Spectral and electric diagnostics of low-current arc plasmas in CO2 with N2 and H2O admixtures

Plasma diagnostics is a key tool to support the further development of plasma-induced chemical conversion of greenhouse gases (such as CO2) into high-value chemicals. For this reason, spectroscopic and electric measurements of low current (below 1.7 A), stationary arc plasmas in CO2 at atmospheric pressure with addition of N2 or H2O are reported. High-speed photography, imaging emission spectroscopy and time-resolved electrical measurements are used to obtain time-space resolved gas temperatures as well as the electric-field current characteristics of the discharge. It is found that the lowest average electric field in a CO2 arc plasma at atmospheric pressure is ∼20 kV mm−1 at a current between 0.8 and 1 A. If the current decreases below this level, the arc remains in vibrational–translational (VT) equilibrium by increasing the electric field. However, VT equilibrium conditions can be only maintained until a threshold minimum current of 0.33 ± 0.05 A, at which the arc transitions into a non-equilibrium condition with further increasing electric fields (reaching 68 ± 15 V mm−1 at 0.03 A). The addition of N2 or H2O did not influence the electrical characteristics of the CO2 arc within to the tested mixtures. However, there is only a significant decrease in the electric field of the formed transition arcs and the threshold minimum current in the presence of N2. The spectra of the low-current CO2 arc is found to be dominated by emission from the C2 Swan band system and the O I 777 nm triplet peak. However, the CN band dominates the spectra even when small amounts (0.5 wt%) of N2 is present in the plasma. The gas temperature at the axis of the CO2 arc plasma decreased slightly with decreasing current, from an estimated 7000 K at 1 A down to 6300 K at 0.4 A. The thermal radius of the arc is estimated to be larger than 1.2 mm, more than two times larger than the optical radius obtained from the emitted radiation. The addition of N2 and H2O (up to 7 and 9 wt% respectively) lead to only to a 500 K decrease in the axial arc temperature.

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Introduction
In recent decades, arc plasmas in CO 2 have been increasingly explored for the efficient conversion of this greenhouse gas into value-added chemicals or new synthetic fuels [1].They can be used to efficiently chemically convert CO 2 at atmospheric pressure into CO while storing surplus electrical energy [2].The produced CO can be subsequently processed together with H 2 (from an electrolyser) to generate syngas, the building block for synthetic chemicals and fuels.Similarly, plasma-induced reactions of CO 2 and CH 4 can also produce syngas in a direct chemical process known as dry reforming of methane [3].This process could be further improved by the addition of N 2 as an additional gas [4].Conversion of CO 2 in the presence of H 2 O is also a possibility to produce syngas as demonstrated for other plasma sources (e.g.[5]).
Gliding arcs have been the plasma source most widely investigated for plasma-induced chemical conversion of CO 2 at atmospheric pressure [2].Gliding arcs are efficient for CO 2 conversion when they are in non-equilibrium between the electronic, vibrational and translational gas temperatures [6].For that reason, such arcs are usually generated under currents lower than 1 A and voltages above several kilovolts to maintain translational temperatures between 2000 and 3000 K.Under those conditions, gliding arcs can provide simultaneously non-equilibrium of chemical reactions as well as high electron density, necessary to drive a highly efficient reaction pathway [2].
Thermal arc plasmas have been recently reported to also dissociate efficiently CO 2 in the presence of a chemical reducing agent [7].Such arc plasmas are operated at lower power conditions than the thermal arcs produced in electric power switchgear (e.g.[8]), high power lasers [9], plasma furnaces [10] or used in metal welding [11].They have high translational temperatures of thousands of kelvins suitable to decompose CO 2 by pyrolysis and electron impact [7].They also require of a reducing agent (carbon) to efficiently quench the reverse reactions producing back CO 2 from the generated CO [7].
In-situ spatial and temporal diagnostics of the plasma source have been recently highlighted as a key tool for the further development of plasma chemical conversion [12].It can provide experimental quantitative information to guide the design of plasma reactors and to enable the validation of simulation models.It is also critical to evaluate the level of non-equilibrium in the plasma and its relation to chemical pathways limiting energy efficiency [13].Therefore, several studies have reported detailed, quantitative diagnostics for other CO 2 plasma sources, including inductively coupled, microwave and dielectric barrier discharge plasmas (e.g.[13][14][15][16][17]).Unfortunately, detailed and systematic studies on spectroscopic properties of low-current arcs are still missing.The existing studies of plasma diagnostics in gliding arcs containing CO 2 have generally used optical emission spectroscopy (e.g.[3,[18][19][20][21]).However, most of them use noncalibrated measurements, allowing only qualitative analysis of emitting chemical species.Calibrated spectra have only been reported in [3,19], although they are unfortunately not resolved in time or space.Thus, they have only delivered averaged plasma temperatures of gliding arcs in CO 2 /H 2 and CO 2 /CH 4 mixtures under specific experimental conditions.
The measurement of time and space-resolved spectroscopic properties of arc plasmas is challenging due to the intrinsic limitations when performing diagnostics on a moving thin plasma channel.In order to overcome these limitations, a weakly-moving, stationary arc plasma is here used to measure spectroscopic and electrical properties under low currents below 1.7 A. Although similar measurements have been reported for CO 2 arcs at atmospheric pressure under high currents (>100 A) [22,23] and intermediate currents (>3.5 A) [8,24], detailed spectra at lower levels are still missing.Similarly, space-resolved spectroscopic measurements of low-current arc plasmas for CO 2 /N 2 and CO 2 /H 2 O mixtures are also not available in the literature.
On the other hand, the electric properties of gliding arcs in CO 2 and its mixtures are generally reported only as voltage and current transient measurements (e.g.[25]).However, voltages strongly depend on the time-varying length of the gliding arc, which is seldom measured or reported.For this reason, the average electric field is a better quantity to specify the electrical conditions of arc plasmas under a given current.On one hand, the chemical and thermal equilibria in the plasma are related to the electric field.Furthermore, knowledge of the electric field in gliding arcs is also key for the design and upscaling of plasma reactors and their required power supply.Unfortunately, electric field as a function of current has only been thoroughly reported for gliding arcs in air [6].Only the electric field at a current of 0.09 A has been reported for gliding arcs in CO 2 /H 2 mixtures [3].
In order to further contribute to the understanding of lowcurrent arc plasmas, experiments are here reported in pure CO 2 and with N 2 and H 2 O admixtures.Diagnostic methods including high speed photography, imaging emission spectroscopy and time-resolved electrical measurements are used.A systematic evaluation of the variation of the electric field of the arc column as a function of currents below 1.7 A is presented.Spectroscopic measurements, averaged as well as resolved in space and time, are also presented together with the corresponding estimated gas temperatures.These measurements are aimed to enable the one-to-one comparison with simulation results of low-current arcs.They can also provide quantitative information to guide the selection and dimensioning of the power supply and the plasma reactor of processes where low-current CO 2 arcs with admixtures of N 2 or H 2 O are involved.

Experimental setup
Figure 1 shows a schematic drawing of the experimental setup here reported.For sake of clarity, the setup will be described separately for each of its three main parts: the arc plasma reactor and its power supply, the gas/liquid fluid control and the plasma diagnostics system.

Arc plasma reactor and power supply
The experiments are performed with an arc plasma ignited in a 21 mm gap between two pencil-shaped tungsten rods (with 3 mm diameter) as shown in figure 1.The plasma in the reactor is confined by a tubular glass envelope, symmetric to the axis of the electrodes.The inner diameter of the glass envelope is 11 mm.The tube is kept in place by using aluminium flanges at each end, with o-rings sealing the reactor.
The plasma is first ignited by a spark produced between the electrodes when an external voltage spike larger than 30 kV is applied with a high voltage source.Then, the transition from the spark into an arc is enabled by applying a decaying current pulse.For this, a 0.6 µF capacitor initially charged at 6500 V is discharged through a 6700 Ω limiting resistor and the plasma.The voltage across the arc (V in figure 1) is measured with a 1000:1 high voltage probe having a minimum readable risetime of 20 µs.The current I is measured with a high-bandwidth current probe from DC to more than 50 MHz.The corresponding signals of the voltage and current probes are recorded with a 20 MHz, 12 bit digital oscilloscope.The total duration of the arc plasma after ignition is less than 10 ms.

Gas/liquid flow control
CO 2 purity grade 4.5 and N 2 grade 5 are taken from highpressure gas cylinders connected with mass-flow controllers to a passive mixing container.CO 2 is used as the main carrier gas flowing with a rate of up to 1.5 l min −1 while N 2 is flowing at a rate of maximum 0.02 l min −1 .Then, the gas flow is connected to a commercial controlled evaporation unit where it is mixed (if desired) with water vapour H 2 O.The vapour is produced by evaporation at the control unit using distilled water flowing with up to 2 g h −1 through a liquid flow controller.A small compressor is used to provide enough pressure for the liquid flow.The gas mixture is then injected into the reactor from the top inlet with tubing that can be heated to 90 • C to avoid condensation when H 2 O is used.Prior to the experiment, the plasma reactor is purged three times during 60 s at the chosen composition.This purging time is sufficiently long to eliminate air within the reactor, as confirmed by an inline measurements with a CO 2 and O 2 gas analyser (not shown in figure 1).
The experiments in pure CO 2 have been performed for flows ranging between 0.2 and 1.5 l min −1 , maintaining atmospheric pressure within the tube (monitored through a pressure gauge P in the mixing box).Under such conditions, the gas flow within the plasma reactor is laminar with a maximum velocity of 0.3 m s −1 (as estimated by computational fluid dynamic simulations not shown here).Such a slow gas flow velocity does not influence the electrical or spectroscopic properties of the plasma as confirmed by our preliminary unreported experiments.
The experiments with the N 2 and H 2 O admixtures are performed at different flows in order to obtain different compositions within the operation limits of the flow controllers.Table 1 shows a summary of the conditions for the gas here reported.

Plasma diagnostics
The spectroscopic diagnostics of the arc plasma are performed using optical emission spectroscopy and high-speed photography.Two separate, complementary spectroscopic systems are here implemented: • An imaging spectroscopic system consisting of an Andor Kymera 328i optical spectrograph and a FASTCAM SA3 CMOS high speed camera (CAM1 in figure 1): this system is used to resolve the spectra in time and space, within a narrow (∼80 nm wide) wavelength band in the visible range between 460 and 800 nm.Combining the spectrograph with the high speed camera allows recording spectra with a high sampling frequency.Thus, spectral images are recorded at 4000 frames per second and with an exposure time of 248 µs each.The recorded 2D images contain side-on spectral information of the plasma as a function of horizontal position and time.In this system, the horizontal arc section located in the middle gap between the electrodes is imaged on the 150 µm vertical entrance slit of the spectrograph.The imaging is performed with a pair of collimating lenses L 1 , L 2 while the mirrors M 1 and M 2 are used to twist the beam 90 degrees.The spectrograph has a focal length of 328 mm and the used grating has 600 lines/mm.Absolute radiance calibration of the side-on spectra is performed by imaging a tungsten strip lamp (OSRAM Wi 17/G) at the location of the plasma reactor.Wavelength calibration of the spectra is performed with Kr and Hg(Ar) penrays.The spectral and spatial resolution of the system is 0.8 nm and 0.16 mm respectively.• A point spectrometric measurement using a four-channel, charged-coupled device optical compact spectrometer (AvaSpec): this measurement detects the irradiance integrated over a 5 mm radius, circular area at the middle of the gap, during an acquisition time of 4 ms.It can be interpreted as a time and space averaged irradiance.It is used to detect the average optical signature of the arc within a broad wavelength window (between 250 and 900 nm) and with good spectral resolution (0.13 nm).A lens L 3 is used to collimate the average light emitted within the imaged circular area into a multi-furcated optical fibre.Four bundles of the optical fibre are connected to the entrance slit of each spectrometer channel (for the spectral bands of 240-400 nm, 400-530 nm, 635-710 nm and 710-800 nm).The relative irradiance and wavelength calibration of the spectrometer is performed with a tungsten strip lamp and Kr and Hg(Ar) penrays.
In addition, a CMOS Kiralux compact scientific camera CAM2 is used to image the shape of the arc plasma ignited between the electrodes.An 8 mm focal distance, f /1.4 camera lens is mounted to focus the arc image on the CMOS sensor of the camera.The images are recorded at a rate of 2000 fps and an exposure of 100 µs.

Electrical measurements and high speed photographs
Figure 2 shows typical electrical measurements recorded in the experiment from the ignition of the spark until the arc extinction.The spark is first ignited between the electrodes due to the applied voltage spike.During the spark-to-arc transition, the discharge voltage rapidly decreases below 1000 V leading to a current overshoot (1.7 A peak) flowing through the plasma.This ignition period lasts for about 0.2 ms.After the ignition period, the current delivered by the main voltage source continuously decreases starting from ∼1.2 A. As it will be later shown in section 3.2, the arc during this period is in vibrational-translational (VT) equilibrium.This VT equilibrium stage with a stable plasma channel continues for several milliseconds until the current reaches a threshold.At this threshold current, the injected power cannot further sustain the arc in VT equilibrium.Thus, the plasma suddenly starts an unsteady decay period.The threshold minimum current level randomly changes from shot to shot between a well-defined range.The measured threshold current is 0.33 ± 0.05 A for arcs in CO 2 only or with the H 2 O admixture, regardless of the tested composition.This threshold current is slightly decreasing when the composition of N 2 increases in the mixture with CO 2 , with a value of 0.25 ± 0.03 A at the highest composition in the experiment.
The voltage during the VT equilibrium period continues decreasing at a lower rate than during ignition, until reaching a minimum of 540 V at ∼0.9 A. Then, the arc voltage continuously increases as the current further decreases, reaching more than 1000 V at the threshold current.The power of the  equilibrium arc plasma in the experiment ranges between 390 and 610 W.
The transition period is characterized by a sudden current decay and the corresponding increase in the discharge voltage.This period lasts for less than 0.5 ms until the discharge cannot be further sustained by the capacitor voltage as seen in figure 2(a).Thus, the discharge is extinguished with no detectable current.Re-ignition of the arc during the extinction period is seldom observed during the experiment.
A typical photograph of the arc plasma during the VT equilibrium regime is shown in figure 3(a).The arc channel is observed as a curvy bright region between the cathode and the anode.Observe that a weaker image of the channel is reflected on the inner surface of the tube (figure 3(b)).However, this reflection should be removed when analysing the footage in order to obtain the two-dimensional arc length l (2D) arc for each frame.For this, the images are brightness-reduced such that the arc column path can be digitally identified between the anode and the cathode (figure 3(c)).The length l (2D) arc along that path is numerically measured from each frame image.The obtained values change randomly between 23 and 38 mm, regardless of the gas mixture used and time.
With a known length of the arc channel for each frame, it is possible to define the average electric field along the arc column E c as a function of time.Assuming that the electric field is uniform along the entire arc column, E c is calculated as: where V meas is the measured voltage across the gap and V c/a is the cathode/anode fall voltage.Unfortunately, V c/a in CO 2 arcs between tungsten electrodes could not be measured in the experiment.However, the V c/a measured in CO 2 arcs between mild steel (with values between 19 and 21.1 V) [26] is here used.Since V c/a is significantly lower than V meas , any uncertainty on the used value has a negligible influence on the calculated E c .The electric fields obtained for different arcing events in CO 2 are then correlated to the applied current as shown in figure 4(a).The obtained electric field-current characteristics have the typical U-shape having three different regimes.At currents lower than ∼0.8 A, E c decreases as the current increases defining the negative-differential resistance regime.Within this regime, the arc is in the VT equilibrium period for currents above ∼0.4 A. Below this level, the arc is in non-equilibrium during the transition period [27].This is the regime where gliding arcs generally operate [25].The arc characteristic reaches a plateau (between about 0.8 and 1 A) where the electric field does not significantly change with current.At higher current levels, E c in the equilibrium arc increases with current in the positive-differential resistance regime.This regime takes place in the experiment during the VT equilibrium and ignition periods.
Even though the stochastic variations in the arc length are partially accounted in the calculation of E c , the obtained characteristics still change randomly from shot to shot.For that reason, the experiments are repeated several times (12 for CO 2 and CO 2 /N 2 and 8 for CO 2 /H 2 O) in order to allow the statistical estimation of the mean value and the maximum variation range.As shown in figure 4(a) for CO 2 , the characteristic has a broader variation from shot to shot at the lowest currents in the negative-differential resistance regime during the transition period.The lowest variations take place at the plateau and then increase as the current augments.For instance, the column electric fields obtained for the CO 2 arcs are about 67 ± 15 V mm −1 , 18 ± 0.22 V mm −1 and 30 ± 5.3 V mm −1 at 0.03 A, 0.9 A and 1.5 A respectively.Notice that this variation of E c cannot be attributed to the small differences (estimated to be lower than 10%) between the true arc column length l (3D) arc and the values of l (2D) arc obtained from the photographs.Thus, these variations are attributed to changes in the electric properties within the arc column.
Interestingly, the addition of N 2 to CO 2 (up to a maximum concentration of 90.1/9.1% as shown in figure 4(b)) produces only a significant reduction of the mean E c for the nonequilibrium arcs (at currents below ∼0.35 A).At the maximum tested concentration of N 2 at 0.03 A, the lowest most column It is important to point out that the average electric fields here measured for a stationary arc represent the lower-bound of E c for a gliding arc.In the case of a non-equilibrium gliding arc, convective losses due to the lateral movement of the arc and the gas flow lead to a larger column electric field [6].As comparison, notice that the electric field of a magnetically-driven CO 2 non-equilibrium gliding arc at 0.09 A have been reported as 151 V mm −1 [3].These gliding arcs moved laterally with a maximum average velocity between 2-6.4 m s −1 (estimated from the rotational frequency and dimensions reported in [3]).This electric field is 2.5 times larger than the ∼60 V mm −1 measured here for stationary arcs (with a limited lateral motion) at the same current (figure 4(a)).

Time-space averaged spectroscopic measurements
An overview spectrum of the CO 2 arc plasma recorded with the point spectrometric measurement is shown in figure 1.In order to observe all possible emission, this spectrum is integrated in time during the first 4 ms of the discharge.During this period, the current through the arc declined from 1.7 to 0.5 A (figure 2(b)).As can be seen, the spectrum of the CO 2 arc plasma at these low currents is dominated by emission from the C 2 (d 3 Π g → a 3 Π g ) Swan band system and the OI 777 nm triplet peak.The O I peak has the highest intensity followed by the radiation of the ∆v = 0 vibrational sequence of the C 2 Swan band.This emission is superimposed to a weak continuum background signal.No other additional atomic emission from oxygen, carbon or tungsten (from the electrode material) is detected.Similarly, no molecular emission from CO (3rd positive or Angstrom (B 1 Σ + → A 1 Π) groups) is observed.Interestingly, the measured spectra is qualitatively similar to that reported for high power microwave [13,14] and inductively coupled [15] atmospheric-pressure CO 2 plasmas.
The CN Violet (B 2 ∑ → X 2 ∑ ) band system also appears with a strong signal in the spectra of the CO 2 arc even with a small 0.5 wt% N 2 admixture, as also shown in figure 5.As the concentration of N 2 further increases, the CN emission dominates the entire spectrum.This effect is enhanced by the reduction of the C 2 Swan band emission with an admixture of 2% or more of N 2 .A similar effect has also been reported for microwave [13] and inductively coupled [15] atmosphericpressure CO 2 plasmas.It has been explained by the mechanisms of CN formation becoming dominant over the production of C 2 as the concentration of N 2 increases [13].
The spectral signature of the CO 2 plasma remains very similar when H 2 O up to the maximum tested composition of 7.6% is added.However, the C 2 Swan band emission decreases only slightly when increasing the concentration of H 2 O. Furthermore, no radiation from hydrogen Balmer lines or OH molecular emission is detected as in studies of CO 2 /H 2 plasmas [3].
The comparison of this measured spectrum with simulated molecular band emission from the C 2 and CN bands allows the estimation of an average temperature for the plasma.For this reason, synthetic spectra is obtained using the Simulation of Platform for Aerodynamics, Radiation and Kinetics (SPARK) Matlab numerical code (formerly known as SPARTAN) [28,29].SPARK is an adaptive numerical code that calculates the line-by-line spectral emission of any plasma at non-local thermodynamic equilibrium (non-LTE).The calculations are performed based on the Gas and Plasma Radiation Database [30] assuming that the species internal modes follow the Boltzmann equation.Then, the vibrational T vib and rotational T rot temperatures are best fitted until good agreement between the measured and simulated spectra is reached.
Figure 6 shows the measured and the synthetic spectra for the ∆v = 0 sequence of the C 2 and CN molecules in the arc plasma under different mixture compositions.The spectra are normalized to the (0, 0) transition headband peak in each case.Observe that the measured normalized spectra for the C 2 Swan and CN violet bands follow a similar emission pattern regardless of the tested composition.This is particularly clear for the CN violet band (figure 6(b)) in which the spectra has a better signal to noise ratio compared with the measurements in the C 2 Swan band.The C 2 Swan in the CO 2 plasma can be best fitted to synthetic spectra with a single temperature for rotational and vibrational levels.The average temperature estimated during the equilibrium period is T r = T v = 5800 ± 1500 K. Interestingly, similar time-and-space-averaged temperature is also estimated for the other tested mixture compositions.
The corresponding calculations from the CN violet band deliver the same temperatures as for the C 2 Swan band, verifying the estimate above.The synthetic spectra calculated for the CN band also show that the difference between T r and T v should be less than 1000 K in order to fit the measured data.This similarity between T r and T v show that the plasma is in VT equilibrium.
Observe that the broad variation in the estimates are caused by the uncertainties introduced by presence of the weak continuum present in the measured spectra.No quantitative analysis of the continuum in the spectra is attempted since the source of this emission is not clear.Observe that this continuum could be produced by chemiluminiscence of CO 2 * due to recombination of O and CO species [31] or by unidentified molecular or atomic spectra (e.g. from W, O, the C 2 Deslandres-D'Azambuja band or the CO Ångstrom system).

Time-and-space-resolved spectroscopic measurements
Typical space-resolved spectral images of the absolute sideon radiance L measured for the CO 2 arc are shown in figure 7.These images correspond to the radiation emitted by a thin horizontal slice of the arc column, which is located at the midgap.Thus, the images show the radiance measured as a function of the x axis and wavelength.In this case, the emission corresponds to the ∆v = 0 sequence of the C 2 Swan band and to the 777 nm O I triplet and its surroundings.The images are taken at two different times (0.5 ms and 3.5 ms) when the current through the plasma is about 1 and 0.5 A. As it can be seen, there are no significant relative differences between the side-on radiation at the two considered currents (in the VT equilibrium regime).However, there are clear differences in the maximum detected radiance in each case.Unsurprisingly, the spectral images have also shown that the optical radius of the arc column emitting radiation changes with wavelength.The optical radius is generally estimated from photographs as the half width, half maximum of the detected optical signal.For instance, the emission from the 516.5 nm headband in the ∆v = 0 transitions of the C 2 Swan band comes from the central region of the arc within a radius of about 0.4 mm (for both currents in figure 7(a)).As the wavelength of the emission within that band decreases, the optical radius is also reduced.Furthermore, the O I triplet in figure 7(b) is emitted within a radius of about 0.5 mm.These changes in the optical radius are naturally caused by the different, non-linear effect of temperature in the emission from different emitting species.For this reason, optical radii measured from spectral images or high-speed photographs as in [3] should not be used as representative of the true arc radius.Instead, the arc radius should be obtained from direct estimations of temperature as it will be later here presented.
In the case of an optically thin plasma, the side-on radiance L (x) corresponds to the spatial integration of the emission along the line of sight through the arc cross section.In order to reconstruct the emission coefficient ε (r) of an axialsymmetric arc as a function of radius r, the Abel inversion process is generally used.The solution to the Abel inversion for an arc with radius R can be expressed as: The solution to this equation is numerically challenging especially since the derivative of L (x) amplifies the noise during measurements.In order to overcome that challenge, the fast Abel inversion method proposed in [32] is used here.
Typical emission coefficients ε (r) obtained from the sideon radiance spectral images of the C 2 Swan band are shown in figure 8.As can be seen, atomic tungsten peaks superimposed to the radiation from the C 2 Swan band are visible only during the ignition period of the arc (see dotted curve in figure 8(a)).
This spectrum had also a significant background continuum radiation.During the VT equilibrium period, the emission from the arc within this spectral window is dominated only by the C 2 Swan band emission.The intensity of this molecular emission decreased with time.However, emission suddenly fell below detection level when the transition decay period started.
An example of the space-resolved emission coefficient at the time t = 0.5 ms when the current is about 1 A, is shown in figure 8(b).It is found that the intensity of the ∆v = 0 transitions of the C 2 Swan band remains relatively constant within the first 0.33 mm from the arc axis.After that, the peak intensities gradually decrease with the arc radius.The measured radiation reached a relatively low signal-to-noise ratio as the radius increased beyond about 1.16 mm.
Further analysis of the space-resolved spectra showed that the background continuum radiation caused larger errors when fitting synthetic spectra to the measurements.These errors significantly increased when the analysis is performed for spectra with low C 2 Swan band peak intensity, away from the axis of symmetry.In such cases, the background continuum influences differently each of the C 2 Swan peaks, in a similar way as reported in other measurements in CO 2 at lower pressures [33].For this reason, the continuum hinders the accuracy of spectrum fitting analysis when performed for an entire vibrational sequence in space-resolved measurements.
In order to overcome the uncertainties caused by the continuum when estimating temperature from space-resolved spectra, a slightly different analysis is now used.Thus, the analysis is performed based on the absolute comparison of the emission coefficient measured and calculated for a single emission peak.This analysis is generally known as the calibrated line method or the single line method since it requires the absolute calibration of (at least) a single spectral line [34].It requires additionally that the radiating specie density is known and that the plasma is optically thin.The (0,0) transition peak at 516.5 nm of the ∆v = 0 sequence of the C 2 Swan band is used here as it has been previously used for the estimation of T r in CO 2 low pressure plasmas [33].To also reduce the effect of the continuum, the peak baseline is taken from the minimum near the bandhead instead of the zero reference of the instrument [33].
In order to calculate the emission coefficient ε, LTE compositions are here assumed to estimate the density of the emitting specie.Observe that there is no conclusive evidence in the experiment showing that complete LTE (with similar electronic, translational and vibrational temperatures) has been reached in the plasma.However, the VT equilibrium found in section 3.2 show that this necessary (although not sufficient) condition for LTE takes place in the experiment.Second, the emission spectrum of an inductively coupled CO 2 atmospheric plasma with similar average VT temperature has been shown to be in thermal equilibrium [16].Third, the average electric fields estimated during the VT equilibrium period in figure 4 range within 20-30 V mm −1 , well within the range typical for thermal arcs [6].
Thus, the total density for the emitting specie is calculated based on the principle of minimization of the Gibbs free energy at a given pressure and temperature [35] Since the Coulomb interaction between charged compounds is increasingly important at high temperature, its effect on the gas pressure is also included [36].The calculations are performed assuming atmospheric pressure.In contrast to continuously-burning arcs constrained within tubes, no steady increase in pressure takes place during the transient plasma in the experiment.Thus, no significant change is detected with the pressure gauge used in the experiment.Under the tested conditions, only a transient pressure overshoot takes place at the front of the expansion shock wave during the start of the ignition period.Then, the arc channel rapidly recovers to atmospheric pressure, followed by an isobaric decrease in gas density in a similar manner as it happens in transient air discharges [37].
Figure 9 shows the emission coefficient ε for the C 2 ∆v = 0 bandhead (0, 0) at 516.5 nm and the O I triplet at 777 nm calculated with SPARK for an equilibrium plasma with temperature.These calculations are performed considering the spectrograph spectral resolution of 0.6 nm.They are here shown for the highest tested compositions of CO 2 , N 2 and H 2 O.The errors of these estimates is mainly limited by the accuracy in the transition probability for spontaneous emission, which is <3% for the O I emission and estimated as less than 10% for the C 2 bandhead.
Observe that ε is strongly dependent on the gas temperature, having only weak changes under the tested CO 2 /N 2 and CO 2 /H 2 O mixtures compared with only CO 2 .Thus, these calculations show that ε for the considered peaks can change by an order of magnitude due to a variation of the gas temperature of less than 500 K. Therefore, they also indicate that the significant changes on the measured emission coefficients in figure 8 are mainly caused by weak changes in the temperature of the hot arc core.
The VT temperatures T v = T r estimated from the emission coefficients from the C 2 ∆v = 0 bandhead for the CO 2 arcs during the equilibrium period as a function of time are shown in figure 10(a).Observe that the arc temperature during this period starts at about 7200 K and decreases slightly to 6500 K at 4.5 ms when the current reaches 0.4 A. Similar estimates (although <3% lower) are obtained when using the emission from the O I 777 nm peak is used instead.These values are also lower but within the range of uncertainty of the time-and-space averaged temperature obtained in section 3.2.Furthermore, the estimated temperatures are similar to those reported for a 220 W microwave CO 2 plasma at near-atmospheric pressure [14].
The similar temperatures estimated from the calculated absolute emission of the O I peak and the C 2 bandhead show that the plasma can be described through one overall temperature.Thus, the excited levels of both emitting species are in equilibrium defining at least a partial LTE.However, proving LTE conditions in a CO 2 arc plasma is a challenging task.Although there are several criteria in the literature to assess complete LTE equilibrium, they are mainly defined for plasmas in hydrogen or hydrogen-like gases [38].Moreover, the electron densities proposed by different authors as main criterion for LTE vary by more than an order of magnitude (even for hydrogen plasmas) [39].According to the widely used Griem criterion [38], the minimum electron density required for LTE at 7000 K in a CO 2 plasma is estimated around 10 21 m −3 .Unfortunately, no electron density could be obtained from the recorded spectra.The only estimate available is the electron density obtained from the equilibrium calculations, which is about 1.4 × 10 21 m −3 at 7000 K.
Unfortunately, the further decrease of the arc temperature with time during the transition decay period could not be estimated in the experiment.As the detected ε continues decreasing below ∼10 3 W m −3 sr −1 nm −1 at lower temperatures, the signal-to-noise ratio of our measurements is not sufficient for a proper estimate.Moreover, the assumption of LTE is no longer justified at lower temperatures.On the other hand, the temperature within the arc core strongly emitting light is found to decrease weakly with radius (figure 10(b)).At a radius of about 1.2 mm, the arc reaches a temperature of about 6200 K and 5800 K at 0.5 and 3.5 ms respectively.Estimates at further radii are also not possible due to the rapid decrease in the emission coefficient at lower temperatures.For this reason, no estimates are possible for the temperature in the cooler envelope around the hot arc core.For this reason, it is only possible to state that the thermal radius of the equilibrium arc core in the experiment is larger than 1.2 mm.Observe that this lower limit for the thermal arc radius is significantly larger (nearly twice) than the optical radius observed from the photographs or the spectral images.
The estimated axial arc temperature as a function of the injected current in CO 2 is shown in figure 11.Observe that the temperature increases rather linearly with current between 0.55 A and 1.3 A. However, a faster rate of increase is found for the CO 2 arc temperature below 0.6 A. The temperatures of the arc when N 2 or H 2 O are added at the maximum tested compositions are surprisingly similar.They are only slightly lower (by about 500 K) compared with the arc temperature in CO 2 only at currents above 0.55 A. Observe that the obtained temperatures in the CO 2 /N 2 arc are similar to that measured for a 3 kW inductively-coupled plasma in [15] at about 6000 K.
Last, it is important to clarify that the discharge in the experiment should not be confused with a glow discharge.Observe that normal and abnormal glows have entirely different characteristics compared to the arc discharge here reported.For instance, glow discharges are strongly non-equilibrium plasmas in which the temperature of electrons (T e ≈ 10 000-30 000 K) and of the gas (T gas ≈ 300-3000 K) differ strongly [40].In contrast, the arc in the experiment is at least in partial LTE, with a maximum gas temperature of about 7000 K. Due to this high temperature, the arc discharge is highly luminous, in comparison with glow discharges [41].On the other hand, while the current density in glow discharges is seldom more than 50 mA cm −2 [2], the estimated value for the reported VT equilibrium arc is be more than 3500 mA cm −2 .This value is estimated assuming a conservative true arc column radius of 3 mm.For further differences between glow and arc discharges, the reader is referred to any of the many books in the subject (e.g.[40,41]).

Conclusions
Different measurements are reported to study the electrical and spectroscopic properties of low-current (<1.5 A), stationary arc plasmas in CO 2 at atmospheric pressure.The experiments are also performed in CO 2 with low concentrations of N 2 and H 2 O, up to 9.2 and 7.4 wt% respectively.A spark is first ignited between the electrodes, and then the plasma is thermalized into an equilibrium arc by injecting a decaying current lasting less than 10 ms.
The U-shaped electric field-current characteristics of the arc plasmas are measured.A minimum average electric field of ∼20 V mm −1 is measured at currents between 0.8 and 1 A under all tested gas conditions.The addition of N 2 and H 2 O into CO 2 did not produce any significant change in the field-current characteristic except for N 2 at currents below 0.4 A. For instance, the average electric field at the maximum tested concentration of N 2 reached 25 V mm −1 at 0.03 A, about 50% lower than for only CO 2 .Furthermore, the addition of N 2 also decreased the threshold current at which the arc can be maintained in vibrational-translational VT equilibrium.This threshold current is 25% lower when N 2 is added to CO 2 .
The optical spectrum of the low-current arc plasmas is dominated by emission from the C 2 Swan band and the OI triplet peak at 777 nm.Although a significant continuum background emission is also measured, no metallic emission is observed during the VT equilibrium arc stage.Furthermore, the CN violet band system is also detected when N 2 is added, even in low quantities (as low as 0.5 wt%).Average temperature estimates by comparison of synthetic spectra with time-andspace-averaged measurements show that the arc is in VT equilibrium.Average temperatures obtained from analysis of the C 2 Swan delivered consistent values 5800 ± 1500 K for all the tested conditions.Similar estimates in the presence of N 2 are obtained when using the CN band, confirming the estimates with the C 2 Swan band.Radiance-calibrated spectral images, resolved in time and space, allowed the estimation of the CO 2 arc temperature as a function of current and radius.It is shown that the axial temperature in a CO 2 plasma decreases with current, from 7200 K at 1.3 A to 6500 K at 0.4 A. These estimates are obtained from emission from the C 2 ∆v = 0 bandhead, with similar values confirmed by estimates based on the OI 777 nm triplet emission.The addition of N 2 and H 2 O at the maximum tested concentration both caused a similar decrease of 500 K in the axial arc temperature.The arc thermal radius is estimated to be larger than 1.2 mm, more than two times larger than the optical radius estimated from the photographs or the spectral images.

Figure 1 .
Figure 1.Schematic image of the experimental setup including diagnostics (not at scale).

Figure 2 .
Figure 2. Typical electrical signals (a) voltage and (b) current recorded for the low current arc in the experiment.The voltage across the capacitor is also included to illustrate the dynamics of the circuit.The different stages during the operation are indicated by the coloured areas.

Figure 3 .
Figure 3.Typical photograph of the CO 2 arc generated between the electrodes.(a) Raw image, (b) colour-inverted image indicating the arc column and the reflection on the glass tube, (c) colour-inverted, brightness-reduced image for arc length calculation.

Figure 4 .
Figure 4. Electric field-current characteristics of the arcs in the experiment (a) for each tested arcing event in CO 2 , (b) average values of all the tests performed in a CO 2 /N 2 mixture at different concentrations, (c) average values of all the tests performed in a CO 2 /H 2 O mixture at different concentrations.The error bands in b and c correspond to the width of the variation band in each case.

Figure 5 .
Figure 5.Typical relative irradiance spectrum of the CO 2 arc plasma detected during the first 4 ms of the discharge and integrated in space at the midgap.Examples of the spectra with the N 2 and H 2 O admixtures are also included for sake of comparison.

Figure 6 .
Figure 6.Comparison between the normalized irradiance spectra measured and simulated for the ∆v = 0 sequence: (a) of the C 2 Swan band in CO 2 only and with the maximum tested concentrations of N 2 and H 2 O, (b) of the CN violet at the different CO 2 /N 2 tested compositions.The simulated spectra correspond to an LTE plasma with Tr = Tv = 5800 K.

Figure 7 .
Figure 7. Example of the measured side-on spectral image of (a) the C 2 Swan band and (b) the O I triplet peak for the CO 2 arc plasma at two different current levels.The colour legend is normalized to the band maximum Lmax in each case.

Figure 8 .
Figure 8. Example of the emission coefficient spectra obtained for the CO 2 arc plasma (a) at different times with a step of 0.5 ms at the axis (r = 0), (b) at different radii at t = 0.5 ms and with a spatial step of 0.166 mm.

Figure 9 .
Figure 9. Emission coefficients of the 516.5 and the 777 nm peaks calculated with SPARK as a function of gas temperature for an LTE plasma in pure CO 2 .The corresponding values for the maximum tested additive compositions of N 2 and H 2 O are also included.

Figure 10 .
Figure 10.Gas temperature estimated from the C2 ∆v = 0 bandhead and the O I peaks for the CO 2 plasma from the emission coefficients in figure 8. (a) As a function of time at the axis (r = 0) and (b) as a function of radius at two fixed time instants.Best fitting curves to the estimated temperatures are included for sake of clarity.

Figure 11 .
Figure 11.Gas temperature estimated from the C2 ∆v = 0 bandhead at the axis (r = 0) of the equilibrium arc in CO 2 plasma and with the maximum additive compositions of N 2 and H 2 O.

Table 1 .
Gas conditions for the different mixtures.