Electric field distribution in a surface plasmaflow actuator powered by ns discharge pulsetrains

M Simeni Simeni1, Y Tang2, K Frederickson1 and I V Adamovich1

1Nonequilibrium Thermodynamics Laboratory, Department of Mechanical and Aerospace Engineering,The Ohio State University, Columbus, OH 43210, United States of America2Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department ofEnergy and Power Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

E-mail: adamovich.1@osu.edu

Received 29 May 2018, revised 17 August 2018Accepted for publication 17 September 2018Published 15 October 2018

AbstractElectric field vector components in a nanosecond pulse, surface dialectric barrier dischargeplasma actuator are measured by picosecond second harmonic generation, for positive, negative,and alternating polarity pulse trains. Plasma images show that in the same polarity train, thepositive polarity discharge develops as two consecutive surface ionization waves, while thenegative polarity discharge propagates as a single diffuse ionization wave. In the alternatingpolarity train, both positive and negative polarity discharge plasmas become stronglyfilamentary. In all pulse trains, the measurement results demonstrate a significant electric fieldoffset before the discharge pulse, due to the surface charge accumulation during previousdischarges pulses. This demonstrates that charge accumulation is a significant factor affecting theelectric field in the discharge, even at very low pulse repetition rates. Peak electric field measuredin the alternating polarity pulse train is lower compared to that in same polarity trains. However,the coupled pulse energy in the alternating polarity train is much higher, by a factor of 3–4, mostlikely due to the neutralization of the surface charge accumulated on the dielectric during theprevious, opposite polarity pulses. This suggests that plasma surface actuators powered byalternating polarity pulse trains may generate higher amplitude thermal perturbations, producinga stronger effect on the flow field. The present results show that the time scale for the electricfield reduction in the plasma after breakdown is fairly long, several tens of ns, including theconditions when the discharge develops as a diffuse ionization wave. This suggests that aconsiderable fraction of the energy is coupled to the plasma at a relatively low reduced electricfield, several tens of Townsend. At these conditions, the discharge energy fraction thermalized asrapid heating would remain fairly low, thus limiting the effect on the flow caused by the high-amplitude localized thermal perturbations.

Keywords: plasma actuator, ns pulse discharge, flow control, electric field, second harmonicgeneration

1. Introduction

Over the last few years, significant progress has been made inapplications of nanosecond pulse dielectric barrier discharge(DBD) plasma actuators for boundary layer separation con-trol, lift enhancement, vorticity generation, and boundarylayer stability [1–9]. In spite of considerable recent advances

in this field, the potential of plasma flow control for aero-dynamic applications remains rather uncertain. One of thereasons for this is that dynamics of these discharges, as wellas mechanisms of their interaction with the flow, remain notfully understood, making predictive analysis of their effect onthe flow challenging. The dominant mechanism of high-speedplasma flow control in nanosecond pulse discharge plasma

Plasma Sources Science and Technology

Plasma Sources Sci. Technol. 27 (2018) 104001 (19pp) https://doi.org/10.1088/1361-6595/aae1c8

0963-0252/18/104001+19$33.00 © 2018 IOP Publishing Ltd1

actuators is due to generation of localized thermal perturba-tions [6, 10]. However, nonequilibrium vibrational and elec-tronic level populations of molecules in the discharge mayalso be a significant factor influencing the effect of the plasmaon the flow field. Discharge input energy partition amonginternal molecular energy states strongly depends on thereduced electric field in the plasma, which is controlled bothby the applied voltage waveform and by the charge accu-mulation on dielectric surfaces. A significant fraction of thedischarge input power may be stored in vibrational andelectronic energy modes of molecules, as well as in moleculardissociation products, and thermalized during the subsequentcollisional relaxation and quenching processes. Mechanismsof molecular energy transfer in nonequilibrium air plasmashave been studied rather extensively. Specifically, the kineticmechanism of ‘rapid heating’, due to energy transfer frominternal molecular energy modes to translational/rotationalmodes on a sub-microsecond time scale have been analyzedin great detail [11–13]. The role of relatively slow vibrationalrelaxation, which may result in a significant temperatureincrease not only in the discharge but also in the afterglowdownstream of the discharge, has received relatively littleattention [14, 15]. This effect may be quite significant whenthe vibrational relaxation time is comparable with the char-acteristic flow residence time [16], such as may occur inhumid air.

Recent experimental and modeling studies yield someinsight into the impact of residual heating of the flow by theplasma on fluid mechanics, specifically on the formation ofcoherent structures in the flow. Specifically, phased-lockedPIV measurements detected formation of large-scale spanwisevortices, resulting in reattachment of the separated boundarylayer over the top surface of the airfoil at a high angle ofattack when the actuator is in operation [2]. These vorticeshave also been detected in several subsequent studies[3, 6, 7, 9]. These results suggested that the flow controlmechanism is due to the excitation of shear layer instabilityby high-amplitude thermal perturbations generated by theplasma actuator. Indeed, CFD modeling incorporating flowheating in ns pulse surface plasma actuators [6] demonstratedthat spanwise vortices are generated by a flow instabilitycaused by the residual localized heating generated in theplasma. The free stream flow is entrained by the vortices intothe flow separation region, resulting in flow reattachment afterseveral discharge pulses, in agreement with PIV velocity fieldmeasurements [6]. Basically, strong temperature gradients inthe relatively low-velocity near-surface flow heated by theactuator generate spanwise vorticity, which has a dramaticeffect on the flow field.

Accurate quantitative prediction of the actuator flowcontrol authority requires knowledge of the time-resolvedtemperature distribution after the discharge pulse, which islargely determined by the electric field in the discharge. Theelectric field controls both the rate of energy coupling to theplasma and its partition among different molecular energymodes, and therefore the rate of energy relaxation in theafterglow. The ns pulse discharge model used in [6] is basedon a self-similar approximate analytic solution for a surface

ionization wave [17], which includes several simplifyingassumptions and therefore has low fidelity. The coupled flow/plasma model [6], which predicts a spanwise vortex ‘roll-up’induced by a flow instability development following eachdischarge pulse, as well as the separated flow reattachmentafter several discharge pulses, is in good qualitative agree-ment with the PIV data. However, quantitative predictions ofthis effect, over a wide range of operating conditions, stillappear to be out of reach. Development and experimentalvalidation of higher fidelity ns pulse discharge models needsdetailed non-intrusive measurements of the electric field in theplasma. Recently, remarkable progress has been made indevelopment of a non-intrusive laser diagnostic technique forelectric field measurements in air plasmas, fs/ps secondharmonic generation (SHG) [18, 19]. This method offersseveral advantages over the reduced electric field measure-ments by optical emission spectroscopy (OES) [20, 21],including straightforward absolute calibration, measurementof individual components of the electric field vector, andcapability of acquiring data over a much larger spatial domainand wider range of time scales, where plasma optical emissionis not detected. Comparison of ps SHG and ps four-wavemixing (FWM) [22] measurements of the Laplacian electricfield in ambient air shows that the former method is far moresensitive, generating a much higher signal at a considerablylower laser power. Unlike OES and FWM, the SHG techni-que is not species-dependent [18], such that it can be used forelectric field measurements in plasmas sustained in gas mix-tures other than air.

The objective of the present work is to use ps SHGdiagnostics for time-resolved measurements of the electricfield vector in a ns pulse DBD surface plasma actuator, toprovide insight into the ns pulse discharge dynamics, and toproduce data sets for detailed validation of high-fidelity,physics-based kinetic models of plasma flow control.

2. Experimental

Figure 1 shows a schematic diagram of a ns pulse, surfaceDBD plasma actuator used in the present work. The actuatoris made of an alumina ceramic plate 0.6 mm thick and twoadhesive copper foil electrodes 25 mm wide and 100 μmthick, attached to the dielectric plate with no overlap. Figure 1also labels the electric field vector components and shows thelocation of the laser beam, directed parallel to the dielectricplate and to the edge of the high-voltage electrode. Theactuator is placed on a rotation stage, mounted on a three-axistranslation stage, and can be moved relative to the laser beamfor spatially-resolved electric field measurements. The elec-trodes are powered by a custom-made high-voltage pulsegenerator producing alternating polarity pulses with peakvoltage up to 15 kV and pulse duration of ∼100 ns FWHM,operated at a 20 Hz pulse repetition rate. The alternatingpolarity pulse train can also be converted to a same polaritypulse train (positive or negative) by using ultra-fast high-voltage diodes (UF1007-T) connected in series between thehigh-voltage terminal of the pulse generator and the actuator

2

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

electrodes, as has been done in our previous work [23].Discharge voltage and current are measured by TektronixP-6015 high voltage probe and Pearson 2877 current probe.Plasma emission images are taken by Princeton InstrumentsPI-Max 3 ICCD camera with a UV lens.

Figure 2 [24] shows a schematic of the ps SHG laserdiagnostics. Briefly, the fundamental (1064 nm), verticallypolarized output beam of an Ekspla PL2143A Nd:YAG laser,with a pulse duration of 30 ps and pulse energy of 2 mJ,operating at 10 Hz, is focused into a region where the electricfield is applied, using a 100 cm focal distance lens. The shot-to-shot reproducibility of the laser pulse energy is approxi-mately 3.5% standard deviation. The laser beam diameter atthe focal point is approximately 200 μm, with the Rayleighrange of about zR ≈30 mm. The second harmonic signalbeam is separated from the fundamental beam using twodichroic mirrors and a dispersion prism, as shown in figure 2.The signal beam is recollimated and focused onto the entranceslit of a monochromator, followed by a narrowband pass filter(see figure 2), and detected by a photomultiplier tube (PMT).Using a polarizer mounted on a rotation stage before thefocusing lens, as shown in figure 2, allows isolating verticallyand horizontally polarized second harmonic signals. Thetiming and the pulse energy of the fundamental beam aremonitored by a photodiode.

The intensity of the second-harmonic signal is [18],

c w w w~

´D

D

w w w

⎡⎣⎢

⎤⎦⎥

[ ( ) ]

( · )·

( )

( ) ( ) ( ) ( )

/

/

I E E E

Lk L

k L

2 , 0, ,

sin 2

2, 1

i ijkl j k l2 3 ext 2

22

where Ejext is the external electric field, w( )Ek and w( )El are the

electric field components in the laser beam, c( )ijkl3 is the third-

order susceptibility, i, j, k, l indicate x or y components of the

electric field in the second harmonic signal beam, externalelectric field, and incident laser beam, respectively (seefigure 1), and L is the interaction length. Vertically and hor-izontally polarized second harmonic signals are generated forEy

ext and E ,xext respectively. In equation (1), the phase-

matching factor between the fundamental and the secondharmonic beams controls the coherent growth of the secondharmonic signal. At the present conditions, the coherencelength, Lc =π/Δk=6 cm, is comparable with the confocalparameter of the lens, b=2zR ≈60 mm. Therefore thepresent diagnostics measures root mean square values of theelectric field vector components, á ñ( ) /E x y t, , ,i z

ext 2 1 2 averagedover the span of the electrodes.

During the experiment, the laser is triggered externally,using the same delay generator that triggers the high-voltagepulser as the master clock. As in our previous work [25], thedischarge voltage waveform, the laser pulse waveform, andthe second harmonic signal for each laser shot are saved by adigital oscilloscope with a 1 GHz sampling rate. The timingof the laser pulse relative to the discharge pulse is determinedduring the data post-processing. The second harmonic signalintensities for each laser shot are placed into the appropriate‘time bins’ 5–10 ns long, much shorter compared to thedischarge pulse ∼100 ns long. The number of laser shots pertime bin varies from ∼30 to ∼60. Unlike the electric fieldmeasurements by ps FWM [22, 25], ps SHG involves onlyone nonlinear process, such that the shot-to-shot signalreproducibility is much better, and the data can be obtainedusing much fewer laser shots. Absolute calibration is obtainedfrom the measurements of a known Laplacian electric fieldbetween two parallel plate metal electrodes. Separate cali-brations are taken for the Ex and Ey components. At thepresent conditions, the second harmonic signal may be sostrong that the PMT detector response would be no longerlinear, such that the calibration curve deviates from a straightline at high electric fields. However, operating in this partiallynonlinear regime somewhat improves the detection limit ofthe diagnostics at low electric fields.

3. Results and discussion

Figure 3 plots voltage and current waveforms for positive andnegative polarity pulses, both for the same polarity pulse train(a) and for the alternating polarity pulse train (b). Figure 3(c)also shows a lower peak voltage, opposite polarity ‘pre-pulse’generated ≈5 μs before the main discharge pulse in thealternating polarity pulse train. In the same polarity pulsetrain, the pre-pulses are blocked. It can be seen that the use ofultra-fast high-voltage diodes to block the opposite polaritypulses somewhat distorts the voltage pulse shape, reducingthe FWHM from ≈100 to ≈70 ns, while pulse peak voltageincreases from ≈12–13 kV to ≈14 kV (see figure 3). In thesame polarity pulse trains, the discharge current pulses arevery similar to each other, with peak values of approximately8 A. In the alternating polarity pulse train, however, peakcurrent measured during the negative polarity pulse is sig-nificantly higher compared to that during the positive polarity

Figure 1. Schematic of the electrode assembly, position of the laserbeam, and electric field vector components in a surface dielectricbarrier discharge plasma flow actuator: (a) side view, (b) top view.Alumina ceramic dielectric plate thickness 0.6 mm, electrode width25 mm, no overlap between high-voltage and ground electrodes.

3

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

Figure 2. Schematic of picosecond second harmonic generation diagnostics. Reprinted from [24], Copyright (2018), with permissionfrom Elsevier.

Figure 3.Voltage and current waveforms for positive and negative polarity pulses: (a) same polarity pulse trains, (b) alternating polarity pulsetrain, (c) alternating polarity pulse train, showing both the pre-pulse and the main pulse.

4

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

pulse, ≈10 A versus ≈6 A. In all four cases, the total mea-sured current exceeds the estimated capacitive current, cal-culated using the applied voltage waveform and the totalcapacitance of the load (the actuator and the external circuit),2.0 pF, by over an order of magnitude. The load capacitancewas determined by measuring the circuit capacitive currentproduced by a 10 V amplitude, 5 MHz frequency AC signal.Therefore at the present conditions, most of the dischargecurrent is conduction current. As expected, the currentreverses direction when the voltage applied to the electrodesbegins to decrease, although the peak current after the reversalis significantly lower compared to the peak current achievedduring the voltage rise. This indicates that the surface chargedeposited on the dielectric during the voltage rise is somewhatdepleted during the voltage reduction, resulting in net surfacecharge accumulation (positive or negative) after the voltagepulse. Also, the energy coupled to the plasma in the samepolarity pulse train, 0.75 mJ/pulse and 0.62 mJ/pulse forpositive and negative polarity pulses, respectively, is muchlower compared to that in the alternative polarity train,2.3 mJ/pulse and 2.9 mJ/pulse, respectively. This is con-sistent with the results of our previous work [23] using aplasma actuator of a somewhat different geometry and thesame pulsed plasma generator. As discussed in [23], higherenergy dissipated in the alternating polarity pulse discharge isdue to neutralization of charge accumulated on the dielectricduring the following opposite polarity pulse, as well as due tothe surface discharge constriction.

Figure 4 shows single-shot plasma emission imagestaken at different moments during the positive polarity pulse,using the camera gate of 5 ns. The image of the entire dis-charge pulse, taken with the camera gate of 400 ns, is also

shown in the figure. These images are qualitatively similar tothe ones observed in a previous study of a ns pulse surfaceDBD with comparable voltage rise/fall time [26], and in ourrecent study of surface charge accumulation and energycoupling in these discharges using the same plasma generator[23]. Specifically, the present images indicate formation of a‘forward breakdown’ surface ionization wave consisting ofmultiple individual streamers, propagating over the dielectricsurface during the voltage rise, from t≈−40 ns to t≈0 (seefigure 4), consistent with the discharge current pulse (seefigure 3(a)). As the voltage continues to increase during thedischarge, a secondary ionization wave front, brighter com-pared with the primary wave, is generated at t≈−20 ns.Generation of the second ionization wave approximatelycoincides in time with the highest current peak at t≈−20 ns(see figure 3(a)). Formation of multiple ionization wave frontshas been predicted by self-similar models of a surface DBD[17, 27]. Qualitatively, this occurs in surface dischargessustained by voltage pulses with a relatively long rise time,dU/dt ∼ 0.1 kV ns−1, when the primary breakdown occursearly during the pulse, at a relatively low applied voltage ofthe order of ∼1 kV. In this case, as the potential on the high-voltage electrode continues to rise, the axial electric field inthe plasma behind the primary ionization wave, only partiallyshielded by the space charge in the wave front, may exceedthe breakdown threshold again, resulting in the secondarybreakdown. When the applied voltage starts to decrease andthe discharge current reverses direction, at t ≈ 0 ns, theplasma emission intensity is reduced considerably (seefigure 4). At t≈20–80 ns, formation of a relatively diffuse‘reverse breakdown’ ionization wave is evident. Peak plasmaemission intensity, achieved at t≈80 ns, approximately

Figure 4. Single-shot plasma emission images taken at different moments during the positive polarity voltage pulse, in the same polarity pulsetrain (camera gate 5 ns). Image of the entire discharge pulse is also shown (camera gate 400 ns).

5

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

coincides with the discharge current maximum during thevoltage reduction. Forward and reverse breakdowns are alsoreadily apparent in the plasma images in a ns pulse DBDplasma actuator in [28], although multiple ionization waveswere not detected due to much shorter voltage rise time,dU/dt≈2 kV ns−1. At the present conditions, plasma emis-sion intensity during the reverse breakdown is much lower,most likely because peak electric field in the plasma duringthe voltage reduction is lower compared to the field producedduring the voltage rise.

Figure 5 shows a collage of plasma emission imagestaken during the negative polarity pulse, at the same condi-tions as in figure 4. Again, the image of the entire dischargepulse is also shown in the figure. It can be seen that during thevoltage rise, at t≈−50 ns to t≈0 ns, the ‘forward break-down’ discharge is propagating as a diffuse surface ionizationwave with a well-pronounced front. After the voltage beginsto decrease at t>0, the ‘reverse breakdown’ wave has amuch less regular structure, with relatively long individualstreamers detected at t≈30–95 ns, as the emission intensityis gradually reduced. Again, this is qualitatively consistentwith the images taken during the forward and reversebreakdown in [26]. Based on the images in figures 4, 5, theplasma is more diffuse when the high-voltage electrode actsas a cathode, i.e. when the electron flux is directed from theelectrode to the dielectric surface.

Operating the discharge in the alternating pulse polaritymode changes the plasma morphology dramatically, as shownin plasma images in figures 6, 7. These figures also showimages of a lower amplitude (≈4 kV) opposite polarity‘pre-pulse’, preceding the main discharge pulse by approxi-mately 5 μs (see figure 3(c)), as well as the entire main pulse,

both taken with the camera gate of 400 ns. At these condi-tions, the plasma is generated much earlier during the pulse(at t≈−100 to −80 ns) and rapidly becomes filamentary.Figure 6 demonstrates formation of an ensemble of long,rapidly propagating positive polarity streamers (up to at least8 mm long) generated early during the voltage rise, att≈−100 ns, before the secondary ionization wave is pro-duced at t≈−80 ns. This is likely to be due to the residualionization produced by the negative polarity pre-pulse, whichreduces breakdown voltage near the high-voltage electrode tosome extent. From figure 6, it can also be seen that the dis-charge rapidly becomes filamentary, with a number of bright,well-defined streamers formed during the ‘forward break-down’ and persisting into the ‘reverse breakdown’ stage.During the ‘forward breakdown’ in the negative polaritypulse, shown in figure 7, the filamentary structure of theplasma in the ionization wave is initially less pronounced,although the wave rapidly becomes unstable and breaks intothe isolated filaments ending in characteristic fan-shapedstructures, previously observed in negative polarity surfacedischarges [10]. Again, well-defined streamers are alsodetected during the ‘reverse’ breakdown.

Summarizing the results of figures 4–7, operating theactuator in the same pulse polarity mode (positive or nega-tive) generates considerably more diffuse, less filamentaryplasma compared to the alternating polarity mode. Thereforethe electric field measurements in the same polarity pulsetrains are expected to be representative of the electric field inthe ‘forward breakdown’ ionization wave (especially for thenegative polarity). On the other hand, a strongly filamentarydischarge generated during the alternating polarity pulse trainresults in a significantly higher coupled energy per pulse (by a

Figure 5. Single-shot plasma emission images taken at different moments during the negative polarity voltage pulse, in the same polaritypulse train (camera gate 5 ns). Image of the entire discharge pulse is also shown (camera gate 400 ns).

6

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

factor of 3 to 4 at the present conditions). This effect cannotbe explained by the difference in voltage pulse waveformsbetween same and alternating polarity pulse trains. In ourprevious work [23], significant coupled pulse energy differ-ence was detected between the pulse trains with essentially

the same peak voltages and voltage rise times. This indicatesthat the difference is due to the alternating polarity rather thanthe voltage pulse shape.

Both higher coupled pulse energy and plasma fila-mentation are conducive to producing higher amplitude

Figure 6. Single-shot plasma emission images taken at different moments during the positive polarity voltage pulse, in the alternating polaritypulse train (camera gate 20 ns). Images of the lower amplitude, negative polarity ‘pre-pulse’ (5 μs before the main pulse), and the entirepositive polarity main pulse are also shown (camera gate 400 ns).

Figure 7. Single-shot plasma emission images taken at different moments during the negative polarity voltage pulse, in the alternatingpolarity pulse train (camera gate 5 ns). Images of the lower amplitude, positive polarity ‘pre-pulse’ (5 μs before the main pulse), and theentire negative polarity main are also shown (camera gate 400 ns).

7

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

localized thermal perturbations, known to be critical forplasma flow control [6, 23]. Therefore plasma characteriza-tion at these strongly filamentary conditions is of considerableimportance for flow control applications. Specifically, mea-surements of the span-averaged electric field in these dis-charges are complementary to the electric field data in diffusesurface plasmas for the same actuator geometry, and mayprovide quantitative insight into the mechanism of ns pulsesurface discharge filamentation [29]. These data can also beused as a comparison metric for three-dimensional surfaceplasma actuator models, to assess their predictive capability.Development of such 3D models is essential for truly pre-dictive kinetic modeling of high pulse energy, filamentaryplasma actuators used for plasma flow control applications.

Figure 8 shows a typical histogram illustrating the dis-tribution of laser shots over 5 ns time bins (during the dis-charge pulse) and 10 ns time bins (before and after thedischarge pulse), during a run of 4300 laser shots. In figure 8,t=0 corresponds to the moment when the voltage pulsepeaks. In the histogram, the time delay between the laserpulse and the discharge pulse varies over 800 ns (fromt=−400 to 400 ns). At −400 ns<t<−150 ns (before thedischarge pulse), the average number of laser shows per timebin is 32 shots/bin, while at 150 ns<t<400 ns (after thedischarge pulse), the average number is 64 shots/bin.The sloping histogram (i.e. the nonuniform distribution ofthe laser shots over time) is an artifact of the laser operation.During the discharge pulse (at t=−150 to 150 ns), theaverage number is 29 shots/bin.

Figure 9 plots PMT signals, averaged over multiple lasershots in a 5 ns bin during the calibration of the vertical electricfield component, using a pair of parallel plate metal electrodeswith sub-breakdown voltage applied to the electrodes. Thehighest field measured during the calibration is approximately25 kV cm−1. The sensitivity limit of the diagnostics at thepresent conditions estimated to be approximately 2 kV cm−1

(see figure 9), although averaging the signal over a largernumber of laser shots (∼120–250) would improve it to about

1 kV cm−1. The sensitivity limit may also be improved con-siderably by increasing the laser power, although this mayresult in PMT saturation at high electric fields. The calibrationdata in figure 8, as well as all data in the ns pulse surfacedischarge, are taken at the laser pulse energy of 2 mJ/pulse.From equation (1), we estimate that increasing the pulseenergy to 20 mJ/pulse would lower the sensitivity limit to100 V cm−1. Even at these relatively high laser pulse energyconditions, optical breakdown in air has not been detected.Although increasing the laser pulse energy might affect thedischarge parameters due to optogalvanic interaction, it isextremely unlikely that this would affect the measurementresults, since the second harmonic signal is generated onlyduring the laser pulse 30 ps long, i.e. on the time scale tooshort for the discharge conditions to change.

Figure 10 shows the results of second harmonic signalcalibration, taken between two parallel plate metal electrodes4.2 mm apart and 25 mm long, measured both for the verticaland the horizontal field. For this, both the electrode assemblyand the polarizer before the focusing lens shown in figure 2were rotated over 90°. Although the theoretical susceptibilityratio for these field components is known, c( )

yyyy3 /c( )

xxyy3 =3

[18], separate calibrations are needed to account for thedependence of the signal collection optics parameters onpolarization. Also, since the second harmonic signal gener-ated by the vertical electric field component is significantlyhigher, the use of the same PMT voltage for measurements ofboth electric field components may result in a nonlinearresponse of the PMT. At the present conditions, the ratio ofthe square roots of second harmonic signals measured for thesame PMT voltage used for Ex and Ey calibration, in the linearregime (i.e. the ratio of calibration line slopes), is approxi-mately 2.2. However, as expected, using the same voltage forEx and Ey calibration resulted in significant nonlinearity of Ey

calibration, due to the partial saturation of the PMT. For thecalibration data plotted in figure 10, a lower PMT voltage wasused for Ey calibration, 750 V versus 900 V used for Ex

calibration. From figure 10, nonlinearity of the calibrationcurves above ∼10 kV cm−1 is readily apparent.

Figures 11–14 summarize the results of electric fieldvector component measurements in the surface DBD in theplasma actuator, both for same polarity pulse trains (panels (a),(b)) and for the alternating polarity train (panels (c), (d)). Notethat the voltage, current, and electric field axes for the negativepolarity pulses (panels (b), (d) in figures 11–14) are inverted, tomake the comparison between different polarities morestraightforward. For these measurements, the laser power andthe PMT voltage were the same as during the calibration.Every data set shown was taken during a single run of over2000 laser shots. To position the laser beam near the actuatorsurface and check if it is parallel to the surface, the actuator wasfirst raised until the laser beam clipped the alumina ceramicplate, which produced easily detectable visible fluorescence,and then lowered by 100 μm. Clipping the surface was alsoreadily apparent from the reduction of the laser signal intensitymonitored by the photodiode. The same procedure was used toposition the beam near the high-voltage electrode. Therefore

Figure 8. Histogram showing distributions of 4300 laser shots andaverage laser pulse energy over 5 and 10 ns time bins.

8

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

Figure 9. PMT signals (averages for 5 ns bins) for different electric fields measured during the calibration of the vertical electric field,between two parallel plate electrodes 4.2 mm apart.

Figure 10. Calibration results for horizontal (a), (b) and vertical (c), (d) electric field components, illustrating PMT detector nonlinearity athigh electric fields. Blue symbols, square root of the second harmonic signal (linear calibration); black symbols, quadratic calibration.

9

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

the near-surface data are taken approximately y≈200 μmfrom the surface, and near-electrode data are taken approxi-mately x≈200 μm from the electrode. For brevity of nota-tions, these locations are referred to as y=0 and x=0throughout this paper.

From figure 11(a), which plots Ex and Ey near the high-voltage electrode and near the dielectric surface (i.e. at x=0,y=0) for the positive polarity pulse train, it can be seen thatboth Ex and Ey have a detectable non-zero offset before thevoltage pulse. Since the second harmonic signal is propor-tional to the absolute value of the electric field, additionalconsiderations are necessary to assign the electric fielddirection. For some of the data points the electric field isinverted, specifically when it is clear that the field changesdirection after approaching zero. This procedure is discussedbelow in some detail. For example, positive residual chargeaccumulation and positive potential on the dielectric surfacefrom the previous (same polarity) discharge pulse are con-sistent with the negative initial offset of Ex and positive initialoffset of Ey in figure 11(a) (i.e. Ex points toward the high

voltage electrode and Ey points down, see figure 1). Asexpected, during the potential increase on the high-voltageelectrode, Ex is first reduced to zero at t≈−60 ns and thenincreases in the opposite direction (now pointing away fromthe high-voltage electrode), such that the Ex data points areassigned negative values before the inversion and positivevalues after. The primary breakdown occurs near the elec-trode at t≈−40 ns, consistent with the discharge currentpeak and with plasma emission images in figure 4. Afterbreakdown, both Ex and Ey drop considerably, indicating theeffect of plasma self-shielding, before increasing again asthe applied voltage continues to rise. However, peak electricfield measured during the primary breakdown is fairly

low, = +E E Ex y2 2 ≈15 kV cm−1, suggesting that the

laser beam may be positioned slightly above the surfaceplasma. Formation of the secondary ionization wave (att≈−12 ns, see figure 4), when the measured electric field isE≈23 kV cm−1, is not readily apparent from the electricfield data, indicating no significant self-shielding behind thesecondary wave front. When the applied voltage begins to

Figure 11. Electric field vector components in the plasma actuator at x=0, y=0, for different polarity pulse trains: (a) positive polarity; (b)negative polarity; (c) alternating polarity, positive pulse; (d) alternating polarity, negative pulse. Voltage, current, and electric fieldwaveforms for negative polarity pulses (panels (b), (d)) are inverted.

10

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

Figure 12. Electric field vector components in the plasma actuator at x=1 mm, y=0, for different polarity pulse trains: (a) positive polarity;(b) negative polarity; (c) alternating polarity, positive pulse; (d) alternating polarity, negative pulse. Voltage, current, and electric fieldwaveforms for negative polarity pulses (panels (b), (d)) are inverted.

Figure 13. Electric field vector components in the plasma actuator at x=2 mm, y=0, for different polarity pulse trains: (a) positive polarity;(b) negative polarity. Voltage, current, and electric field waveforms for the negative polarity pulse (panel (b)) are inverted.

11

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

decrease, both electric field components diminish. The rise ofthe absolute value of Ex at t>20 ns, as the voltage continuesto decrease, indicates that Ex is inverted again and is nowdominated by the field produced by the positive surfacecharge accumulated on the dielectric during the forwardbreakdown, pointing toward the high-voltage electrode.This behavior is also consistent with the discharge currentpulse waveform. Ex continues to increase until the reversebreakdown is achieved at E≈18 kV cm−1, suggesting againthat the laser beam is located above the plasma. After thereverse breakdown, Ex is reduced to near its initial valuebefore the pulse, indicating little or no surface charge neu-tralization on the time scale exceeding a few hundred ns.

The electric field behavior during the negative polaritypulse train, shown in figure 11(b), is fairly similar. Both Ex

and Ey offset values before the pulse are similar to thosemeasured in the positive polarity pulse. In this case, thisindicates negative residual charge accumulation before thepulse. Both electric field components continue to follow theapplied voltage until the forward breakdown, evident from thecurrent waveform and from the plasma images in figure 5,

occurs at t≈−40 ns. During the forward breakdown, peakelectric field value is somewhat higher compared to thatmeasured in the positive polarity pulse, E≈20 kV cm−1,mainly due to the higher peak Ex value. After breakdown,both the horizontal and the vertical field componentsare reduced to near zero, as the surface ionization wavepropagates from the high-voltage electrode (see figure 5). Att≈20 ns, both electric field components are close to zero,although the potential on the high voltage electrode isstill fairly high, U≈10 kV. This indicates that the electricfield is measured in the nearly completely self-shieldedplasma, i.e. that the laser beam is passing through the plasma.At t>20 ns, electric field reversal for both componentsis well pronounced. Peak electric field during reversebreakdown, E≈19 kV cm−1, is slightly higher compared tothat in the positive polarity pulse train.

From figure 11(c), which plots Ex and Ey at x=0, y=0for the positive polarity pulse in the alternating polarity pulsetrain, it can be seen again that both Ex and Ey have adetectable non-zero offset before the voltage pulse, exceptthat now the Ex offset has the opposite sign compared to

Figure 14. Electric field vector components in the plasma actuator at x=3 mm, y=0, for different polarity pulse trains: (a) positive polarity;(b) negative polarity; (c) alternating polarity, positive pulse; (d) alternating polarity, negative pulse. Voltage, current, and electric fieldwaveforms for negative polarity pulses (panels (b), (d)) are inverted.

12

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

figure 11(a). This is due to the previous (negative polarity)main discharge pulse as well as the negative polarity pre-pulse, U≈4 kV, generated at t≈−5 μs (see figures 3(c), 6).As expected, this indicates the presence of the residualnegative charge accumulated on the dielectric surface. Atthese conditions, Ex also exhibits two well-defined maximaduring the voltage rise, at t≈−90 ns and t≈−30 ns.Comparing this with the positive polarity pulse currentwaveforms (see figure 3(b)) and plasma emission images (seefigure 6), these maxima correspond to the primary and sec-ondary breakdowns producing two sudden current increasesand two surface ionization waves (the primary wave beingextremely filamentary). Note that the first breakdown occursvery early during the voltage pulse, when the applied voltageis only U≈1.5 kV, compared to U≈7 kV for the secondbreakdown. In contrast to Ex, Ey exhibits a near-Laplacianbehavior, basically following the applied voltage pulse shape(see figure 11(c)) and not indicating an abrupt reductioncharacteristic for breakdown and plasma shielding. This againindicates that the laser beam may be positioned above thenear-surface plasma. This interpretation is also consistent withthe fact that peak Ex values during the primary and secondarybreakdowns are fairly low, only about Ex ≈13 kV cm−1.Note, however, that both breakdowns occur in air already pre-ionized by the pre-pulse, which is likely to lower the break-down threshold. After the voltage begins to decrease, Ex alsodecreases and starts to rise again in the opposite direction(now pointing toward the high-voltage electrode), consistentwith the discharge current waveform which changes directionnearly at the same time. Ex minimum measured during thefield reversal is above the detection limit, likely due to thefilamentary structure of the plasma (see figure 6), such that thefield is not reversed everywhere at the same time. Followingthe Ex reversal, it reaches a modest peak of Ex ≈8 kV cm−1,which is likely associated with the secondary breakdownin a filamentary plasma (see figure 6), and then graduallydecreases, leaving the residual positive charge on thedielectric.

Finally, figure 11(d) shows the data measured during thenegative polarity pulse in the alternating polarity pulse train,at the same location (x=0, y=0). In this case, it is evidentthat the electric field offset before the main discharge pulse,generated by the previous (positive polarity) main pulse andby the positive polarity pre-pulse, is more significant than infigure 11(c) (both for Ex and Ey). This is consistent with thepre-pulse images (top left frame in figures 6 and 7), whichindicate that the plasma generated by the positive polarity pre-pulse extends over a longer distance over the dielectric sur-face. Ex follows the applied voltage until breakdown occurs att≈−90 ns, at Ex ≈19 kV. The breakdown timing is con-sistent with the beginning of the discharge current rise andplasma emission images (see figure 7). Again, breakdownoccurs early during the voltage pulse, when the appliedvoltage is still quite low, ≈1.5 kV. After breakdown, thehorizontal field gradually decreases to near zero at t≈10 ns.Ey, which initially increases during the ionization wave pro-pagation, subsequently peaks and also diminishes to near zeroat t≈10 ns, nearly at the same time as the horizontal field

(see figure 11(d)). Since this occurs when the potential on thehigh voltage electrode is near its peak of U≈12 kV, thisdemonstrates again that the plasma is self-shielded, indicatingthat the laser beam is passing through the plasma. After theelectric field components are reduced to near zero, both ofthem reverse direction during the voltage reduction andincrease again during the reverse breakdown, at t≈0–100 ns.However, the electric field measured at this stage is notrepresentative of the field in the well-defined, isolated plasmafilaments (see plasma emission images in figure 7). After bothvoltage and current are gradually reduced to near zero, non-zero residual Ex and Ey indicate the negative charge accu-mulation on the dielectric surface, more significant comparedto that after the positive polarity pulse (see figure 11(c)).

In summary, comparing the negative pulse polarity data(see figures 11(b), (d)) with the measurements during thepositive polarity pulse (see figures 11(a), (c)), which indicatenon-zero Ex and Ey when the voltage peaks and the currentreverses direction, suggests that the positive polarity plasmalayer thickness is smaller compared to that of the negativepolarity plasma.

The data taken 1 mm away from the high-voltage elec-trode, near the dielectric surface (i.e. at x=1 mm, y =0),plotted in figure 12, are consistent with the data taken near theelectrode. It can be seen that the horizontal field offset beforethe pulse, due to the residual surface charge accumulation onthe surface, is slightly higher than near the high-voltageelectrode, for all four cases. For positive polarity pulses (bothin the same polarity and alternating polarity pulse trains), themaximum in Ex caused by the primary breakdown near thehigh-voltage electrode (see figures 11(a), (c)) is no longerdetected (see figures 12(a), (c)). This suggests that theionization wave produced during the primary breakdown hasa fairly low amplitude, which rapidly decreases during itspropagation away from the high-voltage electrode. The firstionization wave in the same polarity train is still detectedfrom the Ey maximum (see figure 12(a)). In the alternatingpolarity pulse train, however, Ey peak during the primarybreakdown is barely detectable (see figure 12(c)), most likelydue to the highly filamentary structure of the surface ioniz-ation wave (see figure 6). In this case, the vertical field beginsto increase only when the secondary breakdown occurs att≈−40 ns, a fairly well-defined ionization wave appears(see figure 6), and the horizontal field peaks (see figure 12(c)).In the positive polarity ionization wave after the secondarybreakdown, the electric field behavior is similar to thatobserved at x=0, y=0 (rapid Ex reduction and subsequentreversal, and more gradual Ey reduction, see figures 11(a),(c)). The horizontal field reversal at both locations is muchbetter pronounced in the same polarity pulse train. However,no conclusive evidence of Ey reversal has been observed inpositive polarity pulses at x=0, y=0 and at x=1 mm,y=0, indicating that the surface plasma at these conditionsremains below the laser beam. Contrary to this, in the nega-tive polarity pulse ionization wave, Ex peaks at a much highervalue, Ex ≈25 kV cm−1, Ey is almost completely shieldedafter breakdown, and the field reversal is observed both forthe same and alternating pulse polarities (see figures 12(b),

13

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

(d)), indicating that at these conditions the laser beam passesthrough the near-surface plasma. The Ey peak behind theionization wave front in the same polarity pulse train is muchbetter pronounced compared to the alternating polarity pulsetrain (compare figures 12(b) and (d)), most likely due to thehighly filamentary structure of the negative polarity ionizationwave in the alternating polarity train (compare plasma imagesin figures 5 and 7). This is also the likely reason for twoapparent Ex maxima in figure 12(d). Comparing the horizontalfield directions before and after the discharge pulse, it isevident that the sign of the surface charge remains the samefor the same polarity pulse trains (see figures 12(a), (b)) but ischanges for the alternating polarity pulse train, similar to theresults at x=0.

At x=1 mm, the forward breakdown in the negativepolarity pulses (see figures 12(b), (d)) is better pronouncedcompared to that in the positive polarity pulses (seefigures 12(a), (c)), unlike the reverse breakdown, defined asan Ex maximum after the field reversal. This trend continuesat a longer distance from the high-voltage electrode, x=2 mm,where the negative polarity pulse (in the same polarity pulsetrain) exhibits a clear forward breakdown with the peak field ofE≈27 kV cm−1, without any evidence of reverse breakdown(see figure 13(b)). Since the reverse breakdown at this locationis observed from the plasma emission images (see figure 5), itsapparent absence in the electric field data is likely due to theplasma filamentation. In the positive polarity pulse at thislocation, peak electric field measured during the forwardbreakdown is much lower, almost certainly due to the fila-mentary structure of the forward ionization wave (see figure 4),and the reverse breakdown appears to be absent, in spiteof the strong residual electric field after the pulse, E≈17–27 kV cm−1 (see figure 13(a)). Since the reverse breakdownwave at these conditions is fairly diffuse (see figure 4), the dataof figure 13 indicate that it simply does not reach this axiallocation, leaving significant residual non-neutralized charge onthe dielectric surface.

The trends observed at x=1 mm and x=2 mm are alsodetected further away from the high-voltage electrode, atx=3 mm, as illustrated in figure 14. In the same polaritypulse train, peak electric field measured during the positivepolarity forward breakdown is lower than at x=2 mm,reverse breakdown is not detected, and the residual electricfield is higher (see figure 14(a)). This indicates a significantcharge transfer by the filamentary forward breakdown ioniz-ation wave, while the reverse ionization wave does not reachthis axial location (see figure 4). Note a considerable differ-ence between the electric field values before and after thedischarge pulse in figure 14(a). For the same polarity data setswhere this difference is detected, it indicates that the electricfield between the pulses is affected by the partial neutraliza-tion of the surface charge by the opposite polarity chargetransport from the plasma. This effect, on a microsecond timescale, has been detected in a ns pulse surface discharge anddiscussed in detail in our previous work [22]. Electric fieldbehavior in the negative polarity pulse is completely different,indicating a well-pronounced forward breakdown in adiffuse ionization wave (see figure 5), with peak field of

E≈32 kV cm−1, but no sign of reverse breakdown that canbe observed in the filamentary plasma in figure 5 (seefigure 14(b)). In the alternating polarity pulse train, the delayof the positive polarity pulse ionization wave at x=3 mm,relative both to the voltage pulse and to the data at x=0 andx=1 mm, is readily apparent (e.g. compare figure 14(c) andfigures 11(c), 12 (c)). Also, peak Ex value in the positivepolarity ionization wave front at x=3 mm increases to Ex

≈20 kV cm−1. However, the vertical electric field behind thewave front at x=3 mm is still not shielded (see figure 14(c)),indicating again that the surface plasma layer during thepositive polarity discharge remains below the laser beam. Incontrast, the negative polarity ionization wave remains verywell pronounced, with the peak horizontal field of Ex

≈22 kV cm−1 and the rapid shielding of both electric fieldcomponents behind the wave (see figure 14(d)), showing thatin this case the laser beam propagates through the plasma.Peak electric field measured in the strongly filamentaryplasma in this case remains somewhat lower compared to thefield in the diffuse plasma in the negative polarity pulse in thesame polarity train (see figure 14(b)).

Finally, figures 15 and 16 show the results of electricfield measurements at the same axial location, x=3 mm, andthree different heights above the dielectric surface, y=0,y=1 mm, and y=3 mm, in the same polarity pulse train(figure 15) and alternating polarity pulse train (figure 16). Asexpected, in all cases, both electric field vector componentsare reduced rapidly with the height above the surface, suchthat the surface ionization wave becomes barely detectable.

In the present experiments, peak electric field measured inthe same polarity pulse trains at most axial locations is some-what lower than the breakdown field in air, except for x=3 mm

in the negative polarity pulse, = +E E Ex y2 2 ≈32 kV cm−1

(see figure 14(b)), indicating that the laser beam may be near theouter edge of the plasma layer. In the positive polarity pulse,maximum field at x=0, E≈25 kV cm−1, is reached during theapplied voltage pulse (see figure 11(a)). However, at x=2 mmand x=3 mm, maximum electric field, E≈27 kV cm−1 andE≈25 kV cm−1, respectively, is achieved well after the appliedvoltage pulse (see figures 13(a) and 14(a)). The x=1 mmlocation is an intermediate case, where peak electric field ofE≈22 kV cm−1 is achieved during both forward and reversebreakdown (see figure 12(a)). This behavior illustrates the resi-dual surface charge accumulation at longer distances from thehigh-voltage electrode (x=2–3 mm), where it is not affected bythe reverse breakdown. In contrast, in the negative polaritypulse, peak electric field is always reached during the appliedvoltage pulse, E≈20–32 kV cm−1 at x=0–3 mm, reversebreakdown is not pronounced except at x=0, and the residualfield (i.e. surface charge accumulation) after the pulse is rela-tively low (see figures 11(b)–14(b)).

In the alternating polarity pulse train, peak electric fieldvalues measured during the positive and negative polaritypulses are noticeably lower, most likely due to breakdownthreshold reduction due to pre-ionization in the pre-pulse,approximately 5 μs before the main pulse. However, thecoupled pulse energy in the alternating pulse discharge is

14

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

much higher, by a factor of 3–4 at the present conditions. Asdiscussed in our previous work [23], this difference is pri-marily due to the neutralization of residual surface chargeaccumulated on the dielectric during the previous, oppositepolarity pulse, which results in a higher pulse current. Theeffect of the surface charge neutralization and the horizontal

electric field direction ‘flipping’ (before the pulse versus afterthe pulse) in the alternating polarity pulse train is apparentfrom figures 11(c), (d) and 12(c), (d).

It is well known that increasing the peak reduced electricfield (E/N) in the discharge would result in a higher inputenergy fraction that is rapidly thermalized, mostly during

Figure 15. Electric field vector components in the plasma actuator for positive and negative polarity pulses in same polarity pulse trains, atdifferent locations: (a), (b) positive and negative, x=3 mm, y=0; (c), (d) positive and negative, x=3 mm, y=1 mm; (e), (f) positive andnegative, x=3 mm, y=3 mm. Voltage, current, and electric field waveforms for negative polarity pulses (panels (b), (d), (f)) are inverted.

15

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

quenching of excited electronic states of N2 and O atomsgenerated by electron impact [13]. The discharge energyfraction going to rapid heating by this mechanism is onlyabout 13% at E/N=100 Td and increases by about a factorof two (25%–28%) at E/N=200–300 Td [13]. Significantly

higher peak electric fields in ns pulse discharges can beobtained by using a voltage waveform without the pre-pulseand with a higher voltage rise rate, up to 75 kV cm−1

(E/N≈300 Td) for dU/dt≈3 kV ns−1 [25]. This wouldincrease the amplitude of thermal perturbations produced by

Figure 16. Electric field vector components in the plasma actuator for positive and negative polarity pulses in alternating polarity pulse trains,at different locations: (a), (b) positive and negative, x=3 mm, y=0; (c), (d) positive and negative, x=3 mm, y=1 mm; (e), (f) positiveand negative, x=3 mm, y=3 mm. Voltage, current, and electric field waveforms for negative polarity pulses (panels (b), (d), (f)) areinverted.

16

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

individual discharge pulses. However, as can be seen bothfrom [23] and from the present results, the use of the alter-nating polarity pulse train may well result in a more sig-nificant increase of the total coupled pulse energy, withoutsubstantial reduction in the pulse duration, potentially pro-ducing a stronger effect of the plasma on the flow field.

4. Summary

In the present work, picosecond SHG is used for time-resolved measurements of the electric field in a surface DBDsustained by positive, negative, and alternating polarity trainsof high-voltage ns duration pulses, at multiple spatial loca-tions. The results provide quantitative insight into dynamicsof surface ionization wave development at these conditions,identifying several dominating trends.

During the voltage rise, the forward breakdown in thepositive polarity discharge in the same polarity pulse trainoccurs as a sequence of two surface ionization waves. Thefirst wave, exhibiting a fine filamentary structure, originates ata low applied voltage, with the second wave generated a fewtens of ns later, at a much higher voltage, and propagates overthe plasma produced by the first wave. During the voltagereduction, the reverse breakdown occurs as a single diffuseionization wave. In contrast, the forward breakdown in thenegative polarity discharge in the same polarity pulse traindevelops as a well-defined diffuse ionization wave, whichbecomes filamentary during the reverse breakdown. In thealternating polarity pulse train, the plasma morphologychanges dramatically. In this case, the first ionization wave inthe positive polarity pulse develops as an ensemble of indi-vidual streamers, followed by a somewhat more diffuse sec-ond wave. Well-defined isolated filaments formed during theforward breakdown persist to the reverse breakdown stage. Inthe negative polarity discharge, a single ionization wave frontdisintegrates into isolated filaments during the forwardbreakdown, and the filaments are also observed during thereverse breakdown. In general, surface plasmas generated bysame polarity pulse trains appear more stable and much lessfilamentary.

It should be underscored that the present measurementsyield the electric field vector components averaged across thespan of the actuator. Therefore only the results obtained inrelatively diffuse plasmas, such as occur in surface ionizationwaves in same polarity pulses, are representative of theelectric field in the ionization front. Measurements of theelectric field in well-defined, isolated plasma filaments, gen-erated in alternating polarity pulse trains, would requirehigher spatial resolution, which can be obtained by using ashorter focal distance lens [18], combined with a suitablesignal discrimination technique such as cross-correlationspectroscopy [21].

From the electric field measurements in the positivepolarity pulse (same polarity train), a well-pronounced firstionization wave is detected near the high voltage electrode. Itseffect on the plasma is readily apparent from a nearly com-plete shielding of the vertical field component until the arrival

of the second ionization wave. In the positive pulse of thealternating polarity train, the first ionization wave is much lessapparent, due to its highly filamentary structure. Horizontalfield reversal in the second ionization wave, during the volt-age reduction, is readily apparent both for the same polarityand alternating polarity pulse trains. However, no reversal isobserved for the vertical field, suggesting that the laser beamis positioned above the positive polarity discharge plasma,especially near the high-voltage electrode, where the verticalfield remains close to Laplacian. In the positive polaritypulse train, measurements further away from the high-voltageelectrode demonstrate significant residual surface chargeaccumulation, only weakly affected by the reverse breakdown.

In the negative polarity pulses in same polarity andalternating polarity trains, both electric field components arereduced to near zero during the voltage reduction, such thatthe plasma becomes completely self-shielded, before rever-sing direction when the voltage is reduced. This indicates thatin this case the electric field is measured in the plasma. Sincethe laser beam height above the dielectric surface is the samefor both pulse polarities, the thickness of the surface plasmalayer in the negative polarity discharge is greater compared tothat in the positive polarity discharge. Unlike the negativepolarity pulse in same polarity train, resulting in a well-defined diffuse ionization wave, the ionization wave in thealternating polarity train shows two weakly pronouncedmaxima, due to its strongly filamentary structure apparentfrom the plasma images. Although peak electric field tends todecrease with the distance from the high-voltage electrode,this effect is much less pronounced for the negative polaritydischarge, in which the plasma extends further away from thehigh-voltage electrode.

In all pulse trains, the electric field measurementsdemonstrate a significant field offset before the dischargepulse, due to the surface charge accumulation during theprevious discharge pulses. This demonstrates that surfacecharge accumulation is a significant factor affecting theelectric field during the discharge pulses, even at a very lowpulse repetition rate of 20 Hz. As expected, both electric fieldcomponents decrease significantly with the height above thedielectric. Peak electric field measured in the alternatingpolarity pulse train is lower compared to that in same polaritytrains, most likely caused by the breakdown thresholdreduction due to pre-ionization in the pre-pulse. However, thecoupled pulse energy in the alternating polarity pulse dis-charge is much higher, by a factor of 3–4, primarily due toneutralization of the residual surface charge accumulated onthe dielectric during the previous, opposite polarity pulse.This suggests that plasma surface actuators powered byalternating polarity ns pulse discharge trains may generatehigher amplitude thermal perturbations, producing a strongereffect on the flow field and enhancing the flow controlauthority.

Finally, the present results show that the time scale forplasma self-shielding and the electric field reduction afterbreakdown is fairly long, several tens of ns, including theconditions when the discharge develops as a single, well-defined, diffuse ionization wave. This may have a significant

17

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

impact on the discharge input energy partition, suggestingthat a considerable fraction of the energy is coupled to theplasma at a relatively low reduced electric field, several tensof Td. At these conditions, vibrational excitation of N2 wouldlimit the energy fraction thermalized as rapid heating, redu-cing the effect on the flow caused by the high-amplitudelocalized thermal perturbations.

The present work represents the first systematic study ofthe electric field distribution in a ns pulse surface plasmaactuator, using a novel diagnostic technique with much highersensitivity and wider applicability range compared to pre-viously used methods, such as FWM and OES. The imple-mentation of the second harmonic diagnostics and absolutecalibration of the electric field are straightforward. Thedetection limit and the temporal resolution of the presentmeasurements are approximately 2 kV cm−1 and 5 ns,respectively, although both of them can be improved con-siderably, by increasing the number of laser shots and redu-cing the size of the time bins used for data sampling. Thespatial resolution of the present measurements may be alsoimproved significantly by using a shorter focal distance lens,which would also allow electric field measurements closer tothe dielectric surface, within several tens of microns. Finally,the present diagnostics can also be used for the measurementsof one-dimensional and two-dimensional electric field dis-tributions across the laser beam, if a PMT detector is replacedwith an ICCD camera [30], producing snapshot images of thedischarge energy partition in the near-surface plasma layer.

Acknowledgments

The support of US Department of Energy Plasma ScienceCenter ‘Predictive Control of Plasma Kinetics: Multi-Phase andBounded Systems’, and National Science Foundation grant‘Nanosecond Pulse Discharges at a Liquid-Vapor Interface andin Liquids: Discharge Dynamics and Plasma Chemistry’ isgratefully acknowledged. We would like to thank Dr BenjaminGoldberg from Princeton University for helpful technical dis-cussions of second harmonic generation diagnostics.

ORCID iDs

I V Adamovich https://orcid.org/0000-0001-6311-3940

References

[1] Roupassov D, Nikipelov A, Nudnova M and Starikovskii A2009 Flow separation control by plasma actuator withnanosecond pulsed-periodic discharge AIAA J. 47 168–85

[2] Little J, Takashima K, Nishihara M, Adamovich I and Samimy M2012 Separation control with nanosecond pulse drivendielectric barrier discharge plasma actuators AIAA J. 50 350–65

[3] Rethmel C, Little J, Takashima K, Sinha A, Adamovich I andSamimy M 2011 Flow separation control using nanosecondpulse driven DBD plasma actuators Int. J. Flow Control 3213–32

[4] Kelley C L, Bowles P O, Cooney J, He C, Corke T C,Osborne B A, Silkey J S and Zehnle J 2014 Leading edgeseparation control using alternating-current and nanosecond-pulse plasma actuators AIAA J. 52 1871–84

[5] Correale G, Michelis T, Ragni D, Kotsonis M and Scarano F2014 Nanosecond-pulsed plasma actuation in quiescent air andlaminar boundary layer J. Phys. D: Appl. Phys. 47 105201

[6] Zheng J G, Cui Y D, Zhao Z J, Li J and Khoo B C 2016Investigation of airfoil leading edge separation control withnanosecond plasma actuator Phys. Rev. Fluids 1 073501

[7] Du H, Shi Z, Cheng K, Li G, Lu J, Li Z and Hu L 2016 Thestudy of flow separation control by a nanosecond pulsedischarge actuator Exp. Thermal Fluid Sci. 74 110–21

[8] Du H, Shi Z, Cheng K, Wei D, Li Z, Zhou D, He H, Yao J andHe C 2016 Topological structures of vortex flow on a flyingwing aircraft, controlled by a nanosecond pulse dischargeplasma actuator Appl. Phys. Lett. 108 244105

[9] Komuro A, Takashima K, Konno K, Tanaka N, Nonomura T,Kaneko T, Ando A and Asai K 2017 Schlieren visualizationof flow-field modification over an airfoil by near-surfacegas-density perturbations generated by a nanosecond-pulse-driven plasma actuator J. Phys. D: Appl. Phys. 50 215202

[10] Leonov S B, Adamovich I V and Soloviev V R 2016 Dynamicsof near-surface electric discharges and mechanisms of theirinteraction with the airflow Plasma Sources Sci. Technol. 25063001

[11] Popov N A 2001 Investigation of the mechanism for rapid heatingof nitrogen and air in gas discharges Plasma Phys. Rep.27 886

[12] Aleksandrov N L, Kindysheva S V, Nudnova M M andStarikovskii A Y 2010 Mechanism of ultra-fast heating in anon-equilibrium weakly ionized air discharge plasma in highelectric fields J. Phys. D: Appl. Phys. 43 255201

[13] Popov N A 2011 Fast gas heating in a nitrogen–oxygendischarge plasma: I. Kinetic mechanism J. Phys. D: Appl.Phys. 44 285201

[14] Lanier S, Shkurenkov I, Adamovich I V and Lempert W R2015 Two-stage energy thermalization mechanism innanosecond pulse discharges in air and hydrogen–airmixtures Plasma Sources Sci. Technol. 24 025005

[15] Shkurenkov I and Adamovich I V 2016 Energy balance innanosecond pulse discharges in nitrogen and air PlasmaSources Sci. Technol. 25 015021

[16] Frederickson K, Hung Y-C, Lempert W R and Adamovich I V2017 Control of vibrational distribution functions innonequilibrium molecular plasmas and high-speed flowsPlasma Sources Sci. Technol. 25 014002

[17] Takashima K, Yin Z and Adamovich I V 2013 Measurementsand kinetic modeling of energy coupling in volume andsurface nanosecond pulse discharges Plasma Sources Sci.Technol. 22 015013

[18] Dogariu A, Goldberg B M, O’Byrne S and Miles R B 2017Species-independent femtosecond localized electric fieldmeasurement Phys. Rev. Appl. 7 024024

[19] Goldberg B M, Chng T L, Dogariu A and Miles R B 2018Electric field measurements in a near atmospheric pressurenanosecond pulse discharge with picosecond electric fieldinduced second harmonic generation Appl. Phys. Lett. 112064102

[20] Stepanyan S A, Soloviev V R and Starikovskaia S M 2014 Anelectric field in nanosecond surface dielectric barrierdischarge at different polarities of the high voltage pulse:spectroscopy measurements and numerical modelingJ. Phys. D: Appl. Phys. 47 485201

[21] Hoder T, Loffhagen D, Voráč J, Becker M M andBrandenburg R 2016 Analysis of the electric fielddevelopment and the relaxation of electron velocitydistribution function for nanosecond breakdown in airPlasma Sources Sci. Technol. 25 025017

18

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al

[22] Simeni Simeni M, Goldberg B M, Zhang C, Frederickson K,Lempert W R and Adamovich I V 2017 Electric fieldmeasurements in a nanosecond pulse discharge inatmospheric air J. Phys. D: Appl. Phys. 50 184002

[23] Leonov S B, Petrishchev V and Adamovich I V 2014 Dynamicsof energy coupling and thermalization in barrier dischargesover dielectric and weakly conducting Surfaces on μsec tomsec time scales J. Phys. D: Appl. Phys. 47 465201

[24] Simeni Simeni M, Tang Y, Hung Y-C, Eckert Z,Frederickson K and Adamovich I V 2018 Electric field in nspulse and AC electric discharges in a hydrogen diffusionflame Combust. Flame 197C 254–64

[25] Simeni Simeni M, Goldberg B, Gulko I, Frederickson K andAdamovich I V 2018 Sub-nanosecond resolution electricfield measurements during ns pulse breakdown in ambientair J. Phys. D: Appl. Phys. 51 01LT01

[26] Benard N, Zouzou N, Claverie A, Sotton J and Moreau E 2012Optical visualization and electrical characterization of fast-rising

pulsed dielectric barrier discharge for airflow controlapplications J. Appl. Phys. 111 033303

[27] Lagarkov A N and Rutkevich I M 1994 Ionization Waves inElectric Breakdown of Gases (New York: Springer) ch 4

[28] Starikovskii A Y, Nikipelov A A, Nudnova M M andRoupassov D V 2009 SDBD plasma actuator withnanosecond pulse-periodic discharge Plasma Sources Sci.Technol. 18 034015

[29] Stepanyan S A, Starikovskiy A Y, Popov N A andStarikovskaia S M 2014 A nanosecond surface dielectricbarrier discharge in air at high pressures and differentpolarities of applied pulses: transition to filamentary modePlasma Sources Sci. Technol. 23 045003

[30] Goldberg B M, Dogariu A, O’Byrne S and Miles R B 2017Imaging of DC induced second harmonic generation forspecies independent electric field measurements 55th AIAAAerospace Sciences Meeting (SciTech 2017), AIAA paper2017-1809 (Grapevine, Texas, 9–13 January)

19

Plasma Sources Sci. Technol. 27 (2018) 104001 M Simeni Simeni et al