Optical characterization of nanosecond-pulsed discharge in liquid nitrogen

We report the optical characterization of nanosecond-pulsed plasma ignited directly in liquid nitrogen. Using imaging and optical emission spectroscopy, we estimate neutral temperatures and densities, as well as local electric field values, and the obtained results indicate that the discharge develops via streamer (‘electronic’) mechanism. We show that millimeter-scale plasma propagates in liquid nitrogen at velocities of ∼500 km s−1 with the corresponding required local electric fields as high as 25 MV cm−1, while the estimated local electric fields in the ‘core’ of the discharge are around 6–8 MV cm−1 (corresponding to reduced electric field values of 600–1000 Td). The neutral and electron densities in the ‘main body’ of the discharge were estimated using broadened argon lines, indicating that the neutral densities in the near-electrode region are around 1020 cm−3 (tens of atmospheres), while the maximum recorded temperature is just a few tens of degrees above the surrounding liquid. Electron densities were estimated to be ∼1017 cm−3, about two orders of magnitude lower than those measured for water discharge.


Introduction
Nanosecond-pulsed plasmas in liquids have gained attention in the last decade and as it became clear that by applying very fast rising high voltage pulses to a needle electrode it is possible to produce macroscopic discharge without apparent generation of even microscopic gaseous voids, several exciting opportunities for applications of this type of plasmas became a reality [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].It is important to note that here we focus on short (about 5-20 ns and less) relatively low-energy 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.discharges (on the order of few tens and up to about a 100 mJ) initiated by high voltage pulses with fast rise times (1-2 ns or shorter), which appear to be significantly different from the high-power pulsed plasmas in liquid (long durations and/or high energy on the order of few J or more); the latter are fundamentally related to temperature effects or electrolysis [16].We also exclude nanosecond-pulsed discharges in liquids that are generated at the tips of negatively powered needle electrodes; in this case, their ignition is believed to be related to electron emission processes [17][18][19].It is expected that low-energy positively powered nanosecond-pulsed plasmas would combine the effects of the overall low temperature of liquid phase, the high densities of charged, excited and neutral species, and high local electric fields and radiation (from high-energy x-ray to infrared).One example of the possible applications of cold nanosecond-pulsed plasmas in liquid phase is the synthesis of exotic materials.In our recent studies, we demonstrated the possibility of producing highly energetic, but unstable polynitrogen-a material that was previously observed at extreme conditions of hundreds of GPa and could not be recovered to conditions close to normal [20].Although several theoretical and experimental studies have been conducted to reveal the nature of these types of plasmas, the physical mechanisms of cold nanosecond-pulsed plasma generation in liquids still remain elusive.Fundamentally, it is important to understand if the discharge propagates directly into the liquid via a streamer ('electronic') mechanism, as proposed in [1], or if it is a number of successive streamer discharges that are generated in liquid saturated with so-called nanopores (i.e.'cold leader' mechanisms proposed in [2]).Plasma temperatures and densities are also largely unknown.Therefore, the central problems that we attempted to address in this manuscript are related to the experimental determination (or at least estimation) of the neutral's temperatures and densities, and the maximum local electric field.While most of the work has focused on the production of discharges in water or liquid hydrocarbons, as relatively stable and well-known media, the limited amount of useful spectroscopic information that can be collected when the plasma is ignited in these complex liquids left these questions open for discussion.In our recent preliminary experiments where the discharge was ignited in liquid nitrogen, we were able to register molecular nitrogen emission during the ignition and propagation of the discharge, opening up an opportunity for optical diagnostics of the nanosecond-pulsed plasma in liquid phase.Compared to water and other dielectric liquids, very few studies are available for the discharge in cryogenic liquids, including liquid nitrogen.The following manuscripts (and references therein) report on the discharge development via high-speed photography and shadow imaging [21][22][23], evaluation of the ionization rates and reduced electric fields (REFs) compared to discharges in gaseous nitrogen [24], as well as spectroscopic measurements of the discharge parameters (for longer pulses of sub-and microsecond pulse duration) [22].

Experimental setup
In the experiments, the discharge in liquid nitrogen (Airgas, impurities ⩽5 ppm of O 2 and ⩽10 ppm of CO 2 ) was ignited at the tip of a stainless steel needle electrode with a radius of curvature of 200 µm placed in a vessel that allows optical access to the discharge.The vessel, a double-walled borosilicate glass, was confirmed to be transparent to visible light down to at least 300 nm using a quartz tungsten halogen calibrated lamp (Newport, USA).As a ground electrode, a copper disc placed at the bottom of the vessel at a distance of 2 cm was used.To generate the discharge, we used an FPG 120-01NM10 high-voltage power supply (FID technology, Germany) capable of generating pulses with a maximum amplitude of 120 kV, rise time (10%-90% amplitude) of ∼1 ns and pulse duration at 90% amplitude of ∼8 ns.The pulses were delivered to the high-voltage needle electrode via a long (∼15 m) coaxial cable.
The discharge emission was projected onto the entrance slit of a Princeton Instruments SP-2500i monochromator operating in a single stage with 1800 l mm −1 grating using a quartz lens and recorded with a 4Picos intensified chargecoupled device (ICCD) camera (Stanford Computer Optics, USA).To correct the recorded spectra affected by the camera spectral sensitivity, transmission of optical components and the absorption by the liquid nitrogen, the spectral response of the system in the 300-800 nm range was measured using a quartz tungsten halogen calibrated lamp (63 350, Newport, USA).Emission spectra were recorded at a discharge repetition frequency of 10 Hz.The same 4Picos ICCD camera equipped with VZM™ 450 zoom imaging lens (magnification ×0.75-4.5,Edmund Optics, USA) was used to perform the discharge imaging in a single-shot regime.Synchronization of the system was done using an AFG-3252 function generator (Tektronix, USA).
In order to estimate the local electric field during the discharge, we have separately estimated the REF (E/n) and neutral density (n).To determine the development of the reduced electric field strength in the discharge (E/n), we recorded emission spectra of the second positive (SPS) vibrational transitions of nitrogen and the first negative (FNS) of N + 2 with central wavelengths at 337.1 nm and 391.5 nm respectively.Each spectrum was recorded by an ICCD camera with 50-100 accumulations and 2 or 5 ns exposure.For the estimation of the local neutral density, we used two approaches: (1) measured ro-vibrational transitions of nitrogen were simulated using Specair 3.0.2.0 software to determine gas pressure and temperature, considering several broadening mechanisms, including Van der Waals broadening [25][26][27][28]; (2) fitting of the measured atomic line profiles, with consideration of both Stark and Van der Waals broadening mechanismshere, because no atomic nitrogen emission was detected, we added argon into the liquid nitrogen (argon, 99.9997% certified purity, Airgas, was bubbled through liquid nitrogen at the rate of 1 l min −1 for 20 min).Detailed REF determination and line-fitting procedures are outlined below.We mention, however, that the application of these methods may not be appropriate for the case of very dense media (i.e. when the emission is measured directly from the liquid phaseas shown below, in our experiments the light appears to originate from the gas phase area, albeit at higher pressures) because the collision integral in the Boltzmann equation for the electron energy distribution function cannot be calculated using the binary collision approximation [1].Additionally, these methods will not be applicable in the case of extremely high local electric fields, when ionization and excitation are no longer provided by the direct electron impact, but are related to the electric field itself (see, for example, [29], where field emission processes in nitrogen were studied with application of 200 kV cm −1 electric fields at a picosecond timescale).Nevertheless, our preliminary estimations reported in this paper indicate that the obtained data originate from areas of low density (compared to the density of liquid), modest electron densities and adequate REF, suggesting that the measurement techniques might be applicable in this case.
Here, ∆λ vdW and λ ul , central wavelength, are in Å, M s is the molar mass of species in g mol −1 , M s ′ ̸ =s is the average mass of foreign species, and n s and n s ′ ̸ =s are their densities in cm −3 .For the simulations, we have used a fixed electron density fraction of 10 −5 .

Intensity ratio method for determination of the REF
Determination of the REF in the millimeter-sized discharges at atmospheric pressure is frequently done by a non-invasive method using the intensity ratio of the FNS and SPS optical emissions [26][27][28][29][30]. Here, SPS corresponds to the N 2 , with corresponding band heads located at 394.3 nm and 391.4 nm, respectively.Based on the kinetic model (see, for example, [30][31][32][33] and references therein) of the emission, the intensity ratio between the selected transitions can be shown as: where I 394 and I 391 are the measured intensities of the selected emission bands, and τ eff is the effective lifetime of the radiating species.
To apply the intensity ratio method to our system, excitation of N 2 states from the ground state should be predominantly due to electron impact, which typically means limited heating and absence of meta-stable species.This condition appears to be fully satisfied in our system; as we have shown previously, the maximum discharge temperature estimated from the time-resolved spectra is around 140 Konly ∼60 K above the liquid nitrogen temperature [20].Due to the relatively low pulse repetition frequency used in the experiments (10 Hz), as well as the liquid nitrogen environment, we avoided reignition of the discharge in the pre-existing bubble from the previous pulse, thus ensuring that no meta-stable species affect the excitation processes.
For the dynamic processes, time-dependent SPS and FNS intensity changes must be used in equation (1).Using the method described in [33], we have estimated the effective lifetimes for the FNS and SPS to be ∼1 and 25 ps, respectively, at pressures of 20-50 atm.In the case of a long-exposure intensity recording (5 ns exposure time), the dynamic term dI(t) dt can be ignored, and then equation ( 1) becomes just a ratio of two intensities.Extrapolating the parameters from [33] to pressures of 20-50 atm, for nitrogen plasma we have used ) with a = 17 and b = 105.

Estimation of neutral and electron densities using spectral line broadening
Due to the lack of atomic nitrogen emission, for estimation of both neutral and electron densities we have used Stark and van der Waals broadening of argon lines.To observe argon lines, we have dissolved argon gas by bubbling through liquid nitrogen at a rate of 1 l min −1 for 20 min.Argon emission lines located at 750.3 and 811.5 nm were measured using an ICCD camera with 2 ns exposure and 300 accumulations.
Here, we assume Lorentzian profiles for both Stark and van der Waals broadening and approximate the total line profile using the Voigt function with instrumental broadening (measured as 0.08 nm).Natural and Doppler broadening are assumed to be negligible.To estimate Stark width ω s , we have used the quasi-static approximation calculated by Griem [34] as a function of the electron impact width ω e , electron density N e and temperature T e : where A is ion broadening parameter, and R is Debye shielding parameter.Here, we have used parameters from [34,35].
Van der Waals broadening ω v was estimated using the approximation provided by Griem [36,37]: where λ is the observed wavelength, T is the temperature of the perturber (nitrogen), µ is the reduced mass of the emitterperturber system, ᾱ is the average polarizability of the neutral perturber and N is the number density of the neutral perturber.
R represents the difference between the square of the coordinate vector R2 i of the excited state:

R2
i can be calculated from the Coloumb approximation: where l j is the orbital quantum number and n * j is the effective quantum number.To calculate the effective quantum number, E H is the ionization energy of hydrogen, E ion is the emitter ionization energy and E j is the energy of the upper or lower-level energy of the observed transition.The red shift caused by Van der Waals collisions is approximately one-third of the full half width; however, it varies significantly for different transitions [38].
The shift of the central wavelength ∆λ i can be is calculated using η i,v = 0.36 and η i,S = 0.86 [39]: In order to estimate the densities of neutrals N and electrons Ne, we have solved the equations ( 3) and ( 5) for two lines, using T = 100 K and Te = 1 eV, as well as (3), ( 5) and ( 9) for Ar 811.5 .

Results and discussion
Previously, we have reported the imaging results of the development of the discharge in liquid nitrogen for various applied electric fields (applied voltages) [40].The results of the current study (figure 1) are consistent with these findings: the discharge appears as a streamer-like corona propagating from the needle electrode towards the ground.Here, using a needle with larger curvature, which results in a lower applied electric field at the same applied voltage, we observed a typical discharge propagation length of ∼0.8 mm.With a 1 ns exposure time, we observed a propagation velocity of the discharge of about 0.43 ± 0.05 mm ns −1 , which is about an order of magnitude faster than the typical propagation velocity of these discharges in water (figure 1).
The propagation velocity of a streamer, v s , is dependent on the electric field value E as where µ e is the electron mobility.For liquid nitrogen, the electron mobility can be calculated as where e is the elementary charge, m is the mass of the electron, ν en is the frequency of electron-neutral collisions, k en is the reaction rate coefficient of electron-neutral collisions and n 0 is the neutral density.The neutral density in (11) is the number density of liquid nitrogen is ∼10 22 cm −3 and the coefficient of frequency of electron-neutral collisions k en can be estimated as about 3 × 10 −8 cm 3 s −1 : where σ (ε) ≈ 2 × 10 −15 cm 2 is characteristic collision cross section for streamer electric fields of ∼100 Td and v th electron thermal velocity.Then, the electric field that is needed for the measured streamer propagation velocity can be estimated as 25 MV cm −1 , which corresponds to the electric field strength required for breakdown in gas with density equal to the liquid density from the Townsend model.The time-resolved and time-integrated emission spectra were measured in the 300-400 nm region of molecular nitrogen emission-as reported previously, we were unable to detect any nitrogen atomic lines in the region 300-800 nm.Here, we focused on the emission from the SPS vibrational transitions of molecular nitrogen and the FNS transition of N + 2 that are useful for evaluation of the discharge temperature, neutral density and REFs (figure 2).Using the Specair simulation tool, we have fitted the measured significantly broadened bands to estimate these parameters (figure 3).The results (figure 3) are in good agreement with previously reported estimated temperatures [20]-around 90-120 K.Estimated pressure in the emission region is on the order of 30-40 atm and it needs to be kept in mind that because most of the emission originates from the region close to the tip of the needle, this is probably the lowest value of the density in the discharge.Unfortunately, the present experimental system does not allow usable space-resolved measurements with a highenough signal-to-noise ratio to evaluate densities in the areas of streamer propagation.
Using the measured spectra of the discharge, we have estimated the REF by employing the intensity ratio of the FNS and SPS optical emission methods.Here, the bands located at around 391 and 394 nm were integrated and fed into equation ( 1   is characteristic of streamer discharges.The very first value of around 660 Td probably corresponds to the initial formation of streamers in a higher density region, followed by an increase of the REF value due to the formation of the gaseous area.From here on, most of the light emission and the measured values correspond to the events at the 'tail' end of the discharge, i.e. gas phase processes. Estimations of the neutral and electron densities were also made using broadened lines from Ar added into the liquid nitrogen.For that, we used equations (3)-( 9) for the Ar 811.5 line, as well as (3) and ( 5) for Ar 811.5 and Ar 750.3 .The argon emission was measured with a 2 ns exposure time and a 2 ns delay time step (figure 5).The results indicate that the neutral density in the region with the maximum emission (close to  the needle electrode) steadily decreases from 7 × 10 20 cm −3 -5 × 10 19 cm −3 (about 30-2 atm respectively)-while the initial value corresponds well to the estimated from the nitrogen emission, the final pressure appears to be about an order of magnitude lower.
Electron densities, however, appear to be slowly increasing from about 1 × 10 17 cm −3 to 3 × 10 17 cm −3 .These measured electron densities are about two orders of magnitude lower than those measured from the hydrogen alpha line appearing in water discharge [6,9,10]; however, they correspond well to the absence of the atomic nitrogen emission in the discharge spectrum.Dissociation processes are relatively slow compared to ionization and require much higher electron densities to produce a significant number of atomic species within a few nanoseconds [40].
The strongly dynamic nature of the discharge was combined with the observation of the shockwave in the later stages (reported in [40]).Here, we also attempt to estimate the density changes by considering the Rayleigh flow.To derive the neutral densities at the beginning stage of the streamer propagation, we consider the streamer as a one-dimensional flow with a constant specific heat and a constant cross section.The density relation in the Rayleigh flow can be derived by considering that the initial streamer propagation velocity is equal to the speed of sound (critical state Ma = 1) in liquid nitrogen: where ρ is the pre-shockwave density and ρ * is the postshockwave density (measured density), γ is the heat capacity ratio of nitrogen, and M is the Mach number of the post-shockwave flow.If the streamer propagates with a constant cross section, the propagation velocity decreases with the propagation process and the final velocity (when the streamer reaches the maximum length) can be estimated as: where r is the radius of the streamer cross section, l is the maximum length of the streamer and v c is its initial velocity (set as the speed of sound M = 1 for the critical state).The radius of the streamer cross section can also be calculated from the avalanche head radius [41]: The Mach number can then be estimated from Meek's criterion as M = 1 αl = 20.The density ratio between the pre-and post-shockwaves can then be estimated to be ∼100.Thus, the measured initial density should be estimated as ∼1/100 of the initial density and the measured maximum density for the initial 2 ns of the discharge is ∼10 20 cm −3 .The initial density of the ignition can then be estimated as ∼10 22 cm −3 , which is close to the density of liquid nitrogen.
Using the obtained data for the REF values together with the values of the neutrals densities obtained from the argon line-broadening measurements, we have calculated the local electric field in the discharge (figure 6).The initial values of 6-8 MV cm −1 are almost a half-order of magnitude higher than the applied electric field (maximum 1 MV cm −1 , calculated for the needle electrode with a radius of curvature of 200 mm).

Further discussion on the discharge propagation mechanism
While attempting to describe the development of the discharge in the liquid phase, one of the most challenging aspects is related to the lack of room for the electrons to gain enough energy for efficient ionization [42].The high liquid densities result in high collision rates and fast quenching [43], resulting in very high breakdown electric fields predicted by the Townsend mechanism.For the direct ionization of water, for example, where the typical density is three orders of magnitude higher than that for atmospheric pressure gas: n liquid ∼ 10 3 × n gas , extrapolation of Paschen's curve predicts breakdown electric fields on the order of 30 MV cm −1 .However, in multiple experiments, in-liquid plasma was observed with electric fields closer to ∼ 1 MV cm −1 .Thus, to explain this phenomenon, two broad mechanisms were proposed: (1) the discharge is initiated and its propagation is aided by the formation of nano-scale voids, or pores, driven by the electrostriction forces; and (2) while initiation of the discharge is still probably due to the existence of the aforementioned nanopores, propagation of the discharge is driven by the direct ionization of the liquid phase.These mechanisms can be generally described as the 'dense gas lightning' ('cold' leader) approximation and the hypothesis that streamers are generated directly in the liquid phase.
A hypothesis formulated in [18,44,45] suggests that the discharge initiation mechanism is related to the generation of nanopores in the vicinity of the high-voltage electrode.Electrostrictive forces that appear in polar liquids due to the application of strong non-uniform electric field cause deformation and 'rupture' the liquid.This is followed by the appearance of a region near the high-voltage needle electrode saturated with elongated along the electric field line's nanoscopic voids [18].Inside these voids, virtually free of collisions, electrons can gain enough energy to provide initial ionization and generation of avalanches.Experimentally, the existence of the lower density region in the vicinity of the electrode powered by fast-rising pulses was demonstrated previously using schlieren imaging [18,45].However, due to the high intensity of the plasma radiation, these experiments were performed in the absence of the discharge (i.e. using the application of high voltage pulses with a peak electric field below the breakdown).
The 'lightning' hypothesis of the nanosecond breakdown in liquids is based on the process of the formation of long sparks and lightning in gases and is related to the leader phenomenon [18].In air, the transition from streamers to leaders is related to the detachment of the electrons from the negative ions via a thermal mechanism.Similarly, it has been proposed that the discharge in liquid can propagate via the 'growth' of the 'needle electrode'-or cold leader comprising a positive charge-that provides continuous generation of the nanovoids in front of it, allowing generation of new avalanches and propagation of the discharge.In this case, a continuous increase in the applied voltage is essential for the discharge development.This mechanism suggests that the propagation of the 'leader' is dependent on a constant generation of electrostriction-driven nanopores ahead of the propagating discharge front and thus significantly lower associated local electric fields (since streamers are generated in lower density regions and the local electric field is comparable to the applied electric field).Our results indicate that the neutrals densities, even at the centre of the discharge from which comes most of the registered radiation, are only about 30 times lower than the liquid density, indicating that the discharge actually develops in the high-density environment.Indeed, if the ionization and electron excitation of the radiating molecules and atoms (argon) were happening with the help of nanopores, one could expect much lower pressure broadening.This is because these voids are viewed as 'cracks' in the liquid structure and therefore are initially filled with a 'vacuum'.In [46], it was estimated that time required for filling of a cavitation void by a saturated water vapour is in the range of 20-100 ns, while our experimental results suggest that the pressure inside the gas pocket is, in contrast, decreasing.In contrast, propagation of the streamer directly in liquid would first result in the production of a shockwave or a region with a higher density that would propagate together with the head of the streamer, followed by a lower-density region of the post-shockwave flowas we observed here.Moreover, in liquid nitrogen, a non-polar liquid with dielectric permittivity of ∼1.5, with the applied electric field of ∼1 MV cm −1 , electrostriction-induced cavitation pressure can be estimated as ∼10 kPa, about three orders of magnitude lower than required for cavitation (∼10 MPa [47]).
Alternatively, direct liquid ionization, or a streamer ('electronic') mechanism, is based on the hypothesis that while the initial electron densities are generated with the help of nanopores in the vicinity of the high-voltage electrode, the resulting plasma is a macroscopic streamer propagating directly in liquid.In this case, one can expect that cathodedirected streamer propagation is governed by the generalized Meek criterion for breakdown [48], ´xmax 0 [α (x) − β (x)] dx ⩾ 20, which is associated with local electric fields at the head of the streamer on the order of 30 MV cm −1 and high electron densities in the discharge.Numerical modelling of the streamer development and propagation directly in the liquid phase has been done by Babaeva and Naidis [49,50].The authors considered the 'electronic' mechanism in liquids with a high mobility of electrons, such as liquefied argon, xenon and methane, and is investigated in the sub-nanosecond time range.Numerical models, created for liquid argon and liquid xenon, predicted values for the local electric field (figure 3) and the velocities of streamers in these liquids for applied electric fields on the order of 0.3-0.4MV cm −1 .
The above-presented results indicate that the electric field in plasma propagating in liquid N 2 to about 1 mm in size during a nanosecond may reach values of ∼25 MV cm −1 .These very high values of electric field correspond to the initial suggestions made in the first publications [1] regarding direct breakdown of liquids without the formation of bubbles and voids.According to these, the REF E/n required for the streamer breakdown of gases and liquids (without bubbles and voids) should not be very different.Therefore, while atmospheric breakdown requires about 30 kV cm −1 , breakdown of liquids (about 1000 times denser), should require about 30 MV cm −1 , which is confirmed by the above-presented results.Obviously, in this case, the Meek parameter meets the criterion αd ⩾ 20, where α is the Townsend ionization coefficient and d is the distance between electrodes.
We mention that high electric fields of about 25-30 MV cm −1 and corresponding E/n in the liquid N 2 about 100 Td occur only in the streamer head (outside of the initial plasma 'core') where the liquid is still dense.Streamers propagate significantly faster than shockwaves; therefore, when the streamer already occupies most of the ∼1 mm dense region of liquid nitrogen, the ∼50 times less dense 'core' (effective pressure 20-30 atm) still stays in the ∼10-30 µm initial sphere behind the propagating shockwave.The electric field in the initial 'core' is lower than in the streamer head (about 6-8 MV cm −1 ), but the REF E/n in the 'core' is higher (E/n ∼ 500 Td) because of the lower N 2 density).The high level of the REF E/N in the 'core' results in the majority of radiation coming from there and not from the streamer head, which has been observed experimentally.
The maximum electric field in plasma (about E m = 25 MV cm −1 ) exceeds the applied electric field (E 0 = 1 MV cm −1 ), which indicates the streamer head nature of the maximum achieved electric field.According to the conventional streamer propagation model [41], the relation between applied and maximum electric field can be expressed as a function of the streamer length l and radius r: Assuming the streamer radius is about 1/α [41] and αd ⩾ 20 according to the Meek criterion, this relation gives E m /E 0 = 19, which is very close to the observed ratio and indicates the streamer head nature of the maximum achieved electric field in the liquid.We note that the above E m /E 0 relation requires sufficient conductivity of the plasma following the streamer head to provide its equipotentiality.This means that the RC time of the plasma following the streamer head should be shorter than the streamer propagation time (which is about 1 ns).This requirement is met in the considered system, where the typical electron density on average is at least 10 14 cm −3 , which leads to a characteristic RC time of 10 −10 sec.
It is interesting to point out that the critical Meek αd parameter slightly (logarithmically) grows with the applied electric field (such as const + ln( E0 E00 ), where E 00 = 30 kV cm −1 [41]).Therefore, the effective 'strengthening' E m /E 0 of the applied electric field in the streamer head can be also estimated as: This means that the effective 'strengthening' E m /E 0 of the applied electric field in the streamer head is stronger in the liquid discharges (without bubbles and voids) than in gases.
While the E m /E 0 ratio in gases is usually 3-10 (when E 0 is about 30 kV cm −1 ), the E m /E 0 ratio can be as it has been estimated above up to 20 in the liquid discharges (when E 0 is above 1 MV cm −1 ).Thus, generally, the achieved electric fields in the streamer heads of the liquid discharges (without bubbles and voids) can be extremely high, on the level up to 30 MV cm −1 , which is already about 3% of the intra-atomic electric fields.This hints at a possible contribution of direct ionization by the electric field itself through, for example, tunnelling effects, which surely requires much deeper analysis.

Conclusions
In this work we attempted to evaluate several properties of nanosecond-pulsed plasma generated in liquid nitrogen, including neutral temperatures and densities, as well as local electric field values.Using imaging and optical emission spectra of the discharge, we have shown that: (1) The discharge reaches millmeter-scale sizes with propagation velocity on the order of 0.5 mm ns −1 , which would require local electric field values as high as 25 MV cm −1the electric field strength needed for breakdown in gas with density equal to the liquid density from Townsend model.(2) By using the Specair simulation tool, we have fitted the emission from the SPS vibrational transitions of molecular nitrogen and the FNS transition of N + 2 to evaluate the discharge temperature, which provided values of around 90-120 K, very close to the temperature of liquid nitrogen (77 K).While the presented results indicate that the discharge develops via a streamer ('electronic') mechanism, limitations of the current experimental setup did not allow us to obtain information on the most crucial plasma properties during the very initial (first 1 ns or so) moments nor in front of the propagating channel (streamer head).Although advanced imaging and optical emission spectroscopic measurements are undoubtedly able to estimate densities with the required space and time resolution, predicted values of the local electric fields most likely would not permit application of the intensity ratio method (instead, laser-based diagnostics, such as coherent anti-Stokes Raman scattering and electric field-induced second harmonic generation, should be used).
) in either dynamic (for 2 ns exposure time) or stationary (for 5 ns exposure time) form.The REF was then determined from R 391 394 (E/n) = a exp(−b(E/n) −0.5 ) with a = 17 and b = 105 as described in section 2.3 above.The emission in the bands is strongest around 6-12 ns, while at the beginning and at the trailing end of the discharge signalto-noise ratio was too low for the short-time exposure measurements, the initial REF values were estimated using the 5 ns exposure data taken with 2.5 ns time delay increments.The results (figure 4) show that the discharge ignites at relatively high REF values, followed by a fast decrease in the REF, which

Figure 1 .
Figure 1.Typical single-shot images taken with the exposure time of 1 ns (white bar represents 0.5 mm scale) and corresponding temporal development (maximum observed channel length) of the discharge in liquid nitrogen.

Figure 2 .
Figure 2. Emission spectra of the second positive (SPS) vibrational transitions of N 2 and the first negative (FNS) transition of N + 2 .Inset graphs represent time evolution of the peak intensities.

Figure 3 .
Figure 3. Specair-fitted SPS and FNS emission bands (8 ns time delay, T = 81 K) for various pressures and neutral temperature evolution as a function of time obtained from Specair simulations.

Figure 4 .
Figure 4. Time evolution of the reduced electric field as compared to the voltage pulse waveform (horizontal bars represent exposure time region).

Figure 5 .
Figure 5.Time evolution of the Ar 811.5 and 750.3 spectral lines and calculated neutral and electron densities.

Figure 6 .
Figure 6.Local electric field values estimated from the data presented in figures 4 and 5 compared to the applied electric field (black line).

( 3 )
We have estimated the REF values in the area behind the propagating streamer head by employing the intensity ratio of the FNS and SPS method, suggesting that the discharge ignites at relatively high REF values of around 600-1000 Td, followed by rapid decrease in the REF.The estimated values are characteristic for streamer discharges.(4) Estimations of the neutral and electron densities in the 'main body' of the discharge were done using broadened argon lines, indicating that the neutral densities in the near-electrode region are around 5 ÷ 70 × 10 19 cm −3 (2-30 atm), decreasing with time.Electron densities were estimated to be ∼10 17 cm −3 , about two orders of magnitude lower than those measured for water discharge.(5) Finally, using the data for the REF values together with the values of the neutral densities obtained, we have estimated the maximum local electric field in the 'core' of the discharge to be around 6-8 MV cm −1 .