High voltage nanosecond pulse driven electric discharges in de-ionized water with an argon bubble suspended between two electrodes were experimentally investigated. Two electrode configurations were used to temporally resolve the time scales of the discharge from the applied voltage rise time (7 ns), through the end of the first pulse (30 ns), and longer (>50 ns). We found that, in positive and negative applied voltage polarities, discharge initiates in the water at the tip of the anode. The discharge in the water rapidly extends ( m/s) to the apex of the bubble and light emitted from inside the bubble begins to form. The steep rate of rise of the applied voltage ( kV/ns) and the short time for the development of discharge in the water suggest that cavitation is a likely mechanism for discharge initiation and propagation in water. In addition, the short duration of the applied voltage pulse results in only a partial Townsend discharge inside the bubble.
Gas bubbles in water and other liquid dielectrics have been the topic of extensive theoretical and experimental research due to their ubiquitous presence in water disinfection,1,2 plasma machining,3,4 failing dielectrics,5,6 testing of composition of liquids,7,8 or the presence of impurities.9–11 Gas bubbles may include intentionally injected gases used for water treatment, microbubbles that coalesce, and bubbles that expand thermally under long voltage pulses. The discharge in these complex systems can initiate at the electrodes, in bubbles attached to the electrodes, or bubbles floating in the liquid depending on the rate of rise and duration of the applied voltage.12 Comparing the time scales of the plasma formation with the time scales bound by the applied voltage provides insight into the initiation and time sequence of the electric discharge processes. The discussion of discharge mechanisms below is presented according to a decreasing time scale from milliseconds, microseconds, hundreds of nanoseconds, down to nanoseconds.
Discharges in bubbles submerged in water are generally discharges at atmospheric pressure in the supplied gas (e.g., argon) with saturated water vapor. In a standard Townsend mechanism, electron avalanches form if a seed electron can gain enough energy in the electric field inside a bubble to result in an ionization event. The time for these processes is comprised of the delay time for the appearance of the seed electron and the formation of the initial and secondary avalanches. The initial delay time could range from microseconds to milliseconds depending on the mechanism producing the seed electron. The avalanche formation time is on the order of 10 ns, but the process can continue only if the formation of positive ions is not screened by the negative ions, and hence, the time is limited by the speed of ion drift in the applied electric field. If (1) the field (and thus the first ionization coefficient ) is high enough and (2) the bubble is large enough (typically, macrobubbles with diameters of mm) such that (Meek criterion), then the discharge undergoes an avalanche to streamer transition. The streamer formation is limited by the negative ion drift velocity, , and hence requires a time, , of 100 ns. The total time of a partial breakdown in mm-sized bubbles is generally on microsecond time scales but may extend to the millisecond range due to the delay in obtaining a seed electron and in cases where the field is not strong enough for the avalanche-to-streamer-transition. These principles have been supported by extensive experimental work and modeling, as described below.
Many of the studies of electrical discharges in artificially introduced mm-sized bubbles have involved bubbles attached to an electrode or spanning the gap between the electrodes.13–15 For example, 1 s long voltage pulses with >100 ns rise times, applied to mm and sub-mm size bubbles attached to electrodes, with imaging on ns to hundreds of s time scales, have revealed discharges propagating along the surface of the bubbles; and on long time scales they observed resulting ripple surface oscillations and breathing volume oscillations of the bubbles.13,16,17
Kinetic modeling and experiments have shown that it depends on the ratio of the dielectric constants of the gas and liquid whether the streamer propagates along the gas–liquid interface or directly through the bubble.18,19 For gas bubbles in de-ionized water, the high dielectric constant ratio of 80 corresponds to discharge propagation along the surface of the bubble due to a high tangential component of the electric field along the bubble interface boundary.18
Observations by Sommers and Foster of mm-sized bubbles trapped in an acoustic standing-wave, not in contact with powered electrodes and subjected to applied voltage pulses with a rise time 100 ns, have demonstrated streamer development in water from a positive sharp electrode to the bubble, then followed by multiple streamers inside the bubble.20 The subsequent deformation and physical breakup of the bubbles was followed through on a 10 s time scale. Separately, Wang et al. investigated discharges in mm-sized bubbles under a maximum applied voltage pulses of kV and a rate of rise of kV/ms, as well as a maximum of kV and a rate of rise of kV/ns. The applied voltage pulses and bubble size are similar to our present experiment; however, the images presented by Wang et al. have exposure times of tens of microseconds, hence, the images integrate the entire history of the discharge and a time sequence is difficult to determine.21
In addition to the intentional introduction of macrobubbles, microbubbles on the scale of tens of m can be observed. Microbubbles can be both intentionally introduced or naturally present in liquids. Naturally present microbubbles occur in liquids that have not been thoroughly degassed or after previous discharge cycles. Microbubbles have been observed to form throughout the liquid but are more likely to be found on the electrodes, especially on surface irregularities. The mechanism and the corresponding time delays for the discharge in water aided by microbubbles were first introduced by Korobeinikov.22
Microbubbles are filled with gases at atmospheric pressure; the discharge follows a similar mechanism as that for macroscopic bubbles, except for the important effect of the size of the bubble on achieving the breakdown difference in the potential between the ends of the bubble. Due to the small size of microbubbles, this is only achievable in the vicinity of the electrodes. Hence, the discharge is usually observed only in bubbles directly attached to the electrodes. Elongation of the bubbles, resulting in additional field enhancement, occurs prior to the initiation of the discharge. The time scale for the development of a discharge in microbubbles is on the order of – ns, a time comprised of the production of a seed electron, bubble elongation, and streamer development in the bubble. It should be noted that the production of a seed electron may take longer than the time scale mentioned above depending on the mechanism of origin, which remains the topic of continued investigations.
Microbubbles have been implicated in promoting electric discharge in liquid22–27 by reducing the required breakdown field for discharges in liquids. In particular, they promote the initiation of the breakdown at the electrodes for discharges with applied pulse durations in the microsecond to sub-microsecond ranges. Bubbles with a radius of between 20 and 30 m in fields up to 30 MV/m have shown primary streamers on a time scale of 100 ns, accompanied by deformation within 100–500 ns. Streamers entering water have been observed to develop in 1000 ns.23 Introduction of <100 m bubbles was found to reduce the minimum breakdown voltage between two electrodes submerged in water for 5 s applied voltage pulses,26 similar to the earlier experiments and calculations by Korobeinikov23 and Panov.25 Few works have investigated the source of seed electrons needed for streamer development in bubbles. Babaeva et al.27 have shown that streamers will not form in bubbles that are too small unless there is sufficient initial electron density, e.g., through preexisting charges if the observed discharges are not independent. Furthermore, it had been found that discharges in microbubbles can propagate through a stream of bubbles.
At nanosecond applied pulses, the processes mentioned above do not have enough time to develop. A faster mechanism has been proposed by Shneider and Pekker for discharge initiation on short time scales in strong and strongly inhomogeneous electric fields. This mechanism is based on the formation of reduced pressure regions in a liquid, a phenomenon called cavitation. Due to pressure fluctuations, nanometer-size voids (nanovoids) appear and collapse in a liquid, but a steep voltage rate of rise in a strong and inhomogeneous electric field can produce a net negative electrostrictive pressure. This negative pressure allows cavities to grow so that electrons can gain enough energy to produce ionization events.28,29 These works have shown that for an applied voltage rate of rise of several kV/ns, electrode radii of 25 m, and electric fields of 200 MV/m, negative pressure of >30 MPa leads to the growth of nanovoids. Randomly appearing nanovoids grow to a size large enough to accelerate electrons to ionization energies in tenths of nanoseconds. This produces regions of enhanced electric field at the tip of the nanovoids. Electrons accelerate to ionization potential in the nanovoids and produce ionizations and excitations at the water boundary. The cavity can be filled with ionized and excited water molecules and fragments. The void, in turn, can serve as a sharp electrode to grow a new void. The total time to develop glowing regions starting with nanovoids can take 1 ns. Hence, in 10 ns, propagation of the discharge in water may be recorded.12 This mechanism has been supported by the experimental evidence for ns pulsed discharges in degassed water with electrode radii <50 m and a voltage rate of rise of 5 kV/ns.30
Recent experimental work by Šimek et al. has confirmed the previously reported results and shows that non-luminous structures develop 2–3 ns after the onset of the applied voltage pulse (50–150 kV, duration of 7 ns FWHM), followed almost instantaneously (100 ps) by luminous discharge events.31 Computational investigation of electron multiplication and avalanching in nanovoids has shown that electron avalanches may be created by the emission of secondary electrons caused by a bouncing-like motion of electrons along the cavity.32 In this case, the electron multiplication time scale was determined to be on the order of 1 ps or shorter, leading to a propagation velocity of the electron avalanche of about m/s. Tereshonok et al. present a theoretical and experimental investigation of cavitation and bubble discharge mechanisms. The theoretical description demonstrates the applicability of the cavitation model to the description of discharge initiation at sharp electrodes and steep voltage rate of rise. In addition, they have emphasized that the dependence of dielectric constant of the liquid on the applied electric fields is as important as the voltage rate of rise and water conductivity.33 The change in the dielectric constant with electric field increases the probability of cavitation development of the discharge. Most of the experimental investigations of the cavitation mechanism are concerned with prebreakdown processes in liquids, especially de-ionized water, subject to ns pulsed applied voltage.34
Discharges in 1 mm size argon, methane, carbon dioxide, and propane bubbles in distilled water in a pin-to-pin geometry under an applied voltage of 15 kV—with an initial pulse 20 ns long and followed by damped oscillations up to 1 s—were investigated by Hamdan and Cha.35 The experimental conditions of the above works are similar to those presented in this paper, but the time-integrated imaging of s gate-widths does not reveal the details of the processes happening at the initiation and development of the discharge. In our investigation, the applied voltage pulse and the time resolution of the imaging make it possible to combine 5–500 ns time scales.
This paper presents an experimental study that addresses discharge initiation and propagation in water with Ar macrobubbles subject to pulsed non-uniform electric fields. The combination of a maximum applied voltage rate of rise of 4 kV/ns and subsequent voltage oscillations, sharp electrodes, and a macrobubble positioned accurately between the electrodes during the discharge produces a situation where processes that occur on different time scales become tractable. Therefore, we present a phenomenological picture of each process: from the initiation of the discharge, through its propagation from the positive electrode to the bubble, through emission in the bubble, and effects of the electrode polarity. Our imaging and electrical data demonstrate the complex processes that occur during discharges in this multiphase medium at nanosecond to several hundred nanosecond time scales.
The order of the paper is as follows. We start by describing our experimental methodology addressing bubble geometry and timing methods. For the first time, we present an original method of bubble positioning with control of statistical information of the bubble shape, size, and position between the electrodes. A unique timing scheme is introduced that allows the application of the voltage pulses when a bubble is in the desired position between the electrodes. Finally, the experimental results and discussion section present our evidence for the discharge initiation for two electrode configurations by order of time scale.
II. EXPERIMENTAL METHOD
A. Experimental setup
The experimental setup was designed to reliably capture free-flowing bubbles between electrodes synchronously with an applied high-voltage (HV) ns-pulse. It consists of a rectangular quartz vessel filled with de-ionized water and two tungsten/copper alloy electrodes positioned horizontally. Argon gas passes through a horizontal capillary running along the bottom of the vessel parallel to the electrodes as shown in the image and illustration of Fig. 1. Two different electrode geometries are used for the experiments: (1) a sharp-to-sharp and (2) a sharp-to-flat configuration. Gas bubbles exit a vertical hollow needle affixed to the capillary resulting in bubbles with a diameter of mm (Fig. 2). The hollow needle is aligned so that the bubbles pass between the electrodes. The depth of the water and the gas flow are adjusted to achieve a desired speed and frequency of bubbles as they rise. The argon flow rate of 1 ml/min results in a bubble-detachment frequency of under our conditions. The direction of the bubble flow-path depends on bulk gas velocities in the bubble as addressed in detail in our previous work.36 The triggering system can operate at the bubble-detachment frequency (see Sec. II B); however, every HV pulse and image in this experiment is performed using manual single-shot triggering executed off of the subsequent bubble. Single shot triggering ensures that each discharge is an independent event that occurs under the same initial conditions.
Different regimes of bubble deformation are cataloged along the bubble’s travel-path after bubble detachment from the hollow needle. A region of stability immediately after the bubble detachment is utilized to achieve highly elliptical bubbles and to control bubble eccentricity, , where is the bubble major radius and is the bubble minor radius (Fig. 2). Moving the opening of the needle closer to the electrode gap, such that bubble travel distance decreases, results in decreasing bubble eccentricities. To measure bubble parameters a MATLAB script was written to fit each bubble to an ellipse and quantify its position, major and minor diameters, areas (pixel-counted and fitted), eccentricity, and angle with respect to the horizontal pixel arrays.36 The results of this analysis for several images are included in Table I. See supplementary material for images and values of the bubble statistic results in Supplementary Section A.37
|Source .||Uncertainty .|
|Optical measurements||(spatial resolution)|
|Caliper precision||10 μm|
|Imaged pixel width||4.4 μm (sharp-sharp)|
2.5 μm (sharp-flat)
|Bubble image statistics||bubble position|
σx = 10 μm σy = 3 μm
σa = 3 μm σb = 3 μm
|Electrical measurements||(temporal resolution)|
|SRS DG645 Rubidium timebase||1 ns|
|Pearson current probe||5 ns|
|Textronix HV probe||4.67 ns|
|Andor iStar ICCD||0.035 ns (jitter)|
|Gate signal||2.7 ns (statistical)|
|MegaImpulse pulser||1 ns|
|Source .||Uncertainty .|
|Optical measurements||(spatial resolution)|
|Caliper precision||10 μm|
|Imaged pixel width||4.4 μm (sharp-sharp)|
2.5 μm (sharp-flat)
|Bubble image statistics||bubble position|
σx = 10 μm σy = 3 μm
σa = 3 μm σb = 3 μm
|Electrical measurements||(temporal resolution)|
|SRS DG645 Rubidium timebase||1 ns|
|Pearson current probe||5 ns|
|Textronix HV probe||4.67 ns|
|Andor iStar ICCD||0.035 ns (jitter)|
|Gate signal||2.7 ns (statistical)|
|MegaImpulse pulser||1 ns|
B. Optical triggering
A significant difficulty in ns discharge experiments, with detached gas bubbles in a liquid, is triggering the applied voltage pulse at a specific bubble position and triggering the diagnostics at the desired time during the discharge. We overcome this difficulty by an original optical triggering system based on the free-flowing vertical motion of a stream of bubbles. Our triggering system aligns the electrical and optical parts of the experiment temporally and spatially. Figure 1 shows a photo of the system from the perspective of the ICCD and a cross-sectional diagram of the triggering system. A collimated LED [(a) Thorlabs M740F2 740 nm] is aligned such that its beam passes below the electrode gap and terminates at a photodetector [(b) Thorlabs DET36A2 Si Detector] on the other side of the quartz water vessel. The attenuated signal produced by a bubble obfuscating the path of light is transmitted to an oscilloscope [(c) Tektronix MDO3104] which is set to trigger at the falling edge of the incoming signal. The oscilloscope monitors both the bubble frequency and stability. It is then used as the external trigger for a delay generator [(d) SRS DG645: Rubidium timebase] that calibrates timing for the remaining elements.
The vertical ( axis) bubble position between the electrodes is controlled by delaying the outgoing signal from the delay generator. Three separate delays are routed to a HV nanosecond pulse generator [(e) Megaimpulse NPG-18/100k], LED backlight [(f) Thorlabs M530F2 530 nm], and ICCD [(g) Andor iStar 734]. Pixel-to-m conversions were calibrated by imaging a thin wire with a diameter of 450 m (Table I) between the tips of the electrodes.
C. Electrical measurements
A HV generator (pulser) with external triggering capabilities applies a ns voltage pulse to a submerged sharp electrode while the other electrode (sharp or flat) is grounded. An equivalent circuit of the power source, the bubble/electrode gap, and measurement devices is shown in Fig. 3. The electrical characteristics of the experiment were measured with a HV probe (Tektronix P6015A (75 MHz)) and inductive current monitor (Pearson Model 6600) measured with a 5 GS/s oscilloscope (Rigol DS6104, 1 GHz, 5 GS/s).
Further time calibration between the HV probe and current monitored due to circuit phase delays are carried out by simulating the equivalent circuit for all experiment components (Fig. 3). The large distance (2 mm) and small area () of the electrode gap leads to the concern that reactive elements of the measuring devices in the circuit may have a significant effect on the electric measurements of the system. In particular, if the reactance of the current monitor, , is similar to or larger than the magnitude of the electrode reactance, , the current recorded from the monitor could be delayed on the ns time scale. An equivalent circuit model is simulated in LTspice to determine temporal delay introduced by measuring devices acting as part of the total circuit. To accurately determine the capacitance of the bubble/electrode circuit element, a 3D model of each geometry in Fig. 2 was modeled in ANSYS Maxwell field solver. An overall additional delay of 1.5 ns is added to the cable delay based on the results of the LTspice circuit model with the measurement devices included in the equivalent circuit and the electrode/bubble gap capacitance determined from the ANSYS model (2.0 pF for the sharp-to-sharp configuration and 3.1 pF for the sharp-to-flat configuration). The HV probe parameters, , pF, are from the manufacture’s description. See supplementary material37 for electric field models for electrode configurations. Current monitor inductance, H, is determined by sweeping through inductance values (H) in the LTspice model and fitting simulated current to measured current. The core-loss resistance of the current monitor, , is modeled in parallel with the coupled inductor in the circuit.38 Power spectrum analysis of the measured pulser applied voltage and reflections results in a dominant reflection frequency of MHz. Under this condition, the circuit remains significantly capacitive (; ). See supplementary material for simulated currents of varying inductances in Fig. S7.37
The time-corrected oscilloscope traces used for aligning optical results to electrical results are exemplified by Fig. 4. The applied voltage [Fig. 4(a)] sharply rises to kV from 5%–95% peak value over ns ( kV/ns). The characteristic shape of the HV pulse consists of two rise time sections separated by a 1 ns plateau at 11 kV. The voltage rate of rise for each steep rise is kV/ns. The peak is followed by a slower fall of ns from 95%–5% peak value. The width of the pulse is measured at full-width-half-max and is averaged to be ns. The first maximum occurs ns after the initial steep voltage rise time, which is measured to begin at peak voltage. The beginning of this voltage rise time is defined as the temporal origin for all ICCD gate references hereafter. The bubble position and size change the reactance of the system and can influence the reflections of the pulse. See supplementary material for impedance estimations and power spectrum of the voltage waveforms in Supplementary Section B.37
The reflected oscillations decay with a characteristic decay time of ns. The raw current traces [outlined in green, Fig. 4(b)] are processed with a high-pass filter (HPF) attenuating frequencies below 100 MHz (orange box). This is done to clearly distinguish the high-frequency current oscillations associated with the electromagnetic interference accompanying large discharges.39 The HPF box is placed at the beginning and end of the current trace in Fig. 4 to demonstrate the difference between these current traces. In this paper, the current trace is used for timing purposes and will only be presented with the applied HPF with arbitrary units. Figure 4(c) shows the ICCD gate signal output in relation to the voltage and current peaks, and both the gate delay and gate-width values are indicated on each image. In this paper, the gate-width is presented as the unshaded section of the oscilloscope trace.
The electrode gap is set up by aligning tips as close to the bubble apex as possible, given that the bubble travel-path is established first. After 30 discharge events, degradation in the electrode is detected by persistent discharge attenuations. To investigate the influence of small variations in the distance between the electrode and gas bubble, , the -field simulations modeled in ANSYS Maxwell are used. For the average bubble positioned between two sharp electrodes, small variations in horizontal displacement do little to alter the magnitude of the -field directly at the electrode tips. However, when a bubble drifts too close to the sharp electrode tip, or when grows too large, the difference between the -fields at the boundary interfaces have a noticeable effect on the emission behavior. The ratio between the -fields at the HV electrode tip and the left bubble apex is plotted in Fig. 5 for the sharp-to-flat configuration.
The simulation shows a critical distance from the electrode at which the magnitude of the -field is larger inside the bubble apex boundary than at the electrode tip (m). After this distance, the ratio between the -fields increases linearly up to the point of contacting the flat grounded electrode. Images from this electrode configuration observed around the similar time frames show evidence of this distinction. Figure 5(b) is chosen from an image gated 2 ns after Fig. 5(a) to account for the time taken to propagate a longer distance through water. Figure 5(a) is positioned such that the bubble apex is 76 m from the HV electrode tip and shows similar magnitudes of electrode tip emission and emission observed within the gas region of the bubble. By contrast, Fig. 5(b) measures a bubble apex distance 270 m away from the electrode tip, and tip emission is significantly greater than that in the bubble region emission. As shown by the simulation, at this distance the electrode tip field is over an order of magnitude greater than that at the bubble apex. Bubbles chosen for temporal-resolution results fall within a stable region in which electrode tip -fields remain within an order of magnitude. See supplementary material37 for details of the electrostatic simulations and analysis for our electrodes.
III. RESULTS AND DISCUSSION
In this work, we examine the initiation of a discharge in de-ionized water with and without an Ar bubble between the two electrodes on time scales from nanoseconds to several hundred nanoseconds. We demonstrate that for two electrode configurations—sharp-to-sharp and sharp-to-flat electrodes—and for both applied voltage pulse polarities, the discharge originates at the tip of a sharp positive electrode. A glow at the tips is a persistent feature of our observations. A partial discharge was also observed in the Ar bubbles at certain times of the pulse. Finally, images taken 100 ns later in the discharge present the appearance of the discharge bridging the gap between the electrodes within the argon bubble. We show below that this appearance does not mean that the discharge propagates from one electrode to another, but rather that it originates at different times at each sharp electrode. A time scale approach is utilized in presenting the following results: first, we present and discuss images taken during the voltage rise prior to it reaching its maximum value; then we present the images corresponding to the time when the first pulse is falling; and finally we discuss emissions detected in regions of oscillating pulse decay on longer time scales.
A. Nanosecond pulse time scale: The rise
The earliest images taken within the first nanoseconds of the start of the applied voltage pulse show light emission at the tip of the anode. Figure 6 shows examples of repeated images of the tips of the sharp-to-sharp electrode configuration. To detect the earliest light, the ICCD gate (width of 2 ns) was backed up to the time prior to the start of the applied voltage pulse and then advanced in 2 ns time steps until a glow was observed. Repeated images were captured under the same conditions without changing any of the camera or pulser settings. The images show a glowing discharge region that appears to develop at the tip of the HV electrode, then extinguishing and possibly reappearing again. There are no collection of oscilloscope measurements corresponding to each individual image; instead the timing is calculated between the ICCD activation signal and the HV pulse from the initial measurement of this data set, resulting in a larger temporal uncertainty than images presented with argon bubbles. See supplementary material for traces of the activation signal (Fig. S6).37 Considering the experimental uncertainties, these observations demonstrate the appearance of a glow at the tip of the positive HV electrode in the absence of injected gases. For all the gate delays shown in Fig. 6, the glow is observed within the time of the first voltage pulse and appears to originate within 5 ns of the peak voltage.
In addition, the glow at the tip of the electrode is also observed when Ar gas is bubbled through the water. As described in Sec. II, the applied voltage pulse is timed so that a bubble is positioned between the electrodes. It remains practically stationary during the 500 ns of the first voltage pulse and subsequent decaying oscillations. The uncertainty in bubble position is 10 m (Table I). Figure 7 shows that a faint glow at the tip occurs at the positive HV electrode and is captured before the bubble itself begins to glow. The glow at the tip of the sharp electrode occurs independent of the electrode configuration and has also been observed in the sharp-to-flat electrode configuration as well [Fig. 7(b)].
All the observations discussed so far present images taken within several nanoseconds of the applied voltage pulse reaching the first maximum. The most prominent feature of the images taken on various time scales in our experiments is the glow observed at the tip of the electrodes. This glow is observed with and without the involvement of a macrobubble. However, it should be considered that the water is not degassed and could contain microbubbles due to the dissolved air in a container open to the atmosphere. Small irregularities in the electrode could contain pockets of gas (likely a mixture of air, argon, and water vapor) and form microbubbles with a size of 1 m. Smaller bubbles cannot be sustained in water at atmospheric pressure (Shneider and Pekker, p. 57)12 and larger bubbles would be detected in the backlit images. Therefore, we will begin the discussion of the rationale for the glow initiating at the tip of the electrode submerged in water with the possibility of the discharge initiating in a microbubble.
Gas discharges occur if the field exceeds the minimum required by the value of , a product of the gas pressure, , and the size of the gas gap, , which in this case is the size of the bubble. The small size of the bubble is responsible for a very small value of 0.1 Torr cm; this is lower than the minimum for the gases in our system. Hence, this breakdown would require a potential difference, , of 1 kV across the bubble. The electric field immediately next to the electrode is
where is the maximum applied voltage, is the time from the start of the voltage pulse, is the voltage rise time, is the distance from the electrode tip, and is the radius of the electrode tip. For kV, m, ns, , and , MV/cm. This is an estimate of the maximum value of the field immediately next to the electrode at its tip and it agrees within an order of magnitude with the ANSYS simulation of MV/cm. Both values fall short of providing the required kVs across a microbubble. This means that even if an electron accelerated in the applied field, with a mean free path at atmospheric pressure of m, the microbubbles are too small to develop well-formed electron avalanches. In addition, to grow a microbubble would involve thermal processes that take microseconds, not nanoseconds, to develop (Shneider and Pekker, Chap. 9).12 Hence, we conclude that the observed discharge must initiate and develop by a different, faster, mechanism that also allows for a possible quick expansion of the glowing region. As shown in Figs. 6 and 7, the light from the region next to the electrode tips is recorded at or before the voltage reaches its maximum value of ns.
Discharge initiation by cavitation requires a pulsed nonuniform electric field and depends strongly on the electrode tip radius of the electrode and the applied voltage rise time. Experimental30 and theoretical6,28,29 work have shown that cavities can develop and grow when the electrode tip radius is m and the voltage rise time is <10 ns. In this work, the electrode tips have radii of m, an average voltage rate of rise is kV/ns, and the total time to reach peak voltage of about ns. Under these conditions, electrostrictive cavitation is feasible, and spontaneously formed nanocavities can grow to enable ionization and discharge initiation.12 Experimentally, cavitation was reported by Dobrynin et al.30 for negative electrostrictive pressure of 30 MPa. If we use the electric field near the electrode estimated above, the negative electrostrictive pressure produced close to the electrode is
for ns for all experimentally measured radii of sharp electrodes. In Eq. (2), is an empirical factor for a dielectric liquid, is the permittivity of free space, and is the relative dielectric constant of the liquid. For water, , = 81, and is estimated from Eq. (1). As stated above, light from the electrode region is observed as early as 6–8 ns after the start of the voltage pulse. This time is insufficient for the bulk water to move in and compensate for the negative pressure in the void. Moving at a speed of several meters per second it requires hundreds of nanoseconds to move 1 m—a much greater time than the observed glow at the electrode tips. On a ns time scale, the bulk water does not have time to respond and the cavity can continue to expand. Nano-scale cavities are naturally present in bulk water, but their expansion requires sufficient negative pressure. The expansion of a nanocavity is necessary because there needs to be sufficient distance for an electron to acquire enough energy to produce ionization. The minimum energy required is >12.6 eV, the ionization energy of water molecules. Assuming that the negative pressure in the cavity is sufficient to move the water, the speed of expansion can be estimated as
where is the negative pressure from Eq. (2) and is the water density. For a seed electron accelerating in the -field inside the cavity to gain 12.6 eV, the size of the cavity should be , such that
where is the time needed for a cavity to expand sufficiently such that an electron can gain 12.6 eV. This expression results in an approximate time of, ns. Hence, at our applied voltage rate of rise and amplitude, the voids expand and the electrons in the voids gain sufficient energy for ionizing water molecules on a time scale shorter than the voltage rise time. After electrons sink into the anode, a virtual electrode is formed by the positive ions, and the cavitation process can continue. The basic criterion for the applicability of the cavitation approach is that the rise time of the applied voltage must be shorter than the time required for new water to fill in the region close to the electrode where voids can grow, as discussed. The size of the region depends on the applied voltage and following estimations in Shneider et al.28 is approximately . For our electrodes, m, water moving at the speed of sound of 1500 m/s would take 25 ns to be displaced. Hence, the rise time of the applied voltage pulse in this work is well within the required limits. The time scale estimates here show that the conditions needed for the cavitation model to hold are satisfied in our experiments.12 The cavitation model was first proposed theoretically in Shneider et al.28 and further developed in the author’s monograph.12 Observations by Pekker,40 and Dobrynin et al.30 provide experimental evidence for this model and more recent detailed studies41,42 further validate this it. Moreover, Grosse et al. applied a voltage pulse of a very similar characteristics to the one presented here in our work to de-ionized water using a 50 m radius tungsten wire electrode. Cavitation theory was used to simulate the cavity growth and the results were consistent with experimental observations using shadowgraphy and optical emission spectroscopy (OES).41
Our work contributes to the evidence in favor of the cavitation model but does not directly address the origins of the first electrons. The question on the first electron persists because the usual mechanisms such as cosmic radiation, for example, require a wait time that is too long for the ns pulsed discharges. Other sources have been proposed but are difficult to confirm through direct experimentation. Zhang and Shneider43 show that electron detachment from the hydroxide ion at the surface of cavities may be the most probable source of the initial electrons and also propose a scheme for discharge propagation from one cavity formed by electrostriction to another. We will return to the propagation scheme for later time scales after reporting additional observations occurring within the first applied voltage pulse.
B. Nanosecond pulse time scale: The fall
On this intermediate time scale during the decay of the first half-wave of 12–30 ns, we report two main observations: (1) a glow at the electrode tip that extends to the bubble, and (2) a light forming in the bubble. Images taken with 10 ns and 14 ns delay times with a 2 ns gate width (Fig. 8) in sharp-to-sharp electrode configuration show the glow region extending from the electrode tip to the apex of the argon bubble. Similarly, images presented in Fig. 5 show the glow region extending from the electrode tip to the bubble apex in the sharp-to-flat electrode configuration. In some images, as in Fig. 10(a), the discharge appears to extend from the side of the electrode tip which may be a consequence of this being the closest distance and/or a local irregularity on the surface of the electrode. This underscores the three-dimensional nature of the discharge path and the approximate nature of the velocity estimates. Although the error in the bubble position is only m, the three-dimensional character of the bubble introduces additional uncertainty.
To estimate the velocity of the propagation, images that show the glow just appearing inside the bubble can be used for an approximation. From the images in Fig. 8, the propagation time can be estimated as 10 ns. The distance between the electrode tip and the bubble apex were measured from the back lit images of the bubble-electrode arrangement and hence, from a flat projection of the bubble-electrode arrangement. With this limitation, the distance between the tip of the electrode and the apex of the bubble was estimated as 100 m. The speed of propagation of the discharge from the tip to the bubble is thus m/s, consistent with Fig. 5(b) which yields m/s (270 m distance, 17 ns). Considering the measured uncertainty of our estimations, this speed is in good agreement with the speed of propagation for ns pulsed breakdown in water reported previously by Grosse et al. ( m/s)42 and Ceccato et al. ( m/s).44
Considering the time it takes for the discharge from the electrode tip to reach the apex of the bubble, a very fast mechanism is needed. As discussed, these fast mechanisms could be propagation by cavitation as proposed in Shneider and Pekker,12 and further developed in the recent works;43 or by producing an -field strong enough for the production of local electrons inside the bubble to initiate the avalanche process. In the cavitation propagation mechanism, a nanovoid or cavity elongates to the size sufficient to accelerate the electrons to the energies sufficient for ionization, as described above. These energetic electrons ionize water molecules. Once the newly generated electrons reach and sink into the anode, the cavity acquires a positively charged head and becomes a new sharp anode that initiates a new cavitation process. Since electrons take ps to move through the cavities, the overall process across micrometer will take ns to complete.
The second observation for this time scale is the appearance of the glow in the Ar bubble injected between the electrodes. For a breakdown to occur in the bubble, the field must exceed the minimum breakdown field corresponding to the value of as usual in gas discharges. For a 1.7 mm bubble with Ar gas inside at atmospheric pressure, , which is a large that requires a field on the order of >10 kV/cm. For both geometries in our experiment, , and certainly much smaller than the distance between the electrodes. The electric field in the vicinity of the bubble for a 20 kV applied voltage and a 0.2 cm inter-electrode gap (300 kV/cm) is roughly 10 the breakdown voltage. Hence, conditions are met for the discharge to start during 10–15 ns of the first applied pulse, or until the voltage falls below 1/10 of the max peak value. Under these conditions, V/cm/Torr, and
where (for Ar), , cm Torr (Raizer, Russian edition, p. 150, Table 5.1)45 which gives and for mm bubbles. This is a very large value of the first ionization coefficient meaning that the expression used for this estimation may not hold for large electric fields. For a mm size bubble, the condition of would be satisfied for . This means that there is a likelihood of streamer discharge in an Ar bubble situated between the electrodes provided that there are seed electrons present and if there is enough time for the avalanche to streamer transition. This transition is determined by the negative ion drift velocity because removal of negative ions is required for field enhancement at the head of the streamer. Ion drift velocity is 1000 m/s and, therefore, the time needed is on the order of microseconds. Hence, the time of the applied voltage pulses of 30 ns is insufficient for streamer formation and the discharge remains in the Townsend mode. The sharp-to-flat electrode configuration gated to capture the entire first half-wave of the initial pulse exhibits a similar behavior with only a diffuse glow present in the bubble. Figure 9 captures light emitted over the first 25 ns after the initial applied voltage pulse rise time. The expansion in this mode can be estimated as the speed of the ionization front and is m/s, so the glow is expected to extend about 0.3 mm in 30 ns which falls short of the 1.7 mm across the bubble.
Estimations and ANSYS modeling also show that the electric field inside the bubble depends on the position of the bubble relative to the HV electrode. In cases when the bubble is closer, the discharge in the bubble may initiate sooner and is visible at earlier times together with the glow at the tip of a HV electrode. If the bubble is further away from the HV electrode, the glow may initiate at later times relative to the start of the applied voltage pulse. The fast streamer-like extension of the discharge region from the HV electrode may be acting as an extension of the anode and increasing the field inside the bubble. Therefore, the glow in the bubble may be delayed and seem to appear when the glow region from the electrode tip extends toward the bubble.
To summarize, in the intermediate time regime of 12–30 ns, when the images are taken during the decay of the first half-wave, the discharge in the water is observed to span the region between the tip of the anode and the apex of the bubble, eventually appearing in the bubble. The fast propagation toward the apex of the bubble requires a fast mechanism such as cavitation propagation. The discharge in the gas bubble does not have time to develop into a streamer, although the electric field is strong enough, and remains in the Townsend mode which accounts for the diffuse character of the observed glow inside the bubble.
C. Evidence of anode-initiated breakdown
Experiments were conducted with the first applied voltage pulse in both a positive and negative polarity. In each situation, and for both sharp-to-sharp and sharp-to-flat electrode arrangements, we observe the discharge on the anode side. When the ICCD gate encompasses a positive applied voltage peak, along with a large EMI signal measured on the HPF-applied current trace, the corresponding image detects the glow on the HV side [Fig. 10(a)]. Likewise, when the electrode polarity is reversed in the sharp-to-sharp electrode configuration, using a voltage pulse with opposite polarity, the glow appears on the grounded anode electrode [Fig. 10(b)]. The EMI signal correlates with the side that the emission is detected in the bubble depending on the polarity of the applied voltage at a given measured event. In addition, the glow at the tip of a sharp electrode is sometimes observed at later times during secondary voltage oscillations. Figure 10(c) shows a later discharge event on the grounded electrode at which point the immediate voltage peak is negatively biased, and the grounded electrode is the anode in the configuration. Similarly, when the positive HV pulse is applied to the sharp electrode in the sharp-to-flat electrode configuration [Fig. 7(b)], the discharge appears on the sharp electrode when it is of positive polarity. We do not see any light emission in this geometry when the applied pulse is negative. The glow at the tip of the positive electrode is the most persistent observation in all images where light is recorded.
D. Nanosecond pulse time scale: The decay
In this section we report the results of observations made after the first half-wave of the initial applied voltage pulse, and discuss the behavior of the bubble/electrode system in the presence of the decaying pulse oscillations.
Multiple discharges are observed over the lifetime of the decaying signal initiating at alternating anodes. As depicted in Fig. 10(b) and discussed in Sec. III C, a glow occurs on the grounded electrode during a negatively biased peak, provided a steep enough applied voltage rate of rise () is present. Likewise, later discharges have been observed to initiate multiple times throughout the decay of the voltage oscillations, on both electrodes when they swap anode arrangements [Fig. 10(c)]. The current traces associated with the images in Fig. 11 show examples of multiple discharges occurring over hundreds of ns after the initial pulse. In the case of Fig. 11(a), a negatively biased applied voltage results in the expected electrode-tip-to-bubble-apex breakdown at the grounded anode. The long gate-width, spanning both negative and positive applied voltage peaks, associated with this image also captures the characteristic tip glow on the HV electrode. However, over the course of 100 ns, the emission in the bubble is still limited to diffuse glow similar to the time regime covered in Sec. III B, emphasizing the lack of streamer formation. As discussed above, the 30 ns duration of the first half-wave is an insufficient amount of time to develop a streamer across the bubble, and this holds true for the subsequent reflected waves.
Figures 11(a) and 11(b) share remarkably similar applied voltage and current traces, but with slightly varying gate-widths. Detected emission that appears to bridge the bubble gap [Figs. 11(b) and 4] can only be collected in the sharp-to-sharp electrode configuration where separate discharge initiations are allowed by alternating the anode from the HV electrode to the grounded electrode. The delay between the two images occurs at a positive applied voltage peak and at the initiation of a secondary discharge, as indication by the HPF current signal. As expected, a discharge on the positive voltage pulse is observed at the positive HV electrode. By comparing Figs. 11(a) and 11(b) it is clear that the emission detected between the 20 ns time difference facilitates excited regions of emission that are absent without the presence of breakdown on separate electrodes. This suggests that the emission observed in Fig. 11(b), that spans the length of the bubble, is not the continuation of the initial discharge at the grounded electrode.
In addition, short gate-width images activated at times much later than the initial pulse can detect the history of the multiple discharges by observing decay from slower emission processes. Emission from electron-ion, ion-ion & dissociative recombination and Ar metastable excitation continues to produce photons well after the initial discharge. Argon optical emission can continue for several s under low pressure and hundreds of ns at high pressure.16,46 The oscilloscope trace for Fig. 11(c) shows 2 discharge events as well as a 75 ns time range where high-frequency noise is higher in amplitude than normal. Distinct peaks from EMI noise suggest times where discharge events reach the argon bubble (25–100 ns, 220 ns, & 300 ns). The most noticeable of these signals occurs on a negative pulse 220 ns after the initial applied voltage rise time begins and 140 ns before the opening of the ICCD gate. The corresponding image (short gate width of 2 ns) is open 80 ns after the last emission and retains visible evidence of these previous discharges. Though a single faint gap-bridging structure exists connecting a pair of emission spots within the bubble, the remaining spots are solitary.
Rough estimations for electron-ion recombination emission attenuation (approximating a characteristic decay time of 100 ns for atmospheric pressure) in Fig. 11(c) are: 96%–93% decrease for the initial noise across the first voltage period, 75% decrease for the large EMI event, and 45% decrease for the smaller EMI event. The initial emission intensity for each event is unknown, but the pattern presented across the bubble corresponds with multiple initiations on either side of the bubble over several hundreds of ns. This further emphasizes that long exposure images that capture multiple peaks are likely the collection of multiple discharge events initiated at consecutively alternating anode positions.
Finally, long-gate images are cross-referenced in the sharp-to-flat configuration. In the case where the sharp anode is held constant at one side of the bubble, the gap-extending emission captured in Fig. 11(b) is absent. As expected, all of the EMI signals on the current HPF trace occur within a positive pulse. This means that the breakdown only occurs at a sharp electrode tip at times when it is the positive electrode. The lack of breakdown for negatively biased pulses is consistent throughout the sharp-to-flat images.
Figure 12 shows two images captured over the course of the applied voltage decay. The glow at the electrode tip begins around the peak of the initial pulse [Fig. 12(a)]; but in this case, the large EMI signal is not detected until the third positive pulse (Fig. 12). To compare this electrode configuration with the sharp-to-sharp configuration from Fig. 11, a long gate-width in the middle of the decaying applied voltage pulse is used. The gate collects light over 3 positive and negative peaks but does not show diffuse emission extending any further than what is observed for the first half-wave for the sharp-to-flat electrode configuration in Fig. 9, suggesting that each spot is a new initiation over the course of the oscillating pulse decay.
To summarize all examples, emission detected spanning the gap of the bubble for oscillating ns pulses requires anode breakdown to occur on both sides of the bubble. Despite breakdown on both sides, the emission observed with large gate-widths does not constitute proper streamer formation at our time scales (<500 ns). Instead, short gate-width images show the discharge being restrained to a diffuse Townsend mode and reoccur in this manner over multiple events over the 500 ns oscillation decay.
In this work, we investigate the initiation of the discharge in the presence and absence of 1.7 mm Ar filled bubbles. Our primary observation is that the discharge is first observed at the sharp tip of a positive electrode, within the first 4–8 ns, with and without the Ar bubble present. The ANSYS Maxwell model shows that the presence of the Ar bubble affects the -field in the region between the electrodes, but the field remains strong enough for the persistent presence of the glow at the submerged sharp positive electrode. The short rise time of the applied voltage, and the time it takes for the discharge to bridge the gap between the tip of the sharp positive electrode and the apex of the bubble, suggest the electrostrictive cavitation mechanism for discharge initiation and propagation in water.
The discharge in the Ar bubble appears at times of 10–20 ns or within the first half-wave of the applied voltage. Since the falling voltage does not allow enough time to develop a streamer, the discharge appears to spread in a diffuse form remaining in the Townsend mode.
The same electrode tip and bubble behavior as observed during the first half-wave appears to repeat during some of the subsequent reflected pulses similarly at the sharp anode, which may occur at the opposite sharp electrode at different times. Images taken with long delays (>20 ns) show both electrodes and the bubble glowing, but the processes at the opposite electrodes appear during different voltage pulses and are visible together due to the emission decay times of hundreds of nanoseconds.
The experiment combines discharge in the water and discharge in a gas bubble on very fast time scales. The presented imaging study was possible due to an original optical timing system. The discharge behavior at these time scales is complex enough that estimates do not resolve the entire picture and detailed modeling is needed in order to understand the interactions and processes on this time scale.
The work by N.L.S. was supported by the Integrated University Program Graduate Fellowship. Work by K.S. was in part supported by the National Science Foundation (NSF) under Grant No. PHY2107901. All plasma imaging was conducted at the Princeton Collaborative Research Facility (PCRF) which is supported by U.S. DOE under Contract No. DE-AC02-09CH11466. The work by S.G. was supported by PCRF. N.L.S. and K.S. gratefully acknowledge support from North Carolina State University's Game-Changing Research Incentive Program for Plant Sciences Initiative (GRIP4PSI). The authors thank Dr. M. Shneider for fruitful discussions.
Conflict of Interest
The authors have no conflicts to disclose.
Nicholas L. Sponsel: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (supporting); Investigation (equal); Methodology (equal); Software (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Sophia Gershman: Conceptualization (supporting); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Maria J. Herrera Quesada: Data curation (supporting); Formal analysis (supporting); Software (supporting); Visualization (equal); Writing – review & editing (supporting). Jacob T. Mast: Formal analysis (supporting); Software (supporting). Katharina Stapelmann: Conceptualization (lead); Formal analysis (supporting); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (lead).
The data that support the findings of this study are available within the article and its supplementary material.37 Additional data that support the findings of this study are available from the corresponding author upon reasonable request.