Ignition and propagation of nanosecond pulsed discharges in distilled water -- negative vs. positive polarity applied to a pin electrode
IIgnition and propagation of nanosecond pulseddischarges in distilled water - negative vs. positivepolarity applied to a pin electrode
K. Grosse, M. Falke, A. von Keudell
Experimental Physics II - Reactive Plasmas, Ruhr-Universit¨at Bochum, D-44780Bochum, GermanyE-mail:
Abstract.
Nanosecond plasmas in liquids are being used for water treatment,electrolysis or biomedical applications. The exact nature of these very dynamic plasmasand most important their ignition physics are strongly debated. The ignition itself maybe explained by two competing hypothesis: (i) ignition in water may occur via fieldeffects at the tip of the electrode followed by tunneling of electrons in between watermolecules causing field ionization or (ii) via gaseous processes of electron multiplicationin nanovoids that are created from liquid ruptures due to the strong electric fieldgradients. Both hypothesis are supported by theory, but experimental data are verysparse due to the difficulty to monitor the very fast processes in space and time. Inthis paper, we are using fast camera measurements and fast emission spectroscopy ofnanosecond plasmas in water applying a positive and a negative polarity to a sharptungsten electrode. It is shown that plasma ignition is dominated by field effects atthe electrode-liquid interface either as field ionization for positive polarity or as fieldemission for negative polarity. This leads to a hot tungsten surface at a temperatureof 7000 K for positive polarity, whereas the surface temperature is much lower for thenegative polarity. At ignition, the electron density reaches 4 · m − for positiveand only 2 · m − for the negative polarity. At the same time, the emission of theH α light for the positive polarity is 4 times higher than that for the negative polarity.During plasma propagation, the electron densities are almost identical of the order ofa 1 to 2 · m − and decay after the end of the pulse over 15 ns. It is concluded thatplasma propagation is governed by field effects in a low density region that is createdeither by nanovoids or by density fluctuation in super critical water surrounding theelectrode that is created by the pressure at the moment of plasma ignition. a r X i v : . [ phy s i c s . p l a s m - ph ] F e b
1. Introduction
Plasmas in liquids is a prominent field of research being at the core of many applicationsranging from wastewater treatment, to plasma supported electrolysis, to applicationsin medicine [1]. The discharges are usually ignited by applying a high voltage (HV)pulse to a pin electrode immersed in the liquid opposite to a grounded counter electrode(either a pin or a plane electrode). The high voltage can be applied continuously orin the form of short pulses with a specific temporal structure, which strongly affectsthe ignition and plasma physics of these discharges. For example, if the pulse rise timeis slow in the range of microseconds or longer, Joule heating of the liquid occurs atfirst and the local evaporation of the liquid will form small gas filled bubbles. Thecondition for ignition can then be reached in the gaseous environment and a plasma isformed that causes these bubbles to further expand and to initiate various chemical gasphase reactions. If, however, the pulse rise time is of the order of nanoseconds only, theinertia of the liquid adjacent to the pin electrode is so high, that any formation of amacroscopic bubble and any consecutive gas phase ignition of a plasma is not possible.Nevertheless, luminous discharges are being observed even on nanosecond time scales[2]. We refer to these discharge for simplicity as streamers , although the physics behindmight differ from traditional streamer discharges in gases. The understanding of thecreation of such plasmas inside the liquid is still an open question until today [3, 4],which is addressed by several ignition models: (i) in a seminal work, Seepersad et al. [2]postulated the presence of regions of low density in the liquid in front of a high voltageelectrode that are induced by liquid ruptures caused by the high electric field gradients.Such ruptures induce the formation of so-called nanovoids . It is striking that ignitiononly occurs above electric field strengths that allow also liquid rupture. The ignitionitself may then proceed by a Townsend mechanism for charge multiplication inside thesenanovoids. (ii) Plasma ignition inside the liquid may also occur in previously formedbubbles, which are present in the liquid due to an insufficient outgassing. When thesemicroscopic gas bubbles exist close to the tip of the biased electrode, plasma ignitionin these bubbles may occur [5]. Simek et al. [6, 7] used laser interferometry to analysethe plasma generation on a picosecond scale and observed very dense streamer shadowsemerging from the electrode tip only for the very first pulse of an experiment thatstarted with de-ionized and outgassed water. Even the second plasma pulse in thevery same experiment showed a more inhomogeneous streamer pattern, suggesting thatsome of the created gas from the first plasma pulse remain and influences the ignitionof all consecutive pulses. (iii) Alternatively, the classical breakdown in solids has beenemployed by Devins et al. [8] to describe plasma generation inside transformer oils usingthe Zener theory. Here, electron tunneling between adjacent liquid molecules acts asthe source of ionization during plasma propagation [9].In a recent paper series [10, 11], we analyzed the ignition phase of nanosecondplasmas in water for positive polarity applied to a tungsten wire electrode. The spectraare predominantly composed of a black body background originating from the emissionof the hot tungsten electrode during the pulse. This tungsten electrode exhibits atemperature close to the boiling temperature of tungsten of around 7000 K dependingon the pressure in front of the electrode. On top of this background, the Balmer seriesof hydrogen atoms becomes visible as well as the atomic oxygen line at 777 nm at latertimes after ignition. The modeling of the Balmer series indicated a strong contributionof self absorption, which has been modeled by two contributions to the emission pattern,one originating from the ionization zone at the streamer head with an extension in therange of a few micrometers only showing lines with weak self absorption line profiles andone originating from a recombination region in the streamer channel behind the headwith an extension of 50 to 100 micrometers showing lines with strong self absorptionline profiles. The observed degree of self absorption of the emission line profiles couldonly be explained assuming a very high density environment being close to the liquiddensity. Therefore, the hypothesis of field effects being also relevant for ignition andplasma propagation has been stated. The electron densities had been extracted fromStark broadening of the H α lines yielding values up to a few 10 m − .The interpretation of the observed strong self absorption of the emission lines as anindication of field effects governing plasma propagation is, however, only a very indirectconclusion. Therefore, we attempt in this paper to compare plasma propagation fordifferent polarities of the voltages applied to the electrode immersed in water, becauseit is expected to affect the plasma characteristics. The most prominent example arethe properties of positive versus negative streamer discharges in gases. For example,if ignition processes in the gas phase dominate for these nanosecond plasmas, thosedifferences should also show up in the analysis of our experiments. For example, positivestreamers exhibit a more diffuse structure in comparison to negative streamers since theelectrons created by photo ionization in front of the streamer head are accelerated intoit, whereas negative streamers are usually more localized, since the strong electric fieldcreates a local ionization front [12, 13]. In addition, the electron density in positivestreamer heads is much lower compared to negative streamer heads.The transfer of this knowledge regarding streamers in gases onto the case of plasmaignition at the electrode-liquid interface is not straightforward since two aspects need tobe considered: (i) the temporal development of the medium going through the phasesliquid-gas-plasma in correlation to the temporal development of the applied voltage,and (ii) the contribution of field emission of seed electrons directly at the tip of theelectrodes. Four different models A, B, C and D for the dynamic of the plasma can bedistinguished (see illustration in Fig. 1): • Model A - Ignition via build up of gaseous streamers inside large gas filled bubblesinside the liquid (Fig. 1(a)) : gas filled bubbles may be present from dissolvedair in the liquid or may be created by Ohmic heating and evaporation during therising time of the high voltage pulse. When such gas filled bubbles are present,the development of electron avalanches in the gas phase is the most likely ignitionmechanism. The build up of an avalanche and the formation of a streamer occursover length scales of several 10s of micrometers to millimeters depending on the + 20 kV+ 20 kV +++ -- - (c) nanovoids create internal interfaces at breakdown(a) neg./pos. streamer inside a gas filled bubble + 20 kV ++++ --- hot tungstenelectrode + (b) charge avalanche and propagation by field effects +- x +- x +- x μ m100 μ m10 nm +- x (d) super critical fluid (SCF) 100 µm + 20 kV - gasSCF streamerSCF-streamer nanovoid Figure 1.
Models for plasma ignition and propagation as gaseous streamers insidegas filled bubbles in the liquid (model A), as a charge avalanche that propagates viafield effects (model B), as charge multiplication inside nanovoids or at the interfacesbetween nanovoids and liquid (model C), or as electron channeling in a super criticalfluid (SCF) (model D). pressure. Tereshonok et al. [14, 15] analyzed the time span for the avalancheformation in conjunction to the formation of a gaseous bubble. Due to the finitetime span for such a phase transition to occur, usually rather slow rising times (ofthe order of microseconds) and rather long pules are required for such mechanismto be prevalent.Different polarities of the voltage are expected to have a pronounced effect on theplasma properties similar to the difference between negative and positive coronadischarges in gases and the associated differences between negative and positivestreamers. • Model B - Ignition via charge avalanches that propagate via field effects (Fig. 1(b)) :the formation of a gas filled bubble may be prohibited due the inertia of the liquidat very fast rise times of the voltage. It is reasonable to assume that ionization andpropagation of the discharge occurs via field emission or field ionization due to thestrong gradient of the electric field that propagates through the material. Such amechanism requires a very high electric field and is well known for semiconductorelectron avalanche diodes. Field ionization of water molecules requires electric fieldsof at least 0.2 V/˚A [16, 17] that may occur in the vicinity of small protrusions at theelectrode surface, but also at irregularities at the front of the propagating chargeavalanche.Different polarities of the voltage are expected to have no effect on plasmapropagation since the field effects are very local and the tunneling of an electronbetween adjacent water molecules should not depend on the direction of plasmapropagation in first order. However, the different polarities might have an effecton plasma ignition at the electrode liquid interface due to the difference betweenfield ionization for a positive polarity versus field emission for a negative polarityapplied to the electrode. • Model C - Ignition via charge multiplication inside nanovoids or at the interfacesbetween nanovoids and water (Fig. 1(c)): the high electric fields that are formedby applying a voltage to the sharp electrodes also causes ruptures in the liquid[18, 19]. This creates nanometer sized voids in the medium that may favor ignitionand plasma propagation. The size of these nanovoids, that have not yet beenobserved so far, are expected to be smaller than required for the build up of acharge multiplication avalanche. But, field emission of electrons at the internalsurfaces of the nanovoids, the acceleration of the electrons in the free space of thesenanovoids and ionization at the opposite end may contribute to the ionizationefficiency. Several models tried to analyse such a plasma propagation mechanism[20, 21]. Any experimental verification is still lacking.Different polarities of the voltage may have an effect since the electrons are eitheraccelerated inside the nanovoids towards the electrode or in the opposite direction.If the shape of these nanovoids is affected by the in-homogeneous electric fieldgradient, any differences comparing both polarities could become visible. • Model D - Ignition via charge multiplication in super critical fluid (SCF) of water(Fig. 1d): the existence of regions of lower density might also be explainedby the fact that water is expected to be in the super critical state due to thevery high pressures upon plasma ignition. This state is also referred to as asuper critical fluid (SCF) or as a cluster fluid [22], since the molecules are nothomogeneously distributed, but form rather clusters with space in between. Thecritical temperature of water is 647 K and the critical pressure is 2.2 · Pa.The pressure at the moment of ignition reaches value up to 10 Pa [23] in ourexperiment, which is well above that threshold. It can be assumed that plasmaignition occurs at first by field effects at the electrode-liquid interface leading to suchhigh pressures and temperatures at the electrode tip initially. These pressures andtemperatures are the boundary condition for a spherical pressure and temperaturefield that propagates away from the tungsten tip. Since pressure and temperatureare expected to decrease with distance, one can conclude that also a sphericalregion of water at exactly the critical point has to be present. At its critical point,the medium exhibits strong density fluctuations which may support ionization andacceleration of electrons in the high electric fields via electron channeling [24]. Thishas been studied for the breakdown at the critical point for CO , where a reductionof the ignition voltage at the critical point was observed [25, 24, 22]. The studyof plasmas in SCFs is usually performed by transferring the medium at first in thesuper critical state in a pressurized cell and then igniting a plasma. In the context ofnanosecond plasmas in liquids, it is conceivable to assume that the ignition processcreates this high pressure region initially in which then the plasma may propagate.This should be a self amplified process, since any local plasma creation will instantlybring a neighboring region of water in its super critical state.Different polarities of the voltage may have an effect since the electrons are eitheraccelerated inside the SCF away from the electrode tip or towards the electrodetip. Since the charge multiplication is a very local process the electron densitiesare expected to be the same. But the amount of excited volume might be different,as the electron avalanches propagate towards each other for positive polarity (seeschematic in Fig. 1d) and propagate apart for negative polarity.Given the short time scale of the nanosecond pulsed plasmas, it is reasonable toassume that the ignition physics should properly described by models B, C, or D in Fig.1. Nevertheless, different electron densities are expected for the same voltage that isbeing applied to the electrode tip. For example in model A, the formation of positivestreamers for a positive voltage applied to the electrode should lead to a smaller electrondensity compared to the case of negative polarity. In model B, the electron densityshould not be affected by the polarity of the voltage. In model C the electron densityfor the positive polarity might be higher, because the electrons are now acceleratedinto regions of larger nanovoid density compared to the negative polarity. In model D,the electron densities are expected to be identical. The validation of model C is mostdifficult and field effects at the internal interfaces of the nanovoids are overlapping withionization due to the free acceleration of electrons inside the nanovoids. Both effectsmay counteract or amplify each other.The distinction of models A, B, C, and D has to be regarded with great caresince the dominance of each of the models may change with time during the pulses.For example, at the very beginning of the pulse on the time scale of picoseconds, fieldeffects should dominate leading to a description by model B. As the time progresses,liquid ruptures and/or the transition to an SCF may occur and the effects according tomodel C and D may contribute. Finally, for at least very long pulses, the coalescence ofnanovoids and the expansion of the gas filled bubbles will eventually lead to a dominantcontribution to the plasma formation according to model A.Next to the ionization and the plasma propagation mechanisms in theliquids/gas/plasma phase, also field effects at the electrode surface change whencomparing negative and positive polarity. In the case of negative polarity, the electrodetip is a continuous source of electrons, which are emitted due to the field effect atprotrusions on the surface. This is very efficient and very high electron currents arebeing expected (similar to field emitter tips). This is in contrast to the positive polarity,where the field effect may ionize adjacent water molecules close to the surface at theonset of the high voltage pulse. However, any reduction in the density of the watermolecules due the phase transition to the gas phase will drastically reduce the efficiencyof charge transfer from the medium onto the electrode tip.Summarizing, one may conclude that a comparison between a negative and apositive polarity voltage applied to a pin electrode immersed in water based on anevaluation of the temporal development of the electron density and its absolute valuemay provide information regarding the dominance of one of the four models above.Four experimental quantities will be assessed in this paper: (i) the dissipated poweris deduced from the difference between the forward and backward traveling HV pulsesthat are generated by a nanosecond HV pulser and sent along a transmission line to theplasma electrode, (ii) the total deposited energy depending on the polarity is evaluatedusing cavitation modeling of the bubble radius expansion versus time, (iii) the temporaldevelopment of the electron density is monitored from the Stark broadening of the H α Balmer lines, and (iv) the degree of self-absorption of the hydrogen Balmer lines usused to assess the local density at the location of plasma emission. By comparing thesequantities, the validity of models A, B, C, or D will be judged.
2. Experiment
A detailed description of the setup is published elsewhere [23] and the key elements areonly shortly summarized in the following. Fig. 2 shows a schematic of the experimentalsetup used for time-resolved optical emission spectroscopy of the nanosecond pulsedplasma. The high voltage (HV) pulses are generated by two FID pulse generators (FIDTechnology GmbH) of different polarities, respectively. The pulses have a rising timeof 2-3 ns and a pulse width of 10 ns. A frequency of 15 Hz is applied as well as appliedvoltages of +20 kV or -20 kV, respectively. The cable connecting the power supply andthe plasma electrode is 10 m long with a back current shunt (BCS) mounted at a centralposition along the cable (with a =b = 5m in Fig. 2a). The BCS consists of 11x3.3 Ωresistors welded into the cable shield.The plasma chamber is made of PMMA and three quartz windows are mounted,two from the sides for (shadowgraphic and ICCD) imaging and one at the front forthe collection of light emission during optical emission spectroscopy. The electrodesare positioned at the center of the chamber approximately 10 mm apart, as illustratedin Fig.2b. Distilled water with an electrical conductivity of 1 µ S cm − and a pH ofapproximately 5.5 is used as the liquid. The plasma chamber and the FID pulser areboth surrounded by a common Faraday cage so that electromagnetic interference (EMI)cannot escape the system. The power dissipation in these nanosecond plasmas depends sensitively on the electriccircuitry connecting the power supply to the plasma electrode. The electric pulsesgenerated by the power supply travel along the cable to the electrode tip and generatethe plasma but a part of the electric signal is also reflected, travels back to the powersupply and is reflected again, before it re-ignites the plasma after a time span defined bythe travel time along the cable. This yields an oscillation of the electrical power imposedonto the plasma with period times that can be comparable to the original length of theplasma pulse, as discussed in the literature [26, 27, 23]. This can be avoided by usingeither a matching of the impedance of the plasma by placing a resistor in parallel and inseries to the tungsten electrode or by using a very long cable length so that the reflectedpulse re-ignites the plasma at much later times compared to the first pulse. Here, weused a cable length of 10 m, which yields a delay in between these pulses of 100 ns,which is very much larger than the time span of the plasma development due to theignition by the first pulse.The BCS measures the voltage of the traveling high voltage pulse generated bythe pulser in the middle of the transmission line. When this pulse is reflected at thetungsten electrode, it is reflected and the forward traveling and the backward travelingpulses interfere due to the pulse reflection. This is taken into account by reconstructing
FID
BCS spectrograph I CC D sync ns pulse optical fibres + collimator liquid a bliquid ICCD Xe short arc lamp ns plasma
HV cablecannula50 µmTungsten wire (a)(b) c d
Figure 2.
Sketch of the experimental setup. (a) Layout of the powering of the setupusing a nanpsecond pulser from FID connected to the tungsten electrode with a HVcable where a back current shunt (BCS) is inserted. (b) Layout of the plasma itselfused for shadowgraphy measurements. the voltage at the electrode (in the following: electrode voltage ) from the BCS signalsas follows: The initial and reflected voltage pulses measured at the BCS are summedup with respect to their temporal evolution. This estimation of the electrode voltageresults in a peak amplitude of twice the applied voltage amplitude.The power dissipated in the discharge is assessed from the BCS data by multiplyingthe voltage and current measured at the BCS location according to the procedure bySimek et al. [28]. The absorbed power is then calculated by the difference between thepower of the HV pulse before and after reflection at the electrode and plasma generation.
Shadowgraphy images are taken after the discharge ignition to observe the gas bubbledevelopment in the liquid medium. Therefore, the electrode tip is illuminated by the0light of a Xe short arc lamp and the light is focused onto the ICCD chip of an AndoriStar DH734-18U-03 camera with a lens system. The spectral sensitivity of the cameraranges from 180-850 nm and was triggered by the sync-output of the HV pulsers. Thejitter of only a few ps is negligible. The gas bubble expansion and collapse has beenmonitored by single-shot images with camera gates of 50 ns .The plasma induced bubble formation is modeled by cavitation theory, beginningwith a bubble with radius R and pressure p at the interface between gas and liquidat time t = 0. The pressure in the liquid far away from the bubble is p ∞ . Due toa varying pressure inside the liquid, the sound speed also varies with distance radius r . The expansion of a bubble can be modeled with the well known Rayleigh-Plessetequation [29, 30, 31, 32, 33]: R ¨ R (cid:32) − ˙ Rc (cid:33) + 32 ˙ R (cid:32) − ˙ R c (cid:33) = h (cid:32) Rc (cid:33) + (cid:32) − ˙ Rc (cid:33) Rc ∂h∂t (1)With R the radius of the interface between bubble and liquid, c the speed of soundat the location of that interface. h denotes the enthalpy that is calculated from theequation of state for water as it depends on the pressure p . The experiments in oursetup indicate that the velocity c of the emerging acoustic waves depending on p issignificantly larger than the velocity ˙ R of the bubble radius itself. Therefore, we neglectthe term proportional to ∂h∂t in eq. 1. The pressure inside the bubble is given bythe adiabatic expansion of the water vapor starting with an initial pressure p ,gas thatconstitutes a free parameter for the modeling. The initial radius is set to R = 25 µ mcorresponding to a tungsten tip diameter of 50 µ m. Equation 1 is solved numericallywith the boundary condition of R t =0 = R and ˙ R t =0 = 0. All details of this calculationcan be found in [23]. The emission spectra are acquired by an Andor iStar DH734-18U-03 camera thatis mounted to a triple-grating SpectraPro 750 spectrograph from Acton Research. A50 groovesmm grating blazed at 600 nm is used. The measurements were performed with agate time of t gate = 2 ns and time steps of t step = 2 ns between the spectra. Therefore atime span of 50 ns could be monitored from ignition to the end of the initial pulse. Dueto the size of the CCD chip, the spectrum is composed of three different spectra withthe central wavelengths (CW) of 400 nm, 550 nm and 850 nm, covering a wavelengthrange of approx. 600 nm. The spectra were background subtracted and calibrated witha broadband D-Halogen lamp. Due to internal reflections of the 2nd order onto thegrating, a high pass filter was used for the measurements with CW of 550 nm and 850 nm.The data were processed with a MATLAB script and merged for every step in time.Each spectrum is averaged over 2000 discharges. The acquisition of spectra is performed1using a glass fibre that collects light from the complete region including electrode tipand propagating streamer. Therefore, the light of all propagating plasmas in these2000 discharges is properly collected despite the fact that the streamers propagate inindividual discharges in random directions.The emission spectra consist of a broad continuum and of broadened lines, asillustrated for an experiment monitoring the nanosecond plasmas at 4 ns after ignitionfor a polarity of + 20 kV and of -20 kV (generator output voltage) in Fig. 3a andb, respectively. The spectra contain a contribution from black body radiation from thetungsten tip, which is also the brightest spot in the single shot images. This backgroundmay also contain a short wavelength contribution that may originate from any hot spotsat the electrode (and thus being modeled also with black body radiation with a hightemperature) or from a Bremsstrahlung contribution due to the acceleration of theelectrons in collisions with ions and neutrals. The line emissions contribute only to asmall percentage to the total number of generated photons. The broadened lines arefrom the hydrogen Balmer series (line positions indicated as thin red bars in Fig. 3). The spectra are analysed and quantified following the procedure, as discussedpreviously in [11, 10]. The continuum contains a contribution of black body radiationof the hot tungsten tip, which can be clearly identified in the spectrum using a positivepolarity in Fig. 3a. The intense heating of tungsten can be linked to the electron currentthat is drawn by the positively biased electrode causing typical black body temperaturesof 7000 K. The interpretation of the background as black body spectrum with a singletemperature cannot easily be applied for the spectra collected for negative polarity, asillustrated in Fig. 3b. Instead a short wavelength contribution is visible in all spectra.Such short wavelength contributions may originate from the formation of a hot spoton the electrode, as already discussed in [10] for plasmas using a positive polarity atthe electrode, but may also originate from Bremsstrahlung contribution due to theacceleration of the electrons in collisions with ions and neutrals. The limited signal-to-noise ratio in the data does not allow a clear distinction between black body radiationor Bremsstrahlung radiation in the short wavelength region. Furthermore, the signalcalibration especially at short and long wavelengths below 280 nm and above 800 nmrespectively suffers from the low detector sensitivity at these wavelengths. Therefore, thespectrum is modeled by assuming a short wavelength contribution (orange dashed linein Fig. 3b) corresponding to black body at 20000 K and a long wavelength contributioncorresponding to a varying temperature as indicated in Fig. 3b. Both contributionsare weighted to fit the background. This background fitting approach for the data fromthe experiments for negative polarity is somewhat arbitrary and the short wavelengthcontribution is not discussed any further.2
300 400 500 600 700 8000.02.0x10 s i gna l ( c t s ) l (nm) data @ 4ns blackbody background (T=7000 K) data-background streamer channel streamer head model positve polarity + 20 kV
300 400 500 600 700 8000.02.0x10 s i gna l ( c t s ) l (nm) data @ 4ns background black body background (T=4500 K) short wavelength background data-background streamer channel streamer head model negative polarity - 20 kV Figure 3.
Example for analysis of an emission spectrum at 4ns after ignition for apolarity of +20 kV (a) and of -20 kV (b), respectively. The background is modeled byblack body radiation assuming different temperatures, as indicated. The backgroundcorrected spectrum are modeled with line profiles of the Balmer series of hydrogen(vertical red thin bars) combining a contribution from the streamer channel and thestreamer head. For details see text.
The line contribution to the spectra has been thoroughly analyzed in [11]. Since theplasma is ignited directly in distilled water, line emissions of only H and O containingatoms and molecules are expected. Most prominent is the hydrogen Balmer series, asshown Fig. 3 for H α , H β and H γ (Balmer series indicated as red bars). Due to thehigh temperatures and high densities of electrons and neutrals, all emission lines areaffected by Doppler broadening, van der Waals broadening, or Stark broadening. Dueto the very high electron densities, Stark broadening dominates, as already discussedin [11]. This broadening effect is quantified by using line profiles calculated by Gigososet al. [34] in the form of tables for FWHMs of the hydrogen Balmer series for differenttemperatures. The red shift of the lines due to the Stark effect is usually rather smalland typically only 10% of the FWHM. The example spectra in Fig. 3 are taken at 4 nsafter ignition for which the plasmas show a peak in intensity. The broadened H α lines3are clearly visible, with the lines for the H α lines for the positive polarity being a bitbroader than for the negative polarity indicating a smaller electron density in the lattercase.The high density of species in the nanosecond plasma causes also self absorption ofthe emission lines [35]. This self absorption effect can be seen in the spectrum shown inFig. 3a, and especially in Fig. 3b, as small line reversals of the H α line. Self-absorptionof an emission line takes into account that the emitted photons of a transition may bereabsorbed by the very same species along the optical path. Self absorption by hydrogenatoms generated by the dissociation of water along the streamer channel may also absorbphotons from the black body radiation of the hot tungsten tip. Due to the very localnature of the streamer propagation it is reasonable to assume that the likelihood that thestreamer propagates along the line-of-sight of the optical path is very small. Therefore,blackbody radiation from the hot tungsten tip represents a non obstructed backgroundin the spectra.The Balmer H α , H β , and H γ lines are modeled by assuming different FWHMsand amplitudes, as well as a specific degree of self absorption. Two contribution arepostulated, one originating from the ionization zone of the streamer showing very littleself absorption (bright green line in Fig. 3) and one originating from the streamerchannel showing very large self absorption (blue line in Fig. 3). The sum of those twocontributions (orange line in Fig. 3) is fitted to the background subtracted spectra (thingreen line in Fig. 3). Details of this line fitting procedure are discussed in [11]. Here,we analyse only the H α line profiles and intensity that can easily be separated from thebackground continuum in the data. Thereby, this line analysis is also independent fromany assumptions regarding the nature of the background continuum.4
3. Results
The temporal evolution of the BCS voltage for the positive and negative pulser at ±
20 kV generator output voltage is presented in Fig. 4. The gray areas show the timewindow when the pulses that are reflected at the electrode tip are measured again atthe BCS location. The reflected pulses for both polarities show two distinct peaks,whereas the forward traveling pulses show only one peak at the very beginning. Theconsecutive reflections at the pulser change the signals and the pulses re-appear at theBCS location after 100 ns (indicated by dashed line in Fig. 4). The decrease in voltagewhen comparing the forward with the reflected pulses is used to quantify the dissipatedenergy, yielding 12 mJ for the positive and 18 mJ for the negative polarity. -30-20-100102030 0 20 40 60 80 100 120 140 160-30-20-100102030 B C S v o l t age ( k V ) pos. pulser B C S v o l t age ( k V ) time (ns) neg. pulser t reignition ~ (a)(b) Figure 4.
Voltages measured at BCS for positive (top) and negative (bottom) nspulser with generator output voltage of 20 kV. The gray areas mark the reflectedpulses traveling back towards the pulser. The time between two forward travelingpulses leading to re-ignition of discharge is approximately 100 ns.
The temporal evolution of the voltage is also compared to ICCD images of plasmaemission for negative and positive polarity of -20 kV and of +20 kV in Fig. 5. Theimages are taken during different pulses with an adjusted and shifted time delay. It canbe seen that several ignition locations at the electrode tip can become visible for bothpolarities that also seem to illuminate several streamer channels propagating away fromthe electrode. The plasma pattern in the ICCD images appear for later stages of plasmapropagation rather similar for both polarities. The location of the electrode tip itselfremains the brightest spot of emission independent of the polarity of the voltage. This5is consistent with the observation of a dominant contribution from black body radiationin the spectra (see example spectra in Fig. 3a) that originates from the hot tungstensurface, as already discussed in [23].
Positive polarity + 20kV (b)
Negative polarity - 20 kV (a)
Figure 5.
Images of plasma emission for negative (left) and positive polarity (right).The individual times are indicated. The white line denotes the shape of the electrode.Each image is scaled to its maximum intensity for best visibility. (a)(b) positive polarity emission intensity electrode voltage e m i ss i on i n t en s i t y ( a . u . ) e l e c t r ode v o l t age ( k V ) -10 -5 0 5 10 15 20 25 30 35 negative polarity emission intensity electrode voltage time (ns) e m i ss i on i n t en s i t y ( a . u . ) -60-50-40-30-20-10010 e l e c t r ode v o l t age ( k V ) Figure 6.
Reconstructed voltage pulse from BCS data (black line) for 20 kV generatoroutput voltage for the positive (a) and negative (b) pulser. The integrated lightintensity is shown in blue. The red vertical line denotes t = 0 ns One can clearly see two emission maxima at the rising and falling edge of thepositive and the negative high voltage pulse. In between, a dark phase of the pulse, asalready reported in the literature [2], can be identified.Although the electrode voltages look similar, the temporal evolution of the emissionintensity differs when comparing both polarities. The first emission intensity maximumusing the positive pulse is the strongest, whereas the second intensity maximum is higher7for the negative pulse. This could indicate, that plasma ignition during the rise of thevoltage pulses depends on the polarity.
The nanosecond plasma is eventually initiating the expansion of a cavitation bubbleon time scales of microseconds. Selected shadowgraphs are shown in Fig. 7 that aretaken at different times after ignition for negative polarity of -20 kV (a) and for positivepolarity of +20 kV (b). Fig. 7c shows the temporal evolution of the bubble radius forboth polarities in comparison with cavitation modeling using an initial pressure p ,gas of 1.5 · Pa and of 2 · Pa for an initial volume with radius R of 25 · − m.The pressure in the ambient liquid has been set to p ∞ = 10 Pa. Details are discussedin [23].The dissipated energy given by the product of initial pressure p ,gas of 2 · Patimes volume of a sphere with radius R yields 1.3 · − J, which is much smallerthan the dissipated energy of the order of 10 − J that has been derived from comparingthe BCS data of the traveling high voltage pulses. Such a difference is not surprising,since the initial pressure p ,gas refers to the kinetic energy of species that are created bywater dissociation in the plasma. The energy that is dissipated into dissociation, intoheating the tungsten surface, or into photon emission does not instantly contribute tothe pressure that drives the expansion of the cavitation bubble.The comparison between the cavitation modeling and the observed bubble radiusshows some deviations especially at times earlier than 10 µ s and at times later than 50 µ s: (i) at earlier times, any differences may be associated with the fact that the initialexpansion follows the streamer channels that are not spherical (as shown in Fig. 7a andb) as the spherical bubble in the model; (ii) at later times, when the bubble collapsesagain, the decrease in bubble sizes is much faster in the model compared to the data.This may be associated with the fact that the collapse of the bubble occurs around atungsten wire, whereas the model may be too simple for this phase since it regards onlya collapsing spherical bubble without any adjacent solid surface.It is, however, most striking that the temporal evolution of the bubble radius doesnot depend on the polarity of the voltage applied to the electrode. Apparently, theenergy that is dissipated in the streamers propagating from the electrode into the liquidthat eventually convert water into a hot gas that drives cavity expansion is the same. The tungsten electrode tip surface is investigated before and after discharge treatment.Therefore, new tungsten electrode tips are taken for the measurements with positiveand the negative applied pulses, respectively. The surfaces of the tungsten electrode areinspected using SEM images, as shown in Fig. 8 for the positive polarity of + 20 kVbefore (a) and after plasma exposure for 30 min (b) and for the negative polarity of - 20kV before (b) and after plasma exposure of 25 min (d). It can be seen that the degree8 bubb l e r ad i u s ( m m ) time ( m s) model p = 1.5 x 10 Pa model p = 2 x 10 Pa pos. polarity neg. polarity (a)(c)(b)
200 µm200 µm
Figure 7.
Shadowgraphy images for the negative (a) and positive (b) polarity atdifferent times after plasma ignition. The white line marks the shadow of the electrode.(c) Bubble radius vs. time for negative (black squares) and positive (red squares)polarity. The solid line denotes a Rayleigh-Plesset modelling of bubble expansionusing an initial pressure of 1 GPa and a volume energy of 1 · − J (blue line) and of1.3 · − J (red line). field ionization of water molecules, causes an intense heating which keepsthe tungsten surface at the phase transition liquid-to-vapor. Here, tungsten is soefficiently evaporated that a solid surface remains without any visible melting topologyat the surface after cooling down after the pulse. The high temperatures may alsofavor crystallization of tungsten and the creation of larger grains. The inherent stress ofthese grains becomes visible after cooling down as small cracks at the plasma exposedtungsten surface (see Fig. 8c).In the case of negative polarity, however, electrons are emitted from the tungstenelectrode by field emission . This eventually cools the surface and only the Ohmic heatingof the current passing the tip may heat the electrode at least up to the phase transitionfrom solid-to-liquid. After the end of the plasma pulse, the molten tip solidifies againand molted droplets at the surface remain visible (see Fig. 8d).
Fig. 9 shows the emission spectra for positive (a) and negative polarity (b) versus time.It can be seen that the continuum background is more pronounced for the positivepolarity compared to the negative polarity, as already illustrated for the example spectrain Fig. 3. The broad H α emission can clearly be identified. The continuum is separatedfrom line emission following the procedure from [10, 11], as also illustrated before. Thebackground consists of a black body radiation component with a temperature of 7000 Kfor the positive and a lower temperature for the negative polarity. A short wavelengthcontribution is also visible, which may be linked to the formation of a hot spot on thetungsten electrode or to Bremsstrahlung. Here, we only analyse the broadening andintensity of the H α emission lines.Fig. 10 shows the electron densities derived from the evaluation of the Starkbroadened H α lines and the number of emitting hydrogen atoms as derived from theintegrated line profile of H α (blue circles in Fig. 10). In addition the electrode voltageis shown (red lines in Fig. 10).It can be seen that the electron density follows the electrode voltage rather closely,with electron densities reaching values up to 4 · m − for the positive polarity and up0 b e f o r e p l a s m aa f t e r p l a s m a pos. pulse polarity neg. pulse polarity m m5 m m 25 m m25 m m(a) (b)(c) (d) Figure 8.
SEM micrographs of the tungsten electrode before (a,b) and after (c,d)plasma exposure for positive (a,c) and negative (b,d) polarity. to 2 · m − for the negative polarity. After the end of the plasma pulse the electrondensity decays with a time constant of approximately 15 ns, which is similar to thedecay of the electrical power. Especially, at times larger than 15 ns, oscillations of thevoltage become visible (ringing) that eventually corresponds also to an oscillating powerinput causing the light emission to oscillate as well. Apparently, the electron densityand its dynamic is rather similar when comparing positive and negative polarity. Theline reversal of the H α line is a measure for the degree of self absorption of the H α light.This contribution may be visible only in the very beginning and is again rather similarfor both polarities (not shown).The number of emitting hydrogen atoms is estimated from the H α line profileintegral. At the very beginning, the positive polarity causes an intense light emission ofH α , whereas it is small in case of the negative polarity. At later stages, this integratedH α light is again rather similar, when comparing the positive and negative polarity.1 H a H b (a) polarity + 20 KV (b) polarity –
20 kV
300 400 500 600 700 800 i n t en s i t y wavelength (nm)
300 400 500 600 700 800 i n t en s i t y wavelength (nm) H a H b
28 ns
26 ns24 ns22 ns20 ns32 ns
30 ns
Figure 9.
Temporal evolution of plasma emission for positive (a) and negative (b)polarity. The line positions for the H α and H β lines are indicated. The spectra areoffset for better visibility (horizontal dashed lines).
4. Discussion
The experiments comparing negative and positive polarity applied to a tungstenelectrode immersed in distilled water revealed that some characteristics are almostidentical, whereas others differ significantly. The latter are associated with the interfacesolid-liquid and the differences between field emission and field ionization that causeplasma ignition. The experimental observations can be summarized as follows: • Black body temperature: in case of a positive polarity, a continuum backgroundequivalent to a surface temperature of 7000 K can be seen. This temperature isequivalent to the phase transition liquid-vapor of tungsten. In case of a negative2 n e e l e c t r on den s i t y ( m - ) voltage e l e c t r ode v o l t age ( k V ) H a area H a ( a r ea ) -10 0 10 20 30 40 5001x10 n e e l e c t r on den s i t y ( m - ) time (ns) -50-40-30-20-100 voltage e l e c t r ode v o l t age ( k V ) H a area H a ( a r ea ) (a) (b) Figure 10.
Temporal development of the electron densities in relation to the appliedvoltage for positive (a) and negative polarity (b). Please note that the scales for voltageand electron densities are identical in (a) and (b), but the scale for the H α emissiondiffers by a factor 4. polarity, a significant contribution of black body radiation cannot uniquely beidentified so that the temperature should be significantly lower. Despite a similardissipated energy, the heating of the electrode is apparently more significant for thepositive polarity. • Electron density: the electron densities differ only by a factor of two with respect toits maximum value at the very beginning of the pulse. The densities do not dependon the polarity of the electrode for most of the later temporal development, asillustrated again in Fig. 11. Apparently, the efficiency of ionization during plasmapropagation does not depend significantly on the direction of the electric field. Thisis very different to gaseous streamer discharges, where negative streamers exhibitmuch higher electron densities compared to positive streamers. The decay of the3electron density after the HV pulse is also almost identical, as shown in Fig. 11.The loss of electrons may correspond to the recombination of electrons with ionsindicating that the densities are again rather similar leading to an almost identicaldecay rate. -10 0 10 20 30 40 5001x10 negative polarity positive polarity e l e c t r on den s i t y ( m - ) time (ns) Figure 11.
Comparison electron density for positive and negative polarity (same dataas in Fig. 10) • Emission pattern: the emission pattern in the ICCD images are rather similar forboth polarities. This is in contrast to similar experiments from Seepersad et al.[36], who reported that the emission of a positive and negative pulsed dischargeinside distilled water shows very different emission patterns. The negative pulseddischarge led to a faint glowing structure at the electrode, whereas a positive pulseresulted in a filamentary discharge structure. This was connected to a gas dischargepropagation. The main difference to this work is the longer rise time of 4 ns and apin-to-plane geometry in the experiments of Seepersad et al. • H density: the total number of emitting hydrogen atoms is almost identical forthe negative and positive polarity. Only in the very beginning, the emission by Hatoms is enhanced for the positive polarity.Based on these data, we postulate that the process of plasma ignition at theelectrode-liquid interface induces large differences in the plasma characteristics whencomparing both polarities, whereas the actual plasma propagation appears to be rathersimilar, as discussed in the following.4
The ignition of the plasma is caused either by field ionization of water molecules forpositive polarity or by field emission of electrons from the electrode for negative polarity.In case of field ionization for positive polarity, the layer of water molecules adjacentto the surface is efficiently ionized by tunneling of electrons into the electrode. Inaddition, free electrons from the ionization of water molecules in the high electric fieldare accelerated towards the tungsten electrode and cause an intense heating. At the sametime, a large number of hydrogen atoms is created by for example impact dissociationor dissociative recombination of water ions and electrons. The created excited hydrogenatoms cause an intense H α emission at the very beginning. At later times, when theplasma propagates along the streamer channel, the efficiency of hydrogen excitationbecomes smaller.In case of field emission for negative polarity, an efficient injection of electrons intowater occurs. This field emission appears to create a much smaller electron densityin the beginning and also a much smaller number of hydrogen atoms that are beingexcited. At later times, when the plasma propagates along the streamer channel, theefficiency of hydrogen excitation is similar to that for positive polarity.Apparently, field ionization and field emission create very different electrondensities and thus also different numbers of excited hydrogen atoms during the risingfront of the pulse. At the same time the heating of the tungsten electrode is muchstronger for positive polarity reaching temperatures of 7000 K and only much lowertemperatures for negative polarity.The thresholds in electric field strengths for field ionization and field emission forthe W/H O system are rather similar, namely 0.2 V/˚A [16, 17] and 0.3 V/˚A [37],respectively. It is assumed that these electric fields are reached at small protrusions onthe tungsten electrode. The electric field E can be estimated from the applied voltage U for a surface with curvature radius r as E = U/ (5 r ) [37]. Thereby, a critical fieldstrength of 0.2 V/˚A at a voltage of U = 20 kV, requires a curvature radius of at least r = 2 µ m of small protrusions at the tungsten tip. Such small features can, in fact, beseen in the SEM images in Fig. 8. The threshold field strengths, however, depend alsosensitively on the work function of the tungsten surface, which is 4.5 eV for elementaltungsten, but can rise to 6 eV for oxidized tungsten. Consequently, the local oxidationstage at the surface may have a significant influence on the field effects.The experiments revealed smaller electron densities and a smaller blacktemperatures at plasma ignition for negative polarity, where field emission dominatesrather than field ionization . We argue that this difference is associated with the difficultyof electron emission from a partly oxidized rough tungsten surface in comparison to fieldionization of an adjacent layer of water molecules. The ionization of water moleculesmay occur across a large surface area in front of the electrode, whereas it is assumedthat field emission of electrons may occur only at few spots on the surface, where thework function is the smallest locally. As a result, the current and the plasma power5is localized at a few hot spots at a negatively biased surface, which causes a smallerelectron density and less heating of the tungsten electrode. Plasma ignition by field effects at the electrode-liquid interface may provide someseed electrons, but also volume effects may trigger plasma ignition in the liquidmedium surrounding the tungsten tip. It is for example conceivable to assume electronmultiplication in low density regions in the liquid with the superimposed high electricfield. Such low density regions may either be nanovoids caused by liquid rupture ordensity fluctuation in an SCF at the critical point. • Ignition in nanovoids:
Nanovoids are being created by the electric field pressuregradient surrounding the tungsten electrode tip above a value of 2 · Pa forcavitation to occur to induce liquid ruptures [38]. A seed electron may be generatedat the inner walls of such a nanovoid due to field effects. Due to the very high electricfields, an extension of a few nanometer of these nanovoids is already enough toallow a successful next ionization of such an accelerated electron inside a nanovoid.Simek et al. [28] showed emission spectra for experiments using a very high voltageof 100 kV applied to a pin electrode in water, where the time dependence ofthe spectra evolution in the first 3 ns could be best described by electron-neutralBremsstrahlung that develops in time. They also state that the electron generationis assumed to occur via field effects at nanovoid interfaces (or at the electrodeitself) and the radiation is caused by the acceleration of these created electronsinside nanovoids. Such a region of slightly lower density is also consistent withthe density estimates from the observed degree of self absorption of the hydrogenBalmer lines, as discussed previously [11]. Quantitative modeling of ignition by Liet al. [20] showed, however, that electron multiplication in a single nanovoid mayoccur, but that the density of nanovoids is only 1% so that the development of acomplete charge avalanche is difficult. • Ignition in an SCF: as an alternative, ignition may occur as a volume process byregarding the possible transition of the medium into a super critical state. Thecritical pressure of water is 2.2 · Pa, which is almost identical to the thresholdfor cavitation and liquid ruptures, the critical temperatures is 647 K. Ignition asa volume process my follow three steps in time: (i) at first, local field effects atthe electrode-liquid interface cause ignition that induces a high local pressure oftypically 10 Pa (estimated from the boundary condition of cavitation modellingabove), but also a temperature of the local medium above the critical point of water(estimated from the black body radiation). (ii) Second, a pressure and temperaturefield expands into the medium surrounding the electrode tip, as illustrated in Fig.12 showing a simple r − dependence [29] of the pressure surrounding a bubble withradius of 25 µ m. The interface between the high pressure field and the ambientliquid propagates with the sound velocity outwards after ignition. The velocity of6the pressure wave propagating into the liquid within the first 44 ns after ignitionhad been estimated from the shadowgraphy measurements and ranges between 5500ms − to 9000 ms − depending on the electrode voltage [23]. This can be convertedinto a region with a radius of 55 µ m and 90 µ m that is affected within 10 ns andthat can be converted into the super critical state. (iii) Third, at the front of theacoustic wave, the pressure goes from a value above the critical pressure (markedas red line at 2.2 · Pa in the Fig. 12) to the ambient pressure. Therefore, in theregion of high electric field an acoustic wave front travels outwards that induces theliquid to go through the critical pressure. Finally, the density fluctuations at thecritical point at this acoustic wave front allow ignition. This may be compared witha shadowgraphic image of the discharge taken at 44 ns after ignition but with a gatetime of 70 ns to cover the expansion of the pressure field but also plasma emission,as shown in the insert in Fig. 12. One can clearly see a dark area surroundingthe tip as an indication of the high pressure field and also that plasma propagationitself occurs inside this region. It can be assumed that ignition occurs within sucha region. A similar connection between the region affected by the pressure and theregion where the first streamers becomes visible [2].
26 ns 28 ns gate2ns . mm gate2ns Pressure field in the liquid supercriticalstate
44 ns p crit, H2O bubb l e bubb l e sound speed10 km/s p r e ss u r e ( P a ) distance r (µm) Figure 12.
Pressure field in the liquid after ignition according to cavitation theory.The inserts show shadowgraphy of the ignition phase with a delay of 44 ns and a cameragate of 70 ns. The red line denotes the critical pressure for water.
The ignition via nanovoids or via a SCF should occur rather similarly. However,the experiments reveal large differences with respect to the plasma characteristicsupon ignition. Therefore, we argue that field effects at the interface-liquid should bedominating.7
Plasma propagation for positive and negative polarity are almost identical with respectto the electron density or the number of exited hydrogen atoms, as a measure for thedensity of the medium in which the streamers propagate. Based on the impact ofself absorption on line emission, we assume that the density is slightly lower thanthe liquid density [11]. Any independence of plasma propagation on the polarity isconsistent with our hypothesis of an ionization mechanism in model B and D consistingof electron tunneling in between adjacent water molecules or electron channeling in anSCF, respectively. To some extent also model C may be still consistent with the data,because the acceleration of electrons in small nanovoids may also not be affected by thedirection of the electric field at least in first order. Any gradient in the density of thenanovoids may exist, but since the data for the plasma propagation are almost identical,any influence of such a gradient cannot be seen. Nevertheless, the presented data donot allow to distinguish between plasma propagation via field effects or via accelerationof electrons in an ensemble of nanovoids.The identical electron densities can be explained by assuming that the localionization processes are the same for both polarities. Nevertheless, the data on theH α emission intensity show that the light in case of the negative polarity takes abit longer time to decay after the pulse in comparison to the positive polarity. Onemay speculate that this is caused by different volumina that are being affected by theionization fronts propagating in different direction for both polarities either away from ortowards the electrode tip, as discussed for model D, although more detailed experimentand modeling is required to be able to interpret this. The hypothesis for plasma ignition and propagation is most consistent with model Dand is summarized in the following . The plasmas are ignited via field ionization of watermolecules at the electrode-liquid interface for positive polarity. This ionization occursover a large area in front of the electrode surface. The collected electrons cause a strongheating of the tungsten tip. For negative polarity, ignition occurs via field emissionwhich is more localized at the electrode surface. The initial pressures are of the order of10 Pa and temperatures in the range of 1000 of K. This converts the adjacent water intothe super critical state. In such a state, electron acceleration and multiplication mayoccur via electron channeling in these density fluctuations. One may coin such plasmapropagation as SCF-streamers that propagate towards the tungsten tip for positive andaway from the tip for negative polarity. The electron densities do not depend on thedirection of propagation of the SCF-streamers. This interpretation is consistent withthe data, but remain still be an indirect reasoning and more detailed time and spaceresolved experiments as well as multi physics modeling on an atomistic scale will berequired to uniquely identify the plasma ignition and propagation mechanisms in thefuture.8
5. Conclusion
Plasma ignition and plasma propagation for nanosecond plasmas in water have beenanalysed by optical and electrical diagnostics comparing positive and negative polarityof ±
20 kV applied to a tungsten electrode. It is shown that the plasma ignition byfield ionization creates a larger electron density and thus a larger density of exitedhydrogen atoms compared to plasma initiation by field emission. The heating of thetungsten electrode is much more severe for positive polarity reaching temperatures upto 7000 K, whereas the temperatures are much lower for negative polarity. The electrondensities associated with plasma propagation, however, are rather similar. This led tothe conclusion that plasma propagation is a very local effect for plasmas inside liquidsthat is either governed by field ionization of water molecules around the streamer heador by acceleration and field emission of electrons in nanovoids or sustained by densityfluctuations in water due to its super critical state.9
Acknowledgements
The authors appreciate the help from Susanne Jordans and Felicitas Scholz from Chairof Materials Science and Engineering, Ruhr-University Bochum for their assistance withthe SEM images. This project is supported by the DFG (German Science Foundation)within the framework of the Coordinated Research Centre SFB 1316 at Ruhr-UniversityBochum.
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