Propagation of a pulsed nanosecond discharge on a water surface in non-symmetrical configuration, and comparison with the symmetrical configuration

Non-thermal plasmas produced by pulsed nanosecond discharges at atmospheric pressure are of great interest for fundamental as well as technological and environmental applications due to their high reactivity. When generated in air in contact with water, these discharges induce many physical and chemical phenomena at the interface, including pattern formation. Although the patterns generated in symmetrical configuration have been extensively studied, those produced by asymmetrical discharges are not well characterized. In this study, we report the propagation dynamics of a nanosecond discharge produced in air in contact with water using electrodes mounted in parallel direction relative to the water surface (i.e. asymmetric configuration). The influence of the high voltage polarity and water electrical conductivity on the discharge pattern is investigated using fast imaging and electrical diagnostics. The obtained results demonstrate that under positive voltage polarity, plasma dots are produced along the ionization front. These dots have been previously observed in symmetrical configuration; however, their propagation velocity is greater in asymmetrical configuration, particularly in front of the anode. Under negative polarity conditions, a homogeneous emission pattern is observed, except in the area in front of the cathode, where dots are detected in the ionization front. Based on this data, the E-field threshold beyond which plasma dots are formed is estimated to be ∼5 × 108 V m−1. Overall, the results reported herein provide a fundamental understanding of plasma-water interactions.

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Introduction
Discharges in or in contact with water are widely studied due to unique properties that render them attractive for many applications, including material synthesis [1], water activation [2,3], nitrogen fixation [2], and medical treatment [4,5].Different discharge modes can be sustained above water, namely corona [6], streamer [7], and spark [8].In corona mode, the active plasma phase is produced near a sharp electrode, and the long-lifetime reactive species can reach the water surface (mainly by diffusion) where chemical reactions occur.Unlike the corona mode, discharges in streamer and spark modes exhibit significant plasma propagation and interaction with water surface.Considering that sparks are always preceded by streamers, only the streamer discharge mode is analyzed in this study.
Streamer ignition and propagation have been the focus of numerous studies during the last few decades.Today, the propagation dynamics of streamers in gas medium, including air, is well understood, and the available research indicates that after initiation by electronic avalanches close to the high Efield region, streamers are formed if the number of produced electrons is higher than 10 8 (Meek's criterion) [9].At this condition, the E-field induced by electron-ion separation becomes relatively high (comparable to or higher than the applied field), and thus, it controls the subsequent steps of streamer propagation, mainly by initiating secondary avalanches close to the streamer's head [9].
In practical applications, streamer discharges are typically generated in gaseous media over solid or liquid surfaces, and they come in contact with these surfaces.The propagation dynamics and interactions at the interface are complex phenomena that significantly impact the targeted application; however, they are poorly understood.Previous studies have established the effects of various parameters, including gap distance [7], voltage magnitude and polarity [10], gas composition [11], and electrical conductivity of water [11] on the dynamics of propagation on aqueous surfaces.These studies make use of time-integrated or time-resolved imaging techniques to analyze streamer propagation at the gas/water interface.The former technique shows that depending on the applied conditions, different emission patterns (e.g.plasma dots [7], rings [7], discs [10], etc) are formed on the water surface [10,12].Meanwhile, the latter technique reveals the propagation details at the nanosecond time scale, which is the typical scale of phenomena occurring at the streamer's head.
In general, the pattern formed on the water surface is correlated with plasma-liquid coupling.The literature can be classified into two discharge categories: continuous or pulsed.In the case of continuous DC, the discharge pattern observed on the surface of the solution is sensitive to the experimental conditions (solution electrical conductivity and acidity, voltage polarity, discharge current, gas composition, etc) [13] as well as to the diagnostic technique (time exposure of the camera [10,11,14]).For instance, Bruggeman et al [14] found that when water is cathode, the plasma is filamentary at the water surface; however, it is diffuse when water is anode.Miao et al [15] report that plasmas generated using a DC source and anode water generally have a conical shape that depends on air gap distance, cathode dimension, and water conductivity.As for the exposure-time dependence, Bruggemann et al [14] showed that DC discharge on anode water appears as a homogeneous disc at an exposure time of 20 ms.However, the disc appears as movable dots at an exposure time of 100 µs.Recently, we have investigated the dynamics of single nanosecond discharges produced in air above water.Using the 1 nsintegrated imaging technique.Our results demonstrate that the emission pattern produced on the water surface by a discharge generated under positive polarity voltage evolves rapidly.Indeed, a disc-like emission is observed during the first few nanoseconds, then a ring-like structure, then highly organized plasma dots propagating at the velocity of a few hundred km s −1 ; the propagation velocity was estimated based on 1ns-integrated images [7].The effects of gap distance, voltage magnitude, and water electrical conductivity on the discharge dynamics have also been assessed [7,11].Unlike the positive polarity counterparts, negative polarity discharges do not produce plasma dots on water.Instead, they produce a homogeneous disc-like emission with an ionization front propagating at the velocity of few tens of km s −1 ; the propagation velocity was estimated based on 1 ns-integrated images [16].
The underlying physical processes that give rise to pattern formation are not well understood.However, in the typical configuration of a discharge propagating in gas phase in contact with water, it is proposed that the photoelectron production rate decreases significantly as the discharge approaches the surface, which stops vertical propagation [17].If the radial electric field produced by accumulated charges at water surface is strong enough, radial avalanches are ignited, leading to the formation of radial streamers at or near the surface [17].Therefore, streamer propagation is strongly influenced by the water properties, mainly electrical conductivity, as well as by the electrode geometries.
Previous studies [10,11,16] were conducted in symmetrical configuration, i.e. with the electrode connected to the high voltage power supply placed perpendicularly in air, above water.Herein, we investigate discharge dynamics in asymmetric electrode configuration, i.e. with the electrode mounted at the water surface, in parallel direction.In addition, we examine the effects of voltage amplitude and polarity, as well as water electrical conductivity on discharge propagation dynamics using electrical and optical (integrated and time resolved ICCD imaging) techniques.

Experimental setup
Figure 1 presents the scheme of the experimental setup used herein.Electrical discharges were generated in ambient air in contact with water using a negatively-or positively-polarized pulsed power supply (NSP 120-20-N/P-500-TG-H, Eagle Harbor Technologies) operated in single-pulse mode.The voltage magnitude is adjustable between ±1 and ±22 kV, and the pulse width was kept constant at 500 ns.A tungsten rod (2 mm diameter, Goodfellow) with a mechanically polished tip (∼10 µm curvature radius) was used as anode or cathode.This electrode was mounted in air, with its head directed towards the water surface (figure 1).The distance between the electrode tip and the water surface was fixed ∼20 ± 10 µm.Meanwhile, the grounded electrode was a stainless-steel plate (diameter = 15 mm, thickness = 6.5 mm) placed half in water half in air.The electrical conductivity of the water (60 ml of volume) contained in a Teflon cell was adjusted between ∼5 (distilled water) and 100 µS cm −1 by adding KCl salt.To keep the discharge in streamer mode and avoid spark transition, an inter-electrode distance was fixed to ∼3 cm (relatively large distance).
The electrical characteristics (voltage and current) of the generated discharge were measured using a high-voltage probe (P6015A, Tektronix) and a current monitor (6585, Pearson), respectively.The voltage-and current-waveforms were visualized and recorded using an oscilloscope (MSO54, 2 GHz, 6.25 GS s −1 ).The dynamics of discharge emission at the water surface was monitored by recording images of the dischargestruck surface (12 mm × 12 mm) using a vertically mounted ICCD camera (PIMAX-4, Princeton Instruments).Depending on the investigated phenomenon, images were recorded at 10 ns (gain is 10) or 1.5 µs (gain is 1000) ICCD integration time.The 1.5 µs-integrated images presented below are plotted using the same colormap, which is different from the one corresponding to the 10-ns-integrated images, for both voltage polarities.A delay generator (Quantum Composers Plus 9518 Pulse Generator) was used to ensure synchronization between the ICCD camera and the voltage pulse.

Negative polarity discharge
The electrical characteristics of discharges generated above distilled water (5 µS cm −1 ) at the applied voltage (V a ) values of −13, −16, −20, and −22 kV are shown in figure 2. Although the voltage waveforms (figure 2(a)) show no significant drop, regardless of the V a value, a decrease of a few hundred volts is detected at the breakdown moment.As for the current waveforms, they exhibit peaks corresponding to the displacement current (due to temporal variation of the voltage) at t < 25 ns (figure 2(b)).Moreover, negative and positive current oscillations are observed at t < 100 ns and t > 100 ns, respectively, which indicates that secondary discharges are initiated, as evidenced by image analysis (below).Overall, the absence of a voltage drop and the spiky current profiles confirm that the discharge is run in streamer mode.
The 1.5 µs-integrated images presented in figure 2(c) demonstrate that a single discharge generated at −13 kV produces intense, homogeneous, diffuse-like emission near the cathode pin.When the applied voltage is increased (in absolute value) to −16 kV, the discharge emission zone becomes larger, and dark lines appear in the homogeneous zone (three lines can be identified).As explained in section 4, these lines are related to the development of instabilities in the ionization front.The emission zone further expands when the voltage is increased (in absolute value) to −20 kV, and a filament appears along with the dark lines (only one can be identified in the figure 2(c)).Finally, at −22 kV, the emission zone becomes even larger, and two strong filaments with wide roots and tight heads are observed.Small filaments propagate from each one of these filaments, in perpendicular direction, are visible in the image.
Figure 3 presents the voltage and current waveforms of discharges generated at −22 kV above aqueous surfaces with variable electrical conductivity (5-100 µS cm −1 ).Based on the voltage waveforms (figure 3(a)), the discharges do not exhibit a drop in voltage; however, they present a plateau whose value decreases progressively (by few of kilovolts) with increasing water conductivity.This is probably due to the losses induced by ion displacement in conductive solutions.The current waveforms (figure 3(b)), on the other hand, present the displacement component, as well as several oscillating peaks (magnitude of several amperes).The value of the DC component in the current waveform increases from 0 to ∼1 A as the electrical conductivity is raised from 5 to 100 µS cm −1 .Considering that the measured waveform provides information on the displacement current as well as the conduction current, it provides important information regarding the instantaneous discharge dynamics that can be coupled to the imaging diagnostics (shown below).Such electrical data merit further investigation, e.g. by equivalent electrical circuit approach, to determine the temporal change of plasma impedance.Such analysis is beyond the scope of this study.As shown in figure 3(c), the morphology of the discharge emission changes significantly upon changing the conductivity of the solution.Indeed, the filaments observed at 5 µS cm −1 become thinner and longer when the electrical conductivity is increased, and the small filaments perpendicular to the main ones disappear.At 50 and 100 µS cm −1 , the number of filaments increases, and their propagation length decreases.
To further understand the propagation dynamics of the discharge, images were recorded at 10 ns integration time, for different electrical conductivity conditions.Figure 4 displays images of the emission produced on the surface of 5 µS cm −1 water.It must be noted that these images correspond different discharges that may be ignited with a temporal jitter of ±10 ns.The acquired images are correlated with different times based on the electrical characteristics and camera triggering signal.Based on these images, the discharge is ignited (10 ns-image) near the cathode pin, and with time, it expands (20 ns-image) towards the ground at the water surface.At 20 ns, dark zones are identified in the emission region, and at 30 ns, a half-disc of homogeneous emission with a hot spot at the cathode pin is clearly visible.The disc transforms into a ring that may be correlated with the ionization front at 40 ns.The dark-zonedecorated ring propagates away from the pin, and its thickness varies depending on the position.For instance, the zone located directly in front of the cathode pin is ∼2 mm thick, whereas those located on the sides are ∼1 mm thick.The ionization front continues to propagate away from the cathode pin; however, its intensity and thickness decrease with time, up to 70 ns.Although no important emission is detected between 70 and 290 ns, a low-intensity filament is observed at around 290 ns (a moment in the voltage plateau), and it is connected to the cathode tip.Interestingly, the filament's head is diffuse-like, which is very similar to the morphology of the negative streamers observed in air at long gap distances [18].The filament gains in length at 310 ns, but its head remains diffuse-like.At longer times, even beyond the voltage falling period (730-780 ns), the filament's head disappears, which signifies that ionization is terminated at the front; however, its length remains almost unchanged.Although the images at 290-780 ns show oscillations of the filament in horizontal and vatical directions, it is worth noting that every image corresponds to a different discharge, and the observed movement is linked to the randomly selected images, i.e. not physical movement.In fact, other images can be selected wherein such an oscillation is suppressed.Finally, at 820 and 830 ns, the filament becomes shorter and more intense, then the emission disappears.
Figure 5 shows the 10 ns-integrated discharge emission observed on the surface of 25 µS cm −1 water.At 10 ns, the discharge ignites at the cathode pin, then a strong emission  with half disc shape appears at 20 ns.A larger disk with a thick, dark-zone-decorated ring is observed at 30 ns, and the ring continues to propagate, albeit with reduced thickness at 40 and 50 ns.At 60 and 70 ns, the ring seems to be decomposed into single dots (i.e.plasma dots) similar to those produced by symmetrical positive discharges ignited from an anode pin mounted perpendicularly above a water surface [10].Note that when the cathode is perpendicular to the water surface (i.e.symmetrical negative discharge), only a homogeneous circular ring is observed [16].At 80, 90, and 100 ns, the emission morphology remains the same; however, the emission intensity decreases significantly.At 120-140 ns, short filaments reignite at the cathode pin, and they propagate on the water surface via two modes.These two modes can be explained by the temporal jitter.Indeed, since the discharge can ignite at ±10 ns, the discharge current may vary by a few amperes, resulting in different discharge evolution.The first mode is characterized by the formation of few filaments that are relatively long and intense with a diffuse head.Meanwhile, the second mode implicates shorter filaments whose diffuse heads appear later.Compared to the mode 1, the diffuse heads of mode 2 are smaller and less intense.Between ∼420 and 480 ns, the two modes behave similarly, as only one filament with low intensity is identified.Finally, short and intense filaments reignite at the cathode pin at 590 ns.With time, the length of these filaments increases, but their intensity decreases until the emission is extinguished at about 810 ns.
The discharge emission observed on the surface of 50 µS cm −1 water (figure 6) is similar to that detected at lower electrical conductivity (25 µS cm −1 ), with some minor differences.For instance, the transition from a ring to filaments is observed earlier at 50 (90 ns) than at 25 µS cm −1 (140 ns).Moreover, a larger number of filaments in mode 2 is detected at the higher electrical conductivity condition.Although similar filament propagation profiles are detected between 420 and 430 ns, the emission produced at 50 µS cm −1 is more intense than that generated at 25 µS cm −1 .In the final phase, i.e. reignition of short filaments at the cathode pin, similar emission behaviors are detected at both conductivity conditions, and extinction occurs at ∼840 ns in both cases.No significant changes are observed upon further increasing the water conductivity to 100 µS cm −1 (figure 7).However, the intensity of the emission observed during the first phase of propagation (10-50 ns) decreases at higher conductivity (e.g. 100 vs. 50 µS cm −1 ).Nevertheless, plasma dots may still be observed in the ionization front at 50 ns.The two modes appear at ∼130 ns, and their propagation is very similar to that observed under lower conductivity conditions.Finally, extinction is detected beyond ∼830 ns at the 100 µS cm −1 condition.

Discharge in positive polarity
This section presents the results obtained under positive polarity conditions.Notably, negative polarity discharges could not be ignited above 100 µS cm −1 , and the probability of successful discharge decreased with increasing water conductivity between 1 and 50 µS cm −1 .Indeed, the probability was found to be 98, 52, and 16% at 5, 25, and 50 µS cm −1 , respectively.Figures 8(a) and (b) present the voltage and current waveforms of typical occurred discharges, respectively.Although statistical variations are observed due to stochastic discharge behavior (i.e.discharges may occur at different moments in time during the pulse, even when the same conditions were applied), it is clear that the voltage-current waveforms of occurred positive polarity discharges do not significantly depend on the water conductivity conditions.For instance, the breakdown moment is characterized by a ∼1-2 kV voltage drop and a ∼5-8 A current peak, regardless of electrical conductivity.
Figure 8(c) shows 1.5 µs-integrated images of the discharge emission observed on the surface of 5, 25, and 50 µS cm −1 water.Based on these images, the electrical conductivity of water has no significant effect on the discharge emission morphology, within the range of conditions investigated herein.In general, a strong zone of emission is observed near the anode pin, followed by less intense, long, and organized filaments that propagate beyond the field-of-view of the camera.
The temporal evolution of the discharge emission observed on the surface of 5, 25, and 50 µS cm −1 water is presented in figure 9.At 5 µS cm −1 (figure 9(a)), a homogeneous 2 mmlong emission with a high intensity zone near the anode pin is detected during the first 10 ns (first image in figure 9(a)).The emission becomes much longer (∼8 mm) during the next 10 ns, and some pattern starts to develop in the discharge head zone.At 22 ns (third image), a pattern of filaments can be clearly discerned.These highly organized filaments separate and detach from the anode pin at 24 ns, but a hot spot and an intense short filament remain visible near the anode.With time, the individual filaments, as well as the one reignited at the anode pin propagate further in the gap, and their intensity gradually decreases.At 90 ns, the lowest intensity is detected; however, reignition is observed at the anode pin just a few nanoseconds later.The reignited emission is filamentary, and it is extinguished within less than 50 ns.As in the case of negative polarity discharges, the temporal evolution of the emission patterns obtained on 25 and 50 µS cm −1 water (figures 9(b) and (c), respectively) is very similar to that of the 5 µS cm −1 emission.However, the transitions from one phase to the other occur later in time when the electrical conductivity is higher.For instance, at 5 µS cm −1 , the organized filaments extend beyond the camera field of view at 29 ns, compared to 36 and 41 ns at 25 and 50 µS cm −1 , respectively.Similarly, the extinction time is 170 ns at 5 µS cm −1 , compared to 244 and 262 ns at 25 and 50 µS cm −1 , respectively.This indicates that the discharge propagates faster when the electrical conductivity is low.

Discussion
Along with the results obtained for positive and negative polarity discharges in symmetrical configuration (i.e. when the pin is perpendicular to the water surface) [7,16], the findings reported herein provide deep insight into the emission morphology and propagation of discharges generated in air in contact with water.In this section, we compare the four discharge conditions (positive and negative discharge in symmetric and asymmetric configurations) that lead to different discharge behaviors and report the conditions at which plasma dots are formed.Before delving into the details, it must be noted that the studies reporting the influence of similar parameters on nanosecond discharges with liquid are scarce.The available studies on nanosecond surface dielectric barrier discharge show that positive discharges propagate faster than the negative ones [19].To the best of our knowledge, the influence of electrode configuration on the discharge at the dielectric surface has not yet been investigated; however, Babaeva et al [20] have simulated the influence of the angle between a helium plasma jet and dielectric surface, and their results demonstrate a strong dependence of the plasma spot size on the angle, dielectric permittivity, and electrical conductivity.
In the context of this study, the negative discharges generated in symmetrical configuration exhibit no pattern, and the disc-like emission is homogeneously distributed around the cathode pin.In this case, the propagation velocity of the ionization front is in the order of tens of km s −1 , as shown in figure 10(a).Comparatively, the positive polarity symmetrical discharges develop a pattern of plasma dots just a few nanoseconds after ignition.These dots are evenly distributed in a circle centered at the anode pin, and their propagation velocity is in the order of a few hundred km s −1 (figure 10(b)).Based on the available results, the formation of plasma dots may be attributed to the development of instabilities in the ionization front upon the ignition of radial avalanches.Such instabilities distort the ring and induce its decomposition into dots.This mechanism of plasma dot formation has been highlighted in a simulation study conducted by Xiong and Kushner [21].At the interface, the discontinuity of physical properties, such as dielectric permittivity, strongly influence the E-field distribution (magnitude and direction), and thus, the interface acts as a guide for the propagation of the discharge.In our study, an asymmetric E-field distribution is obtained in asymmetrical discharge configuration (i.e. when the electrode is positioned in parallel direction relative to the water surface).When the voltage polarity is negative, the asymmetrical discharge forms an ionization front that propagates on water surface, and some instabilities resembling those observed under positive polarity appear.Figure 10(c) shows selected images corresponding to the moment when plasma dots are clearly observed at different conductivities.At this stage, it becomes clear that the electrode configuration has a great influence on the formation of plasma dots as well as on their propagation velocity.This influence is mainly attributed to the Efield (magnitude and direction) at water surface, which in turn is induced by the applied voltage and charge accumulation.Interestingly, the development of instabilities in the ionization front is enhanced when the electrical conductivity of water is increased from 5 to 25 µS cm −1 , and the plasma dots are more clearly identified, particularly in the region facing the cathode; see images at 60 ns for 5 (figure 4), 25 (figure 5), and 50 µS cm −1 (figure 6).The temporal evolution of the discharge emission observed at 50 µS cm −1 is similar to that recorded at 25 µS cm −1 ; however, the emission intensity is higher, and the propagation speed seems to be lower.At 100 µS cm −1 , the plasma dots become less resolved, and the propagation speed decreases further.Notably, the plasma dots do not appear at higher conductivity.Compared to the positive polarity symmetrical discharges, the plasma dots of the asymmetrical discharges are more clearly resolved, and they propagate much faster.However, the propagation velocity is non-uniform, with higher velocities detected in the region facing the anode pin.
The following discussion addresses a series of questions regarding variations between the four sets of conditions summarized in figure 10.
Figures 10(b) and (d) present 10 ns-integrated images of the emission patterns corresponding to positive polarity discharges in symmetrical (taken from [10]) and asymmetrical (obtained in this study) configuration, respectively.In symmetrical configuration, patterns of highly organized plasma dots appear at the very beginning, and they propagate at the speed of ∼200 km s −1 .Their propagation velocity in asymmetrical configuration is almost twice.Moreover, the electrical characteristics of the symmetrical and asymmetrical discharges are similar; data for symmetrical configuration can be found in [7].Therefore, it may be assumed that they have similar injected charges.Considering that in symmetrical configuration the charges are deposited initially over a greater area compared to the asymmetrical configuration (full circle/disc vs. half circle/disc ionization front), the space charge field produced at the discharge head in the latter condition is almost twice as large, resulting in a higher propagation speed.

4.2.
In asymmetric positive polarity configuration, why is the discharge dynamics independent of electrical conductivity in the interval of 5-50 µS cm −1 , and why do discharges fail at higher conductivity?
In the range of 5-50 µS cm −1 , the dynamics of a positive polarity discharge is independent of solution conductivity, and no discharge occurs at higher conductivity.To explain these results, we must recall the so-called polarization time or Maxwell time (τ) [22], defined as τ = ε 0 ε r /σ (ε r ∼80 is the relative dielectric permittivity of water and ε 0 ∼8.85 × 10 −12 F m −1 is the dielectric permittivity of vacuum).τ decreases with increasing conductivity (σ), which means that the ions require less time to reorganize in response to the applied field.At 5, 25, 50, and 100 µS cm −1 , τ is ∼1400, 280 140, and 70 ns, respectively.Considering that the polarization time (∼70 ns) at 100 µS cm −1 is shorter than the rising period of the high voltage (∼90 ns), no breakdown occurs at this condition, and the field induces ion displacement in the solution.At lower conductivity conditions, the discharge propagates rapidly at the water surface before ion reorganization, and thus, it does not significantly depend on σ.

In asymmetric negative polarity configuration, why does the ionization front become instable and plasma dots appear? And why are the dots observed only in a particular region in the ionization front?
In symmetrical configuration, the discharge propagates first in the air gap, then at the water surface.The surface propagation is mainly initiated by accumulated electrons that diffuse in outward direction and induce ionization.Considering the high mobility of electrons, the electron-induced ionization process produces a homogeneous circular ionization front.In asymmetrical configuration, the discharge ignites directly at the water surface, where the E-field distribution is inhomogeneous.This induces space-dependent variations in the ionization rate, with the highest rate detected in the region directly facing the pin.In general, streamer propagation is driven by the applied E-field and space charge field at the streamer head, both of which are expected to be high in the absence of a voltage drop.In asymmetrical configuration, charges are deposited in an asymmetric half-circle/half-disc, resulting in the development of a non-uniform space charge field.Thus, inhomogeneous discharge propagation in asymmetrical configuration may be attributed to the movement of charges under the action of the non-uniform field.As for the pattern, it generally appears due to instabilities that associated with the inhomogeneous radial gradient of the E-field at the ionization front, as detailed below.The inhomogeneous E-field gradient significantly influences the rate of ionization, and thus, it affects the space charge field distribution, which in turn induces a gradient in the propagation speed.Considering that discharge propagation in the zone facing the pin is fastest, plasma dots are produced in this region, and the front is rather homogeneous elsewhere.

Why does the emission pattern depend on electrical conductivity in negative polarity? And why do the dots disappear at high conductivity?
The water electrical conductivity influences the emission pattern observed in negative polarity.In fact, the pattern becomes more visible at 25 and 50 µS cm −1 , but less resolved at 100 µS cm −1 .Such variation may also be attributed to Efield modification upon changing the conductivity of water.Indeed, the presence of free ions leads to solution reorganization when an E-field is applied.As mentioned earlier, the characteristic time τ deceases with increasing σ, and at 50 and 100 µS cm −1 , τ is comparable to the period when instabilities are observed in the ionization front.This indicates that the free ions in solution can interact with the charges present at the ionization front, thereby decreasing the space charge field and reducing the instability, as demonstrated by the experimental results.At 25 µS cm −1 , τ is ∼280 ns, which means that only partial reorganization occurs before the pattern formation.The appearance of a more resolved pattern at this condition may be attributed to a change in the dynamic of water molecule polarization.

What information can be derived from the homogeneous and inhomogeneous ionization fronts?
To provide an estimate of the propagation speed, 10 nsintegrated images showing well-resolved structuration were selected, and the contour of the ionization front in these images was traced.Figures 11(a)-(c) show the ionization front contours and emission zone lengths corresponding to an asymmetric negative discharge, a symmetric positive discharge, and an asymmetric positive discharge, respectively.Using the measured length values, the speed of propagation during the 10 ns time interval was determined.In the well-resolved image of a negative asymmetric discharge (50 µS cm −1 ) at 50 ns (figure 11(a)), two zones are identified: a structured zone and a homogeneous one.The longest propagation lengths in the former zone is ∼1 mm, whereas that in the latter zone is ∼0.8 mm.Values between these two limits correspond to a transition from one zone to the other.In contrast, the image of the symmetrical positive discharge (figure 11(b)) shows plasma dots along the ionization front, with a propagation length of ∼1.2 mm.Plasma dots are also observed along the ionization front of the asymmetric positive discharge (figure 11(c)); however, the propagation length varies depending on the position.The shortest length is ∼1 mm, which is greater than the threshold length needed to observe plasma dots (>0.8 mm).Using this value (0.8 mm), we determined the threshold E-field and charge number based on a simple calculation applied in previous studies [7,11].Assuming that the plasma dot mobility (µ) in a symmetrical positive discharge remains constant at 1.5 × 10 −4 m 2 Vs −1 [7], and considering that the speed (v) of a dot observed at the threshold length of 0.8 mm (during 10 ns integration) is 8 × 10 4 m s −1 , the threshold E-field given by E = v/µ is ∼5 × 10 8 V m −1 .Beyond this value, we assume that instabilities are triggered in the ionization front.Using Gauss's law, the threshold charge associated with a typical plasma dot (100 µm radius [7]) is estimated to be ∼0.55 nC, which corresponds to a threshold charge number of ∼3.4 × 10 9 .Compared to the plasma dots propagating in a symmetrical positive discharge [7], the threshold charge and E-field values correspond to the beginning of plasma dot extinction, i.e. the moment when the space charge field becomes insufficient to induce further propagation.This further supports the threshold approach to trig instabilities in the ionization front propagating on water surface.

Conclusion
In this study, we investigated the morphology and propagation dynamics of a streamer discharge generated over a water surface in asymmetrical configuration.The effects of water electrical conductivity and voltage polarity were also analyzed.The obtained results demonstrate that unlike the symmetrical configuration, the initial E-field distribution in asymmetrical configuration is not homogeneous, which impacts the emission pattern produced.Interestingly, plasma dot formation is observed under negative polarity due to the nonhomogeneity of the E-field, which induces non-homogeneous electrons propagation on the water surface.Compared to the symmetrical positive discharge, the asymmetrical counterpart exhibits increased discharge propagation velocity on the water surface, as the ICCD images showed.Changes in water conductivity induce charge reorganization in the liquid after Efield application.Such reorganization influences the charge density and E-field distribution at water surface, which in turn affects the pattern produced by negative polarity asymmetrical discharges.Furthermore, the non-homogeneity of the E-field at the surface leads to the formation of a pattern in front of the cathode (where the field is high), with homogeneous emission observed elsewhere (where the field is low).This behavior suggests a threshold phenomenon.Analysis of the speed along the pattern and homogeneous region reveals that the threshold E-field is ∼5 × 10 8 V m −1 ; this value is similar to the value reported for symmetrical configuration discharges when the dots disappeared.Beyond this threshold, instabilities are triggered in the ionization front, leading to the formation of plasma dots.The findings reported in this study provide new insights into the dynamics of nanosecond discharges on water surfaces, and they can be used to develop/optimize various applications in liquid processing.

Figure 1 .
Figure 1.Scheme of the experimental setup used to produce discharges at the surface of water with different electrical conductivities.

Figure 2 .
Figure 2. (a) Voltage and (b) current waveforms of discharges generated in ambient air above the surface of distilled water (5 µS cm −1 ) at −13 > Va > −22 kV; the inset in (b) shows a zoom of the current waveform when the discharge occurred.(c) 1.5 µs-integrated ICCD images of the discharge emission at different conditions.

Figure 3 .
Figure 3. (a) Voltage and (b) current waveforms of discharges generated in ambient air above the surfaces of aqueous solutions with different electrical conductivities (5, 25, 50, and 100 µS cm −1 ), at the applied voltage of −22 kV; the inset in (b) shows a zoom of the current waveform when the discharge occurred.(c) 1.5 µs-integrated ICCD images of the discharge emission at different conditions.

Figure 4 .
Figure 4. 10 ns-integrated ICCD images showing the temporal evolution of discharge emission at the surface of distilled water (5 µS cm −1 ) at an applied voltage of −22 kV.

Figure 5 .
Figure 5. 10 ns-integrated ICCD images showing the temporal evolution of discharge emission at the surface of water + KCl (25 µS cm −1 ) at an applied voltage of −22 kV.

Figure 6 .
Figure 6. 10 ns-integrated ICCD images showing the temporal evolution of discharge emission at the surface of water + KCl (50 µS cm −1 ) at an applied voltage of −22 kV.

Figure 7 .
Figure 7. 10 ns-integrated ICCD images showing the temporal evolution of discharge emission at the surface of water + KCl (100 µS cm −1 ) at an applied voltage of −22 kV.

Figure 8 .
Figure 8.(a) Voltage and (b) current waveforms of discharges ignited above the surface of 5, 25, and 50 µS cm −1 water at an applied voltage of +22 kV.(c) 1.5 µs-integrated ICCD images of the discharge emission at different conditions.

Figure 9 .
Figure 9. 10 ns-integrated ICCD images showing the temporal evolution of discharge emission at the surface of (a) 5, (b) 25, and (c) 50 µS cm −1 water at an applied voltage of +22 kV.

Figure 10 .
Figure 10. 10 ns-integrated ICCD images showing the propagation of the discharge emission on the surface of water under different conditions.(a) Negative (−20 kV) and (b) positive (+14 kV) polarity discharges in symmetrical configuration at σ = 5 µS cm −1 .(a) Reproduced from [16].© The Author(s).Published by IOP Publishing Ltd.CC BY 4.0.(b) Reproduced from [10].© IOP Publishing Ltd.All rights reserved.(c) Negative polarity discharges in asymmetrical configuration at various conductivities.The selected images correspond to the moment when plasma dots are clearly observed.(d) Positive polarity discharges in asymmetrical configuration at σ = 25 µS cm −1 .

Figure 11 .
Figure 11.Representation of the emission contours of (a) asymmetric negative discharge, (b) symmetric positive discharge, and (c) asymmetric positive discharge when structuration is maximum.(d) The 10 ns-integrated images used to trace the contours.