Breakdown and quasi-DC phase of a nanosecond discharge: Comparison of optical emission spectroscopy measurements with numerical simulations

A nanosecond atmospheric pressure plasma jet operated in pure nitrogen is studied by spatially and temporally resolved optical emission spectroscopy complementing the companion paper (Kuhfeld et al 2023 Plasma Sources Sci. Technol. 32 084001), where the discharge is investigated by means of Particle-in-Cell/Monte Carlo collisions (PIC/MCC) simulations and fluid models. Two temporal phases of the evolution of the discharge are identified: a fast breakdown and a quasi-DC phase. It is shown that during the breakdown phase several ionization waves develop, while after the breakdown the discharge has a structure similar to DC glow discharges, in agreement with the modeling predictions. The results of the measurements of the spatial-temporal dynamics of the light emission are compared with the distribution of densities of the N2+(B2Σu+) and N2(C3Πu) states reconstructed from the PIC/MCC simulations. A good agreement is demonstrated.


Introduction
Recent studies of a nanosecond atmospheric pressure plasma jet (ns-APPJ) by picosecond electric-field induced second harmonic generation [1,2] have shown two distinct phases of the discharge: a fast breakdown phase at high electric fields was * Author to whom any correspondence should be addressed.
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. followed by a quasi-DC phase at lower permanent electric field and high electron density. Remarkably, the bulk electric field in the quasi-DC phase was independent of the amplitude of the voltage applied to the discharge and, consequently, the electric field strength during breakdown. Thus, it was concluded that plasma generation, which almost entirely occurs in the breakdown phase, and the subsequent quasi-DC phase are separated and can be controlled independently in order to optimize excited species production. An example of such control is given in [2,3], where vibrational excitation and transfer in the ns-APPJ were studied by coherent anti-Stokes Raman scattering spectroscopy. In these works, different fractions of the vibrationally excited nitrogen molecules were obtained by varying the high voltage (HV) pulse duration and the amplitude of the applied voltage.
In order to optimize discharge parameters for applications, it is required to investigate in more detail the nature of such two-mode discharge. This is accomplished by means of Particle-in-Cell/Monte Carlo collisions (PIC/MCC) simulations in a companion paper [4] combined with the present work, where the discharge is studied by spatially and temporally resolved optical emission spectroscopy (OES).
In order to study the discharge structure and its development the emission of the (0-0) transition of the first negative system (FNS) (bandhead at λ = 391.4 nm) and the (2)(3)(4)(5) transition of the second positive system (SPS) of nitrogen (bandhead at λ = 394.3 nm) is considered: Comparison of the FNS and SPS emission intensity provides information about the electric field distribution in the discharge gap due to significantly different excitation thresholds of the N + 2 (B 2 Σ + u ) and N 2 (C 3 Π u ) states, which are 18.74 eV for N + 2 (B 2 Σ + u ) and 11.05 eV for N 2 (C 3 Π u ) [5], so a dominating ion emission indicates presence of highly energetic electrons. In general, a quantitative analysis providing an absolute value of E/N is possible [6][7][8][9][10]. However, this requires a valid collisional-radiative model and the following conditions to be fulfilled: (i) the problem is quasistationary or the temporal derivatives of emission intensity are taken into account; (ii) the field is uniform in space or the emission of both selected states comes from the same discharge region; (iii) non-local effects are not important. Although, the present experiment, see section 2, is organized in a way that conditions (i)-(ii) are satisfied, non-local effects affect some discharge regions such as the sheath, the negative glow, the Faraday dark space and possibly the anode glow (see the companion paper [4]). Therefore, no conclusions about the electric field distribution in these regions are made based on the experimentally measured emission intensities. However, an analysis of the temporal behaviour and the spatial distribution of the emission and their comparison with the results of the PIC/MCC simulations [4] are performed, since PIC/MCC modeling provides the spatially and temporally resolved electron energy distribution function (EEDF) and, consequently, excitation source terms for the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states taking into account nonlocal behavior of the electrons. Such a comparison serves as a semi-quantitative validation of the PIC/MCC simulations in addition to comparison of the numerical results with electrical measurements performed in [4].

Experimental setup
The discharge is generated between two 1 mm thick flat molybdenum electrodes with a length of 20 mm mounted between two glass plates at 1 mm interelectrode distance, see figure 1(a). Pure nitrogen at room temperature is supplied through an orifice in one of the glass plates at the center of the inter-electrode gap. A constant flow rate of 20 sccm is maintained by a mass-flow controller (MKS Instruments). The discharge cell is installed in a vacuum chamber to control the atmosphere and maintain a constant pressure of 200 mbar during the measurements.
High voltage pulses of negative polarity are generated at a repetition rate of 1 kHz by a home-made pulser based on a fast HV switch (Behlke HTS 81) with an on-time of 175 ns fed by a DC voltage with 3 kV amplitude. In order to protect the switch, the electric current is limited to < 30 A using a 255 Ω series resistor installed between the switch and the cathode of the plasma jet. A 2 kΩ resistor is installed parallel to the discharge cell to remove any residual charges in the circuit between the discharge pulses. The voltage at the powered electrode is monitored with a 400 MHz HV probe (LeCroy PPE 6 kV). The electric current in the discharge is measured by a 200 MHz current probe (Tektronix CT2) installed on the wire connecting the anode with the electrical ground. All electrical signals are recorded by a 3.5 GHz oscilloscope (LeCroy WavePro 735Zi). For a more detailed description of the discharge, please refer to the previous works [1,2].
A schematic view of the experimental setup used for OES measurements is shown in figure 1(b). The light from the discharge is collimated and focused onto the 150 µm input slit of a spectrometer (SPEX 1704: 1 m focal length, 100 mm × 100 mm grating with 1200 grooves per mm and 500 nm blaze wavelength) by a pair of 1 inch achromatic lenses (Thorlabs AC254) with focal lengths of 150 mm and 250 mm, respectively. The spectra are recorded by an ICCD camera (Andor DH720-18F) with a minimum gate time of 5 ns installed at the focal plane of the spectrometer. For measurements with higher temporal resolution, a streak tube (Hamamatsu C10910) coupled with a CCD camera (Hamamatsu ORCA-R2) is used. In this case, see figure 1(b), a second pair of 1 inch achromatic lenses (Thorlabs AC254) with focal lengths of 150 mm and 300 mm are used to collimate and focus the dispersed light leaving the output slit of the spectrometer onto the input slit of the streak camera. To suppress the influence of residual room background light during the measurements, an interference filter with a central wavelength of 400 nm and FWHM bandwidth of 40 nm (Thorlabs FBH400-40) is mounted in front of the input slit of the streak camera. To provide simultaneous spatially and temporally resolved measurements, a pair of mirrors with planes crossed at 90 • is used to rotate the image of the vertical output slit of the spectrometer in order to match it with the horizontal input slit of the streak camera. Due to the low intensity of the dispersed light, averaging of the signal over multiple discharges is required. To acquire one image, the signal is accumulated on the CCD detector for 1 s. Then, 1000 images are accumulated. At a repetition rate of 1 kHz, this corresponds to 10 6 single discharge pulses in total. The background signal is collected in the same way with the discharge being switched off.
To measure the dynamics of the emission intensity, the band heads of the corresponding transitions are projected onto the 30 µm input slit of the streak camera. To control the spectral selectivity of the streak camera measurements, a flipmirror is used to guide the focused light to the ICCD camera recording the spectra at fully opened (3 mm) and at set to the 300 µm output slit of the spectrometer for each spectral region of interest. The corresponding spectra for the FNS (0-0) and SPS (2)(3)(4)(5) transitions are shown in figure 2.
It should be noted that the width of the input slit of the streak camera is much smaller than the width of the image of the output slit of the spectrometer on which it is projected. As a result, the streak camera measures only part of the spectra shown in red in figure 2. Although, it was attempted to guide the light in a way that the streak camera detects the maximums of the red curves shown in figure 2, it is hard to state which part of these were exactly used. This would complicate a comparison of the relative intensities of the FNS (0-0) and SPS (2)(3)(4)(5) transitions, since the form of the red curves is rather steep and the possible uncertainty is significant. To avoid this problem, relative intensities of the transitions are determined from the spectroscopic measurements performed with the ICCD camera mounted on the spectrometer as a detector. In order to perform the integration over the wavelength required to obtain the total intensity of the transitions, the FNS (0-0) and SPS (2)(3)(4)(5) bands were decoupled by subtracting a fit of the SPS (2-5) band from the experimentally measured spectrum. The fitting has been performed using the SpecAir software [11] with rotational temperature, T rot , of the N 2 (C 3 Π u ) state equal to 340 K.
A parasitic discharge observed in the gap between the glass plates and the electrodes as well as rounded electrode edges, see figure 1(a), extends the detected emission region beyond the discharge gap. Consequently, in order to determine the positions of the electrodes required for spatial resolved measurements, a calibration is performed. Since white light from an ordinary lamp or an LED has too low spectral radiance to illuminate the discharge gap observed through the spectrometer at a given wavelength, a low pressure mercury lamp is installed behind the discharge cell to illuminate the polyethylene housing of the APPJ. Two mercury lines at 390.187 nm and 390.637 nm [12], recorded with a fully opened (3 mm) input slit of the spectrometer sufficiently illuminate the discharge gap in the spectral region of interest at 391-394 nm, see figure 3(a). Then, the positions of the electrode edges are determined. They are denoted by dashed horizontal lines in both figures 3(a) and (b), where the time integrated intensity profile of the FNS (0-0) is shown. One can see that at the anode the electrode position corresponds to a local peak of intensity, while at the cathode the electrode edge is located at about 30% of the maximum intensity. These relations are used as a guide for spatially resolved measurements presented in this work.

Voltage and current measurements
In figure 4 the voltage and current waveforms are given (note that the polarity of the HV pulse is negative). Two phases of the discharge can be identified: the fast breakdown is followed by a quasi-DC phase with a constant voltage (900 V) and an  almost constant current (6 A). Moreover, the electric field in the middle of the discharge gap after the breakdown was shown to be constant as well (about 80 Td) [2]. The electric current of 6 A and the electric field of 80 Td correspond to an electron density of about 2 · 10 13 cm −3 . For the complete temporal profile of the electron density calculated based on the measured electric current and electric field, please refer to [3].

Discharge imaging
A time integrated image of the discharge emission (second positive system of nitrogen) is shown in figure 5. A few regions can be distinguished in the emission intensity distribution along the discharge gap: a bright region near the cathode is followed by a dark space, then a region with an almost uniform intensity is clearly seen. The structure of the discharge shown in figure 5 is similar to the emission intensity distribution typical for a glow discharge [13]: starting from the cathode side, the narrow cathode sheath is followed by the bright negative glow, the Faraday dark space and the positive column. Light emission, corresponding to the anode glow is also observed at the positive electrode. A similar structure of a nanosecond discharge in plane-to-plane geometry was observed in hydrogen [14,15] and helium discharges [16] as well.
The spatial discharge structure remains almost unaltered at different amplitudes of the DC voltage used to feed the HV switch (referred to as the applied voltage), see figure 5(a), which agrees well with the results of [2], where it was shown that the voltage at the cathode in the quasi-DC phase and the electric field in the middle of the discharge gap are not sensitive to the applied voltage. In contrast to the applied voltage, the pressure variation influences the discharge, see figure 5(b). It is clearly seen that at lower pressures the positive column shrinks, which is typical for glow discharges [13].

Spectroscopic measurements
In order to study the spatial and temporal dynamics of the FNS and SPS emission, spectrally resolved measurements are performed. An example of the spatially resolved spectrum integrated over the discharge duration is shown in figure 6(a). One can see (please note that the intensity scale is logarithmic) that emission of the ionic band (FNS) dominates near the cathode and in the plasma bulk it is much less intensive, while the neutral N 2 (C 3 Π u ) emission (SPS) has comparable intensity both near the electrodes and in the plasma bulk, although near the electrodes the intensity is slightly higher (cathode and anode glows). In figure 6(b), a spectrum averaged over the positive column recorded during 40-45 ns and normalized to the intensity of the SPS (2-5) transition is shown. The ratio of the densities of the N 2 (C 3 Π u , v = 2) and N + 2 (B 2 Σ + u , v = 0) states in the positive column estimated from the spectrum is Einstein coefficients from [17] were used to obtain the density ratio from the ratio of the intensities. The high uncertainty in the density ratio is caused by the limited range of the wavelengths, where decoupling of the FNS (0-0) and SPS (2-5) bands is possible. Moreover, it was noticed that, in contrast to the SPS   (2-5) band, the FNS (0-0) transition cannot be approximated by a synthetic spectrum with T rot = 340 K or any other rotational temperature value. Differences in the rotational temperatures of the N 2 (C 3 Π u , v = 2) and N + 2 (B 2 Σ + u , v = 0) states might indicate the presence of a population channel of the N + 2 (B 2 Σ + u , v = 0) state in addition to the direct electron impact [18].
To provide temporally resolved measurements of the intensity distribution, the spectra are taken with a 5 ns ICCD camera gate and a time step of 2-10 ns. The signals corresponding to the FNS (0-0) and SPS (2)(3)(4)(5)   discharge (breakdown and quasi-DC) can clearly be seen. The emission of the FNS dominates near the cathode during the whole discharge, forming the negative glow. The FNS has noticeable intensity in the plasma bulk during the breakdown only. The emission of the SPS is intensive in the whole discharge gap only during the breakdown. During the quasi-DC phase, it is much weaker in the bulk. However, the Faraday dark space, the positive column and the anode glow are clearly seen immediately after the breakdown, figure 7(b).
Although the dynamics of the emission is well resolved in the quasi-DC phase, the ICCD camera gate of 5 ns is too large to track the emission behavior during the breakdown. Therefore, streak camera measurements have been performed using the setup shown in figure 1(b). The parts of the molecular bands selected by the spectrometer are shown in figure 2. It should be noted that since the corresponding transitions are spectrally very close, no correction to the transmission/sensitivity of the equipment is required. However, a drawback of this is that the contribution of the SPS (2-5) tail into the FNS (0-0) signal should be taken into account. This is estimated from spectroscopic measurements similar to the ones shown in figure 2 and is found to be 0.001 of the band head of the SPS (2-5) signal. Thus, the images corresponding to the SPS (2-5) multiplied by 0.001 are subtracted from the raw data corresponding to the FNS (0-0).
The results of the streak camera measurements are presented in figures 8-10, where the detected emission intensity is shown as a function of time and distance from the cathode. The results presented in figure 8 are in good agreement with figure 7. Higher temporal resolution allows to resolve a few waves of emission of the FNS (0-0) during the breakdown, see figure 8(a). Formation of the plasma bulk and the sheath are better resolved as well.
More details are seen in figure 9 obtained with four times higher temporal resolution compared to figure 8. Here, three waves of the FNS (0-0) emission can be clearly resolved, see figure 9(a). The first wave (short dash arrow) moves from the anode to the cathode. When it reaches the middle of the discharge gap, the second wave (dashed arrow) starts to move in the opposite direction, while the first one continues crossing the gap. Once both waves reach the corresponding electrodes, the emission intensity decreases for 2 ns and then increases uniformly in the whole gap simultaneously (dotted line). Such transient events are successfully resolved due to the short lifetime of the N + 2 (B 2 Σ + u , v = 0) state under the present conditions, 1.07 ns, while the lifetime of the N 2 (C 3 Π u , v = 2) state is significantly larger, 4.4 ns, so no waves of the emission intensity are observed in figure 9(b). The quenching rate constants and the radiative lifetimes for N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) are taken from [19,20], respectively.
The features of N + 2 (B 2 Σ + u ) emission are caused by ionization waves with high E/N propagating between the electrodes. They are clearly seen in the temporal profile of the electric field shown in figure 11 in [4].
In figure 10 the results of the measurements with about five times higher temporal resolution compared to figure 9 are presented. The waves of the FNS (0-0) emission are seen similarly to figure 9(a). The emission distribution dynamics allows to determine the velocity of the first ionization wave. The slope of the dotted line shown in figure 10(a) corresponds to a velocity of 0.35 ± 0.01 mm ns −1 . The same result is obtained from the SPS (2-5) emission dynamics, see figure 10(b).
From figure 10(a) it is also clearly seen that a region with the strongest N + 2 (B 2 Σ + u ) emission is formed at a point located about 100 µm from the cathode, when the first wave reaches it. During the second and the third waves this region moves further towards the cathode indicating sheath layer formation (see [4]). A similar pattern near the cathode is seen in figure 10(b) for the N 2 (C 3 Π u ) emission, with the only difference that the emission intensity in the plasma bulk is significant as well.
Similar dynamics of N + 2 (B 2 Σ + u ) and N 2 (C 3 Π u ) emissions have been observed during breakdown in dielectric barrier discharges (DBDs) [21][22][23][24][25]. However, naturally, a quasi-DC phase is absent in DBDs due to the charging of the dielectric layers covering the electrodes, while both the breakdown and quasi-DC phases with glow discharge structure similar to those shown in figures 7-10 have been observed in discharges with uncovered metal electrodes [14][15][16].

Comparison with the results of numerical simulations
In this section, the temporal development of the excited species densities reconstructed using the results of a PIC/MCC simulation is compared with the experimentally measured intensity dynamics. For a detailed description of the numerical modeling, please refer to the companion paper [4].
The densities of the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states are considered, see (1) and (2). The density of the upper state N * is calculated by integration of the corresponding time derivative in assumption of zero initial density: where k e is the rate constant of the excitation by direct electron impact, [N 2 ] is the nitrogen density, N e is the electron density, k q is the rate constant of collisional quenching by N 2 and τ 0 is the radiative lifetime of the excited state. As mentioned earlier, the quenching rate constants and the radiative lifetimes for N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) are taken from [19,20], respectively.
The excitation rate constants k e for the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states are calculated from the results of the numerical simulations [4] using the EEDF and the corresponding excitation cross sections Q FNS v=0 and Q SPS v=2 , respectively. For the N + 2 (B 2 Σ + u , v = 0) state, only the emission crosssection of the FNS (0-0) transition, Q FNS 0−0 , is available [26]. However, the excitation cross-section can be obtained using [26] where A 0−0 and A v=0 are the band and total transition probabilities. Based on the Einstein coefficients from [17]  the ratio A 0−0 /A v=0 = 0.71 is used for the calculations, so Q FNS v=0 = 1.408 · Q FNS 0−0 . For the N 2 (C 3 Π u , v = 2) state, the excitation cross-section is obtained from the cross-section of the excitation of the N 2 (C 3 Π u ) state, Q N2(C) exc [27,28], by where q v=2 = 0.106 [17] is the Frank-Condon factor from the ground vibrational state of nitrogen. The results of the density calculations are presented in figures 9(c), (d) and 10(c), (d). A good agreement between the reconstructed density and the experimentally measured emission dynamics is clearly seen both for the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states. The negative glow, the Faraday dark space, the positive column and the anode glow are well distinguished similarly to the experimental results. The three waves of N + 2 (B 2 Σ + u , v = 0) density are observed in the simulations as well.
Although, the 2D images presented in figures 9 and 10 allow a comparison of the simulation results with the experimental results, such a comparison is only qualitative, especially due to the logarithmic scale. For a more detailed analysis, cuts of the corresponding images are also plotted: figure 11 shows the emission intensity as a function of time at a fixed distance from the cathode (475-525 µm) and figure 12 presents the emission intensity as a function of distance from the cathode at a fixed time (40-50 ns). Please note that the temporal profile of the N + 2 (B 2 Σ + u , v = 0) density has been smoothed due to the low signal-to-noise ratio of the experimental data. Nevertheless, the main features, such as the relative peak intensities and their positions have been preserved.
The experimental results obtained in arbitrary units are scaled to the simulation results in the following way. The emission intensity of the SPS (2)(3)(4)(5) transition is scaled to fit the peak of the N 2 (C 3 Π u , v = 2) state density in figure 11(b). Thus, arbitrary units from the experiment are linked to the absolute units from the simulations for the N 2 (C 3 Π u , v = 2) state. The same scaling factor is then used in figure 12(b). To obtain  (475-525 µm). The N 2 (C 3 Πu, v = 2) density profile measured experimentally in arbitrary units shown in subplot (b) is scaled to fit the absolute density profile obtained from the simulations. The relative units for the N + 2 (B 2 Σ + u , v = 0) profile are obtained using the ratio of the densities of the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Πu, v = 2) states at 40-45 ns estimated from the spectrum shown in figure 6(b) using Einstein coefficients from [17]. Pure nitrogen, 200 mbar, 3 kV pulse. Densities of the (a) N + 2 (B 2 Σ + u , v = 0) and (b) N 2 (C 3 Πu, v = 2) states measured experimentally together with the densities reconstructed from the simulations as functions of distance from the cathode at a fixed time (40-50 ns). The units for the experimentally measured profile of the N 2 (C 3 Πu, v = 2) state density are obtained using the profiles shown in figure 11(b). The relative units for the N + 2 (B 2 Σ + u , v = 0) profile are obtained using the ratio of the densities of the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Πu, v = 2) states at 40-45 ns estimated from the spectrum shown in figure 6(b) using Einstein coefficients from [17]. Pure nitrogen, 200 mbar, 3 kV pulse.
'absolute' densities of the N + 2 (B 2 Σ + u , v = 0) state, the ratio of the N + 2 (B 2 Σ + u , v = 0) and the N 2 (C 3 Π u , v = 2) densities at 40-45 ns estimated from the spectrum shown in figure 6(b) is used. The relatively high uncertainty of the density of the N + 2 (B 2 Σ + u , v = 0) state shown in figures 11 and 12 is caused by the uncertainty in the intensity of the FNS (0-0) band, which has to be decoupled from the SPS emission, as it was mentioned in section 3.3.

Discussion
One can see from figure 11(a) and, especially from figure 12(a), that the density of the N + 2 (B 2 Σ + u , v = 0) state measured experimentally in the quasi-DC phase (please keep in mind that the density measurements are not absolute and provide only N + 2 (B 2 Σ + u , v = 0) density relative to [N 2 (C 3 Π u , v = 2)]) is much higher than the values predicted by the simulations. This indicates an additional population of the N + 2 (B 2 Σ + u , v = 0) state during the quasi-DC phase of the discharge, which agrees well with the difference in rotational temperatures of the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states mentioned in section 3.3. Since the very complex nitrogen kinetics cannot be treated in the framework of the PIC/MCC simulations, the nature of the additional population of the N + 2 (B 2 Σ + u ) state observed experimentally is not discussed in the present paper. Extensive studies of the dynamics of the relative N + 2 (B 2 Σ + u , v = 0) density in the discharge and its afterglow supported by numerical kinetics modeling of the plasma bulk in 0D approximation has allowed to identify possible mechanisms of additional N + 2 (B 2 Σ + u ) population during the quasi-DC phase observed experimentally and will be presented in a follow up paper.
The difference between the experimentally measured N + 2 (B 2 Σ + u , v = 0) density and the density reconstructed from the simulations during the breakdown phase is much smaller, see figure 11(a), since during the breakdown the direct electron impact is a dominant population channel for the N + 2 (B 2 Σ + u , v = 0) state due to high reduced electric field. The slightly lower N + 2 (B 2 Σ + u , v = 0) density obtained in the simulations is attributed to the initial conditions set in the modeling, which were selected based on the agreement of the simulation results with electrical measurements [4]. Supplementary test calculations have shown that a lower seed electron density leads to higher peak values of the N + 2 (B 2 Σ + u , v = 0) density. It should be noted that the quenching rate constant of the N + 2 (B 2 Σ + u , v = 0) state, k q , used for the reconstruction affects There is a discrepancy between the values of the quenching rates available in the literature, see tables 1 and 2 in [29], where the rates reported by different groups and obtained by different methods are presented. The difference is especially high for the N + 2 (B 2 Σ + u , v = 0) state: the most extreme values are obtained by selective laser excitation, 8.84 · 10 −10 cm 3 s −1 [30] and excitation by a pulsed discharge, (1.37 − 2.17) · 10 −10 cm 3 s −1 [31]. The quenching rate used in the present paper, 2.1 · 10 −10 cm 3 s −1 [19], is selected based on the analysis presented in [18], where the ratio of the intensities of the FNS(0-0) and SPS(0-0) transitions measured experimentally in [8] was compared with the results of numerical calculations with different sets of the quenching rates from the literature. It has been concluded that the quenching rate constant of the N + 2 (B 2 Σ + u ) state taken from [19] and the quenching rate constant of the N 2 (C 3 Π u , v = 0) state taken from [20] allow one to reproduce the experimentally measured [8] ratio of the intensities relatively well. The selected rate constant value is close to the lowest limits reported in the literature. The peak and quasi-DC values of the reconstructed N + 2 (B 2 Σ + u , v = 0) density would be about 3.5 and 4.2 times lower, respectively, if the highest value of k q available in the literature is used.
A good agreement is seen in the shapes of the temporal profiles: both the experimentally measured and the computed profiles shown in figure 11(a) consist of two main peaks representing the ionization waves seen also in figures 9 and 10. Nevertheless, two major differences between the profiles are seen. First of all, the ratio of two peaks in the experiment is about 1:1.2, while the simulation result shows a ratio of about 1:2.6. Also, it is clearly seen from figure 11(a) that the first peak observed in the experiment is delayed relative to the first peak in the simulation. As in the previous case, the difference is attributed to the initial parameters used in the modeling. In this case, the additional test simulations have shown that a lower value of the capacitor representing the stray capacitance of the electrical cables powering the discharge cell (see [4] for the details) leads to the first peak being higher in amplitude and appearing later in time, while the second peak weakly changes. As a result, the computed profile of the N + 2 (B 2 Σ + u , v = 0) density agrees better with the experiment.
It should be noted that a change of the seed electron density or the stray capacitance value affects the current and voltage waveforms obtained in the simulation. Due to the long run time of the simulations [4], simultaneous fine tuning of the electrical circuit parameters and seed electron density to achieve the best agreement in both the measured temporal profiles of the excited states during the breakdown and the electrical measurements is hardly possible.
The shape of the temporal profile of the N 2 (C 3 Π u , v = 2) state reconstructed based on the results of PIC/MCC simulations, see figure 11(b), agrees well with the experimentally measured profile during the breakdown. Again, it should be emphasized that the experimentally measured profile in arbitrary units is scaled to fit the computed one. The scaling factor is then used to compare densities in figures 11 and 12. During the quasi-DC phase, however, the computed N 2 (C 3 Π u , v = 2) density is slightly higher than the experimentally measured one, see also figure 12(b). A possible explanation is that the simulation returns E/N = 100 Td in the quasi-DC phase of the discharge, see [4], while the experimentally measured reduced electric field is about 80 Td [2]. Thus, the N 2 (C 3 Π u ) excitation in the simulation is overestimated. The reason for the different values of the reduced electric field is most likely the underestimated electron density during the quasi-DC phase, since the model does not include additional ionization in reactions between excited nitrogen states, i.e. associative ionization [32].
Both temporal profiles of the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states, shown in figure 11, clearly demonstrate that the densities of these excited species reach a steady state in the quasi-DC phase. This allows to additionally validate the diagnostic module of the PIC/MCC simulation, i.e. the calculation of the rates based on the EEDF and the subsequent calculations of the densities of the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states. A steady state density of the excited state can be calculated from equation (3) assuming dN * /dt ≈ 0: where τ is the lifetime defined as Thus, the ratio of the stationary [N + and depends only on the reduced electric field at fixed gas density (i.e. fixed lifetimes), since the electron density cancels out. In the companion paper [4] it is shown that in the plasma bulk the EEDF obtained in the PIC/MCC simulations in the quasi-DC phase can be approximated by the Multibolt Boltzmann solver [33], which uses 6 terms Boltzmann equation model. Thus, Multibolt is used here to obtain k N + 2 (B) e and k N2(C) e , so that the ratio of the excited state densities (7) is calculated independently from the PIC/MCC code using the same cross-sections. At 45 ns, the reduced electric field returned by the simulation is about 95 Td. At this reduced field value the ratio of the densities (7) calculated using the Multibolt is 3.85 · 10 −4 , while from figure 11 one gets 3.15 · 10 −4 , which is a reasonably good agreement taking into account that the full steady state has been assumed and the EEDF returned by PIC/MCC has been approximated by the Boltzmann solver. The good agreement between the ratios [N + 2 (B 2 Σ + u , v = 0)]/[N 2 (C 3 Π u , v = 2)] obtained by the two different approaches confirms the validity of the modeling and supports the conclusion that [N + 2 (B 2 Σ + u , v = 0)]/[N 2 (C 3 Π u , v = 2)] observed in the experiment during the quasi-DC phase, see figures 11(a) and 12(a), is much higher than the computed one due to the additional N + 2 (B 2 Σ + u , v = 0) population in the discharge and is not a result of an underestimation of [N + 2 (B 2 Σ + u , v = 0)] in the model. It should be noted that the ratio of the FNS (0-0) and SPS (2)(3)(4)(5) intensities obtained experimentally in [8] for wide range of E/N is not used here for comparison with the simulation results, since the measurements of [8] were performed in air meaning different EEDF at the same E/N, since in the present paper a discharge in pure nitrogen is considered.
The spatial distribution of the N + 2 (B 2 Σ + u , v = 0) and N 2 (C 3 Π u , v = 2) states obtained in the simulation are compared with the experiment in figure 12. A good agreement is demonstrated: all distinct regions of the discharge-negative glow, Faraday dark space, positive column and anode gloware clearly seen in both the simulations and the experiment and have the same dimensions and positions of their boundaries. It should be noted, however, that in the experiment some sharp details, e.g. transition between the Faraday dark space and the positive column or negative and anode glows, are slightly smeared out compared to the simulation results, most likely, due to finite focal depth of the optical system used to collect the light.

Conclusions
A ns-APPJ has been studied by spatially and temporally resolved optical emission spectroscopy. Two phases of the discharge (breakdown and quasi-DC) have been identified. It has been demonstrated that the breakdown phase consists of several ionization waves, while after the breakdown the discharge has a structure similar to low pressure glow discharges: the cathode sheath and the negative glow are followed by the Faraday dark space, the positive column and the anode glow. Emission of excited nitrogen ion, N + 2 (B 2 Σ + u ), dominates in the negative glow during the whole discharge pulse indicating highly energetic electrons coming from the sheath layer. Emission of the positive column formed by excited nitrogen molecules is significant only during the breakdown phase, when the reduced electric field is high. It is also shown that the discharge morphology weakly depends on the applied voltage, which agrees well with the results of electric field measurements [2].
A good agreement between the experimentally measured emission dynamics/structure and the density of the corresponding excited states reconstructed from PIC/MCC simulations have been demonstrated both for breakdown and for quasi-DC phase. Such an agreement serves as a validation of the PIC/MCC simulations in addition to a comparison of the numerical results with electrical measurements, see [4].

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.