Nanosecond pulsed discharges in distilled water: I. Continuum radiation and plasma ignition

The nanosecond plasma evolution is observed by ICCD imaging shown in figure 4(a) where the position of the electrode is indicated by gray lines. The position is taken from a shadowgraphic image as shown in the top left image of this figure. The corresponding temporal variation of the electrode voltage is shown in figure 4(b). The temporal evolution of the electrode voltage and of the light emission is adjusted in time by aligning the rising edges of both signals.

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The voltage curve is calculated from the line current I measured at the BCS according to the following equations. The voltage drop over the BCS can be written as:

$$\begin{equation}{U}_{\mathrm{B}\mathrm{C}\mathrm{S}}={R}_{\mathrm{s}\mathrm{h}\mathrm{u}\mathrm{n}\mathrm{t}}\cdot I\end{equation} \tag{ 6 }$$

with the current I inside the coaxial cable and R the total resistance of the shunt with R_shunt = 0.3  Ω. We derive a line current according to:

$$\begin{equation}I=\frac{1}{0.3}{{\Omega}}^{-1}\cdot {U}_{\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{p}\mathrm{e}}\end{equation} \tag{ 7 }$$

With that, the actual voltage pulse can be determined according to Ohm's law:

$$\begin{equation}U={R}_{\mathrm{c}\mathrm{o}\mathrm{a}\mathrm{x}}\cdot I\end{equation} \tag{ 8 }$$

with the cable resistance R_coax = 50  Ω.

The quantification of the signals from the oscilloscope is similar to the reference [11], although here the impedances of the cables as well as the oscilloscope are all matched to 50 Ω. The BCS measures the voltage signal of the traveling HV pulse in the middle of the cable. After reflection at the electrode it travels back along the BCS cable with the opposite sign resulting from the different direction of traveling (data not shown). The real sign of the pulse changes only during its second reflection at the pulser. The difference between the shape of the forward and backward traveling pulses is often used to estimate the absorbed power in the plasma. This absorption originates from the fraction of the HV pulse that travels to the grounded electrode and dissipates in the plasma and in the liquid. The voltage curve shown in figure 4(b) represents the voltage pulse at the electrode reconstructed from the initial and the reflected voltage pulses detected at the BCS (shown in figure 4(c)). Due to the constructive interference between the forward and backward traveling pulse with itself directly upon reflection at the electrode tip, the actual voltage at the tip can be up to twice the value that is measured at the BCS depending on the actual reflection coefficient. The electrode voltage is then reconstructed by adding the initial and the time shifted and inverted reflected pulses that are measured at the BCS location. Such a doubling of the voltage is only valid for the reflection at an open ended cable. Any losses at the end may damp and distort the signal. The inspection of the shape of the traveling pulses (shown in figure 4(c)) indicates, however, that any distortion and damping is rather small, so that the simple addition of the traveling pulses remains a good estimate. Nevertheless, a more detailed electrical analysis of pulse shapes to describe the electrode voltage accurately remains a task of the future. In the following, we distinguish between 'BCS voltage' measured directly at the BCS and 'electrode voltage' which is a reconstructed pulse from the BCS voltage.

As discussed in the section above, the voltage measurements show reflections of the initial pulse but at much later times in comparison to the first 30 ns after plasma ignition. The time t₀ = 0 ns is defined by the rise of the voltage pulse. Figure 4(b) shows the integrated intensity of the ICCD images. Two intensity maxima can be seen, which correlate with the rising and falling edge of the HV pulse. A minimum in emission is seen during the plateau phase of the pulse. This so-called 'dark phase' was already reported in the literature [26] (this minimum cannot directly be derived from figure 4(a), because all images are normalized to the maximum).

The ignition of plasmas in liquids by nanosecond pulses cannot easily be explained by an initial bubble formation followed by an electron avalanche inside that bubble to create the plasma. Such a macroscopic bubble formation is prohibited by the inertia of water at these short time scales preventing any displacement of the heavy species. Instead, the formation of nanovoids due to the differential pressure by the electric field around a tip is postulated serving as nucleation sites for an electron avalanche ignition. However, these nanovoids have not been observed so far and the gas density in such a small void might be even too small to allow for a plasma to develop.

In order to gain a better understanding of the exact position of the discharge, ICCD images for different pulses were taken (figure 5) 6 ns after the ignition of the discharge. In these images the position of the plasma at the tungsten electrode was monitored by single shot ICCD images. The images show, that the plasma ignites at different locations of the tungsten tip for different pulses which leads to the hypothesis that small protrusions at the tungsten surface are the sites of ignition. Furthermore, one can see that ignition may also appear at two or more locations simultaneously. The dimension of the emitting areas is of the order of 10 μm. This illustrates that the microscopic topology of the surface is more important than the macroscopic curvature radius of the tungsten wire.

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To understand the surface structure of the electrode material in our experiment, we compared two electrode materials tungsten and a platinum/iridium alloy and analyzed the surface after operation with a scanning electron microscope (SEM), as illustrated in figure 6. The electrode using the platinum/iridium alloy was intentionally sharpened by chemical etching with a manufactured tip radius of only a couple of 100 nm for optimum plasma ignition. The tungsten wire was cut sloping before clamping it into the cannula. The experiments showed that the plasma operation with a tungsten tip was continuously possible despite significant material erosion, whereas the plasma operation using the platinum/iridium tip was only possible for approximately one hour.

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The SEM inspection of this platinum/iridium tip after operation revealed a very smooth surface and a larger tip radius, as shown in figures 6(c) and (d). This is in contrast to the electrode surface of the tungsten tip shown in figures 6(a) and (b) where individual sharp micrometer sized protrusions are present.

Such sharp protrusions at the tungsten tip electrode are apparently rather durable or reappearing even during long operation of the plasma when the electrodes are being eroded continuously. The erosion of electrodes for in-liquid plasmas was studied by Lukeš et al [27, 28]. The comparison of platinum, tungsten and stainless-steel as electrode material showed the highest erosion rates for tungsten [28]. Furthermore, the surface topology of tungsten electrodes showed peculiar protrusions in their study. The authors linked the appearance of these protrusions to the high melting temperature and high thermal conductivity of tungsten that cause very transient melting and solidification processes of the tungsten surface during the plasma pulse.

It is assumed, that the plasma operation for a tungsten tip continuously regenerates these sharp protrusions in a cycle of melting and solidification in each plasma pulse. Due to the lower melting temperature and lower thermal conductivity of the platinum/iridium alloy, a larger surface area on the tip remains in the molten state for a longer time implying also a slower solidification process after the end of the plasma pulse. As a result, the surface tension of the platinum/iridium alloy leads to small curvature protrusions and any electric field enhancement effect is smaller compared to tungsten as electrode material. Therefore, we postulate that these sharp protrusions act as ignition sites.

In order to explain the lifetime of the different material electrode tips, we postulate plasma ignition by field emission in case of a negative polarity or by field ionization for a positive polarity at the protrusions on the electrode tip surface. In this case, after a specific time of operation, the tip of the platinum/iridium alloy becomes too smooth so that ignition by field effects is no longer possible and plasma generation stops.

In general, a strong electric field at the electrode–liquid interface acts on the adjacent water molecules and distorts their electronic ground state as illustrated in figure 7. In the beginning of the pulse, a positive potential between electrode and surrounding (figure 7(a)) may lead to electron generation by field ionization from the H₂O molecule tunneling into the tip. A layer of positive water ions adjacent to the electrode surface is created. At the end of the pulse a negative potential is created due to a strong residual positive space charge close to the tip (figure 7(b)). Electrons generated by field emission may tunnel from the tip into the water and populate an excited state of the water molecule or simply ionize the water molecule by electron impact. This would be the case for the positive charge in a streamer head as will be discussed in part II of this paper.

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The threshold electric field E_threshold for tunneling to occur is in H₂O 0.2–0.5 V Å⁻¹ (H₂ = 0.7 [29]). The field at the tip used in these experiments can be estimated as follows [29]:

$$\begin{equation}{E}_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}}\approx V/\left(5{r}_{\mathrm{t}}\right)\end{equation} \tag{ 9 }$$

with the applied voltage V and the tip radius r_t. The voltage in our experiment was set to 20 kV resulting in a field of 0.016 V Å⁻¹ assuming a tip radius of 25 μm. This is too small for field emission effects to occur. However, a close inspection of the tungsten tip in operation indicated that plasmas can only be ignited if the 25 μm radius tip is intentionally sharpened yielding local radii in the range of 1 μm. This in turn implies local electric fields of the order of 0.4 V Å⁻¹ which is identical to the required threshold fields E_threshold for water field ionization or field emission [13].

The gas temperature inside the plasma can be derived from the ideal gas law for a known pressure, plasma volume and particle density. Recently, we used cavitation theory to model bubble expansion [19]. In this model, the expansion of the cavitation bubble with an initial radius of R₀ = 25 μm or a volume ${V}_{0}=4/3\cdot \pi {R}_{0}^{3}$ and an initial pressure p_0,gas is modeled showing excellent agreement with the temporal evolution of the bubble radius as deduced from shadowgraphy. The main fitting parameter of this model is the initial energy that is deposited by the plasma that eventually drives cavitation. This initial energy corresponds to the volume energy p_0,gas V₀. Due to the high inertia of water molecules during the short plasma pulse itself, it is reasonable to assume that the species density inside the initial bubble with volume V₀ is identical to the liquid water density n_water. Based on this information, we can assess a temperature by using the ideal gas law from p_0,gas = n_water k_B T to convert the fitted initial pressure p_0,gas yielding temperatures from 2000 K for experiments using an applied voltage of 14 kV to 70 000 K for experiments using an applied voltage up to 26 kV. This determination of the temperature provided a good input parameter to model the water chemistry inside the expanding bubble [30]. Nevertheless, it remains a crude assumption with a significant error bar. For example, the initial volume V₀ might be smaller and the initial pressure p_0,gas higher yielding an identical initial volume energy. A smaller volume, however, corresponds to a smaller absolute number of water molecules at a higher temperature to yield the same dissipated energy. Consequently, we seek independent information on the temperatures based on spectroscopy.

The time-resolved emission spectra of the first 34 ns after plasma ignition are shown in figure 8 for a nanosecond pulsed plasma with approximately 15 ns width and 2–3 ns rising times at 20 kV and 15 Hz. The ICCD gate is 2 ns and each spectrum is averaged over 1000 discharges. The individual spectra are stacked in the graph and scaled for best visibility of the spectral features. In the beginning, the broadband continuum is evolving and the Balmer series of hydrogen becomes visible with H_α being very broad due to Stark broadening. The continuum may either originate from Bremsstrahlung or from black body radiation leading to different spectral shapes, especially at long wavelengths, because Bremsstrahlung follows a 1/λ² dependence whereas black body radiation follows a 1/λ⁵ dependence, respectively:

• Bremsstrahlung background 1/λ² at long wavelengths: Bremsstrahlung originates from the energy loss of an electron in a collision with an ion or a neutral. These free–free transitions are described by equations (3) and (4) with a 1/λ² dependence of the emission coefficient.
• Hot tungsten surface emitting black body radiation with 1/λ⁵ dependence at long wavelengths: the power input onto the small electrode tip leads to electrode heating and to the emission of black body radiation (equation (5)). The ICCD images indicate that most of the emission is located very close the electrode surface (compare with figure 4(a)) so that we assume that the tungsten surface is the source of black body radiation.

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Both possible continua are evaluated in comparison with typical data of a sensitivity calibrated emission spectrum at 4 ns after ignition shown in figure 9. The red line corresponds to black body radiation assuming a temperature of 7000 K, the black solid line corresponds to Bremsstrahlung of electrons in collisions with neutrals at a temperature of 9500 K. It is expected that the Bremsstrahlung of electrons in collisions with neutrals dominates in comparison to the collisions with ions, because ionization degrees of the order of only 10⁻³ are found, as discussed in the second part of this paper series [31].

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The continuum spectra are scaled arbitrarily to fit the data. Broadened hydrogen lines for H_α , H_β and H_γ may be identified. At the position of the OH molecular bands around 300 nm no clear interpretation is possible. From this graph, it is obvious that a 1/λ⁵ dependency of black body radiation fits better to the continuum in comparison to the 1/λ² dependency of Bremsstrahlung since line emission provides additional contributions. Therefore, the origin of the broad continuum background will be assumed to be black body radiation from the hot tungsten electrode.

The fitting of the continuum background due to black body radiation is shown in figure 10 for different times of the pulse. The analysis of the data shows that the assumption of a single unique temperature for the complete tungsten tip is not sufficient to describe the complete data set. Instead, a variation of the continuum at short wavelengths is observed. It is postulated, that this behavior can be best fitted by a two temperature model of the hot tungsten surface during plasma operation exhibiting two distinct regions being motivated as follows:

• Black body radiation of the hot tungsten surface: the black body emission from the tungsten electrode is shown as green line in figure 10. The temperatures are typically at 6000 K or higher corresponding to the boiling temperature of tungsten at varying partial pressures of tungsten due to the ongoing evaporation process. Such a fit with a black body continuum and a unique temperature showed excellent agreement with the data taken at 2 ns, 4 ns, and 6 ns.
• Black body radiation of a hot spot on the hot tungsten surface: the continuum background of the data taken at 8 ns and later cannot easily be fitted by a single black body background at one unique temperature. Hence, the additional black body emission from a very small hot spot at the tungsten electrode (shown as red line in figure 10) is postulated. The temperature of this hot spot is set to 20 000 K arbitrarily. It is well known from arc discharges that the nonlinear interplay between thermionic emission and local heating of the surface leads to the formation of a 'hot spot', a very localized region, where the plasma is contracted and where the surface temperature can be much higher at the expense of a small reduction of the overall temperature of the remainder of the electrode [32]. The area of this hot spot may be only in the percent range of the complete hot tungsten surface. Due to the T⁴ dependency of the Stefan–Boltzmann law, even a small area but at a high temperature can significantly contribute to the emission. A very high temperature of this hot spot of 20 000 K creates a maximum emission at wavelengths well below the wavelength range of our spectra. Therefore, the emission of this hot spot contributes with a second 1/λ⁵ continuum to the emission at short wavelengths.

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Due to the limited wavelength range an exact determination of the temperature of such a hot spot is not possible. It is also conceivable that these hot spots are the locations of the small protrusions that had been found by Lukes et al [28] on the plasma electrode after operation.

In general, the assumption of the presence of a hot spot is reasonable, but remains a very crude assumption and any exact quantification of both, the temperature and the area ratio of such a hot spot, remain very ambiguous. One could also assume that the observed variation in the spectra at short wavelengths corresponds to a modulation due to a varying recombination radiation that correlates with the propagation of the plasma. However, this would imply that the continuum is composed of two very distinct sources of emission (Bremsstrahlung and black body radiation). Such a composition should lead to more complicated spectral shapes of the continua, because black body radiation and Bremsstrahlung can affect very different parts of a spectrum. This is not observed. The presence of several temperatures on the hot tungsten surface is, however, much more likely, so that one source of continuum emission, namely black body radiation, can more easily explain the observed variation and modulation in the spectra.

The fitting shows that in the beginning of the pulse, a black body emission with temperatures between 7000–8000 K fits well to the continuum background, consistent with findings in the literature [14]. The emission from the hot tungsten (green line) is ranging between 5000–8000 K for a time span of 25 ns.

The fitting of the continuum background using the two-temperature model in figure 10 is quantified by the two parameters in figure 11 of the (i) temperature of the hot emitting tungsten surface (green) and (ii) the fraction of the surface corresponding to a hot spot being at 20 000 K (red). The dashed line indicates the boiling temperature of tungsten at ambient conditions. The temporal evolution of the electrode voltage is plotted for comparison as black line. The hot spot may form a few nanoseconds after ignition and then contribute to the continuum radiation. This results in the 1/λ⁵ contribution in the short wavelength range from 250–300 nm (red line in figures 10(c) and (d)). The continuum fitting indicates that the temperature significantly exceeds the boiling temperature at the beginning and the end of the pulse, when the electric field is the highest. The fraction of the hot spot is out of phase with the variation of the temperature of the hot tungsten surface. This leads to the assumption that the surface is initially overheated, before the hot spot is formed and the temperature decreases to the boiling temperature after 12 ns after plasma ignition. A similar observation can be made at the end of the pulse where another overheating due to the assumed field from the positive propagating plasma initiates as second increase of the hot spot contribution at about 20 ns. The percentage of the hot spot agrees reasonably well with the ratio between the dimension of the protrusions of micrometer and the observed dimension of the total emitting areas.

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When the applied voltage pulse of 20 kV arrives at the electrode, field ionization becomes possible at the electrode liquid interface: due to the high electric field, the potential barrier between the water molecules and the tungsten tip becomes distorted (illustrated by the dashed line in figure 7). When the distortion of this reference energy is large enough so that the ground state level in the water molecule is above the Fermi level of the electrons in the tungsten electrode, an electron in the water molecule may tunnel into the tungsten electrode and field ionization occurs. This process requires electric fields of the order of 0.4 V Å⁻¹ that can be present at 1 μm radius protrusions at the electrode tip. Protrusions of that size or even smaller are visible in the SEM micrographs (figure 6). Field ionization creates positive water ions at the electrode liquid interface. This effect induces also an electric field gradient inside the liquid, where more water molecules may be ionized by tunneling effects. A positive space charge is formed that is able to propagate in the liquid (figure 12). Unfortunately, no modeling is available for such a plasma propagation directly in liquids and the characteristic behavior may only be compared with the streamer propagation in air at high pressures [33]. The exact nature of this process will be analyzed in the second part of this paper series.

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The high electric field at one or more protrusions at the tungsten tip surface leads to electrons being accelerated toward the tip and electron impact leads to heating of the tungsten surface. The temperatures of the tungsten surface are in the range of 6000–8000 K. This temperature range is consistent with the fact that the boiling temperature T_B of tungsten is at ${T}_{\mathrm{B},{p}_{0}}\enspace \simeq$ 5828 K at ambient conditions corresponding to a vapor pressure p₀. Here, we also have to take into account that the vapor pressure p of tungsten in front of the tungsten tip can be very high due to evaporation, which increases this transition temperature according to the Clausius–Clapeyron equation as:

$$\begin{equation}T={\left(1/{T}_{0}-\frac{R\enspace \mathrm{ln}\enspace \frac{p}{{p}_{0}}}{{\Delta}{H}_{\mathrm{v}\mathrm{a}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{z}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}}\right)}^{-1}\end{equation} \tag{ 10 }$$

with R the gas constant and the heat of evaporation of tungsten of ΔH_vaporization = 774 kJ mol⁻¹. This yields higher boiling temperatures of for example 8189 K for p/p₀ = 100 or 6810 K for p/p₀ = 10. Due to the very high heat of evaporation at this phase transition, it is assumed that the tip of the tungsten electrode is always at the boiling temperature, which may, however, vary during the pulse due to the intense evaporation of tungsten. This evaporation becomes visible as a non-negligible erosion of the tungsten tip during operation. At such high temperatures, the black body radiation is in the visible wavelength range and thereby dominating the spectrum.

Due to the local nature of the discharge it is expected that this temperature is not homogeneously distributed over the surface of the tungsten tip, but a small hot spot forms due to the contraction of the plasma to particular locations where the surface temperature is the hottest. Therefore, the overall black body radiation may be composed of the emission of the tungsten tip at boiling temperature plus a hot spot at even higher temperatures. The latter effect gets significant, when the plasma current and the electron emission at the electrode is the highest. This occurs at the rising and the falling edge of the plasma pulse leading to an additional contribution to the broad band continuum at smaller wavelengths.

This hot spot is assumed to have a temperature of 20 000 K and covers only a small percentage (approx. 0.5%) of the total emitting surface area. This area is likely to evaporate due to the high local temperature. Therefore, with each discharge a small part of the tungsten tip is evaporated that explains the typical loss of the tungsten wire of 1 mm h⁻¹ in our experiment.

Such a hot spot formation has not been reported in literature for these in-liquid discharges. The comparison of ICCD images reported from groups working with similar setups [17, 26] is challenging because higher voltages were applied and therefore a higher power input is given. The emission from the propagating plasma is proportional to the electrode voltage whereas the black body radiation is limited by the boiling temperature of the surface material. This temperature of approximately 7000 K has also been observed by Marinov et al [14], although they claimed that molecular bands could also be responsible for this continuum. This should be investigated in future experiments.

The lines from the hydrogen Balmer series are evaluated with respect to the various broadening mechanisms, as discussed in the second part of this paper series [31]. From this, two emission regions of the propagating plasma are identified, a trailing recombination region and a leading ionization region. From the Stark broadening of the H_α emission from the ionization region, electron densities up to 5 × 10²⁵ m⁻³ are determined. Such electron densities are also typical for discharges in liquids for a wide range of pulse lengths [8, 9, 34]. The H_β and H_γ emission is assumed to originate from the recombination region where the water ions and electrons recombine.

At the end of the ns pulse, the plasma may have traveled a distance of approximately several micrometers or even millimeters depending on the propagation velocities. The plasma channel may correspond to an equipotential region connecting the plasma to the HV at the electrode tip in a coarse similarity to high pressure streamers. When the voltage is switched off at the end of the pulse, a high electric field will form due to space charges at the interface between electrode and liquid because the propagating plasma represents an electrical potential of +20 kV. This causes a significant distortion of the reference potential energy of the free electrons, as illustrated by the dashed line in figure 7. Now, the electrons from the electrode tip material may tunnel into the adjacent liquid and trigger an intense emission signal.

This interpretation of dominating field effects at the beginning and end of the pulse may explain the observation of emission maxima in phases of the pulse with high dV/dt and a 'dark phase' in between.

The velocity of the propagating plasma can be calculated from ICCD images (figures 12 and 13). The radii of the propagating plasma together with the evolved time yield a velocity of v_propagation = 46 km s⁻¹ which is comparable with the propagation velocities 30 km s⁻¹ determined by Ceccato et al [35, 36] (20 ns rise time, 40 kV applied voltage). In this study, previously formed microbubbles were observed due to Joule heating resulting from the longer rise time of the voltage pulse. Different values for streamer propagation in liquids were found by [26] with estimated streamer channel velocities of 250 km s⁻¹ (150 ps rise time, 112 kV applied voltage). Šimek et al [17] determined propagation velocities in the order of 100 km s⁻¹ (1–2 ns rise time (estimated, not given), 50 kV applied voltage). Lesaint [37] studied various electrode configurations and powering schemes and found propagation velocities of plasmas in liquids between a few and several 1000 km s⁻¹. A direct comparison between all reported streamer velocities is difficult because the values were determined for different times after the ignition and the setups as well as the discharge parameters varied.

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This explanation of the continuum emission is consistent with the different sources of emission observed in the ICCD images. The emission spectra are fitted with a dominant contribution of black body radiation which constitutes 90% of the total emission intensity. The ICCD images also indicate that most of the emission is located very close the electrode surface whereas the streamer channels appear much fainter, as can be seen in figure 13.

At later times after the voltage pulse, the energy dissipated by recombination leads eventually to vaporization along the plasma channel. These plasma channels, filled with hot gas, coalesce to form a spherical bubble due to the surface tension of the surrounding liquid. Cavitation occurs until a maximum bubble diameter of typically 1 mm is reached [19].

Summarizing, we postulate that the continuum emission is dominated by the hot tungsten surface, which is mainly heated by electron transfer due to field effects at the electrode–liquid interface. This heating can become localized due the contraction of the plasma to a hot spot. The characteristic black body temperatures are at the boiling temperature of tungsten of 5828 K or even higher in synchronization with the change of the tungsten pressure in front of the electrode. It is possible that this high temperature also represents the temperature of the adjacent water layer where the dissociative recombination of water ions with electrons triggers the chemistry of these plasmas. It needs to be noted, that this fluid model approach cannot resolve smaller structures or discontinuities. However, the ignition process can be explained by assuming field emission only, without the pre-existence of nanovoids. Therefore, it can be assumed, that the initial ionization process if predominantly driven by field dependent ionization.