Characterization of a filamentary discharge ignited in a gliding arc plasmatron operated in nitrogen flow

A gliding arc plasmatron (GAP) is a promising warm plasma source for the use in gas conversion applications but lacks an understanding of the plasma dynamics. In this paper, the gliding arc plasma conditions of a GAP operated with nitrogen flow (10 slm) are characterized using optical emission spectroscopy (OES) and numerical simulation. A simultaneously two-wavelength OES method and Abel inversion of the measured images with a spatial resolution of 19.6 μm are applied. The collisional radiative model used in this study includes Coulomb collisions of electrons. An iterative method of plasma parameter determination is applied. The determined values of the electric field up to 49 Td and electron density up to 2.5∙1015 cm−3 fit well to the plasma parameters received with different diagnostics methods in comparable plasma sources. Additionally, the electric current, which is calculated using the determined reduced electric field and electron density, is compared with the measured one.


Introduction
Interaction between a filamentary discharges and a gas stream impinging perpendicular to it is applied in a quantity of industrial arrangements.In dependence on the electric field and the electron density that can be thermal, so called arc in cross flow [1], and non-thermal (cold or warm) plasmas (e.g.gliding arc (GA) [2][3][4]).These discharge types have different commercial applications, like circuit breakers and wire arc spraying (arc in cross flow [1]) and gas conversion or combustion enhancement Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
(gliding arc [2][3][4][5][6]).Thermal plasmas with gas and electron temperature (T g , T e ) of about 10 4 K, are very dense, with electron density higher than n e > 10 16 cm −3 , and are sustained by thermal collisional excitation and ionization.A conventional gliding arc is a nonstationary plasma discharge, which in its simplest configuration is ignited between two flat horn-shaped electrodes and is shifted along the electrodes with the gas flow (see e.g.[2][3][4]).The length of the gliding arc channel increases during this movement up to a maximum value, which corresponds to the extinguishing of the GA.After that, a new GA channel is produced at the shortest distance between the electrodes.A gliding arc is ignited in the spark mode with a strong current peak [7] and then turns into a stable stage.It was supposed in [4] that the so-called 'gliding arc' is actually the glowtype discharge, which is sustained due to the high electric field, whose role is to provide sufficient gas ionization in the positive column.For different plasma chemical applications, the gliding arc has the advantages of simultaneously achieving a high level of non-equilibrium, a high electron temperature, but at the same time, elevated electron density [8][9][10].
The flat geometry and the overheating of the electrodes of conventional GA plasma sources limits their effectivity for plasma-chemical applications, like gas flow conversion [11].This can be solved by using a 3D geometry like a gliding arc plasmatron (GAP), where a gas swirl is produced inside two hollow electrodes to increase the residence time and to stabilize the plasma.This plasma source has been found to increase the efficiency of the plasma-chemical applications compared to a typical gliding arc [11,12].The elevated gas temperature and electron density, the small dimension and the simple setup make the GAP attractive for different applications.
The gas temperature, the electric field and the electron density of the gliding arc channel are the most important parameters, which must be taken into account by consideration of the GAP for one or another application.Optical emission spectroscopy (OES) and numerical simulations are applied usually by the determination of the gas temperature of the gliding arc channel [13].The measured emission bands of diatomic molecules are compared with spectra simulated by different rotational temperatures and the best fit is determined.Thermal equilibrium between translational and rotational degrees of freedom of diatomic molecules is assumed at atmospheric pressure conditions [13,14].Different molecules and radical transitions, like N 2 (C-B), C 2 (d-a), OH(A-X), CO(B-A) were applied to determine the gas temperature in the GA channel [4,6,[15][16][17][18].The electric field and the electron density are determined using current-voltage measurements and the geometry of the plasma channel (length and cross section).For this approach, several assumptions must be made, like a known voltage on the cathode fall and homogeneous plasma conditions of the 'positive column' region [6,19].OES methods like line ratio (argon [20] and OH-radical [21]) and line broadening (argon [18] and hydrogen [16,17,22,23]) were applied by GA plasma characterization.All aforementioned diagnostics methods provide effective plasma parameters, but characterize the GA channel without temporal and spatial resolution, though different plasma conditions are expected in different development stages and different regions of the plasma channel [4,6,19,24].
To solve this problem, OES with temporal and spatial resolution is applied to characterize the GAP channel.A twowavelength simultaneously diagnostics method is used in the presented study.The basic of this method is an absolute calibrated spectroscopy, a simulation of the electron distribution functions by solving the Boltzmann equation and a known collisional-radiative model, which uses reliable cross-sections of electron impact excitation.The diatomic nitrogen molecule is chosen as a test gas, but this method can be used in general in nitrogen containing plasmas, even with low nitrogen admixtures, to characterize the plasma.The molecular nitrogen emission spectrum in UV/VIS spectral ranges consists of two electronic systems: N 2 (C-B) (second positive system) and N 2 + (B-X) (first negative system) with very different energies of the upper states, namely 11.05 eV and 18.74 eV.Because of this large difference, the intensity ratio of these emission bands is very sensitive to variations of the electron velocity distribution function (EVDF) in nitrogen-contained plasmas.The electric field and the electron density are determined separately and consecutively [14,25].A spatial resolution of several micrometers can be achieved by application of a calibrated intensified charge-coupled device (ICCD) camera and Abel inversion of the measured images [14].Reliability of this diagnostics method was successfully verified at different plasma conditions by comparison with an electric probe [26,27], multipole resonance probe [28], capacitive probe [29] and laseraided electric field induced second harmonics [30].
In the presented paper, a spectroscopic characterization of the plasma conditions with spatial resolution of the GAP plasma channel near the anode spot is introduced.Because of the expected elevated electron density and the relative low electric filed, the Coulomb collisions are taken into account for the plasma characterization based on nitrogen molecular photoemission [14].

Experimental setup
A GAP was developed in [11,31,32].In the presented study a slightly modified scheme of the reverse-vortex plasmatron is used (figure 1).Further information about the geometry can be found in [33].The gas flow enters through six tangentially gas inlets with a diameter of 2 mm into the outer cylindrical vessel, where the outer swirl is produced.The inner swirl with much higher velocity is produced inside the hollow cathode and is transferred to the outlet tube, which is used as anode.
The minimum gap between the anode and the cathode amounts to 3 mm.Stainless steel electrodes are used.The inner anode diameter amounts to 7 mm.The GAP is operated with a nitrogen flow of 10 slm with a purity of 99.999% (Alphagaz, Air Liquide).The applied DC power supply (XR10000, Magna Power Electronic) delivers a maximum voltage of 10 kV and a maximum current of 600 mA.In this work, the power supply is operated in the current limiting mode at 0.23 A. A 15 kΩ resistance is connected in series with the GAP to limit the electric current during the discharge ignition to protect the power supply from electrical shorts.The voltage and current during the operation of the GAP can be seen in figure 2. The sawtooth like behavior is due to the extension of the plasma channel because of the perpendicular gas flow, increasing of the voltage between axial channel and the anode and formation of a new channel inside of the anode tube with lower length and resistance.This event is repeated with a frequency of about 770 Hz ± 133 Hz in our experiment.The temporal behavior of the GAP plasma is studied by using a high-speed camera (Phantom VEO 440 l 1MP, Vision Research).The frame rate of 18-35 kHz and the image resolution of 512 × 256 pixels are matched for a reliable study of the temporal behavior of the GA plasma.The current-voltage characteristics are measured using a current monitor (CP030A, Teledyne LeCroy) and a voltage probe (P6015A, Tektronix) connected to an oscilloscope (Waverunner 8254 2.5 GHz, Teledyne LeCroy).An echelle spectrometer (ESA4000, LLA Instruments) with a spectral resolution of 0.015 nm < ∆λ < 0.06 nm in the spectral range of 200 nm < λ < 800 nm is used for the OES plasma characterization.The spectrometer is provided with a condenser lens and a pinhole diaphragm with a diameter of 0.5 mm as shown in figure 1.With this optical arrangement, the spectrometer collects the photoemission of a cylindrical volume parallel to the GAP axis.The spectral efficiency of the echelle spectrometer was determined using both a tungsten ribbon lamp and a deuterium lamp, each calibrated by the Physikalisch-Technische Bundesanstalt (PTB, Berlin) [14].Temporary averaged emission spectra are measured.The gas temperature in the discharge is determined by using the rotational distribution in the emission spectrum of the N 2 (C-B,0-0, λ = 337.1 nm) vibrational band, under the assumption that the translational and rotational degrees of freedom in the ground state of nitrogen molecules (N 2 (X)) are in equilibrium.The electronic impact excitation of diatomic molecules is limited by the selection rule ∆J = 0, ±1.Therefore, the rotational distribution in the excited molecular state is approximately equal to the rotational distribution in the ground state of the molecule.With an in-house software, the emission spectrum of the N 2 (C-B,0-0) vibrational band is simulated with different rotational temperatures and a spectral resolution equivalent to that of the used spectrometer.With that, the rotational structure of the simulated spectra represents a big number of unresolved bands.With a spectral broadness of about ∆λ = 0.1 nm, the simulated bands consist of three lines of different rotational line progressions.The mean intensities of some of these bands are determined for different rotational temperatures, normalized to the maximum value at λ = 337.1 nm and fitted with a polynomial fit.The same calculation procedure is applied to the measured spectra and a relative mean intensity is determined in the same chosen spectral intervals.The rotational temperature, which in our case is equal to the gas temperature, is evaluated using the relative mean intensity values of the measured spectra and compare it to the polynomial fitted values of the calculated data.The mean value of the gas temperature and the standard deviation is determined using five chosen spectral intervals in 10 measured emission spectra.The standard deviation of the mean value is used by the determination of a confidence interval of the measured gas temperature.
The gliding arc channel near the anode spot is characterized in the presented paper using OES.This part of the GAP filament is a transient discharge, which moves around the electrode surface [34].To characterize this transient discharge, a two-wavelength simultaneous arrangement [14,35], that consists of two optical beam splitters, two band-pass filters and two mirrors in combination with an ICCD camera, is used (see figure 1).This optical setup is focused on the top edge of the anode, so that the images of the plasma are recorded a few microseconds before the gliding arc exits the anode and reaches its maximum length.Using this optical scheme, two discharge images for the N 2 (C-B) and N 2 + (B-X) molecular emissions are displayed simultaneously and separately on the CCD chip of the camera.An UV enhanced ICCD camera (4 Picos, Stanford Computer Optics) is used for this study.The exposure time of the camera can be varied from a minimum of 200 ps to 1000 s.To obtain the spatial distribution of the N 2 (C-B) and N 2 + (B-X) emissions, two band-pass filters with the transmittance at either 380 ± 5 nm or 390 ± 5 nm (Thorlabs GmbH) are aligned with two achromatic lenses to receive a high spatial resolution.At this condition, the pixel length of the measured images amounts to 19.6 ± 0.1 µm.For the purpose of plasma characterization with spatial resolution, the Abel inversion of the measured images is performed in the presented study.This mathematical method can be applied only for objects with cylindrical symmetry.The GAP channel is a transient discharge with continual changing filament form and plasma spot position on the electrode surface.This change depends on the velocity of the gas stream, which is lowest near the surface of the anode tube.Due to the image splitting (see figure 1), the insufficient transmission of the band-pass filters and sensitivity of the ICCD camera used, the simultaneous two-wavelength diagnostics requires elevated intensity of the examined object.An insufficiently high signal causes an increased statistical dispersion, a low signal-to-noise ratio and an artificial radial intensity distribution created by Abel inversion of the image.A low measured intensity of the examined object can be partially compensated by increasing the exposure time.The disadvantage of a long exposure time is the movement of the studied transient plasma object during the measurement time and the formation of an artificial object shape in the measured images.In this study, an exposure time of 15 µs has been found to give a good signal to noise ratio.
The plasma channel of the GAP with reverse-vortex stabilization consists of three areas: a stable central plasma filament and two channels connecting this central filament to the electrodes [34,36].Figure 3 shows the GAP plasma channel when it just exits the anode nozzle (left), as well as shortly before it extinguishes (right).The connecting channel rotates along the electrode surfaces, due to the working gas swirl while the stable plasma filament, which length amounts to several centimeters, is placed near the GAP axis.The intensity of the photoemission in longitudinal direction of the stable plasma filament is much higher than the intensity of the rotating part of the GA channel (see figure 3).To exclude a saturation of the CCD chip during the OES plasma characterization, the entrance lens of the optical arrangement is placed in a position, where the stable plasma filament is not observed by the camera (see figure 1).A point-like (diameter of 0.6 mm) microwave plasma and a calibrated spectrometer are used for the absolute calibration of the ICCD camera with the twowavelength simultaneous diagnostics arrangement [14].The + (B-X,0-0) are measured for this plasma source using the echelle spectrometer.The microwave plasma source is placed in the same position as the studied GAP and its image is recorded using the ICCD camera with the simultaneous two-wavelength diagnostics arrangement.From the measured absolute intensities of nitrogen bands of the pointlike source, the ICCD camera is absolutely calibrated simultaneously with both filters [14].
The ICCD signal measured with the two-wavelength arrangement must be corrected because of a partial overlapping of the nitrogen bands due to the wide transmission profiles (∆λ = 10 nm) of the applied filters.This correction is done by using the measured emission spectrum and the transmission of the filters.The transmission profiles of the applied optical band-pass filters are measured using a broadband light source (DH-Mini, OceanOptics) and a grating imaging spectrometer (QE65000, OceanOptics) with spectral resolution of 1.3 nm.The broadband light source is connected to the collimator lens via an optical fiber and produces a parallel light beam.After passing the band-pass filter, the parallel light beam is collected by the second collimator and guided by an optical fiber to the spectrometer.

Applied diagnostics method
As was mentioned before, the emission spectrum of nitrogen under atmospheric pressure conditions consists of two intensive emission systems N 2 (C-B) and N 2 + (B-X).The scheme of energetic levels and electron impact excitation transitions, which are applicable for OES diagnostic at the GAP plasma conditions, are presented in figure 4.Under the elevated pressure conditions, the molecular emission N 2 (C-B) and N 2 + (B-X) can be excited by direct electron impact of the nitrogen ground state N 2 (X) or stepwise via the nitrogen metastable N 2 (A) and the ground state of nitrogen ions N 2 + (X) [14].The former excitation scheme is characteristic in high electric field plasmas, like dielectric barrier discharges (see e.g.[37]).The latter is a basic excitation mechanism at elevated electron density and low electric field, like in a high frequency plasma [38].Based on the estimation of the plasma conditions of GA plasmas [4,39,40] and previous characterizations of nitrogen plasmas using OES diagnostics [14,35] a stepwise mechanism for the excitation of the nitrogen molecular photoemission is assumed for the GA channel (see figure 4).Electron impact ionization N 2 (X)-N 2 + (X) is presented in figure 4 with dotted arrow only in a purpose of completeness and is not included in the considered radiative-collisional model.
The rate constants, presented in figure 4, are calculated using the known cross sections of the electron impact excitations (σ exc ) [41][42][43] and the EVDF (f v (E)).The latter is determined by solving the Boltzmann equation numerically for nitrogen plasmas and for different reduced electric field values.For this purpose, the program code 'EEDF', developed in the group of Prof.A Napartovich, Moscow Institute of Physics and Technology [44], is applied.The EVDF in kinetic energy scale ( f v (E kin ) in eV −3/2 ) and the electron drift velocity (in cm s −1 ) are calculated.The EVDF is normalized to fulfill equation (1).
The rate constants for electron impact excitations are calculated with equation ( 2) where E kin is the kinetic energy of the electron, m e the electron mass and the coefficient In the frame of the stepwise excitation model, the intensities of the nitrogen UV photoemission I N2(C) and I N + 2 (B) can be presented by equations ( 3) and ( 4) (3) where and n e are the respective number densities, B1 = 0.5 and B2 = 0.5 are correction factors, which correspond to a partial population of the N 2 (C,v ′ = 0) vibrational state by electron impact excitation from the N 2 (A) state and the branching factor of the N 2 (C-B,0-0) transition by photoemission from the N 2 (C,v ′ = 0) vibrational state [14].The quenching factors are calculated in equations ( 5) and ( 6 , from [45].The influence of the elevated gas temperature on the efficiency of the quenching process is considered by substituting the rate constants for the collisional induced deactivation of electronically excited nitrogen states in equations ( 5) and ( 6) in Arrhenius form. (5) Equation ( 4) contains the unknown density of diatomic ions n N + 2 (X) .In assumption of quasi-neutrality and based on analysis presented in [14] is assumed in this work.This assumption will be validated below.The reduced electric field (E/N in Td) and the electron density can be determined separately and consecutively by using equations ( 7) and (8), respectively.
The discharge current density of the gliding arc channel (j) can be calculated using the determined electron density, the calculated drift velocity v d of the electrons and the elementary charge (e) (equation ( 9)).
To simplify the determination of the plasma parameters and the calculation of the discharge current density equations ( 7)-( 9) are fitted with polynomials shown in equations ( 10)- (12), respectively.
As mentioned in [14], Coulomb collisions affect the shape of the simulated EVDF at elevated electron densities and low electric field strengths and can cause systematic errors in the OES plasma characterization (see figure 5).To obviate this problem, an iteration method is introduced in this work.
Therefore, the Boltzmann equation is solved for different electron densities, ranging from 10 13 cm −3 to 10 16 cm −3 on a logarithmic mesh as well as for different reduced electric fields, as was described above.
Based on that, the respective EVDFs and the drift velocity are determined and the respective excitation rate constants are calculated.In the next step, the functions F1, F2 and F3 were fitted with polynomials for each electron density (see figure 6).The real electron density is not known a priori and at first approximation, the influence of Coulomb collisions on the EVDF is excluded (n e = 0) from consideration and respective polynomials for F1 and F2 are chosen.Using the measured photoemission intensities and the chosen polynomials, the reduced electric field and the electron density are determined in first approximation.From the results of [14] it can be concluded that the electron density is overestimated if the Coulomb collisions are not taken into account in the OES characterization of the nitrogen plasma.This overestimated electron density is rounded to the nearest value used for the calculation of the polynomials and respective F1 and F2 polynomials are chosen for the next iteration.The electron density determined in the second iteration with the same measured intensities of nitrogen photoemission is then underestimated because of the overestimated density value used by choosing F1 and F2 polynomials.
Iterations are then continued until the results of subsequent iterations will be equal or their difference is lower than the step size of the electron density mesh (see figure 6).The averaged values (reduced electric field and electron density) between these last overestimated and underestimated values are used as results of the iteration process.The confidence intervals of the determined plasma parameters caused by the iteration procedure will be discussed below.

Experimental results
The emission spectrum of the gliding arc channel near the anode surface is measured longitudinal with a lens and a pinhole diaphragm (see figure 1).The gas temperature of 1474 ± 30 K was determined by using five bands in the rotational structure of the N 2 (C-B,0-0) transition of ten measured spectra.
To estimate the vibrational temperature of the nitrogen molecule in the filamentary plasma near the anode spot, the measured spectra of N 2 (C-B) bands (figure 7) and the calculated Franck-Condon factors (FCF) for N 2 (C-B) [46] and N 2 (X-C) [47] transitions were used.The vibrational degree of freedom is excited in the nitrogen GAP plasma by electron impact of the N 2 (X) ground state, namely by direct vibrational excitation (e-V) and by electron impact excitation of the N 2 (A,B,C) states because of the difference in equilibrium internuclear distances to the ground state.Because of frequently collisional quenching and a short lifetime of the electronic excited states of the nitrogen molecules at GAP plasma conditions, the vibrational excitation of the N 2 (A,B,C) states is irrelevant for plasma sustenance and plasma chemistry.The steady state density of these excited nitrogen states in the GAP plasma is in the ppm and ppb ranges.To determine the steady  10)- (12) in assumption of different electron densities (see supplementary information).state vibrational excitation of the ground state N 2 (X), the relative intensities of the N 2 (C-B,v ′ -v ′′ ) bands are determined using the measured emission spectrum (see figure 7) and the steady state population of the N 2 (C,v ′ ) levels are calculated by applying the FCF from [46] (see figure 8).The N 2 (C) state is excited at GAP plasma conditions mainly by electron impact of the N 2 (X) state.The population distribution of the N 2 (C) state is caused by the vibrational population distribution of the ground state N 2 (X) and the FCF of the N 2 (X-C) [47] transition.Figure 8 shows the steady state population of the vibrational levels of the N 2 (C) state (■), determined using the measured emission spectra of the GAP plasma (figure 7).The error bar shows the confidence interval, which is caused by possible inaccuracy of the calculated FCF and partial overlapping and insufficient intensities of the different vibrational bands.The solid line with triangles (▲) presents values of the relative vibrational population of N 2 (C), which are calculated in assumption of electron impact excitation only from the ground vibrational level (v ′′ = 0) at T vib = 0 K.The empty circle symbol (•) shows the population of vibrational levels N 2 (C) states in assumption of a Boltzmann distribution of the vibrational degree of freedom in the ground state with a vibrational temperature (T vib = 1500 K), which is equal to the gas temperature inside the plasma.It can be seen in figure 8, that the vibrational populations of the N 2 (C) state, which are calculated under the assumption of an equilibrium between the translational and the vibrational degrees of freedom (T g = T vib ) and were measured using the photoemission of the GAP plasma, show a deviation which is smaller than the confidence interval from the vibrational distribution, which is calculated under the assumption of electron impact excitation only from the ground vibrational level (T vib = 0 K).Due to that it can be concluded, that the vibrational excitation of molecular nitrogen is low at GAP plasma conditions and cannot be reliably determined using OES.
Figure 9(a) shows an image of the gliding arc plasma channel near the anode spot measured with the non-synchronized ICCD camera and the optical arrangement for the simultaneous two-wavelength OES diagnostics shown in figure 2. To minimize the systematical error in the Abel inversion, which is caused by an incline of the GA channel axis, the measured images are rotated counterclockwise by 16 degrees (see figures 9(b) and (c)) using the rotate-function of Python.To remove a possible systematical error in the determination of the plasma parameters caused by this procedure the calibration of the ICCD camera is carried out with and without the additional image rotation.No difference between the efficiency of the ICCD camera measured in these two cases was established.
The optical imaging system (ICCD camera and the simultaneous two-wavelength arrangement) is calibrated as was mentioned in chapter 2.1 using a point-like high frequency light source operated with 2 slm nitrogen and a calibrated echelle spectrometer.The ICCD signal measured with a bandpass filter of 380 nm is corrected for the calibration and  the plasma characterization, because of an overlapping of the N 2 (C-B) and N 2 + (B-X) molecular bands in the transmission spectral range of this filter (see chapter 2.1).The correction factor for the ICCD signal measured with the 380 nm filter amounts to 22% for the calibration procedure and 24% for the GAP characterization.The ICCD signal measured with the 390 nm filter not need any corrections because participation of N 2 (C-B) photoemission in The optimal pixel length of 19.7 µm and the exposure time of 15 µs were chosen in the present study to strike a balance between signal-to-noise ratio, reliable profile of the GAP plasma channel in the measured images and sufficient spatial resolution.This optimization cannot completely solve the problem, which was mentioned above.Therefore, the profile of the measured GAP plasma channel has a tail in direction against the gas rotation.To reduce the influence of this factor on the reliability of the determined plasma parameters, only the front half of the GAP plasma channel cross section (toward the moving direction) near the anode surface, at the distance about 0.5 mm, is used for the Abel inversion and following plasma characterization.Under the assumption of cylinder symmetry the evaluated image section is then mirrored, to represent the whole diameter of the GAP plasma channel (see figures 9-12).The radial distributions of the N 2 (C-B) and N 2 + (B-X) molecular emission transitions, which are determined using the Abel inversion of the measured images are presented in figure 10.To determine the radial distributions of the plasma parameters, the images are corrected for their background.Afterwards, the images are calibrated in photons•s −1 cm −3 [14], corrected for overlapping of the emission bands (see above) and collisional quenching by the nitrogen molecules (equations ( 5) and ( 6)).Finally, the collisional-radiative model (see chapter 2.2) is applied to every single volume pixel (19.7 µm × 19.7 µm × 19.7 µm) using the fitted polynomials F1 and F2 (equations ( 10) and ( 11)) to receive the reduced electric field and the electron density (figure 11).The iteration procedure is used to take into account the Coulomb collisions.Mostly 3-4 iteration are needed to receive reliable plasma parameters.
Using the spatial distribution of the reduced electric field, calculated drift velocity and the electron density the electric current density is calculated by using equation (9) (see figure 12).The electric current of the gliding arc channel of the GAP calculated (equation ( 13)) in assumption of cylindrical symmetry of GA plasma I = 2π ˆj (r) rdr (13) amounts to 2.1 ± 0.1 A. Accuracy and reliability of the calculated values and comparison with measured electric current are presented in the following chapter.

Verification of the applied collisional-radiative model
Based on the low electric field conditions of the gliding arc [4,39,40] it was assumed in this study, that a stepwise excitation mechanism of the nitrogen molecular emission best describes the process [14].To valid this assumption the electric field needed to excite the measured emission spectrum of the GAP plasma channel is estimated.The intensity ratio between the N 2 + (B-X) and the N 2 (C-B) emission band amounts to about four in our experiment.At that, quenching of molecular nitrogen excited states at experimental conditions is taken into account.A hypothetic electric field, which can ensure the measured intensities ratio in assumption of electron impact excitation of the ground state N 2 (X) (direct excitation mechanism), amounts at GAP plasma conditions to about 36 kV.The maximum voltage of the applied power supply is 10 kV.The measured voltage applied to the GAP amounts to about 1 kV.Based on this estimation we conclude, that the excitation of nitrogen molecular emission by electron impact excitation of the ground state N 2 (X) (direct excitation mechanism) is negligible at GAP plasma conditions.

Plasma parameter of the GA channel
The assumption of quasi-neutrality in a pure nitrogen plasma is shown in equation ( 14) Due to the high chemical activity of nitrogen atoms [48] and the low cross section of the electron impact ionization of atomic nitrogen [49], the relative density of atomic nitrogen ions and the three-atomic ions, which are formed by participation of neutral nitrogen atoms or atomic ions [48], can be neglected (equation ( 15)).
At steady-state plasma conditions the density of N + 2 ions is proportional to the electron density (equation (18)) Because of the relative low gas temperature of the GA plasma (∼1500 K), the term K (n e , T e , T g ) can be up to about 0.2 in the presented study.The presence of N + 4 in the GA plasma causes a systematical error in the determination of the plasma parameters [14].The reduced electric field is slightly overestimated, up to 0.5%, and the electron density is underestimated down to about 7%.These systematical errors are negligible in comparison to other inaccuracies of the measurement and the simulation and are excluded from consideration in the presented study.
The results of the presented study show, that Coulomb collisions are important for the formation of the electron distribution function under plasma conditions of the GAP (see figure 4).A reduced electric field lower than 50 Td and an electron density about 10 15 cm −3 are characteristic of a GAP plasma.Neglecting of Coulomb collisions in the OES characterization can cause a big systematical error (see figure 5).The iterative procedure applied in the presented study can successful solve this problem.At that, the final inaccuracy of the received plasma parameters depends on the mesh size of the simulation of the fit functions E N (I emission ) and k exc E N (see equations ( 10) and ( 11)) with different electron density values.The iteration procedure starts in assumption of negligibility of Coulomb collisions.The results of the sequence steps of the iteration procedure are the under-and overestimated values of the electron density.The iteration is finished when the underestimated and overestimated values correspond to their neighbor mesh values.The final iteration result is received by averaging the plasma parameters, reduced electric field and electron density, calculated in assumption of these two values.Three to four iteration steps are needed in the presented study to achieve this result.The maximum inaccuracy of the reduced electric field and the electron density, which is received by this procedure amounts to values lower than 1% and 10%, respectively.Accuracy of the iteration procedure can be heightened by application of a denser mesh.The electric field, which is measured in the anode spot, amounts to about 40 Td or 2 kV cm −1 (see figure 11).The electric field of a gliding arc is estimated in different papers using voltage measurement in assumption of glow-like spatial distribution of the voltage drop in the plasma column.In conventional and magnetic gliding arcs, operated with air flow and an electric current of 0.2 A, an electric field of about 10 Td was estimated under these assumptions [4,19].From the other side, it was established in [51] that the gliding arc at a moderate current and an elevated gas flow is a transition discharge and contains of two phases: equilibrium and non-equilibrium.An analysis of the kinetic balance of the transient regime between these phases in air flow shows that the electric field is about 40 Td, if the gas temperature amounts to 1500 K [24].This result is very similar to the plasma conditions established in this work.
The electron density of a magnetic stabilized gliding arc operated in an air flow was also estimated to about 5 × 10 14 cm −3 with an electrical current of 0.2 A [19] in the frame of a glow-like assumption, mentioned before.This value is very similar to n e = 6.9 × 10 14 cm −3 measured by application of the line ratio method in argon flow in a so-called 'GA jet', stabilized with a magnetic field [21].Stark broadening of emission lines was also used to determine the electron density in hydrogen and argon containing gliding arc plasmas and values from 1.4 × 10 14 cm −3 [17], ∼10 15 cm −3 [16], 1.32 × 10 15 − 5.74 × 10 15 cm −3 [18] up to 1.9 × 10 16 cm −3 [23] were measured.The here presented result of about n e = 10 15 cm −3 near the anode spot of the GAP hit the middle of the above mentioned interval.To valid the reliability of the electron density measured in the frame of aforementioned collisionalradiative model, measured intensity of N 2 (C-B,0-0) emission and equation ( 8), we determine electron density using intensity of N 2 + (B-X,0-0) and equation (19) in assumption of .
The received electron density values are very similar to the presented ones in figure 11, but with some deviation caused by the participation of N + 4 ions in balance of charge species in quasi-neutral plasma.Based on the similarity of the electron density values measured using photoemission of neutral and ionized nitrogen molecules, we conclude that the result presented here is reliable.A big difference of electron density values measured without spatial and temporal resolution in different experiments mentioned above is caused possibly by the transient character of the gliding arc discharge and existence consecutive thermal and non-thermal discharge phases.

Accuracy of determined plasma parameters
The accuracy of the OES plasma characterization of the GA plasma is analyzed based on the accuracy of the measurements and the calibration procedure.Based on the results of [14], the accuracy of the echelle spectrometer efficiency amounts to 8% in the complete spectral range.The standard deviation of the intensity measurement, using the calibrated echelle spectrometer and the plasma parameters, is determined using quadratic error propagation.The gas temperature of the GAP plasma channel measured using the N 2 (C-B,0-0) spectrum amounts to 1474 ± 30 K. The inaccuracy of the ICCD camera calibration, using a point-like MW plasma source and the calibrated spectrometer, amounts to 2.6% measuring N 2 (C-B) and 3% when determining the intensity of N 2 + (B-X).The inaccuracy of collisional quenching of N 2 (C-B) and N 2 + (B-X) amount to 6% and 14% at the considered experimental conditions [45].The inaccuracy of the cross sections of excitation of N 2 (C-B,0-0) and N 2 + (B-X,0-0) emission by electron impact of N 2 (X) and N 2 + (X) are 14% and 4% respectively [41,43].Inaccuracy of the intensity determination of N 2 (C-B,0-0) and N 2 + (B-X,0-0) emission bands amount to 10% and 15%, respectively.Plasma parameters, namely the reduced electric field and the electron density, are determined in the frame of the above presented collisional-radiative model with inaccuracy of 1% and 23%, respectively.

Measured and calculated electric current
The electric current of the GA channel, calculated using the measured plasma parameters and equation ( 13), is approximately ten times higher than the measured current of the GAP.This is a very surprising result and the reliability of the calculation must be verified.The reliability of the calculated current depends on the reliability of the plasma channel cross section, the drift velocity of the electrons, which are calculated using the measured electric field, and the electron density.The diameter of the plasma channel near the anode spot of the gliding arc is observed in our experiment with different cameras and with different distances and zoom.Based on these observations we can conclude that the full diameter of the plasma channel of 600 µm (see figure 14) is a reliable value.The drift velocity of the electrons is calculated with the 'EEDF' program.This program has been used in many studies (see e.g.[14]) where reasonable results were received.Therefore, the reliability of the calculated electric current depends on the reliability of the plasma parameters, namely the electric field and the electron density.Based on the previous discussion, we can conclude that the determined plasma parameters correspond to the expectations for transition discharge of gliding arc and are reliable.
One possible reason for this surprising difference between the measured and the calculated electric current is a circular current of the GAP plasma channel, which can be caused by axial magnetic field.To produce the circular current of electrons an axial magnetic field is needed.This hypothetic magnetic field will cause a circular moving not only of the electrons but also of the ions, which will receive additional kinetic energy.Generally, the ions are accelerated in the electric field of the plasma and have elevated kinetic energy in comparison to the neutral species.As was mentioned before, translational and rotational degrees of freedom of diatomic molecules, neutral and ionized, are in equilibrium at atmospheric pressure conditions and population distribution of rotational levels, namely, rotational temperature, of the ions differs in plasma to the neutral molecules.This difference can be used for the determination of the drift velocity of the ions [52] or vice versa.Based on the calculated and the experimental data presented in [52] we can conclude that the difference of the rotational temperature of nitrogen molecular ions and neutrals is about 100 K at plasma conditions of GAP plasma channel (E/N = 40 Td).The rotational temperature of the nitrogen diatomic ions is determined in our experiment by applying the same method as by the determination of the gas temperature, namely using five chosen unresolved spectral bands in ten measured emission spectra.The rotational temperature of N 2 + (B) ion measured in emission spectrum of GAP plasma (see figure 7) amounts to T rot (N 2 + (B-X)) = 2903 ± 33 K.This value is to ∆T rot = 1429 ± 44 K higher to the gas temperature of GA plasma measured with rotational distribution of nitrogen molecular band N 2 (C-B) (see figure 13).In other words, the kinetic energy of nitrogen molecular ions is fourteen times higher than can be expected at GAP plasma channel conditions.Based on the spectroscopic characterization of the GAP plasma, it can be concluded, that the nitrogen ions are under some influence, possibly an axial magnetic field.
Another event concerning the GAP plasma channel presented in [33] confirms the formation of a circular current of the anode spot.Due to the high electric current during the GAP ignition phase, the anode spot of the gliding arc channel, possibly in thermal stage [2,51], produces erosion traces on the anode surface near the ignition gap.These traces have a toroidal structure.These structures have the form of a crater of molten and partially vaporized metal, with a round area in the center with non-disturbed steel.The reason of the possible circular current and axial magnetic field of the GAP plasma channel has no rational explanation now and needs additional theoretical and experimental studies.

Conclusions
The plasma conditions of the GAP plasma channel operated with nitrogen flow are characterized by OES.The plasma channel has two different regions, the movable gliding arc channel and the stable axial plasma filament.The measured gas temperature of the gliding arc is 1474 ± 30 K. Plasma parameters of the gliding arc channel are characterized near the anode surface in the frame of a collisionalradiative model, using a simultaneously two-wavelength OES method and Abel inversion of the measured ICCD images.The reduced electric field and electron density show peak values of 2.4 • 10 15 cm −3 and 49 Td respectively.At that, Coulomb collisions are important for the formation of the EVDF, which are considered in the applied model.The electric current of the GA channel is calculated using the measured plasma parameters.This value is about ten times higher than the measured GAP current.Moreover, the measured rotational temperature of N 2 + (B) ions of 2903 ± 33 K testifies surprising high kinetic energy of molecular ions.A circular current of the GA channel is supposed.Additional experimental and theoretical studies are needed to valid this assumption.

Figure 1 .
Figure 1.Scheme of the experimental setup for the spectroscopic characterization of the plasma channel of a gliding arc plasmatron.The left side shows the setup to gather optical emission spectra and on the right side, the two-wavelength ICCD camera setup is shown.

Figure 2 .
Figure 2. Voltage and current during the operation of the gliding arc plasmatron.

Figure 3 .
Figure 3. Tangential (top) and longitudinal (bottom) images of the GAP plasma channel, operated with a nitrogen flow of 10 slm.A sketch of the anode and the inner diameter of the nozzle are shown for clarity.The images on the right hand side are measured with a delay of 170 µs to the images on the left.The exposure time amounts to 30 µs.

Figure 4 .
Figure 4. Collision-radiative model of molecular nitrogen with electron impact excitations (solid arrows, black) and spontaneous emission (dashed arrows, red).The denominations of the rate constants of the electron impact excitations are presented near the corresponding arrows.The dotted arrow presents all electron impact ionization processes, which are not included in the considered model.
) using the known Einstein coefficients (A N2(C) , A N + 2 (B) ) of the respective emission transitions, N 2 (C-B) and N 2 + (B-X), and the rate constants of the collisional quenching by nitrogen molecules,

Figure 5 .
Figure 5. Electron velocity distribution functions (EVDF) simulated using 'EEDF' code (see text) in nitrogen plasma for a reduced electric field of 50 Td and different electron densities.

Figure 7 .
Figure 7. Emission spectrum of the GAP plasma channel near the anode, measured longitudinal with the optical arrangement presented in figure 1.The nitrogen flow amounts to 10 slm.Observed electronic transitions of molecular nitrogen and assignment of most intensive vibrational bands are presented.

Figure 8 .
Figure 8. Relative population of vibrational levels of N 2 (C) state determined (■) using measured emission spectrum of GAP plasma in nitrogen near the anode spot.The solid line with triangles (▲) shows the vibrational population of N 2 (C) under the assumption of excitation only from the vibrational ground state (v" = 0) (T vib = 0 K).The empty circle symbol (•) shows vibrational distribution of N 2 (C) state by a vibrational temperature of 1500 K in ground state N 2 (X).

Figure 9 .
Figure 9. ICCD image of the GA channel, measured with band-pass filters 390 nm ± 5 nm (left) and 380 nm ± 5 nm (right) in nitrogen flow of 10 slm and with an exposure time of 15 µs.(a) Shows the original image, (b) and (c) show the by 16 degrees rotated and zoomed images of the respective nitrogen molecular bands.

Figure 11 .
Figure 11.Spatial distribution of reduced electric field (left) and electron density (right) in the GA channel of the GAP, determined using the measured emission of N 2 (C-B,0-0) and N 2 + (B-X,0-0) in the frame of the considered collisional-radiative model.

Figure 12 .
Figure12.Spatial distribution of the current density of the GA channel calculated using the determined plasma parameters and calculated drift velocity (equation (9)).

Figure 13 .
Figure 13.Measured and simulated rotational structure of N 2 (C-B,0-0) (left) and N 2 + (B-X,0-0) (right) vibrational bands, which are used by determination of the gas temperature and kinetic energy of molecular ions in GAP plasma, respectively.Simulated spectra, which are shown for visual verification, are shifted for clarity.