High‐Speed Spectroscopy of Lightning‐Like Discharges: Evidence of Molecular Optical Emissions

High speed spectra (between ∼380 nm and ∼800 nm) of meter‐long lightning‐like discharges recorded at 672,000 fps and 1,400,000 fps (with 1.488 and 0.714 μs time resolutions and 160 ns exposure time) show optical emissions of neutral hydrogen, singly ionized nitrogen, oxygen, and doubly ionized nitrogen which are similar to those found in natural lightning optical emissions. The spectra recorded in the near ultraviolet‐blue range (380–450 nm) and visible‐near infrared (475–793 nm) exhibited features of optical emissions corresponding to several molecular species (and emission bands) like cyanide radical (CN) (Violet bands), N2 (Second Positive System), N2+ (first negative system), C2 (Swan band) and CO (Quintet and Ångström bands). Molecular species can be formed at regions of the lightning‐like channel where the gas temperature would be milder and/or in the corona sheath surrounding the heated channel. We have quantified and compared electron densities and temperatures derived from different sets of neutral and ion line emissions and have found different sensitivities depending on the lines used. Temperatures derived from ion emissions are higher and change faster than those derived from neutral emissions.

derived from other neutral (H α at 656.30 nm) and ion (N II at 648 and 661 nm) lines. A discussion on these results follows in the study.

Instrumentation and Experimental Setup
The results presented here have been obtained with an ultrafast and high spectral resolution (between 0.29 and 0.75 nm) spectrograph named GALIUS. GALIUS is a portable, ground-based spectrograph able to record spectra of natural/triggered or lightning-like discharges with submicrosecond time resolution. GALIUS can be set up with a total of 22 configurations made of combinations of 10 collector lenses (focus lengths ranging from 25 to 200 mm), two different collimator lenses in the UV and visible-NIR range (105 mm with F#4.5 and 50 mm with F#1.2) and four interchangeable volume-phase holographic (VPH) grisms for spectral ranges from the near ultraviolet (380 nm) to the near infrared (805 nm) and high-spectral resolution (0.29-0.75 nm depending on the grating used). More details about GALIUS and its configurations can be found elsewhere (Kieu et al., 2020;Passas et al., 2019).
For all spectra presented here, GALIUS was set up in slit mode (50 μm × 3 mm), using the high-speed FASTCAM SAZ camera, 12-bit ADC pixel depth constructed on a very high sensitivity (monochrome ISO 50000) CMOS sensor with sensor size of 1,024 × 1,024 20 μm square pixels. In the near-ultraviolet blue range, the camera was set up with two collimator lenses (105 and 50 mm) and collector lens 50 mm (F#1.5) controlled by the grism R1 with central wavelength in 357 nm, spectral resolution 0.29 nm and 2086 lines/ mm. The recording speed in this configuration was 672,000 fps (160 ns exposure time) and the spectra was recorded in the range 380-450 nm. In the visible-near infrared range, GALIUS used two similar collimator lenses (50 mm, F#1.2) and a collector lens (50 mm, F#1.67 for long sparks). Spectra in this region were recorded at 672,000 fps (160 ns exposure time) using the grism R2 with central wavelength in 656.30 nm, spectral resolution 0.75 nm and 1,015 lines/mm. This was the widest spectral range recorded. The recorded images showed spectral emissions from 475 nm upto 793 nm. Finally, the camera was set up to allow submicrosecond time resolution in the near-infrared spectral range. These spectral images were obtained at 1,400,000 fps (0.714 μs time resolution and 160 ns exposure time) within the 770-805 nm spectral range. We used grism R4 with central wavelength in 778 nm, spectral resolution of 0.34 nm and 1,727 lines/mm. The collimator and collector lenses were the same as with the set up used with grism R2.
In 2019, we moved GALIUS to the facilities of the company DENA Desarrollos in Terrassa (Spain) to work with ∼1-m-long lightning-like discharges produced by a 2.0 MV Marx generator. This generator can produce sparks up to 900 kV in Switching Impulse (SI) and Lightning Impulse (LI) modes. The experimental setup used here can be found elsewhere (Kieu et al., 2020). In the SI mode, the voltage slowly rises up to its maximum peak in 100 μs and then it decays in ∼0.5 μs. In the LI mode, the voltage rapidly reaches its peak in 0.5 μs, keeping a plateau of 2-3 μs and then decaying in 0.5 μs. Opposite to voltage, the current in the SI mode reaches its peak and immediately decays, while the current in the LI mode rises up fast (0.3-0.5 μs) but decays slowly in about 100 μs. The LI mode is most similar to triggered and natural lightning where the current rise time is relatively fast (several μs) and the current decays in tens to hundreds of μs (Walker & Christian, 2019). Natural lightning can exhibit peak currents much higher (15-150 kA) than the ones usually available in experimental facilities. In spite of this, we have obtained similar temperatures (and only slightly lower electron densities) than obtained in natural (Orville, 1968b) and triggered lightning (Walker & Christian, 2019).
In the following sections, we will show and discuss spectra of lightning-like discharges in the SI and LI modes produced with the same voltage (800 kV) and that generates ∼1-m-long discharges ∼8.5 m away from GALIUS.

GALIUS Spectra in the Near Ultraviolet-Blue (380-450 nm)
Time-resolved spectra in the near-ultraviolet were recorded by grism R1 at 672,000 fps (1.488 μs time resolution) from 380 to 450 nm, as shown in Figure 1 for discharges generated in the LI mode. A zoom in of the spectral region between 400 and 425 nm is shown in Figure 1 (b). No spectra could be recorded in the SI mode in this spectral region due to the faint luminosity and short life time of the discharge. To identify emitting species, we have labeled these spectra with their corresponding wavelengths and ionization states, for example, neutral nitrogen (N I), singly ionized nitrogen (N II), and doubly ionized nitrogen (N III). Figure 1 shows the presence of singly ionized atomic nitrogen and oxygen, doubly ionized atomic nitrogen together and molecular optical emissions that were labeled in green, purple, blue and black color, respectively. The doubly ionized nitrogen lines at 409.7 nm, 410.3 nm were first reported by Walker and Christian (2017) but the 419.6 and 420.0 nm reported here were not seen before in this region. They only appear in the first frame (at 1.28 μs) of the near-ultraviolet spectra. Many optical emissions in this near ultraviolet blue region are due to molecular species. Optical emissions of the CN violet band system (B 2 Σ + , v′ → X 2 Σ + , v′′) contributed with the presence of the line 388.3 nm (v′ = 0 -v′′ = 0). The N 2 second positive system (SPS) shows two transitions at 394.3 nm (v′ = 2 -v′′ = 5) and 405.8 nm (v′ = 0 -v′′ = 3) (Gordillo-Vázquez et al., 2012;Luque & Gordillo-Vázquez, 2011). The N 2 + FNS can be identified by humps at 388.4 nm (v′ = 1 -v′′ = 1), 391.4 nm (v′ = 0 -v′′ = 0) and 427.81 nm (v′ = 0 -v′′ = 1). Some of these lines were earlier reported in lightning spectra (Salanave et al., 1962;Wallace, 1960). After these early molecular detections, there were no modern reports on molecular emissions in lightning spectra.
KIEU ET AL.
10.1029/2021JD035016 4 of 18 Figure 1. Time resolved R1 (380-450 nm) spectra of a meter long lightning-like discharge produced with the Lightning Impulse (LI) mode of a Marx generator with 800 kV. Panel (a) shows the entire spectral range. Panel (b) displays a zoom of the 400-425 spectral gap. The spectrum was recorded at 672,000 fps (160 ns exposure time) with spectral and time resolutions of 0.29 nm and 1.488 μs, respectively. Spectral lines of singly ionized atomic nitrogen and oxygen, doubly ionized atomic nitrogen and several molecular species (N 2 ,  2 N , C 2 , CN, and CO) are visible and marked with green, purple, blue and black labels, respectively.
The presence of ground state and electronically excited CO in lightning-like discharges could be explained by the action of thermal dissociation of CO 2 (CO 2 → CO (X 1 Σ g , v ≥ 0) + O( 3 P)), electron-impact dissociation of CO 2 (CO 2 + e → CO (X 1 Σ g , v ≥ 0) + O( 3 P) + e), N + CO 2 → NO + CO (X 1 Σ g , v ≥ 0) and electron-impact excitation of ground state CO (CO(X 1 Σ g , v ≥ 0) + e → CO(B 1 Σ, a′′ 5 Π, a′′ 5 Π, v ≥ 0) + e) taking place in the shocked air surrounding the lightning-like channel, which is cooled rapidly by hydrodynamic expansion (Levine et al., 1979;Ripoll et al., 2014). This mechanism would prevent CO from further dissociation and could support the detection of CO (Levine et al., 1979). If, on the contrary, CO was produced in the slower-cooling inner core of the lightning channel, no CO would be produced (it would have been lost by thermal dissociation) and no CO would be detected (Levine et al., 1979). Once ground-state CO(X 1 Σ g ) is produced, excited electronic states producing Ångström and Quintet states can be produced by thermal and/or electron-impact excitation.
It is interesting to note that although traces of CO are detected in the present spectroscopic analysis of lightning-like discharges as well as with chemical detectors in previous studies (Levine et al., 1979), global atmospheric chemistry circulation models predict that CO is slightly depleted by the action of lightning Murray, 2016). A possible explanation for this could be that once CO is produced in the lightning channel, it is depleted by reactions involving lightning produced OH and ground state oxygen atoms O( 3 P) like CO + OH → CO 2 + H, CO + OH + O( 3 P) → CO 2 + OH and CO + OH + O 2 → CO 2 + HO 2 .
The detection of C 2 and, in particular, the formation of C 2 (d 3 Π g , v) underlying the Swan band optical emissions can be explained in terms of the presence of CO(X 1 Σ g , v) in the lightning-like channel. At relatively high temperatures (4000-6000 K) typical of air in the edge of the expanding channel of a lightning-like discharge, ground state C( 3 P) atoms can be efficiently produced through the reaction CO(X 1 Σ g , v 1 ) + CO(X-1 Σ g , v 2 ) → CO 2 + C( 3 P) (Carbone et al., 2020). Once C( 3 P) is formed, Little and Browne (1987) proposed a possible three step mechanism for the formation of C 2 (d 3 Π g , v) producing the Swan band through: (a) C( 3 P) + C( 3 P) + M → C 2 ( 5 Π g , v) + M, (b) C 2 ( 5 Π g , v) + M → C 2 ( 5 Π g , v = 0) + M and (c) C 2 ( 5 Π g , v = 0) + M → C 2 (d 3 Π g , v = 6) + M, where 5 Π g is a metastable (quintet) state for which a crossing exists between the v = 6 level of the d 3 Π g and the v = 0 of the 5 Π g state (Carbone et al., 2020).
The presence of CN and its violet band (due to the radiative deexcitation of CN(B 2 Σ + )) in the R1 spectra can be explained by competing mechanisms for the formation of C 2 and CN that promote and go in favor KIEU ET AL.

Table 1 Molecular Species and Vibro-Electronic Optical Transitions Detected in the Present Study
of the formation of CN in aN 2 rich environment like air. According to Dong et al. (2014), once atomic carbon and molecular C 2 are available, CN radicals can be formed by C( 3 P) + N 2 → CN(X 2 Σ + ) + N, C( 3 P) + N → CN(X 2 Σ + ) and C 2 + N 2 → 2 CN(X 2 Σ + ), C 2 + 2 N → 2 CN(X 2 Σ + ). The excitation energy of CN(B 2 Σ + ) is about 3 eV so that it can be easily produced by thermal and/or electron-impact excitation of ground state CN(X 2 Σ + ) in the lightning-like channel. Alternative kinetic mechanisms for the formation of CN(X 2 Σ + ) and CN(B 2 Σ + ) would require the presence of the metastable N 2 ( (Crispim et al., 2021). These reaction paths should also be possible in mild temperature regions of the lightning-like channel so that ground state N 2 can be excited by electron collisions before dissociation occurs. Figure 2 shows the fit of synthetic spectra of heated humid (80% relative humidity [RH]) air to the measured R1 spectra (normalized with respect to the 399.5 nm N II ion line) corresponding to the early times (from 1.28 μs to ∼10.20 μs) of a meter-long LI discharge. As time increases, the measured gas temperatures decreases. The synthetic spectra are based on equilibrium calculations of thermal air plasmas (see supplementary material of Kieu et al., 2020). Calculated spectra include all possible lines of atoms, singly and doubly ionized ions that can appear in the R1, R2, and R4 spectral ranges explored in this study and considered in Kramida et al. (2020). The only molecular species considered is N 2 and, in particular, the Lyman-Birge-Hopfield (LBH) band, First Positive System (FPS), and Second Positive System (SPS). Stark broadening of nonhydrogenic (Bekefi, 1976) and hydrogenic lines (Griem, 1964) are included and convolved with instrumental broadening (0.29 nm for R1 and 0.75 nm for R2) using the measured electron densities and gas temperatures. Since no electron densities could be measured in the near ultraviolet-blue spectral range using grism R1, we used the electron concentrations measured with grism R3 (see panel [b] in Figure 6) in our previous paper since the spectral resolutions of R1 and R3 are similar (Kieu et al., 2020). From the measured R1 gas temperatures (see panel [d] in Figure 6), the corresponding equilibrium concentrations and partition functions of chemical species (atoms, ions and molecules) were calculated to generate the synthetic spectra.
The agreement between synthetic and measured R1 spectra is fine except for some N II ion lines (383.8, 403.5, 404.1, 404.3, 417.6, 422.8 nm, 423.7, and 424.2 nm), which predicted intensities are below the measured values and a few transitions of CO and of the  2 N FNS not included in the synthetic spectra calculation. Since the measured R1 spectra mostly include ionic emissions, their intensity rapidly decreases as the gas temperature evolves toward lower values. For instance, the strong N II ion lines at 399.5 and 444.7 nm fade away as time evolves.
The use of simulated spectra is justified because they contribute to detect the limits of our knowledge (accuracy of available spectroscopic constants and calculated Stark broadening mechanisms) and model approximations (equilibrium assumptions).

GALIUS Spectra in the Visible-Near Infrared (475-793 nm)
Time-resolved spectra in the visible-near infrared range from 475 to 793 nm were recorded with grism R2 at 672,000 fps as shown in Figures 3a and 3b, 3c for ∼1 m-long, 800 kV discharges in SI and LI modes, respectively. We can see in the first frame (at t = 0.930 μs [SI mode] and t = 1.250 μs [LI mode], see panel [b]) of both figures the sharp rising of the singly ionized nitrogen (N II) at 500 nm. Then, in the second frame (at t = 2.418 μs (SI mode) and t = 2.738 μs [LI mode], see panel [b]), the 500 nm ion line reaches its maximum intensity. Similarly, Figure 3 also shows the evolution dynamics of the 777 nm neutral oxygen line with its rising from the first frame to its maximum at later times of around ∼2.418 μs and ∼8-10 μs for the SI and LI modes, respectively. The maximum intensity of the 500 nm N II line is much larger than the peak of the 777 nm O I line in these early times. However, the neutral 777 nm O I line lasts much longer (see panel [c]) than the singly ionized 500 nm N II line. The explanation for this is that ion emissions appear in the early time and remain excited only for a short time (a few microseconds) while the neutral emissions appear later but last much longer since they are easier to excite.
The second interesting feature in the R2 spectra of Figure 3 is the presence of a line at ∼517 nm. This line was first identified by Orville (1968a) in an attempt to prove the existence of singly ionized oxygen lines in lightning spectra. However, when Orville (1968a) used it to calculate temperatures, the result yielded too high values in the range 40,000-70,000 K which considerably exceeded the temperature values 20,000-30,000 K previously derived by the same authors (Orville, 1968b). The singly ionized oxygen line at 517.5 nm seems to be a weak one (Kramida et al., 2020). This means that the line in this position of the R2 spectra may result from the overlapping of that oxygen ion line and another emission lines from other species. In particular, the C 2 emission at 516.5 nm corresponds to the band head (0-0) which is the KIEU ET AL.   strongest transition in the C 2 Swan band system (see Section 3.1). Therefore, it could be very possible that the recorded emission at ∼517 nm corresponds to the overlapping of the C 2 (0-0) 516.5 Swan band and the singly ionized oxygen at 517.5 nm that could not be well resolved because of the limited spectral resolution (0.75 nm) of the R2 spectra.
Finally, other interesting line emissions present in the R2 spectra are those of several doubly ionized nitrogen at 485.8, 486.7, 532.0, and 532.7 nm in early times (from 0.93 μs to ∼2 μs). These ion lines were recently identified in triggered lightning return stroke spectra recorded at 672,000 fps (Walker & Christian, 2017). However, in their identification the doubly ionized nitrogen lines were only present in the first frame of their spectra. Figure 4 shows the fit of synthetic spectra of heated humid (80% RH) air to the measured R2 spectra (normalized with respect to the 500 nm N II ion line) corresponding to the early times (from 1.250 μs to ∼10.178 μs) of a meter-long LI discharge. In a time gap of ∼9 μs the measured gas temperatures decrease from ∼34,000 K to ∼17,000 K as derived from the ratio of the 648 and 661 nm N II ion lines (see Figure 6e). The R2 synthetic spectra were calculated using as inputs the measured R2 electron densities (obtained from the H α line) and gas temperatures (see Figure 6). From the measured gas temperatures, the corresponding equilibrium concentrations and partition functions of chemical species (atoms, ions and molecules) were calculated to generate the corresponding R2 synthetic spectra.
There is a reasonable agreement between synthetic and measured R2 spectra except for the 656.30 nm H α line and the 567.9 nm line of the N II ion, which predicted intensities are below the measured values. The 777 nm line of O I is not well matched at 2.738 μs. On the other hand, the C 2 Swan band peak at 516.5 nm was not included in the synthetic spectra calculation and so there is no synthetic line able to match that peak.

GALIUS Spectra in the Near-Infrared (770-805 nm)
In the near-infrared spectral region we focus the study on the dynamics of two neutral oxygen triplet lines at 777 and 795 nm. Their spectra were recorded at 1,400,000 fps with submicrosecond time resolution (0.714 μs and 160 ns exposure time) as shown in Figure 5. The spectra recorded in this spectral range did not exhibit any molecular emissions. Figures 5a, 5b and 5c, 5d show the optical emissions from ∼1-m-long spark produced with 800 kV in the SI and LI modes, respectively. The neutral O I line at 777 nm is in reality a triplet with sublines at 777.19, 777.42, and 777.54 nm. The O I line at 795 nm is also the combination of three lines at 794.75, 795.08, and 795.21 nm. These two triplet O I lines are among the longest lasting emission lines in lightning spectra, around 25 μs in the SI mode and about 100 μs following the duration of the input current of the LI mode. Neutral emissions usually appear a bit later but last longer than ion lines (Kieu et al., 2020;Walker & Christian, 2019). In spite of this, the emergence of the 777 nm line can be seen in a time as early as 0.25 μs in the SI mode (see Figure 5b) and ∼0.55 μs in the LI mode (see Figure 5d). The emergence of the 795 nm line is weaker than the 777 nm one because, though they have very similar Einstein coefficients, the excitation energy of the 795 nm triplet is higher (∼14.04 eV) than that of the 777 nm triplet (∼10.73 eV). It is interesting to note that, as it is seen from high speed photometric recordings from space, lightning 777 nm optical radiation inside thunderclouds has a duration of several milliseconds due to scattering by water and/ or ice particles before it is finally absorbed Soler et al., 2020). Lightning near-infrared optical emissions inside thunderclouds are more absorbed than near-ultraviolet and blue radiation .
The nonscattered (by clouds) lightning 777 nm optical emission (mainly connected to the heated channel luminosity) is of interest for diagnostic purposes since its temporal dynamics closely follows that of lightning currents (Cummer et al., 2006;Fisher et al., 1993;Kolmašová et al., 2021;Walker & Christian, 2019). It is also tightly correlated to the distant quasi-static (≤0.1-400 Hz) magnetic field signature attributed to lightning continuum currents that have been associated to delayed sprites (Cummer & Füllekrug, 2001;Cummer et al., 2006). Recent results by Kolmašová et al. (2021) have demonstrated that, in addition to high-peak current of causative lightning strokes, the velocity of the current wave and the conductivity of the heated channel of the return stroke are important factors that control the intensity of elves. Cho and Rycroft (1998) had previously shown that the amplitude and the rise time of lightning affect the intensity of elves. The amplitude relates to the lightning channel conductivity and the rise time influences the current wave velocity of the lightning return stroke pulse.
The electrical conductivity of the (heated) lightning channel can be affected by the ambient relative humidity which depends on season, environment, that is, coastal, maritime or inland, and regional climate. For instance, in high-altitude plateaus, the conductivity can be up to 20%-40% lower (Guo et al., 2009). We have explored the temporal dynamics of the electrical conductivity in a spot of the heated, highly ionized lightning-like channel.

Electron Density
Stark broadening is often used to estimate the electron density in lightning discharges (Orville, 1968b  independent of assumptions on the equilibrium state of the plasma. Consequently, electron densities are usually derived from the full width at half maximum (FWHM) of a line profile. However, it is well known that ion dynamics affects both the line widths and their shapes. This effect is especially important for the H α and H γ lines, but it is nearly negligible for the line H β (Gigosos et al., 2003). Therefore, Gigosos et al. (2003) suggested an alternative method to calculate the electron density from the Stark broadening of the H α line using the full width at half area (FWHA) of the H α with the equation: Electron densities obtained from the FWHA of the Stark broadened H α line in the visible-near infrared spectra (using grism R2) recorded at 672,000 fps are shown in Figures 6a and 6b (see red line) for ∼1-m-long sparks in the SI and LI modes, respectively. For comparison, electron densities derived from short spectral range (using grism R3) recorded at 2,100,000 fps are also shown in Figures 6a and 6b (see yellowish dots and line). Even though our electron densities are obtained from lightning-like discharges, the results are similar to those derived by Orville (1968b) in real lightning.
For comparison with the FWHA method, the FWHM of a Stark broadened line can also be used to estimate the concentration of electrons. Griem (1964) provided a convenient equation (see below) to derive electron densities from the Stark FWHM broadening of spectral lines corresponding to neutral or singly ionized atoms: We have included for comparison electron densities and temperatures reported in a previous paper (see yellowish line) using grism R3 (645-665 nm) recorded at 2.1 Mfps for the same discharge and setup (Kieu et al., 2020). Note that the inset marked with (e) in panel (d)  ( 2) where ω(T) is a tabulated function (in units of Å) that depends on the temperature and on the line transition wavelength considered. Equation 2 is only valid for electron densities in the range 10 16 -10 18 cm −3 and it provides values of the electron density with an error within 20%-30%. Griem's calculation for ω(T) only considered the broadening of the 777.19 nm, the strongest subline in the 777 triplet. For this subline ω(T) varies between 1.99 × 10 −2 Å at 2,500 K and 5.56 × 10 −2 Å at 40,000 K Griem (1964). To make the calculation more precise, we interpolated the tabulated function ω(T) and measured the Δλ Stark of the 777.19 nm subline extracted from the full Stark broadening of the triplet. To find out the FWHM of each subline belonging to the triplet 777 nm, we built a triplet Lorentzian function (L 3 ) to fit the experimental data. Since the O I 777 nm triplet is the combination of sublines 777.19, 777.41, and 777.53 nm with relative intensities 870, 810, and 750 Kramida et al. (2020), the Lorentzian function (with six fitting parameters) for the 777 nm triplet line can be written as:  The electron densities obtained from the Stark broadening of the 777.19 nm subline of the O I 777 nm triplet for spectra recorded with grisms R4 and R2 are shown in Figures 6a and 6b (see green and pink lines for R4 and R2, respectively) for the SI and LI modes of a ∼1-m-long spark produced with a peak voltage of 800 kV. We see that the maximum electron density derived from the 777.19 nm always stays above the one obtained from the H α spectral line (656.30 nm) and it seems to flatten at later times (∼4 μs and ∼10 μs for the SI and KIEU ET AL.

10.1029/2021JD035016
13 of 18 LI modes, respectively). This might be due to the fact that the FWHM method is less sensitive when the broadening of the line is not sufficiently large. We conclude that the analysis of the FWHM could be used as a first rough estimate of the electron density. The FWHA under the Stark broadened H α line seems to be more sensitive (than the FWHM) to the time dynamics of the electron concentration within the heated channel.

Temperature
The most common method to determine the temperature of a hot plasma channel is to measure the relative intensities of different spectral lines of the same species. To calculate the gas temperature from the time resolved spectra of lightning-like discharges recorded in this work, we will assume the criteria previously established by Prueitt (1963) and Uman (1969), and also recently used by Walker and Christian (2019) for deriving the gas temperature in triggered lightning. In particular, we consider that (a) the channel of the lightning-like discharge is optically thin (there is no light absorption through the line of sight), (b) the temperature is relatively uniform along the lightning-like channel radial cross section (temperatures are similar at the edge and the center of the lightning channel), and (c) that thermal equilibrium controls the concentration of the different atoms and ion energy levels emitting light due to spontaneous radiative deexcitation, that is, the density of excited atoms and ions follow Boltzmann's law. We also assume that local thermal equilibrium (LTE) applies so that the derived electron temperature equals the gas temperature.
Therefore, the gas temperature is calculated from the intensity ratio of different pairs of lines depending on the grism used and assuming that the corresponding emitting energy levels are populated following Boltzmann's equilibrium law. In particular, for the near-ultraviolet blue spectra recorded with grism R1, we used two singly ionized nitrogen lines at 399.5 and 444.7 nm. For visible-near infrared spectra recorded with grism R2 we used the pair of lines at 648 and 661 nm associated with singly ionized nitrogen, and the pair of O I neutral lines 715 and 777 nm. Details of these calculations can be found in Kieu et al. (2020). Finally, for spectra recorded with grism R4 in the near-infrared the temperature was calculated from the ratio of the line intensities of the triplets 777 and 795 nm.
The estimation of the error in the electron temperature is evaluated with equation (11) in Walker and Christian (2019) that depends on the uncertainties in the intensity ratio and assuming a 10% uncertainty in the tabulated Einstein coefficients (Kramida et al., 2020). The uncertainty in the intensity ratio is calculated using the bootstrap method also adopted to quantify the error in the electron density. Figures 6c and 6d show the temperatures for, respectively, the meter-long SI ( Figure 6c) and LI (Figure 6d) discharges. The use of the pair of ionic lines 648 and 661 nm provide consistent temperature values with each other when used with spectra obtained with grisms R2 and R3, recorded at 672 kfps and 2.1 Mfps, respectively. The pair of N II ion lines 399.5 and 444.7 nm in the spectra recorded at 672 kfps with grism R1 (only for LI discharges) also provide consistent temperature values with those derived with grisms R2 and R3. The temperatures measured with ion lines can only be tracked for relatively short times between 2 and4 μs (SI mode) and up to ∼10 μs (LI mode). However, when neutral lines (O I 777 and 795 nm, or O I 777 and 715 nm) are employed the obtained temperatures are slightly lower (maximum of ∼28,000 K) than the ones obtained when with ion lines (maximum of ∼33,000 K) but can be tracked for longer times (than with ion lines) between ∼11 μs (SI mode) and ∼50-60 μs (LI mode) since neutral lines last longer. These results resemble those derived from 5-m-long lightning-like discharges in air produced with 6.4 MV by Orville et al. (1967), where it was mentioned that the ion radiation is mostly emitted from the hotter region of the channel while the neutral radiation is emitted from the cooler regions. Finally, it should be noticed that, since the 715 nm line of O I is weaker than the 795 nm line of O I, the derived temperature can be followed for shorter times when evaluated from R2 spectra (compared to R4 spectra that include the O I line at 795 nm).

Time Dynamics of the Electrical Conductivity
Once the electron concentration and gas temperature are known, we can estimate the variation in time of the electrical conductivity in the heated (and highly ionized) lightning-like channel. We assume isotropic collisions so that the momentum transfer cross section σ tr = σ c , with σ c being the cross section for electron-neutral collisions. Since the heated channel is highly ionized (N e /N ≥ 10 −3 ), it is reasonable to assume that the ion (N i ) and electron (N e ) densities are similar (N i = N e ) and, consequently, the effective collision frequency for momentum transfer ν m = Nvσ tr + N e vσ Coulomb ≃ N e vσ Coulomb , where N is the gas density, v is the mean thermal velocity of electrons, and σ Coulumb is the cross section of electron-ion collisions dominated by Coulomb forces. For instance, for electron (and gas) temperatures (T e = T) ∼1 eV (11,600 K) and N e = 10 13 cm −3 , σ Coulomb ≃ 2 × 10 −13 cm 2 , while σ tr ≃ 10 −16 -10 −15 cm 2 (Raizer, 1991). Thus, we can consider that the electrical conductivity σ in the heated lightning-like channel is controlled by σ Coulomb as σ = e 2 N e /mν m = (with e and m being the electron charge and mass, respectively) = 1.9 × 10 4 × T e (eV) 1.5 (lnΛ) −1 S m −1 with lnΛ = 13.57 + 1.5 log(T e (eV)) − 0.5 log(N e (cm −3 )) (Raizer, 1991). According to Figure 8, the electrical conductivity decreases from 1.35 × 10 4 S m −1 to 6 × 10 3 S m −1 (approximately a factor of two) in ∼ 50 μs mostly following the decay time scale of the temperature (see Figure 6d) from ∼ 27,000 K to ∼ 15,000 K. This indicates that high current flows are only favored in the very early times of a cloud-to-ground lightning stroke. The conductivity values obtained in this study are slightly smaller than those previously reported (∼1.6-2.2 × 10 4 S m −1 ) using non-time resolved lightning spectra of cloud-to-ground strokes (Guo et al., 2009). Interestingly, our conductivity values are higher and close to those recently reported in stepped leader tips (∼4.3 × 10 3 Sm −1 ) and dart stepped leaders (∼1.1 × 10 4 S m −1 ), respectively, where, by using 20 μs slit-less spectroscopy, the measured electron densities and gas temperatures were ∼10 15 cm −3 (stepped KIEU ET AL.

Conclusions
In this study, we reported on high-speed time-resolved spectroscopic analysis of lightning-like discharges recorded by a fast and very sensitive spectrograph named GALIUS. The spectra were recorded in three separate spectral regions: near-ultraviolet blue (380-450 nm), visible near-infrared (475-793 nm), and near-infrared (770-805 nm). GALIUS spectra in the near-ultraviolet blue range, recorded at 672,000 fps (time resolution 1.488 μs), exhibited early time optical emissions associated to singly ionized nitrogen, oxygen, doubly ionized nitrogen, and several molecular species. In addition to the spectral features of the CN violet transition, N 2 second positive system and N 2 + FNS reported in some previous studies, we found spectroscopic signatures of optical emissions due to the Swan band (516.5 nm) of C 2 and of several electronically excited states of CO. These molecular species could exist in the mild temperature regions of lightning-like plasma channels and/or could be produced due to the chemical activity of streamers surrounding a heated lightning channel. Spectra in the visible-near infrared range (475-793 nm) exhibited the strongest optical emission from singly ionized nitrogen 500 N II lasting from the onset of the discharge to about 10 μs.
Molecular species such as CN and N 2 were found in high-temperature (6,000-7,000 K) combustion environments accompanied with nitrogen oxide (NO) optical emissions in the 140-340 nm spectral range (Hornkohl et al., 2014). While the 140-340 nm spectral gap is presently outside the detection range of GALIUS, our detection of molecular emissions in lightning-like channels opens the door to detect and quantify NO production by lightning using high sensitivity spectroscopic techniques. We speculate that the sensitivity of the sensor can play a key role in determining the presence of molecular species in lightning spectra.
The spectra recorded in the near infrared at 1,400,000 fps (time resolution 0.714 μs) showed the dynamics of two distinct O I triplets at 777 and 795 nm. Optical emissions from the 777 nm triplet, which are the strongest ones, begin almost at the onset of the discharge at about 0.25-0.55 μs and last up to ∼100 μs following the input current. These O I triplets and the O I 715 nm line were used to calculate the gas temperature inside the lightning-like channel. The gas temperature was also evaluated from the ratio of two pairs of N II ion lines (648 and 661 nm, and 399.5 and 444.7 nm) and compared with the temperature derived from pairs of neutral O I lines. The temporal dynamic of the gas temperatures is conditioned by the lifetime of ion and neutrals lines. Thus, while the final temperatures are roughly the same (∼15,000 K) for the LI mode, ionic lines can provide more reliable temperatures in the early times (≤2 μs) but neutrals can be followed longer and can better account for the thermal relaxation of the lightning-like channel.
We have completed our measurements with simulated spectra. The comparison between measured and synthetic spectra reveal some disagreements that could be due to inaccuracies of available spectroscopic constants, calculated Stark broadening mechanisms and/or underlying model approximations (equilibrium assumptions).
Finally, the concentration of electrons within the heated channel was determined by the analysis of the Stark broadening of spectral lines. We compared the electron densities resulting from the FWHA under the H α line, and from the FWHM of the neutral 777.19 nm O I line. For the H α broadening, electron densities were in a good agreement with those obtained in real lightning (Orville, 1968b) but the estimations from the FWHM of the 777.19 nm overestimated electron number concentrations and can be considered as a rough estimation.

Data Availability Statement
The spectroscopic data (processed data and source python scripts used for figure generation) presented in this article are available through figshare (https://cutt.ly/zcRpNzK).