e)).It displays the highest temperatures of around 2700 K close to the discharge, quickly dropping to 2000 K over a distance of 15 mm and leveling off at around 1600 K. Absolute number densities n O of ground state oxygen atoms (2p 4 3 P 2,1,0 ) measured in the effluent of the CO 2 discharges at radial positions y 0 = 0 (red), y 1 = 5.5 mm (blue), and y 2 = −5.5 mm (black).For better visibility, the uncertainties are displayed for one out of 60 data points along the axial direction.The conversions χ for each condition are included for reference.

Number densities
The absolute number densities of the atomic oxygen ground state 2p 4 3 P 2,1,0 are depicted for the different operating conditions in figures 14(a)-(e).The uncertainties of the measurements are discussed in section 3.2.The random uncertainties are displayed as error bars.Additionally, the results are subject to a systematic uncertainty of ±45% of the absolute number density values, which is not displayed here as it affects all measured number densities equally.
The measured atomic oxygen number densities fall within the range 10 20 m 3 < n O < 2.5 × 10 21 m 3 with the lower end being limited by the sensitivity of the detection.Overall, the number densities at different radial and axial positions behave very consistently for a given operating condition.The differences between the three radial positions agree within the range of random uncertainty, indicating a relatively homogeneous radial distribution of oxygen atoms.However, the number densities measured 5.5 mm above the center line (blue profiles) consistently display the highest values, indicating that the radial profile could be slightly asymmetrical.It should be noted that the oxygen atoms are detected at different distances from the plasma depending on the discharge conditions.Perhaps the most striking feature of the axial number density profiles is the general trend that can be observed for all conditions: the number densities increase along the axial direction, reach a peak and then decrease again.
The effect of pressure variation can be seen in figures 14(a)-(c).The ground state oxygen atoms reach sufficiently high number densities for successful detection at a distance of around 25 mm from the discharge at 1.2 mbar.As the pressure increases, the distance grows larger and reaches 80 mm at 5 mbar.The absolute values of number densities for the pressure variation in figures 14(a)-(c) are also different for the three operating conditions with the highest number densities being detected for the 3 mbar condition.The overall highest number densities are measured for the high power condition (figure 14(e)), which also displays the highest conversion χ.Doubling the power from 600 W to 1200 W (figures 14(d) and (e)) leads to an increase of the measured number densities of around 50%, the same trend is observed for the conversion, which increases from 57.4% to 90.3%.Increasing the flow rate by a factor of five (figures 14(c) and (d)) at a constant pressure of 5 mbar and comparable translational temperatures (figures 13(c) and (d)) leads to higher ground state atomic oxygen number densities in the effluent, even though the conversion χ is significantly lower for the higher flow rate condition.This illustrates that the connection between postdischarge atomic oxygen number density and conversion is not straightforward and kinetic modeling would be required for a detailed interpretation.
As already mentioned, all of the number density profiles follow similar trends along the axial direction of the effluent peaking at distances of several centimeters from the active discharge.An increase in ground state atomic oxygen number density implies that oxygen atoms are either produced through dissociation, ion recombination, or that the energetic ground state gets increasingly populated via de-excitation of already present electronically excited oxygen atoms.Due to the significant distances from the active discharge at which the oxygen atoms are detected, neither dissociation nor ion recombination appear to be suitable explanations for the measured axial number density evolutions.The decrease in number density following the peak could be the result of recombination reactions.Specifically recombination to O 2 can be expected to have a large impact due to the generally high conversions measured further (see table 1).
The initial dissociation of CO 2 in a discharge can follow different pathways.The expected strong non-equilibrium nature of the low-pressure discharge conditions investigated here (see also discussion in section 4.1) indicates that thermal dissociation can be expected to only have a small impact on the overall dissociation [13].Due to the low energy efficiencies 2% and 7%, dissociation through step-wise excitation can also be excluded as a major source of dissociation as it is the most energy efficient dissociation mechanism, only requiring around 5.5 eV per molecule [2].As a result, dissociation via direct electron impact can be expected to account for a significant portion of the dissociation in the plasma.Direct electron impact dissociation of a CO 2 requires >7 eV to form CO alongside metastable O( 1 D) and >11 eV to form CO and metastable O( 1 S) [2].Both pathways of direct electron impact dissociation are achievable with specific energy inputs between 22.4 eV/molecule and 111.9 eV/molecule (see table 1).The metastable states of atomic oxygen are by principle long-lived, with radiative lifetimes in the range of several minutes [36], and thus potentially survive into the post-discharge regime providing a delayed source of ground state oxygen atoms after de-excitation in the effluent.In addition, neutral collisions of O( 1 S) can potentially lead to production of additional O( 1 D) in the post-discharge regime [59,60].
Figure 15 compares the normalized axial atomic oxygen ground state number density profiles of the radial center line position for different operating conditions.The translational temperatures for the conditions in figure 15(a) are for the most part between 1000 K and 1400 K with the 5 mbar condition displaying the lowest temperatures of the three conditions (see figures 13(a)-(c)).The conditions in figure 15(b) display a larger difference in translational temperature: up to 2700 K for the high power condition and around 1000 K for the low power condition (see figures 13(d) and (e)).
It can be observed that the ground state number densities start to increase and also reach their peak closer to the end of the plasma for lower pressures (figure 15(a)) and higher temperatures (figure 15(b)).The number densities of the other two radial positions exhibit exactly the same trends and are therefore omitted from figure 15.Considering the hypothesis that quenching of metastables is the cause for the increasing ground state population, this behavior is particularly interesting as the frequency of quenching of metastables through collisions with other atoms or molecules in the gas phase increases with increasing pressure and decreasing temperature (see for example the rate coefficients for quenching of O( 1 D) from Streit et al [61] or Dunlea and Ravishankara [62]).Thus, quenching through heavy particle collisions does not appear to be a suitable explanation for the observed trends.
The other pathway for the quenching of metastables to consider is deactivation via collisions with the inner wall of the quartz tube.The probability of quenching to occur when a metastable atom collides with the wall is typically considered to be 100% [63][64][65].Therefore, the diffusion rate to the wall corresponds directly to the rate of quenching via wall collisions.To investigate the expected trends for quenching of metastable atoms via wall collisions, a simplified two-species model for diffusion of O in CO is considered here.This is a reasonable approximation for the investigated operating conditions as they exhibit large degrees of conversion and therefore the bulk of CO 2 is expected to be dissociated in the investigated region of the effluent.The diffusion rate τ −1 d is determined according to Möller [66] as from the ratio of diffusion coefficient D and mean diffusion length Λ.The diffusion coefficient D is calculated as for the gas temperature for a tube with the inner radius r tube and length l tube , and r tube ≪ l tube as is the for the tube geometry.The resulting wall diffusion rates for T and p are depicted in figure 16.
They exhibit a strong increase with decreasing pressure as well as temperatures, which is qualitatively consistent with the observed trends from figures 15(a) and (b).In this context, it is worth noting that for all conditions at axial positions closest to the discharge, the number densities of atomic oxygen for the off-center radial positions (see blue and black profiles in figures 14(a)-(e) are consistently roughly twice as large as the number densities at the radial center line.The peaks in the axial number density profiles also appear earlier in the effluent for the radial off-center measurements, though the distances to the peaks of the center line measurements vary for different conditions.
In order for the quenching of metastables to contribute in a significant way to the observed post-discharge increase in ground state density, their concentration needs to be sufficiently high.Number densities of metastable atomic oxygen resulting from kinetic modeling (usually involving only O( 1 D)) of various different oxygen containing low-pressure plasmas are typically found to be significantly lower than the ground state number densities, ranging from five orders of magnitude difference [68] all the way down to less than one order of magnitude [69] and everything in between [60,64,65,[70][71][72].This wide spread of metastable concentrations suggests that the ratio of ground state to metastable density is highly dependent on the specific discharge conditions.In fact, simulations of low-pressure O 2 discharges performed by Lee et al [63] indicate that an increase in power deposited into the discharge can raise the O( 1 D) number density by several orders of magnitude.As a result, significant concentrations of atomic oxygen metastables are not implausible for the high specific energy inputs investigated here.
For a more detailed quantitative analysis of the results, a sophisticated modeling approach would be required including at the very least a detailed kinetic model for CO 2 (plasma)chemistry-explicitly including metastable excited states and particle-wall interactions.In addition, CFD simulations could provide insights into the characteristics of the flow in the effluent of the discharge, e.g. to which degree the swirling flow caused by the tangential gas injection persists through the discharge.
The complex kinetics determining the gas composition in the effluent of the discharge cannot be fully understood by considering a singular diffusion rate.Nevertheless, the qualitatively observed number density evolutions with regard to temperature and pressure dependence provide clues that could help explain the observed behaviour.These clues indicate that metastable oxygen atoms and gas-surface interactions could play a key role here.Certainly, for a complete understanding the complex interplay between numerous reactions involving O production and loss channels as well as excitation and deexcitation pathways will have to be considered.

Conclusion
A diagnostic setup for axially resolved TALIF measurements of atomic oxygen ground state (2p 4 3 P 2,1,0 ) number densities and translational temperatures along the effluent of a microwave-powered CO 2 discharge has been developed.Oxygen radicals are one of the most important intermediate species for the CO 2 conversion process as the recombination reactions following the dissociation in the plasma determine the obtainable CO retention.The conversions at different operating conditions of the source are obtained via MS.The TALIF setup has been characterized with regard to its saturation behavior, the number density threshold for the onset ASE could be estimated, and decay rates due to collisional quenching as well as natural lifetimes have been determined experimentally.Reference measurements with xenon 6p ′ [3/2] 2 are used for absolute number density calibration.Furthermore, measurements of the downstream plasma elongations for different operating conditions of the plasma source facilitate downstream placement of the results relative to the end of the active discharge for the different operating conditions.The result is a large data set for different operating conditions of the plasma source detailing the obtained conversions, axially resolved translational temperatures of oxygen atoms along the effluent of the discharge as well as axially resolved absolute ground state number densities of oxygen atoms for three different radial positions.
The number densities of ground state atomic oxygen are initially increasing along the effluent, even at significant distances of several centimeters downstream of the active discharge.The most likely explanation for this behavior is quenching of metastable oxygen atoms that are formed via direct electron impact dissociation of CO 2 .The observed trends for this downstream evolution of number densities are qualitatively consistent with wall collisions being the dominant quenching mechanism of the metastable atoms.Therefore, the obtained results offer interesting insights into the kinetic behavior of oxygen radicals in the plasma effluent, putting special emphasis on the key role of metastable species as well as the importance of considering particle-wall interactions when trying to accurately predict post-discharge concentrations.
The developed TALIF experiment offers the unique opportunity to probe ground state oxygen atoms in the volatile postdischarge regime where the transition from dissociated and energetically excited plasma products to ground state species and recombined molecules takes place.Thus, the data lend themselves very well to future benchmarking attempts for kinetic models that aim to capture not only the active discharge composition in a CO 2 microwave plasma, but the postdischarge regime as well.

Figure 1 .
Figure 1.Schematic of the plasma source; not to scale.

Figure 2 .
Figure 2. (a) Measurement of the plasma emission intensities around 844 nm inside of the downstream chimney for different operating conditions with applied linear fits, and (b) average downstream plasma elongations for different operating conditions and optical filters.

Figure 3 .
Figure 3. TALIF setup for 1D-resolved axial detection of atomic oxygen in the effluent of the CO 2 plasma; not to scale.

Figure 4 .
Figure 4. Two-photon absorption transitions of ground state atomic oxygen and xenon.

Figure 5 .
Figure 5. TALIF data of atomic oxygen recorded in the effluent of the CO 2 discharge at the radial center position (p = 5 mbar, Γ CO2 = 370 sccm, P abs = 600 W).

Figure 7 .
Figure 7. (a) Example Voigt fit to a xenon profile recorded at a pressure of 0.3 mbar (∆λ G = 0.91 pm, ∆λ L = 0.32 pm, HWHM), and average line width contributions (HWHM) along the laser beam incidence for different xenon cold gas pressures.

O
= 1.90.Overall, the uncertainty of the relative cross section used for calibration leads to a systematic uncertainty of around ±45% for the determined absolute number density values.

Figure 8 .
Figure 8. TALIF signal intensities of atomic oxygen for different laser pulse energies at a single pixel position with fitted slope (a) and results of the fits along the axial pixel positions of the measurement (b).

Figure 9 .
Figure 9. Experimental setup for the measurement of fluorescence decay rates; not to scale.

Figure 12 .
Figure 12.Overview of the most important parameters of the TALIF experiment; not to scale.Blue and red example profiles for T and n O respectively are included as a reference for the position of the measurements.

Figure 13 .
Figure 13.Translational temperatures T of oxygen atoms measured in the effluent of the CO 2 discharges at radial center position y 0 = 0.For better visibility, the uncertainties are displayed for one out of 60 data points along the axial direction.

Figure 14 .
Figure 14.Absolute number densities n O of ground state oxygen atoms (2p 4 3 P 2,1,0 ) measured in the effluent of the CO 2 discharges at radial positions y 0 = 0 (red), y 1 = 5.5 mm (blue), and y 2 = −5.5 mm (black).For better visibility, the uncertainties are displayed for one out of 60 data points along the axial direction.The conversions χ for each condition are included for reference.

Figure 16 .
Figure 16.Wall diffusion rates of O in CO within the quartz tube for different pressures and temperatures in the effluent.

Table 2 .
Overview of radiative lifetimes τ 0 , ordered by publication date.
T, total number density n tot = p/(k B T) and the masses of oxygen atoms m O and carbon monoxide m CO .The collisional cross section σ O−CO is approximated as the hard-sphere cross section σ O−CO = π(r O + r CO ) 2 with kinetic radii r CO = 184.5 pm and r O ≈