Nanosecond pulsed discharges in distilled water-Part II: line emission and plasma propagation

Figure 1 shows a schematic of the experimental setup used for time-resolved optical emission spectroscopy of the nanosecond pulsed plasma. The HV pulses are generated by a pulse generator FPG 30-01NK10 (FID Technology GmbH). The pulses have a rising time of 2–3 ns and a pulse width of approximately 15 ns. A frequency of 15 Hz was applied as well as a voltage of 20 kV. The cable connecting the power supply and the plasma electrode is a 12 m long coaxial cable (RG213) with a back current shunt (BCS) mounted at a central position along the cable (with a = b = 6 m in figure 1(a)). The BCS is used to measure the current flowing inside the coaxial cable which can be used for calculating the voltage pulse. A direct measurement of the current at the electrode tip is not possible due to electromagnetic interference inside the Faraday cage. Nevertheless, the current I can be estimated from the dissipated energy E that is derived from a comparison of the initial with the reflected pulses yielding E = 3 mJ. If we assume a voltage pulse length of approx. 15 ns at a voltage amplitude of 20 kV, the current can be calculated from the energy yielding roughly I = 10 A. The current density at the tungsten tip would be even more relevant for the analysis of the plasma since the current density may also vary locally due to the effects such as self-contraction being typical for high current density discharges. This is, however, not analyzed here, because it would be only based on the rough current estimates and better experiments would be required for any robust interpretation.

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The electrical circuitry powering the nanosecond plasma can have a significant influence on the plasma by reflections and oscillations of the high voltage pulse inside the cable, if the plasma load is not matched to the impedance of the cable. The length of the cable connecting power supply and plasma electrode is a crucial parameter to distinguish between the forward and backward traveling pulses in the BCS signal. In the case of the 12 m long cable, the separation between the forward (initial) and backward (reflected) traveling pulse is approximately 60 ns and therefore, the voltage waveform at the electrode can unambiguously be determined. The difference between the initial and the reflected pulse can be used for determining the dissipated power and energy for a pulse of 15 ns which are in this case 200 kW and 3 mJ, respectively.

The electrodes are mounted into a PMMA made plasma chamber with three quartz windows for optical access (see figure 1(b)). They consist of copper rods insulated by glass tubes. Stainless steel cannulas are inserted in the copper rods to clamp a tungsten wire (diameter 50 μm) as electrode. Distilled water with an electrical conductivity of 1 μs cm⁻¹ and a pH of approximately 5.5 is used as the liquid. The plasma chamber and the FID pulser are both surrounded by a common Faraday cage so that electromagnetic interference (EMI) cannot escape the system.

For imaging and optical emission spectroscopy (OES) measurements an Andor iStar DH734-18U-03 camera is used. For OES the camera is mounted to a triple-grating SpectraPro 750 spectrograph from Acton Research, which used a 50 $\frac{\text{grooves}}{\text{mm}}$ grating, blazed at 600 nm. The system has an effective spectral resolution of about 2 nm. The camera is synchronized to the discharge via the synchronization output of the FID pulser and a defined delay time to compensate for the cable length was set. The maximum jitter of the synchronisation signal is 0.5 ns and can, therefore, be neglected. By combining three spectra at different central wavelengths spectra of an overall wavelength range of approx. 600 nm could be recorded. Two connected UV suitable optical fibers from CeramOptec GmbH are used to couple the plasma emission into the spectrograph and to prevent EMI to escape from the Faraday cage. A collimator at the end of fiber d, which is mounted in front of the plasma chamber, collects the emitted light of the plasma into the optical system from a distance of about 4 cm. The 4 cm include a water layer of 1 cm from the electrode tip to the optical window. The system is calibrated with a broadband D₂-Halogen lamp. The measurements are performed with a gate time of t_gate = 2 ns and time steps of t_step = 2 ns between the spectra within an interval of 30 ns. Each spectrum is averaged over 1000 discharges.

A more detailed description of the setup can be found in part I of this paper series [24].

A single shot image taken of the plasma at 12 ns after ignition is shown in figure 2(a). In this phase, the plasma emission in the visible spectral range is the most intense. The image of the discharge shows that the maximum of emission is located in the direct vicinity of the electrode tip. Whereas the propagating plasma is only visible by faint structures developing up to the dotted circle. When the area of brightest emission is blackened, these structures become more visible, as discussed in the first part of this paper series (figure 13 in [24]). The diameter of the faint structures can be estimated roughly to be 100 μm from these images. Here it is important that the emission maximum is not located at the front of the propagating plasma (comparable to streamer head in gas discharges) but the location is close to the electrode tip. The good fit of black body radiation with temperatures of 6000–7000 K similar to the boiling temperature of tungsten led us to postulate that on the one hand black body radiation is the dominant source of the continuum radiation and that on the other hand the emitted black body radiation is likely to originate from the hot tungsten electrode [24].

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Figure 2(b) shows a typical sketch of a plasma that propagates into the medium. In principle, one could start with the model of a positive streamer [25, 26]. However, the exact mechanism of plasma propagation in the very dense medium of a liquid may differ from the classical streamer in the gas phase, because recombination is more dominant and the mean free path of the electrons is reduced to inter molecular distances in liquid water. Therefore, we describe the nature of the propagating plasma in more general terms: the plasma is expected to propagate similar to a positive space charge region where a cloud of positive ions creates a high electric field in the surrounding that causes further ionization events. The newly created electrons are transported to the positive space charge where recombination occurs. In this simple picture the plasma structure should consist of a leading edge where ionization is dominant and a trailing part where recombination is prevalent. When this plasma propagates through the liquid, a channel should be created along its path where the energy from the recombination events eventually leads to dissociation and heating of the water. This propagation of the plasma occurs with a velocity of approximately 46 km s⁻¹ in our experiment [24], as described in part I of this paper series. Summarizing, we separate the propagating plasma into three regions: a leading ionization region, a trailing positive space charge region or recombination region and a plasma channel along the propagation path where dissociative recombination converts the liquid into hydrogen and OH.

With respect to light emission, we may postulate four contributions: (i) the black body emission from the tungsten tip at boiling temperature, (ii) black body emission from a hot spot at the tip of the tungsten electrode at the root of the plasma channel, (iii) light emission from a region where recombination dominates, (iv) light emission from a small region at the leading edge of the propagating plasma where the electron density is high and ionization dominates. The background of the spectrum is dominated by the contribution from black body radiation (i) and (ii), the line features in the spectra are dominated by the contributions from (iii) and (iv).

In the first part of this paper series, we discussed the nature of the continuum. This continuum is dominated by black body radiation of the hot tungsten tip. Due to the high local current density an intense heating of tungsten occurs. This leads to typical black body temperatures of 7000 K or even higher. This temperature is consistent with the fact that the boiling temperature T_B of tungsten is at ${T}_{\text{B},{p}_{0}}$ = 5828 K at ambient conditions corresponding to a vapour pressure p₀. During plasma operation, non-negligible erosion of the tungsten tip occurs due to evaporation. This creates a higher tungsten vapour pressure in front of the electrode surface, that may cause the equilibrium surface temperature of the tungsten tip to increase even further. For example, if the partial pressure is increased by one or two orders of magnitude, the equilibrium temperature of a boiling tungsten surface may easily reach temperatures of 8000 K or higher.

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 on the hot tungsten surface may form, as it is known from arc lamp discharges [27], because the discharge current contracts the plasma to a particular location 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 dominates, 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, as discussed in [24].

In this paper, we regard the line emissions that become visible in the spectra. Since the plasma is ignited directly in distilled water, line emissions of only H and O containing atoms and molecules are expected. Any clear identification of emission lines is difficult, due to the very dynamic temporal evolution of the plasma, significant broadening effects and a limited signal-to-noise ratio at this high temporal resolution. Consequently, very many species may be formed during the dissociation of water, but a unique identification of, for example, OH emission with the prominent A-X bands at 306 nm is not possible. The only line emission that is clearly visible is the Balmer series of hydrogen, which is discussed in the following in detail.

Figure 3 shows the signature of spectral features at the line positions of the hydrogen Balmer series for H_α , H_β and H_γ . At later times after plasma ignition also a broadened oxygen emission line at 777 nm (OI(777 nm)) is observed. Due to the high temperatures and high densities of electrons and neutrals, all emission lines may be affected by Doppler broadening, van der Waals broadening or Stark broadening. The inspection of the spectra indicates full width at half maximum (FWHM) values of the lines of several nanometers at least, which is much larger than the Doppler broadening at temperatures of a few 1000 K. Therefore, only van der Waals and Stark broadening effects are discussed in the following. For these effects, the emission line should follow a line profile P(λ) of a Lorentzian for a central wavelength of λ₀:

$$\begin{equation}P\left(\lambda \right)=\frac{1}{\pi }\frac{\left(\frac{{\Delta}}{2}\right)}{{\left(\lambda -{\lambda }_{0}-{\lambda }_{\text{s}}\right)}^{2}+{\left(\frac{{\Delta}}{2}\right)}^{2}}\mathrm{d}\lambda \end{equation} \tag{ 1 }$$

with Δ the FWHM and λ_s a possible red shift of the line. The integration of the line profile yields ∫P(λ)dλ = 1.

Other spectral features as e.g. emission from molecular components as e.g. H₂O or OH cannot be identified. The limited spectral resolution combined with the signal noise and the broadening of the lines prohibit any unambiguous identification even of ro-vibrational bands.

Stark broadening of emission lines in plasmas occurs due the perturbation of the emission process by electrons and ions surrounding the emitting atom or molecule. This broadening effect is quantified for the hydrogen Balmer series by Gigosos et al [28] in the form of tables of FWHMs for different temperatures and different reduced masses μ. This reduced mass μ describes the relation between the emitter atom hydrogen and the perturbing mass of the surrounding ions. Since, we assume that hydrogen emits and that the dominant ion is a water ion, we may use μ ≃ 1 amu. The value for the reduced mass can change in the case of non-equilibrium situations to μ* = μT_e/T_g for different electron and heavy particle temperatures. In the case of a high electron but low heavy species temperature, smaller Stark FWHM values [15, 29] compared to thermal equilibrium conditions are obtained.

According to the tables of Gigosos et al, the Stark effect at a temperature of 20 000 K and an electron density of 10²⁴ m⁻³ yields an FWHM = 5 nm for the H_α line, an FWHM = 23 nm for the H_β line, and an FWHM = 27.8 nm for the H_γ line. The H_α FWHM varies typically by 5% for a temperature variation of a few 10 000 K, whereas the H_β and H_γ FWHM vary by 15% to 20%. Consequently, the H_β line is often used for Stark width analysis in plasma science since the line broadening is significant and the line is also sensitive to the plasma temperature [30]. The line width of H_α is rather insensitive to temperature changes and simpler line width formulas consistent with the tables of Gigosos et al are available. One example are FWHMs ${{\Delta}}_{{H}_{\alpha }}$ and red shifts λ_s,α of the H_α line as given by Kielkopf and Allard [31]:

$$\begin{equation}{{\Delta}}_{{H}_{\alpha }}\left[\mathrm{\mathring{\text{A}}}\right]=1.55\cdot 1{0}^{-11}{\left({n}_{\text{e}}\left[{\text{cm}}^{-3}\right]\right)}^{0.70{\pm}0.03}\end{equation} \tag{ 2 }$$

$$\begin{equation}{\lambda }_{s,\alpha }\left[\mathrm{\mathring{\text{A}}}\right]=1.23\cdot 1{0}^{-16}{\left({n}_{\text{e}}\left[{\text{cm}}^{-3}\right]\right)}^{0.92{\pm}0.03}\end{equation} \tag{ 3 }$$

The estimates are only validated up to electron densities of 10²⁵ m⁻³ and any application at higher electron densities is an extrapolation. The red shift of the lines due to the Stark effect is usually rather small and typically only 10% of the FWHM.

In the extreme nanosecond plasmas in liquids, the visibility of lines and their separation from the background of the spectrum makes the identification of lines and their FWHM and shift very challenging. For example, a broadened hydrogen H_α line is clearly visible in the spectra with an FWHM of typically of 80 nm, as shown below. Since the center of the line is shifted by 10% of the FWHM, the Stark effect is identified as the line broadening mechanism. Consequently, one would expect to also observe Stark broadened H_β and H_γ lines. The line intensities of H_β and H_γ , however, are one or two order of magnitudes smaller due to the lower population of the upper states and the much lower transition probabilities of H_β and H_γ in comparison to H_α (Einstein coefficients for spontaneous emission are ${A}_{{\text{H}}_{\alpha }}$ = 4.41 × 10⁷ s⁻¹, ${A}_{{\text{H}}_{\beta }}$ = 8.419 × 10⁶ s⁻¹, and ${A}_{{\text{H}}_{\gamma }}$ = 2.53 ⋅ 10⁶ s⁻¹, respectively). Consequently, if one observes a Stark broadened H_α line with an FWHM of 80 nm, an order of magnitude smaller H_β or H_γ line with a typically 4 times larger FWHM compared to the FWHM of H_α cannot easily be distinguished from the background continuum.

The second broadening mechanism that influences the FWHM of the hydrogen Balmer series is likely van der Waals broadening that is induced by collisions of hydrogen with surrounding collision partners. The van der Waals broadening is extracted from the formulas of Konjevic et al [32] yielding an FWHM:

$$\begin{align}\hfill w\left[\text{cm}\right]& =8.18{\times}1{0}^{-12}{\lambda }^{2}\left[{\text{cm}}^{2}\right]{\left(\alpha \left[{\text{cm}}^{2}\right]{R}^{2}\right)}^{2/5}\hfill \\ \hfill & \quad {\times}\enspace {\left(T\left[K\right]/\mu \left[\text{amu}\right]\right)}^{3/10}n\left[{\text{cm}}^{-3}\right]\hfill \end{align} \tag{ 4 }$$

with λ the wavelength of the emission in [cm], α the polarizability of the collision partners [cm²], T the temperature of the gas [K], and μ the reduced mass describing the collision of hydrogen and the collision partners [amu]. The factor R² can be extracted from the quantum numbers of the transition by ${R}^{2}={R}_{\text{u}}^{2}-{R}_{\text{l}}^{2}$ with

$$\begin{equation}{R}_{\text{u}}^{2}=0.5{n}_{\text{u}}^{2}\left(5{n}_{\text{u}}^{2}+1-3{l}_{\text{u}}\left({l}_{\text{u}}+1\right)\right)\end{equation} \tag{ 5 }$$

$$\begin{equation}{R}_{\text{l}}^{2}=0.5{n}_{\text{l}}^{2}\left(5{n}_{\text{l}}^{2}+1-3{l}_{\text{l}}\left({l}_{\text{l}}+1\right)\right)\end{equation} \tag{ 6 }$$

with n_u, n_l the main quantum numbers of the upper and lower state of the transition. l_u, l_l are the angular momentum quantum numbers of the upper and lower states. The polarizability α may range from 1.45 × 10⁻¹⁸ m² for water to 0.8 × 10⁻¹⁸ m² for oxygen or 0.66 × 10⁻¹⁸ m² for hydrogen as collision partners. If we assume that van der Waals broadening of hydrogen atoms is induced by collisions with water molecules at a density of 3 × 10²⁸ m⁻³ corresponding to the liquid density of water. Previously, we analyzed the pressures during plasma evolution and expansion by a modelling based on cavitation theory [23]. This yielded a gas density of liquid water and a temperature of a few thousand K during the plasma phase at the very beginning. If we use the very same estimate to assess the van der Waals broadening, one would expect FWHMs of 65 nm for H_α , of 34 nm for H_β and of 26 nm for H_γ . These high values should correspond to an upper limit. It is reasonable to assume that collision partners consist of hydrogen or oxygen atoms with much smaller polarizabilities and that the local densities at the location of the emitting atoms can be somewhat smaller than the liquid water density. If we assume for example hydrogen as emitter inside water at a reduced density of 3 × 10²⁷ m⁻³ and a temperature of 7000 K, one obtains FWHM values of 6.5 nm for H_α , 3.4 nm for H_β and 2.6 nm for H_γ . An FWHM of up to 80 nm, as visible for the H_α line in the spectra could only be explained by water molecules as collision partners at a density of liquid water of 3 × 10²⁸ m⁻³ and a temperature of 15 000 K. This seems unrealistic.

The van der Waals effect causes also a shift to the red of 33% of the FWHM [33], which is much larger than the shift of 10% of the FWHM due to the Stark broadening. Therefore, the nature of the broadening mechanisms for very broad lines can easily be identified by regarding both, the FWHM and the shift of the line. For example, the H_α line with an FWHM of 80 nm that is observed in the data at 14 ns after plasma ignition is shifted by 8 nm only, consistent with the Stark effect being the line broadening mechanism. Therefore, we assume that the impact of van der Waals broadening is much smaller in comparison to the line broadening by the Stark effect for very large FWHM values.

The high density of species in the nanosecond plasma, causes also self absorption of the emission lines [34, 35] and can be seen in the spectrum shown in figure 3 as small line reversal of the H_α line. Self absorption of an emission line takes into account that the emitted photons of a transition may be reabsorbed by the very same species along the optical path. This effect can be calculated by using an optical depth p given by:

$$\begin{equation}p=\frac{h{\nu }_{0}}{c}BP\left({\lambda }_{0}\right)\int {n}_{\text{a}}\left(x\right)\mathrm{d}x\end{equation} \tag{ 7 }$$

with h Planck's constant, ν₀ the frequency of the emission line, B the Einstein coefficient of absorption and P the line profile. The integral ∫n_a(x) dx = N_a yields the total number of absorber species N_a along the optical path. The Einstein coefficient B for absorption is connected to the Einstein coefficient for spontaneous emission A via:

$$\begin{equation}A=\frac{2h{\nu }^{3}}{{c}^{2}}B=\frac{2hc}{{\lambda }^{3}}B\end{equation} \tag{ 8 }$$

with c the velocity of light. This yields a modification of an emission line I(λ) with a line profile P(λ) and amplitude I₀ passing a layer with absorbing atoms of the same identity of [34]:

$$\begin{equation}I\left(\lambda \right)={I}_{0}P\left(\lambda \right)\mathrm{exp}\left(-p\frac{P\left(\lambda \right)}{P\left({\lambda }_{0}\right)}\right)\end{equation} \tag{ 9 }$$

This is the simplest case of a spatial separation of emitters and absorbers. Since the nanosecond plasma is very much localized, we assume that this situation describes our case and the hydrogen emitting at the center of the plasma in the recombination region or in the ionization region are affected by dissociated cloud of hydrogen atoms in the surrounding.

Self absorption of emission lines mainly affects the center of a line and leads to a peculiar change of the line shape. This needs to be distinguished from a regular absorbing medium, which influences the overall line intensity but not the line shape. The absorption coefficient of liquid water in the wavelength region of the Balmer series is very small of the order of 10⁻⁴ to 10⁻² cm⁻¹ and can be neglected. More important is the influence of the optical path x. Along this path, a significant density of the lower states of the transition of the emitting species needs to be present for the self-absorption effect to become visible. In case of the hydrogen Balmer series, this constitutes to the n = 2 state of hydrogen. Such states are excited states of hydrogen and should only be dominant in the plasma filaments, either at the leading edge or in the recombination region behind the streamer head. From the inspection of the ICCD image above, we estimate that such optical lengths are in the range of 100 μm at most.

The temporal evolution of the initial and reflected BCS voltage and of the electrode voltage are shown in figures 4(a) and (b), respectively. Additionally, figure 4(b) shows the integrated light from the camera images. One can clearly see two intensity maxima in the emission which are correlated to the rising and falling edge of the high voltage pulse. In between, a dark phase of the pulse, as already reported in the literature [19, 36], can be identified. The synchronization of electrical and optical signals can also be performed by correlating the voltage plateau and the dark phase in emission. A direct synchronization between optical and electrical signals could not be realized for the present measurements. In the first part of this paper series, we connected these emission maxima with the ignition phenomenon at the beginning of the pulse corresponding to field ionization of water molecules at small protrusions at the tungsten electrode tip. This instantaneous formation of positive ions in proximity of the tungsten electrode leads to the seed ions for the plasma to propagate following a mechanism similar to a streamer mechanism in the gas phase, as discussed below. These fast ionization processes may induce light emission due the acceleration of the electrons in the high local fields inducing that emission maximum. At the end of the pulse, the voltage is being switched off and an electric field acts on the plasma channel, leading to an acceleration of residual electrons and to field emission at small protrusions at the tungsten electrode tip. A second maximum in emission becomes visible as shown in figure 4. The postulated temporal correlation of the voltage evolution and emission intensity needs to be validated in future experiments by an accurate synchronization of both signals. Nevertheless, these processes describe the discharge behaviour and evolution inside the liquid reasonably well under the assumption that the correlation between intensity and voltage is given.

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The voltage measured at the BCS and the acquisition by the camera and by the emission spectrometer are synchronized, but the absolute time delay between these data sets is difficult to calibrate. Instead, we used the most characteristic point in the data at the end of the plasma pulse at the maximum of the voltage, to shift the voltage curves, the camera images and the emission spectra by a few nanoseconds to fix a common unique time axis. Such a shift may seem arbitrary, because delays between voltage and emission are well known to occur for gaseous streamers and ionization avalanches [37]. But, as it is known from literature [14], the plateau of the voltage pulse is equivalent to the time of lowest intensity and therefore this assumption is taken for shifting both axes.

The corresponding emission spectra taken at high temporal resolution are shown in figure 5 (same data as in part I of the series). The individual spectra are stacked in the graph and scaled for best visibility of the spectral features. One can clearly see a pronounced and very broad H_α peak, especially at later times after plasma ignition. Complex spectral features at the location of the H_β and H_γ lines are also clearly visible. At later times, a broadened line at the position of OI(777 nm) also appears. The temporal development of the spectra indicates that the Balmer lines are not much shifted with respect to the standard line positions. This indicates that Stark broadening appears to be the dominant broadening mechanism at least for the broad H_α line.

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The analysis of the line emissions in the spectra requires first the subtraction of the background and then the fitting of the emission lines of the Balmer series. At first, the black body radiation from the hot tungsten tip including the possible formation of a small hot spot at the foot print of the plasma, as discussed in part I of this paper series is modelled. Then, the background subtracted spectra are fitted using an emission model for the hydrogen Balmer series. The best fit is obtained, if two main contributions are being postulated for hydrogen Balmer line emission:

• Balmer series emission from hydrogen atoms in the ionization region: the ionization region is the location of high electron densities and it is reasonable to assume that Stark broadening dominates line emission of the hydrogen lines from this location. The leading edge of the propagating plasma, where the electric field is expected to be the highest is also a very small region in comparison to the complete plasma channel, so that self absorption of the lines should play only a minor role.In addition, excitation of hydrogen by fast electrons that are accelerated in the electric field around the leading edge of the propagating plasma should be the dominant process. This should lead to a population of excited states of hydrogen that can be described by an electron temperature. In this case, the line emission from H_α in the Balmer series will dominate.

• Balmer series emission from hydrogen atoms in the recombination region: the recombination region behind the ionization region of the propagating plasma exhibits lower electron densities and Stark broadening effects might be similar to van der Waals broadening in this region. In addition, the recombination region represents almost the complete volume of the propagating discharge so that any self absorption effects may influence the emission line shapes much stronger than for the emission from the ionization region.In a recombination reaction of a proton and an electron, higher states of hydrogen are populated first inducing light emission from cascade processes. In this case, strong deviations from a thermal population of the excited states of hydrogen are expected. For example, if recombination leads to the population of the n = 5 state in hydrogen first, the line emission of H_γ in the Balmer series will be enhanced. In general, the differences in energies of the n = 3, n = 4, and n = 5 states in hydrogen are only ≃1 eV. At an estimated temperature of 7000 K, the differences in population are therefore only a factor 5 at most assuming a Boltzmann equilibrium, but not orders of magnitude.

This separation in two regions of origin of the hydrogen Balmer series generates a typical spectrum, where the emission from the ionization region is dominated by a Stark broadened H_α line with H_β and H_γ being barely visible, because these lines are much smaller, but also much broader due to their higher sensitivity to the Stark effect. This is in contrast to the emission from the recombination region, where H_β and H_γ radiation from recombination dominates and the much stronger H_α emission is reduced due a strong self absorption effect. Using this simple model of two hydrogen emission populations, the background corrected spectra can be very well fitted as shown in figure 6.

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Figures 6(a)–(e) show the data at different times after plasma ignition and the corresponding modelling of the continuum background consisting of black body radiation assuming a temperature between 5200 K and 7900 K as indicated and a second contribution of black body radiation at a very much higher temperature. Details of this are discussed in part I of this paper series. Figures 6(a')–(e') show the residuum (signal-background) on a same scale. It can be noted that the residuum exhibits a deviation from zero especially at wavelengths above 750 nm and also below 280 nm, which is especially pronounced when the absolute signal intensity is small as can be judged from the different scales in figures 6(a)–(e). These deviations are an artifact from the calibration procedure and originate from the subtraction of the background light from the data. This induces significant error in the wavelength region where the detection system exhibits a poor sensitivity as it is the case below 280 nm and above 750 nm.

This fit is based on the parameters amplitude and FWHM for each Balmer line originating either from the recombination or from the ionization region. In addition, a total number of absorbers is used to describe the self absorption for the complete Balmer emission for each of the regions. The black body background is described by a temperature and an amplitude. This yields 10 free parameters for this fitting. Such a large number of fitting parameters can render a model ambiguous, but different parameters are affecting very different parts of the spectra and different features of the Balmer series that can easily be separated from the continuum background. The most robust parameters are the FWHM and amplitude of the H_α line originating from the ionization region and the corresponding number of absorber atoms. The emission lines from the recombination region suffer all from strong self absorption, which makes the fitting of the amplitude, of the FWHM, and of the absorber numbers much less reliable. The error bars for these fitting parameters express the ambiguity in their absolute values. The amplitudes of the lines depend very much on the excitation process, but also on the volume of the emission region. This will be discussed below. At first, we discuss the line shapes in the spectra in figure 6 as follows:

• at 4 ns after ignition (figure 6(a)): the H_α line originating from the ionization region shows a small degree of self absorption indicating the existence of absorbing hydrogen atoms in the optical path at the very beginning of the discharge. The H_β and H_γ line show strong self absorption line shapes. At the central position of the H_β and H_γ line, a broadened line without any self absorption is still visible. Such a contribution indicates hydrogen emission in the absence of self absorption. These emitting hydrogen atoms cannot originate from the ionization region, because the FWHM should be much larger than the FWHM of the H_α line from the very same region. Instead, these small H_β and H_γ contributions may originate from a separate region of hydrogen atom emission outside of the central part of the propagating plasma. This is just a hypothesis and further experiments would be required to uniquely identify this small contribution.
• at 6 ns after ignition (figure 6(b)): the amplitude of the H_α line is increasing and the line shows less self absorption. The FWHM is also larger indicating a larger electron density. This trend can be easily understood. At the beginning of the discharge, more and more hydrogen atoms are being ionized, which causes an increase in electron density, but at the same time a decrease in hydrogen absorbers inducing self absorption. The plasma propagation apparently outruns the formation of neutral hydrogen atoms due to field effects in the vicinity of the electrode.
• at 12 ns after ignition (figure 6(c)): the FWHM of the H_α line is very large and shifted typically by 10% of the FWHM indicating the Stark effect being the broadening mechanism. At the same time, the emission pattern of the H_β and H_γ line remains unaltered, but their contribution in relation to the H_α line becomes smaller. At later stages in the plasma propagation, the density along the plasma channel might decrease and the electron temperature cools down, so that the hydrogen emission from this region becomes fainter as the plasma propagates.
• at 16 ns after ignition (figure 6(d)): the H_α line shape is very similar to the spectrum at 12 ns. The typical slight asymmetry to the red of the Stark broadened line becomes visible. A broad line for the OI(777 nm) emission appears at 777 nm.
• at 24 ns after ignition (figure 6(e)): the H_α line is dominant in the spectrum with a smaller FWHM indicating lower electron densities. The spectral signatures of the H_β and H_γ line become weaker indicating that during the decay of the plasma, the electron temperature in the plasma channel may decrease causing the lines to become rather faint very quickly.

The good agreement between data and emission model assuming two major contributions of emitting hydrogen atoms yields line parameters for the H_α , H_β , and H_γ lines for the ionization regions and the recombination region and two numbers of absorbing species. The parameters line amplitude, FWHM and number of absorbers causing self absorption are coupled and lead to a certain ambiguity in the absolute values. The most robust parameters are the absorber numbers and the line parameters for the pronounced H_α line of the emission from the ionization region. The detailed fitted parameters of the H_β and H_γ lines are discussed only to a small extent in the following, because they may suffer from larger error bars and also from the effect that the recombination region may be composed of different spatially separated parts. Here, the simple model of a unique distribution of hydrogen atoms may be an oversimplification.

A good fit is obtained by assuming a number density of N_a = 4 × 10¹⁶ absorber atoms along the optical path for the hydrogen atoms emitting in the recombination region. The plasma propagates in random directions from the tungsten electrode, so that most of the light emission from the recombination region escapes along the sides of the plasma channel. If we assume an optical path length of photons escaping from this channel of typically 100 μm, one may deduce a density of absorbing hydrogen atoms of n_a = 4 × 10²⁰ m⁻³. Then = 2 state of hydrogen is 10.2 eV above the ground state. If we assume the black body temperature of the tungsten tip of typically 7000 K being also representative for the gas temperature in the recombination region, we can derive a ground state density of n₀ = n_a exp(10.2 eV/7000 K) of 8.8 × 10²⁷ m⁻³. This is close to the liquid density of water and leads to the conclusion that water may be completely dissociated within the recombination region, producing a very high local density of hydrogen atoms. This complete dissociation of water in the recombination region is consistent with chemical kinetics calculations of the water chemistry in the nanosecond plasma [38].

An absorber number N_a of only a few 10¹³ absorber atoms along the optical path for the hydrogen atoms emitting from the ionization region is necessary to fit the data. This much smaller number may be compared to the estimate for the self absorption in the recombination region: when an absorber number N_a of 10¹⁶ corresponds to a length scale of 100 μm in the recombination region, an absorber number of 10¹³ should correspond to an optical path for self absorption of light from the ionization region of the order of 1 μm or even below. This is consistent with typical models for propagating plasmas in the literature such as streamers. As a streamer propagates, only at the very tip a high electric field is created that accelerates electrons into the streamer head. If we transfer this typical picture of streamer discharges to the in liquid discharge, excitation and emission would occur in a very thin layer of around 1 μm at the head of the filament.

The line profiles of the H_α line originating from the ionization region are fitted assuming Stark broadening including the effect of self absorption. The electron densities are then derived from the FWHM using equation (2). The temporal evolution of the electron density is shown in figure 7(a) together with the temporal evolution of the voltage for comparison. The electron density reaches very high values of the order of 5 × 10²⁵ m⁻³ at the end of the pulse (this implies the validity of the extrapolation of equation (2) to electron densities slightly above 10²⁵ m⁻³). These data are consistent with our previous experiment [23], as shown in figure 7(b) comparing the new data taken at a temporal resolution of 2 ns with the previous data taken at a temporal resolution of 30 ns. Such electron densities are typical for discharges in liquids for a wide range of pulse lengths [8, 9, 39].

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It is striking that the electron density follows closely the voltage applied to the electrode during the rising and falling edge of the pulse. In nanosecond plasmas in gases at atmospheric pressures, the voltage and current exhibit usually a delay in between with the voltage rising first followed by the current due to the delayed build-up of the electron density in the ionization avalanche. During the plasma propagation in the liquid, however, the density of species is three orders of magnitudes higher, so that the build-up of charges is expected to be much faster compared to the variation of the voltage. The same also holds for recombination that should exhibit time constants of the order of ps at these densities. The actual electron density is then a balance between generation of free electrons in the high electric fields and their loss due to recombination. This is consistent with the observation that the electron density follows also the decrease of the voltage with a time constant of 8 ns (shown as solid line in figure 7(a)). The decay of the electron density is not a free decay due to recombination, but rather follows a decreasing equilibrium value as a competition between ionization and recombination.

A close inspection of the data indicates also an oscillation of the electron density during the decay with a period of 10⁻⁸ s. This is similar to the time constant of the nanosecond pulse itself. Any further interpretation of the temporal evolution of the electron densities at 20 ns after plasma ignition and later remains ambiguous, because the effects of van der Waals broadening on the FWHM cannot easily be distinguished from the Stark broadening at electron densities below 10²⁵ m⁻³ in our high pressure nanosecond plasmas.

The interpretation of the H_α line width using the Stark effect may be questionable taking into account that pressure broadening might also be significant given the very high pressures in our plasmas. However, Stark broadening and pressure broadening can be distinguished based on the shift of the lines, which is only 10% in case of Stark broadening but 30% of the wavelength in case of pressure broadening. In our experiment we see only a shift of 10%. Therefore, we assume that Stark broadening is dominant and that the shift of the H_α line and its width can be directly connected to an electron density.

In the following, we discuss the line parameters of the most prominent H_α emission originating from the ionization region. Figure 8 shows the temporal evolution of the number of absorbers N_a (a), the amplitude of the H_α line (b), and the temperature of the hot tungsten tip (c) for comparison. The temporal evolution of the voltage and of the electron density, as shown in figure 7, are also plotted as reference.

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The number of absorbers is of the order N_a = 3 × 10¹³ at the very beginning of the discharge (figure 8(a)). It decays to zero at 10 ns simultaneously with the increase in electron density. This behaviour can easily be explained. At the beginning of the discharge, field ionization creates the first positive ions in the vicinity of the tungsten tip. This positive space charge starts to propagate and causes dissociation and excitation of water molecules and their dissociation products. As the plasma propagates more and more hydrogen atoms are converted into hydrogen ions and are thereby not able to act as absorber atoms anymore or the total numbers of hydrogen atoms in front of the propagating plasma becomes so small that any self absorption cannot longer be identified in the line profiles.

The amplitude of the H_α emission from the ionization region is a measure of the volume or the size of the plasma that is propagating (figure 8(b)). At the beginning of the discharge, the amplitude is rather large, whereas the electron density is still small. This is consistent with a distribution of emitting hydrogen atoms over a large area in the vicinity of the tungsten surface, where field effects cause ionization and excitation. As time progresses, the amplitude decreases sharply and the electron density increases. This can correspond to a localization of the plasma at the electrode tip and may resemble a typical dynamic of the formation of an arc spot. This is in line, with the observed variation of the radiation from the tungsten tip: simultaneously with a localization of the H_α emission, the black body temperature of the tungsten tip decrease whereas the contribution from a hot spot causing a shift of the continuum to shorter wavelengths becomes visible, as can be deduced from the fitting parameters of the black body continuum shown in figure 8(c). At the location of the hot spot, tungsten is efficiently evaporated inducing evaporation cooling leading to a lowering of the temperature in the region surrounding this hot spot. At the end of the pulse, the amplitude of the H_α line goes through a short maximum, because the change in the electric fields during the falling edge of the pulse accelerates again free electrons and/or induces field effects that lead to light emission. The amplitude of the H_α emission quickly drops to very small values, although the electron densities decrease quite slowly. Apparently, the electron temperature for exciting the Balmer series drops much faster than the electron density. This is also typical for most afterglow plasmas.

Figure 9 shows the amplitude of the H_α emission from the ionization region (same data as in figure 8) in comparison with the amplitudes of the H_β and H_γ emission from the recombination region. One can see that the amplitudes of lines from the ionization region and recombination region follow the same trend. One can also notice that the ratio between the H_β and H_γ amplitude drops as the plasma propagates. If one corrects the amplitudes for the different Einstein coefficients for these transitions, one may deduce a rather high population of the higher states, as being typical for recombination being the source of emission.

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