Effects of liquid properties on the development of nanosecond-pulsed plasma inside of liquid: comparison of water and liquid nitrogen

In this manuscript, we report on observations of the development of nanosecond-pulsed plasma in liquids and examine liquids with two drastically different properties: water and liquid nitrogen. Here, we compare the discharge appearance using high-speed imaging, examine bubble formation using shadow imaging, and measure the time-averaged optical emission spectra of these plasmas. Because the liquid nitrogen plasma is ignited in a liquid that is at boiling temperature, we also study the water discharge at various temperatures, up to boiling. We demonstrate that the discharge development appears not to be affected by this type of liquid. Optical emission, however, is strikingly different: in water, we observe continuum emission in the UV region only and no black-body continuum or atomic lines, whereas the liquid nitrogen spectrum is populated by molecular and longer wavelength broadband emissions.


Introduction
Strong electric fields applied to liquids have been studied for various applications in chemistry, biology, and physics.For example, they can be used for water sterilization or high-power switching.Generally, electrical discharges observed in liquids are either corona (or corona-like) discharges or pulsed arcs (or sparks).In all cases, the discharge is initiated in the gas phase due to the local heating of the liquid with the formation of gas bubbles [1,2].Recently, several groups have investigated a distinct type of breakdown in liquids, where the discharge is 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.generated before bubble formation by applying rapidly rising short high voltage pulses.This nanosecond-pulsed discharge exhibits a sub-nanosecond time scale of development and can propagate with velocities of up to 5000 km s −1 [3].It is fundamentally different in nature than discharges initiated by electrical pulses with a longer rise time [4][5][6].Nanosecond-pulsed discharges in liquids are typically characterized to have relatively small sizes, ranging from hundreds of microns to a few mm, and high densities, varying from 10 17 to 10 20 cm −3 in different experiments [7][8][9].It is believed that these discharges are generated, or at least initiated, directly in the liquid phase before the formation of gaseous voids or bubbles [3,7,10].The exact mechanisms of their initiation, however, are still largely unknown.Although time-resolved spectroscopic measurements of heavy particle temperature are extremely challenging in low-energy nanosecond-pulsed discharges, particularly in the case of water discharges where the emission spectra exhibit a broad-band continuum [3,7,9], estimations based on OH emission from the secondary 'bubble' phase of the discharge indicate that the discharge is actually nonthermal, with an associated temperature increase of approximately 100-200 K [11].
Typically, nanosecond-pulsed discharges are studied in water and various types of liquid hydrocarbons.However, obtaining detailed plasma parameters in these liquids using optical emission spectroscopy methods has proven to be difficult: for example, at the early stages of the discharge, spectroscopic analysis of the plasmas in water reveals a broadband continuum emission, which only later, after the high voltage pulse ends, reveals line emission [7][8][9].Based on the observed hydrogen and atomic oxygen emission lines, several groups have determined electron densities in the water plasmas [7][8][9].In our recent experiments, when the discharge is ignited in liquid nitrogen, we were able to register molecular nitrogen emissions during the ignition and propagation of the discharge [12].Using liquid nitrogen as a medium for nanosecond-pulsed discharges provides an opportunity to observe the evolution of the plasma parameters with temporal resolution.Unlike water and other dielectric liquids, there have been very limited studies on plasmas in cryogenic liquids, including liquid nitrogen.The following manuscripts (and references therein) report on the discharge development via highspeed photography and shadow imaging [13][14][15], the evaluation of the ionization rates and reduced electric fields compared to discharges in gaseous nitrogen [16], and spectroscopic measurements of the discharge parameters (for longer pulses of sub-and microsecond pulse duration) [14].In [14], streamer development was observed by the application of relatively long pulses with variable width from 100 ns to several µs.The recorded spectra showed the main bands of the second positive system of nitrogen (C 3 II u → B 3 II g ) and vibrational bands of the first negative system.From the analysis of the N 2 second positive system, a rotational temperature of about 500 K and a vibrational temperature of about 4000 K have been estimated.Our previous study reported on the observations of molecular nitrogen emission spectra from the discharge ignited in liquid nitrogen and estimated temperatures of ∼110 K [12].
The goal of this study is to draw an analogy between the basic characteristics of nanosecond-pulsed plasmas ignited in liquid nitrogen and water.Here, we compare the discharge appearance using high-speed imaging, then examine bubble formation using shadow imaging, and measure the timeaveraged optical emission spectra of these plasmas.Because the liquid nitrogen plasma is ignited in a liquid that is at a boiling temperature (77 K), we also take a look at the water discharge at various temperatures (room, 50 • C, and boiling).

Materials and methods
In the experiments, the discharge in liquid was ignited at the tip of a needle electrode placed in a vessel that allows optical access to the discharge (steel needles with radius of curvature of 7.5 and 55 µm were used).For the generation of discharges in liquid nitrogen and water, a double-walled borosilicate glass that allows an efficient transmission of light down to at least 300 nm (as confirmed by measurements using a Newport quartz tungsten halogen-calibrated source lamp) was fixed in an evacuated enclosure equipped with quartz windows (figure 1).A copper disc affixed at the bottom of the liquid-containing vessel's outer surface was acting as a second grounded electrode.Liquid nitrogen (LN) with impurities of ⩽5 ppm O 2 and ⩽10 ppm CO 2 was purchased from Airgas.For the generation of the discharge in water, Optima LC/MS grade water (Fisher Chemical) was degassed by boiling under reduced pressure provided by a vacuum pump for at least 15 min.To examine the discharge behavior at various temperatures, a copper vessel (∼50 ml volume) equipped with quartz windows was placed on a hot plate, and temperature was monitored using a HH806AU thermocouple (OMEGA).In the case of boiling water, liquid was allowed to reach volumetric boiling with the generation of large bubbles (as opposed to boiling on chamber walls), which, due to their relatively slow movement, does not affect discharge generation and imaging.
To generate the discharge in liquids, we have used FPG 120-01NM10 high-voltage power supply (FID technology) capable of generating pulses with a maximum amplitude of 120 kV, rise time (10%-90% amplitude) of ∼1 ns, and a pulse duration at 90% amplitude of ∼8 ns.For the generation of discharge in water, FPG 20-1NM10DD highvoltage power supply (5-20 kV, 10 ns duration, and 2-3 ns rise time) was also used.In both cases, long (∼15 m) coaxial cables were equipped with back current shunts to monitor pulse shapes (figure 2) and diagnostic equipment synchronization.
Imaging of the discharge was performed using 4Picosintensified charge-coupled device (ICCD) camera (Stanford Computer Optics, USA), equipped with VZM™ 450 zoom imaging lens (magnification 0.75-4.5X),and synchronized with the power supply using AFG-3252 function generator (Tektronix, USA).A 75W Xe arc lamp (6251NS, Newport) was used as a source of back light for shadow imaging.The discharge emission spectra were recorded using the Princeton Instruments-Acton Research, TriVista TR555 spectrometer system operating at a single stage with 1800 l mm −1 grating via 1 m single-leg fiber optic bundle with nineteen 200 µm fibers (190-1100 nm, Princeton Instruments, USA).Spectra of the discharge in water were taken using the PIMAX digital ICCD camera, and in liquid nitrogen-4Picos ICCD camera.To account for the camera detector spectral sensitivity, transmission of optical components, and absorption by the liquids, the spectral response of the system in the 300-800 nm range was measured using a quartz tungsten halogen calibrated source lamp (63 350, Newport) for both liquid nitrogen and water.Emission spectra measurements were performed while the discharge was operating at a repetition frequency of 10 Hz, whereas imaging was done in a single-shot approach.From the imaging examination, the repetition frequency of 10 Hz was sufficiently low not to affect bubble/void generation (i.e., the ignition of the discharge in the pre-existing bubble from the previous pulse).

Results and discussion
A number of studies [7,8,[17][18][19][20] have investigated the discharge development in water, and the results included here are consistent with these findings.In this report, we compare discharges ignited in low molecular weight liquids with drastically different polarizability constants: water and liquid nitrogen.This allows us to determine whether the previously observed discharge phenomenology is specific to water, especially at room temperature far from the critical boiling point that affects bubble formation, or intrinsic to the application of short high voltage pulses in liquids in general (to some degree, it was studied in [7,11], where discharge was ignited in hydrocarbon liquids at room temperature).Typical timeresolved images of single-shot discharges ignited in water and liquid nitrogen are shown in figure 3. The results of the discharge imaging allow us to draw an immediate qualitative conclusion: the discharge dynamics is similar in both water and liquid nitrogen and is independent of water temperature.In all cases, the discharge appears at the rising edge of the high voltage pulse, along with the 'first stroke, dark phase, and return stroke' emission pattern (figure 4).This is consistent with previous findings (7,11,17).This can be interpreted while keeping in mind that a major difference in the evolution of discharges in different liquids is significantly attributed to differences in their polarizability and therefore dielectric permittivity, which depend on the effective frequency of the applied electric fields.The differences in the polarizability and dielectric permittivity of water and liquid nitrogen are mostly due to the strong contribution of dipolar orientation polarization, which is very high in water.The typical time of dipolar orientation polarization in room temperature water, however, is in the range of nanoseconds, resulting in a low contribution of the dipolar polarization of water during nanosecond pulsing.It suppresses the significant difference in dielectric behavior of water and liquid nitrogen in this case and explains the observed virtual identity of the discharge evolution in liquids with significantly different characteristics: liquid nitrogen and water.Nevertheless, the differences in the dielectric properties of the liquids affect the overall discharge brightness, channel propagation length and velocity, as shown below.
However, the luminosity and discharge size appear to be dependent on the liquid properties.In water, with the increase in temperature, the discharge overall brightness and maximum propagation length seem to decrease; this can be related to the dependence of water dielectric constant on temperature: ε = 80 at 20 • C, ε = 69.9 at 50 • C and ε = 57-56 at 95 • C-100 • C [21].Similarly, in [11], it was shown that discharge ignited in hydrocarbon liquids (with the smallest dielectric constants) produced noticeably weaker emission  and propagated shorter distances, whereas water and methanol solutions allowed stronger, brighter, and longer channel generation.
The typical maximum discharge size produced in both water and liquid nitrogen was on the order of mm. Figure 4 shows temporal development of the discharge.For water, the maximum length of channels generated with 20 kV pulses was about 310 µm for room temperature, 270 µm for 50 • C, and about 210 µm for boiling water.The velocity of the channel propagation was estimated to be 44 ± 3 km s −1 for room temperature water, 39 ± 3 km s −1 at 50 • C, and 37 ± 3 km s −1 for boiling water (note that these images were taken with 3 ns exposure time and therefore resulted in somewhat lower estimated propagation velocities).Similar velocities were reported previously: for example, 30-60 km s −1 for 15 kV pulses with ns exposure time (5 ns rise time, 30 ns duration) in [22]; however, with the application of faster rising and higher amplitude, pulses reported streamer propagation velocities were almost an order of magnitude higher: 200 km s −1 for 100 kV pulses (2 ns gate time, 7 ns FWHM) [17], and 230 km s −1 for 160 kV pulses (500 ps gate time, 7 ns FWHM) [23].A faster velocity of 5000 km s −1 , close to the velocity of streamer propagation in air, was reported in water when 220 kV pulses (200 ps gate time, 150 ps rising time, 400 ps duration) were applied [3].In liquid nitrogen, the discharge was generated using higher voltage pulses of 60 kV, and the typical maximum size was about 1.2 mm.With 1 ns exposure time, we observed a much faster discharge development than that in water: at 60 kV, channel velocity was estimated to be ∼500 km s −1 (0.5 mm per ns).Applied voltage amplitude significantly affects the discharge size and maximum channel length.Here, we examine this relation for water and liquid nitrogen (figure 5) using the FPG 120-01NM10 high voltage power supply.Plotting of the data as a function of the maximum applied electric field is calculated using the maximum applied electric field at the maximum of the voltage pulse V: (where r is the needle radius of curvature, d-distance to the second electrode), and compared with data for polydimethylsiloxane (C 2 H 6 OSi) n transformer oil (PDMS) that has a dielectric constant of ∼2.3-2.8 from [11, data obtained for 5 µm needle], we note that in water discharge, the size dependence on applied voltage is weaker than that for liquid nitrogen and PDMS.We attribute this result to a faster screening effect of space charges in liquids with higher dielectric permittivity.The discharge of liquid inevitably leads to the generation of gaseous voids and associated acoustic waves.Shadowgraphic imaging was performed in both liquids to study these effects (figure 6).In the discharge event, plasma emission overpowers the background light.However, right after the discharge is extinguished, bush-like gaseous structures in that occupy former channels' positions are clearly visible in both water and liquid nitrogen.The shape and size of the structures correspond to those of the previously generated plasma.About 30 µs later, the gaseous structure becomes spherical (with a rising temperature of the liquid, this seems to have happened a few µs earlier), and eventually leaves the electrode.In liquid nitrogen, however, due to significantly lower surface tension, a spherical bubble takes its shape at later time points-around 50-60 µs.It should be noted that both power supplies effectively absorb the reflected high voltage pulses, resulting in no additional energy deposition into the liquid.
In water, at around 70 ns after discharge initiation (corresponding to about 40 ns after the discharge emission ends), we observed initial shockwave formation around the gaseous channels (figure 7).Similarly, in liquid nitrogen, wave formation was also observed, but at a significantly later time pointaround 450 ns after the high voltage pulse arrived at the electrode.In water, at all temperatures, the initial shockwave velocity was measured to be ∼4 km s −1 .At around 150 ns, it becomes an acoustic wave traveling with the speed of sound (∼1.4 km s −1 ).In liquid nitrogen, the fastest wave velocity was measured to be 0.85 km s −1 at a speed of sound.From the x-t graph shown in figure 7, the observed waves form at significantly later time points after the discharge extinguishes (while in water they are of a cylindrical geometry, originating from the gaseous channels) and therefore are most likely not related to the electrostriction phenomenon.Assuming a constant liquid density and using Hugoniot equations for the shockwave velocity, we estimate the initial cavitation pressure to be a few GPa for water.Comparable values were reported for room temperature water in [19,22].
Spectroscopic measurements of the discharge emission in the range 300-800 nm were taken without spatial and temporal resolution.In these experiments, long exposure time measurements were taken with 10 µs (water), 2 µs (liquid nitrogen) exposure times and 50 (water), 200 (liquid nitrogen) accumulations at the discharge repetition frequency of 10 Hz.Quartz tungsten halogen calibrated source lamp (63 350, Newport) was used to calibrate the optical system for both water and liquid nitrogen setups to account for the camera sensitivity function, the transmission of optical components, and the absorption by the liquids in the range of 300-800 nm.Measured spectra were then corrected using the calibration function.Figure 8 shows a striking difference in the discharge emission spectra in water at different temperatures versus liquid nitrogen.At all temperatures in water, we observed no line emission accompanied by a strong increase in the emission intensity toward the UV region (spectra shifted vertically for clarity).
The liquid nitrogen plasma emission spectrum looks very different from the spectra obtained in water: we observed strong molecular emission from the first and second positive systems, as well as weak emission in the UV range, with a maximum of the continuum emission around 700 nm.The presence of molecular nitrogen emission, in principle, allows the determination of vibrational and rotational temperatures.Since the vibrational and rotational structures are not sufficiently resolved in the present experiments, as well as due to long exposure measurements (i.e., the emission signal is collected from the whole pulse and represents a superposition of signals from different discharge stages), we did not attempt to estimate the corresponding temperatures.In an effort to do so (using Specair 3.0 [24]), we note that nitrogen bands are significantly broadened, indicating that emission, at least partially, originates from high-density regions: Specair 3.0 allows the   modeling of line shapes considering several broadening mechanisms, including van der Waals broadening.Using this software, we estimate the pressure to be at least 1-10 MPa.Timeresolved emission measurements will allow a detailed study of the discharge temperatures and densities.
In both water and nitrogen plasma emission spectra, we were unable to detect any of the well-known hydrogen, oxygen, or nitrogen atomic lines.This result is in contrast with our previous studies, where we reported on integrated emission spectra taken from discharges generated using an older pulsed power supply, where atomic hydrogen and oxygen emissions were observed due to multiple discharge reignitions [7].At the same time, similar water emission spectra were reported in [8,17] during the primary pulse at its later stages: strong emission in the UV region, a 'structureless' continuum and absence of atomic line emission.The early emission spectra (during the first 3 ns) measured by the same group were attributed to electron-neutral bremsstrahlung continuum emission [25].As also noted in [25], several reports have proposed black-body radiation spectra originating from the tungsten electrode tip in similar experiments.It is also worth noting that dissociation processes happen at much longer timescales compared to ionization, and it would require relatively high electron number densities to produce a significant number of atomic species during the few nanoseconds-we estimate this electron density would need to be at least ∼10 19 cm −3 , which is comparable with the densities reported in [9,19] where the authors were able to detect H α emission in water plasma.

Conclusions
Nanosecond-pulsed discharge in liquid was studied using imaging and spectroscopic techniques.We show that discharge development appears to be virtually identical in liquids with significantly different characteristics: liquid nitrogen and water (barring corresponding distinctions in sizes).Although in general, plasma development in various liquids appears to be very similar, we noted a few differences.For water, the temperature of the liquid was found to play a minor role, slightly affecting only the propagation length and velocity: the higher the temperature, the smaller and slower the channel .Ignition of the discharge in liquid nitrogen requires higher applied voltages, but the observed size of the plasma region is similar to that in water and is on the order of a millimeter.Perhaps due to the lower dielectric constant, channels in liquid nitrogen propagate to longer distances with the increase of the applied electric field, compared to water.Estimations of the channel propagation velocity in liquid nitrogen (∼500 km s −1 ) are close to those in water generated with similar pulses, and about an order of magnitude higher than for pulses with slower rise times.Shadowgraphic imaging of the discharge shows generation of gaseous voids followed by shockwave formation in water and slow acoustic waves in liquid nitrogen.In both cases, we note that waves appear at significantly later time points after the discharge.
Optical emission spectra of the discharge ignited in water and in liquid nitrogen are strikingly different: in water we noted continuum emission in the UV region (which is presumably due to electron-neutral bremsstrahlung) but no blackbody continuum or atomic lines, whereas the liquid nitrogen spectrum is populated by molecular and longer-wavelength broadband emission.These spectroscopic features of the liquid nitrogen plasma are believed to be useful for further studies to better understand the mechanisms of the discharge formation in liquids: allowing not only the measurements of the discharge temperature but distinguishing between the proposed mechanisms of direct streamer propagation in liquid phase versus electrostriction-driven 'leader' formation.This could be possible by the determination of local densities from the line broadening, accompanied by measurements of reduced electric fields from the ratio of the emission intensities of the second positive (SPS) vibrational transitions of nitrogen and the first negative (FNS) of N 2 + .

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).

Figure 1 .
Figure 1.Schematics of the experimental setups used for generation of the nanosecond-pulsed plasma in liquid nitrogen (left) and in water at different temperatures (right).

Figure 2 .
Figure 2. High-voltage pulse shapes used in this study.

Figure 3 .
Figure 3.Typical discharge images taken in water at different temperatures and in liquid nitrogen.Exposure time 3 ns.White bars show 100-µm scale.

Figure 4 .
Figure 4. Temporal development-maximum observed channel length-of the discharge in water (left) and in liquid nitrogen (right).

Figure 5 .
Figure 5. Dependence of the observed maximum channel length in various liquids on the peak applied electric field.

Figure 6 .
Figure 6.Shadowgraphic images of the post-discharge events in water at various temperatures and in liquid nitrogen.White bars show 100 µm scale.

Figure 7 .
Figure 7. Representative shadowgraphic images of the shockwaves in water and measured shockwave radii at different times post discharge in different liquids.

Figure 8 .
Figure 8. Optical emission spectra of the discharge in water (left, spectra shifted vertically for clarity) and in liquid nitrogen (right).