surface ionization wave propagation in the nanosecond ......oct 11, 2019 · sdbd using the er...

Surface ionization wave propagation in thenanosecond pulsed surface dielectric barrierdischarge: the influence of dielectricmaterial and pulse repetition rate

Bangdou Huang1 , Cheng Zhang1,2,6 , Igor Adamovich3 ,Yuri Akishev4,5 and Tao Shao1,2,6

1 Beijing International S&T Cooperation Base for Plasma Science and Energy Conversion, Institute ofElectrical Engineering, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China2University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China3Nonequilibrium Thermodynamics Laboratories, Department of Mechanical and Aerospace Engineering,Ohio State University, Columbus, OH 43210, United States of America4 State Research Center of Russian Federation TRINITI, 108840, Moscow, Troitsk, Pushkovykh Str.,Vladenie 12, Russia5NRN University MEPhI, 115409, Moscow, Kashirskoe Shosse 32, Russia

E-mail: [email protected] and [email protected]

Received 11 October 2019, revised 9 February 2020Accepted for publication 20 February 2020Published 26 March 2020

AbstractIn this work, the propagation of the surface ionization wave (SIW) in the nanosecond pulsedsurface dielectric barrier discharge with different dielectric materials and pulse repetition rates isinvestigated. The current waveforms at different locations along the route of the SIWpropagation are obtained, based on a specially designed ground strip array geometry. Thetemporal evolution and spatial distribution of the electric field during the SIW propagation aremeasured by using the electric field induced second harmonic generation method. Thedistribution of the residual surface potential after the discharge is mapped with a Kelvinelectrostatic probe, which verifies both the existence of the residual electric field and its oppositedirection to that during the SIW propagation. It is found that with the dielectric material onwhich the surface charges decay faster, there are the well-pronounced primary and secondarySIWs with a higher velocity on the voltage rising edge and both the peak current and the peakelectric field are also higher, with a less spatial attenuation along the SIW propagation route. It isdemonstrated that the residual surface charges with the same polarity as the high-voltage pulsesuppress the development of the SIW.

Keywords: nanosecond pulsed discharge, surface ionization wave, electric field

1. Introduction

Surface dielectric barrier discharge (SDBD) at atmosphericpressure driven by high-voltage (HV) nanosecond pulses hasbeen a promising discharge form, which has its potential

application in different fields, such as the plasma flow control[1–5] and the plasma assisted ignition and combustion [6–9].

The breakdown process of the nanosecond pulsed SDBDis generally accompanied by a discharge propagation alongthe dielectric surface, which is usually called the surfaceionization wave (SIW) [10]. Except for the nanosecondpulsed SDBD, the phenomenon of SIW also widely exists indifferent kinds of atmospheric pressure discharge, such as the

Plasma Sources Science and Technology

Plasma Sources Sci. Technol. 29 (2020) 044001 (14pp) https://doi.org/10.1088/1361-6595/ab7854

6 Authors to whom any correspondence should be addressed.

0963-0252/20/044001+14$33.00 © 2020 IOP Publishing Ltd1

https://orcid.org/0000-0002-1523-7380https://orcid.org/0000-0002-1523-7380https://orcid.org/0000-0003-1512-2820https://orcid.org/0000-0003-1512-2820https://orcid.org/0000-0001-6311-3940https://orcid.org/0000-0001-6311-3940https://orcid.org/0000-0001-8379-5782https://orcid.org/0000-0001-8379-5782https://orcid.org/0000-0002-5738-1241https://orcid.org/0000-0002-5738-1241mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://doi.org/10.1088/1361-6595/ab7854https://crossmark.crossref.org/dialog/?doi=10.1088/1361-6595/ab7854&domain=pdf&date_stamp=2020-03-26https://crossmark.crossref.org/dialog/?doi=10.1088/1361-6595/ab7854&domain=pdf&date_stamp=2020-03-26

plasma-liquid and the plasma-catalyst interaction [11–14]. Aninvestigation of the SIW is valuable for both a deeperunderstanding of the atmospheric pressure discharge and animprovement of its plasma application.

As its name suggests, the SIW is one kind of dischargeform with a strong coupling between the gas and the surface.The dielectric surface, as the boundary of a thin layer ofplasma, and plasma-surface interaction processes can have astrong impact on the discharge evolution [15–17]. However,performing an on-line investigation on the plasma-surfaceinteraction, especially at atmospheric pressure, is extremelychallenging, as a non-intrusive diagnostic method with aspatial resolution down to micrometer and a temporal reso-lution down to nanosecond is needed. One example is usingthe electro-optical effect to measure the charge distribution onthe dielectric in DBDs and the interaction between theatmospheric pressure plasma and the dielectric material hasbeen investigated [18, 19]. Electric field induced secondharmonic (EFISH) generation is a burgeoning diagnosticmethod for the electric field in the plasma and it has beenapplied to different form of discharges, such as the fastionization wave and SIW [20–24]. As both the charges in thegas phase and those on the surface will contribute to themeasured electric field in the plasma region, measuring theelectric field using the EFISH method can provide an indirectroute to investigate the plasma-surface interaction at an ele-vated pressure.

Except for the dielectric surface, another factor influencingthe repetitively nanosecond pulsed SDBD is pulse repetitionrate (PRR), which determines the time interval between therepetitive pulses and the initial condition of each pulse [25]. Theimpact of PRR on the nanosecond pulsed discharge and its gas-phase kinetics has been investigated in a quantitative way in ourprevious work [26, 27]. However, the effect of PRR on the SIWpropagation is still needed to be explored.

In this work, the SIW driven by repetitive nanosecondHV pulses is generated in a specially designed SDBD geo-metry with the metal strip array as the ground electrode.Measuring the current flowing through the distributed groundelectrode array, the SIW propagation process is monitored.The temporal evolution and spatial distribution of the electricfield during the SIW propagation is also measured using theEFISH method. The distribution of the residual surfacepotential after the discharge is mapped, which is related to theresidual electric field from the EFISH measurement. More-over, the influence of the dielectric material and the PRR onthe SIW propagation is illustrated.

2. Experimental methods

In this work, the SDBD geometry is constructed with theprinted circuit board (PCB, as shown in figure 1). Both theflame-retardant-4 epoxy resin (ER, relative dielectric constantεr≈4.3) and the polytetrafluoroethylene (PTFE, εr≈2.1)are used as the PCB dielectric material with a thickness of1 mm and a size of 6 cm×6 cm. The electrodes are made ofcopper strips with a thickness of about 50 μm. In particular,

the ground (GND) electrodes are made of copper strip arraywith a width of 1.5 mm and a length of 30 mm and the gapbetween two strips is 1 mm [28].

In order to measure the current flowing through eachground strip, a shunt resistor (R0≈3 Ω) is used and anotherresistor R1 is used to achieve an impedance matching to the50 Ω coaxial cable, as shown in figure 1(a). The length of thecoaxial cable connecting each shunt resistor and the oscillo-scope is kept exactly the same (3 m). Attenuators (20 dB) areused to reduce the signal reflection. A large number of ferritecores are clamped on the coaxial cables to suppress thecommon mode signal [28, 29]. The voltage waveform on theHV electrode is measured using a HV probe (Pintech,P6039A). The time synchronization between the voltage andthe current measurement has been corrected as follows, whichhas been introduced in [28]. The HV electrode is extendedwith a square copper foil, which covers all ground strips. Apulsed voltage below the breakdown threshold is applied onthe HV electrode and the time-deviation of the voltagewaveform, which represents the displacement current in thiscase, and the measured current waveform are synchronized intime. By comparing the signal amplitudes from differentshunt resistors in this case, their amplitude responses are alsochecked, which have a maximum variation of about 10%between different shunt resistors.

The discharge is generated using a homemade nano-second HV generator (positive polarity) with a peak voltageof approximately 14 kV, a full width at half maximum ofabout 250 ns, and a rising edge (20%–80% of the peak value)

Figure 1. A schematic diagram for the geometry of the surfacedielectric barrier discharge with the ground strip array, (a) side view,(b) top view. The unit of the dimensions is in millimeter. Note thatthe dimensions in this diagram are not to scale.

2

Plasma Sources Sci. Technol. 29 (2020) 044001 B Huang et al

of about 200 ns. The PRR of the discharge is varied from10 Hz to 500 Hz. In this work, argon is blown out from anozzle (with a cross section of approximately 1 mm in heightand 6 mm in width) attached to the HV electrode. The gasflow rate is 0.3 standard liter per minute. The purpose ofintroducing an argon flow is to extend the discharge length, asa result of which, the current when the SIW propagates can bemeasured by the ground strip array. In fact, it is very chal-lenging to obtain the flow geometry and the gas component inour current experimental setup, even though the particleimage velocimetry could be applied to visualize the flowgeometry, which is already out of the main scope of thisinvestigation. The influence of the gas component on theEFISH measurement will be discussed in detail below. Here,the Reynolds number of the argon flow Re =ρmvf Lf/μ isestimated to be 720, where ρm is the density of argon (ρm≈1.78 kg m−3), vf is the flow velocity (vf≈1 m s

−1), Lf isthe characteristic length of the flow (Lf ≈1 cm), and μ is theviscosity of argon (22.9 μPa s). It can be seen that the argonflow from the nozzle is laminar flow in the discharge region.

An intensified charge coupled device (ICCD, Andor iStarsCMOS) camera is used to obtain both the single shot dis-charge image and the averaged image over multi-pulses. Thegate width of the ICCD camera is 500 ns. The start time ofthe ICCD gate with respect to t=0 (when the HV reachesits peak value) is set to be −280 ns in the ER case and it is−210 ns in the PTFE case, as the breakdown happens later inthe PTFE case. With these settings, most of the dischargeemission during both the voltage rising and falling edges canbe captured. The length scale of the discharge images iscalibrated using the distance between the ground strips, whichcan be seen in an image of the SDBD geometry without thedischarge taken with the same optical setup.

Figures 2(a) and (b) show the single shot images of theSDBD using the ER dielectric with different grey scales andfigure 2(c) shows the averaged image over 50 pulses,respectively. For comparison, those with the PTFE dielectricare also shown in figures 2(d)–(f). It can be seen that theemission intensity of the SDBD with the ER dielectric isstronger than that with the PTFE dielectric by one order ofmagnitude. This result is consistent with the measured currentamplitude using these two kinds of dielectric materials (sub-sequently shown in figure 5). In addition, the dischargemorphology with the ER dielectric is more filamentary, whilethat with the PTFE dielectric is more diffuse. Notice that,except for the main streamer in the argon flow region, thereare also multi short streamers outside the argon flow with bothdielectric materials, whose intensity is below 10% of theintensity of the main streamer.

In this work, the EFISH generation system is used tomeasure the temporal evolution and spatial distribution of theelectric field. A detailed description of the EFISH method hasbeen given in [20–24] and only a brief introduction of theexperimental setup used in this work is given as follows(shown in figure 3).

The horizontally (x direction) polarized 1064 nm funda-mental output beam of a nanosecond Nd:YAG laser (Beam-tech SGR-S400, pulse width 7–9 ns, 10 Hz) is focused to the

discharge region (near the nozzle) using a plano-convex lens(with a focal length f of 55 cm). The laser energy is set as15 mJ per pulse in this work. The 1/e2 radius of the laserbeam at the focus, measured by traversing a knife edge acrossthe laser beam, is approximately 130 μm. When using ashorter focal length lens, the beam radius around the focuswill be less and the spatial resolution of the EFISH mea-surement will be improved [20]. However, as a nanosecondpulsed Nd:YAG laser is used in this work, the risk of the laserinduced breakdown will increase with a short focal lengthlens. Therefore, we choose to use a relatively long focallength lens. After the laser beam passes through the dischargeregion, a prism is used to disperse the fundamental laser andthe second harmonic light in space. A polarizer is used toselect the horizontally polarized component of the secondharmonic and a band pass filter (BPF) is used to select thewavelength of the second harmonic (532 nm). The intensitiesof the fundamental laser and the second harmonic light aredetected with a photodiode (PD, Thorlabs, DET10A2) and aphotomultiplier (PMT, Hamamatsu, R1828-01), respectively.The Nd:YAG laser and the nanosecond HV generator aresynchronized with a delay generator (SRS, DG645), whichdetermines the time interval between the laser output and theHV pulse. The frequency-division method is used when theSDBD has a higher repetition rate than the laser.

The SDBD structure is mounted on a three-dimensionaldisplacement platform and the electric field at differentlocations can be obtained without changing the laser

Figure 2. (a) and (b): The single shot images of the SDBD using theER dielectric with different grey scales, (c): the averaged image over50 pulses with the ER dielectric. (d)–(f): The corresponding imageswith the PTFE dielectric.

3


alignment. When performing the EFISH measurement, theSDBD structure is firstly adjusted using an air level. Next, theSDBD structure is raised until the laser is shot onto the side ofthe dielectric (and the laser is blocked by the dielectric). Then,the SDBD structure is moved lower-down slowly while thelaser energy is monitored by the photodiode, until the laserenergy recovers to the value without blocking. The beamwaist of the laser at the edge of the dielectric surface isapproximately 0.15 mm (according to equation (7)), which istaken as the distance between the observation point and thedielectric surface. At each time point and at each position,signal average over 1000 pulses is performed.

In order to obtain the relationship between the intensityof the EFISH signal (I(2ω)) and the electric field strength (E),a calibration of the system is needed. When performing theEFISH calibration, both a static voltage and a nanosecond HVpulse are applied across the parallel-plate electrodes (34 mmby 12 mm, gap 2.5 mm) in order to obtain a known anduniform electric field. The laser beam passes through theparallel-plate electrodes along their short side (as shown infigure 3), i.e. in the calibration configuration, the interactionlength between the laser and the electric field is 12 mm.

When the static voltage is larger than about 2.9 kV inargon, breakdown occurs between the parallel-plate electro-des, which means that an electric field larger than about11.6 kV cm−1 cannot be obtained in this case. In order toextend the range of the electric field in the EFISH calibration,a nanosecond HV pulse with a peak voltage of 5.3 kV and apulse width of 80 ns is applied, which does not induce abreakdown in argon (due to the pulsed breakdown delay

effect [30, 31]), and a maximum electric field of 21 kV cm−1

is obtained in argon. Similarly, in air, a nanosecond HV pulsewith a peak voltage of 8 kV is applied and a maximumelectric field of 32 kV cm−1 is obtained.

Figures 4(a) and (b) show the relationship between theintensity of the second harmonic light (I(2ω)) with the squareof the electric field (E2) in argon and in air, respectively. Itcan be seen that the measured I(2ω)–E2 relationship can befitted well with a linear function, which agrees with thetheoretical relationship [21]

( ) [ ( ) ( )

( ) ( )] ( · )·

( )

( )

⎡⎣⎢

⎤⎦⎥

/

/

w c w w w w

w w

µ -

´D

D

I N E E

E Lk L

k L

2 2 , 0, ,

sin 2

2. 1

i ijkl k

l

30 0 1,

1,2 2

2

Here, N is the gas density. L is the interaction length betweenthe laser and the external electric field. E0(ω0) represents theexternal electric field with a frequency of ω0. E1(ω) representsthe electric field of the fundamental laser with a frequency ofω. The frequency of the laser electric field is much larger thanthat of the external electric field (ω?ω0). χ

(3) is the third-order nonlinear susceptibility (hyperpolarizability) and theratio of χ(3) in air and χ(3) in argon (χ(3)[Air]/χ(3)[Ar]) is 0.79from [32]. Note that a mixture fraction weighted hyperpo-larizability for air is used in this work, i.e. χ(3)[Air]=0.8χ(3)[N2]+0.2 χ

(3)[O2], which has been done in [33]. Δk isthe wavevector mismatch of the fundamental laser and itssecond harmonic, i.e. Δk=2k1−k2 and ki =2πn(λi)/λi,where n(λi) is the refractive index of the light with a wave-length of λi. c is the light velocity in vacuum. It has been

Figure 3.A schematic diagram of the electric field induced second harmonic generation system. LPF: long pass filter, FL: plano-convex lens,BPF: band pass filter, PD: photodiode, PMT: photomultiplier tube.

4


calculated that Δk in argon (Δk[Ar]) is 0.47 cm−1 and Δk inair (Δk[Air]) is 0.50 cm−1 [34, 35] and the coherence lengthLc =π/Δk is about 6 cm, which is much larger compared tothe span of the HV electrode.

In the calibration of this work, the ratio of the slope of theI(2ω)–E2 relationship (i.e. the calibration coefficient) S[Air]/S[Ar] is 0.8 from the fitting of the measured data and the squareroot of this ratio (S[Air]/S[Ar])0.5 is 0.89, which is close toχ(3)[Air]/χ(3)[Ar] of 0.79 from [32].

Figure 4(c) shows the temporal evolution of the electricfield between the parallel-plate electrodes from both theEFISH signal and the voltage over the electrode gap (V/d),when a HV pulse is applied in argon. It can be seen thatif a calibration coefficient obtained in air, S[Air], is used,there is an overprediction of the electric field by about 10%compared with the V/d, illustrating the difference between the

hyperpolarizabilities of argon and air. However, when S[Ar]is used, the EFISH data fall on the V/d curve. This obser-vation agrees with the effect of varying gas species on theEFISH signal in [33]. Notice that even small variations of theV/d pulse shape are reproduced by the EFISH measurements.

In addition, a Kelvin electrostatic probe (Trek-6000B-6)and an electrostatic voltmeter (Trek 347) are used to measurethe surface potential distribution on the PTFE dielectric afterthe discharge, by mounting the SDBD structure on a two-dimensional displacement platform, as has been performed in[36, 37]. The distance between the tip of the electrostaticprobe and the dielectric surface is approximately 5 mm. Thisdefinitely limits the spatial resolution of the surface potentialmeasurement, which is estimated to be at least 5 mm, basedon the measurement of the spatial distribution of the potentialgenerated by applying a static voltage on a metal plate with asharp edge [26, 29].

3. Results and discussion

3.1. The current flowing through the ground strip array

Figure 5(a) shows the voltage waveform on the HV electrodeand the current waveforms flowing through each ground stripwith the ER dielectric. The peak voltage is 14 kV and thePRR is 100 Hz. The zero point of time is set at when thevoltage reaches its peak value.

It can be seen that on the voltage rising edge, the currentwaveform through the first three ground electrode stripspresents a two-peak feature, indicating the primary and thesecondary SIWs [21]. The peak value of the current through aground strip further away from the HV electrode is reachedlater, as a result of the SIW propagation. The velocities of theprimary and the secondary SIWs are estimated to be about0.29 mm ns−1 and 0.25 mm ns−1, respectively, obtained fromthe relationship between the location of different groundstrips and the time when the peak current through each strip isreached.

It can also be seen that the peak current of the secondarySIW is 3 times higher than that of the primary SIW. This isdue to the fact that the secondary SIW propagates in theconductive channel left over by the primary SIW. The currentattenuation during the propagation of the secondary SIW isalso less than that of the primary SIW. The current waveformthrough the fourth ground strip, located at where the SIWextends to its maximum length, presents only one peak duringthe period of the secondary SIW propagation, which meansthat the primary SIW hardly reaches this position.

On the voltage falling edge, the current through eachground strip turns to be negative, indicating a reverse dis-charge. Note that, during this period, the negative currentthrough the first ground strip is much larger than that throughstrips further away from the HV electrode. This means thatthere are residual positive charges left far away from the HVelectrode (which may be like an isolated island). This effectwill also be proved by the measured electric field as well as

Figure 4. The relationship between the intensity of the secondharmonic light (I(2ω)) with the square of the electric field (E2) (a) inargon and (b) in air; (c) the temporal evolution of the electric fieldbetween the parallel-plate electrodes from both the EFISH signalusing different calibration coefficients and the voltage over theelectrode gap (V/d), when a high voltage pulse is applied in argon.

5


the distribution of the residual surface potential after thedischarge (shown below).

Figure 5(b) shows the HV waveform and the currentwaveforms flowing through each ground strip using the PTFEdielectric with a peak voltage of 14 kV and a PRR of 100 Hz.Differing from the case with the ER dielectric, the currentwaveform with the PTFE dielectric presents much less pro-nounced two-peak feature on the voltage rising edge, whichmeans that there may not be well-distinguished primary andsecondary SIW propagation processes. The velocity of theSIW propagation on PTFE is estimated to be about0.08 mm ns−1, which is much slower than that on ER. Thepeak current with PTFE is much smaller than that with ER byone order of magnitude, which agrees with the huge differ-ence in the emission intensity shown in figure 2. The peakcurrent through each ground strip with PTFE also attenuatessignificantly away from the HV electrode, in contrast with thealmost constant (second) peak current in the ER case.

Figure 6(a) shows the current waveform through the firstground strip using the ER dielectric with different PPRs of10, 100, and 500 Hz. The peak voltage is kept at the same

value of 14 kV. It can be seen that the two-peak feature onthe current waveform is less obvious with a high value ofPRR (500 Hz) compared with that with a low PRR (10 and100 Hz), which means that the primary and the secondarySIWs are less distinguished with a high PRR. This featureagrees with what has been observed in the fast ionizationwave propagating in a shielded dielectric tube, which shows alesser difference between the peak electric field and that afterthe breakdown with a high value of PRR [26].

Figure 6(b) shows the current waveform through the firstground strip using the PTFE dielectric with different PRRsand with the same peak voltage of 14 kV. Similar as the casewith the ER dielectric, the two-peak feature of the currentwaveform is slightly more obvious with a low PRR of 10 Hz.Other than this, the current waveform is almost the same withdifferent values of PRR.

The following estimation is performed, trying to give aninterpretation about the influence of dielectric material on thecurrent during the SIW propagation (I(t)), which can roughly

Figure 5. The voltage waveform on the HV electrode and the currentwaveforms flowing through each ground strip. The peak voltage is14 kV and the PRR is 100 Hz. (a) ER dielectric, (b) PTFE dielectric. Figure 6. The current waveform through the first ground strip with

different values of pulse repetition rate and with the same peakvoltage of 14 kV. (a) ER dielectric, (b) PTFE dielectric.

6


be given as follows [38, 39]:

( ) ( ( ) · ( )) ( ) · ( ) ( ) · ( )

( )

= = +I tC t U t

tC t

U t

t

C t

tU t

d

d

d

d

d

d.

2

Here, U(t) is the voltage waveform. C(t) is the capacitancebetween the plasma slide and the ground electrode, whichchanges with time due to the SIW propagation andthe extension of the plasma slide. C(t) and dC(t)/dt can bewritten as:

( )( ) ( )

·( )

· ( )

e e e e

e e

= =

=

C tW L t

d

C t

t

W

dL t

t

W

dV

,d

dd

d. 3

p p

e

p

e

p r p

e

r 0 r 0

0SIW

Here, ε0 is the vacuum permeability and εr is the relativedielectric constant of the dielectric material. de is the thicknessof the dielectric. Wp and Lp are the width and the length ofthe plasma slide, respectively. Here, Wp is assumed to be aconstant during the SIW propagation, while Lp extends with avelocity of VSIW.

Combining equations (2) and (3), the following rela-tionship can be obtained,

( )( )

· ( ) · · ( ) ( )e e e e

= +I tW L t

d

U t

t

W

dV U t

d

d. 4

p p

e

r p

e

r 0 0SIW

The first term on the right side of equation (4) is the classicaldisplacement current due to the variation of the voltage acrossa capacitor, while the second term is due to the extension ofthe conductive plasma slide and the variation of the capaci-tance, which is called the dynamic displacement currentin [38].

It can be estimated that for the ER dielectric case whenthe SIW has a relatively high velocity (about 0.3 mm ns−1),the first term on the right side of equation (4) contributes acurrent on the order of 0.2 A, while the second term con-tributes a current on the order of 1 A. However, for the PTFEdielectric case when the SIW has a relatively low velocity(about 0.08 mm ns−1), both terms contribute to a current onthe order of 0.1 A. As one can see, the velocity of the SIWpropagation and the dynamic displacement current help toexplain the huge difference in the measured current (by oneorder of magnitude) when different dielectric materials areused, which goes beyond the influence of the relative di-electric constant (εr≈4.3 for ER versus εr≈2.1 for PTFE).

It is worth to notice that in the above estimation, weignore the voltage drop across the plasma slide, which has acertain resistance and is not a perfectly conductive medium[40, 41]. Even so, the purpose of this estimation is to give aqualitative explanation on the huge difference in the measuredcurrent with different dielectric materials. Further detailedanalysis considering the spatial distribution of U(t) based onthe measured electric field distribution will be given in theappendix.

3.2. The electric field: temporal evolution and spatialdistribution

Figures 7(a) and (b) shows the measured temporal evolutionof the horizontal electric field (Ex) at different locations usingthe EFISH method with the ER and the PTFE dielectrics,respectively. The peak voltage is 14 kV and the PRR is100 Hz.

Note that there is already a non-zero electric field beforethe HV pulse, which is due to the existence of residual surfacecharges from the previous pulse. The direction of the electricfield is inverted when it reaches a local minimum point (thesame as what has been done in [21]).

It can be seen in figure 7(a) that as the voltage starts torise, Ex near the HV electrode starts to increase firstly, whileEx at locations further away from the HV remains more or lessunchanged. This means that before the breakdown happens,the electric field near the HV electrode is a superposition ofthe Laplacian field and the field due to the residual surfacecharges.

When Ex near the HV electrode reaches a peak value of26 kV cm−1, it starts to drop and a local minimum value is

Figure 7. The temporal evolution of the horizontal electric field atdifferent locations with a peak voltage of 14 kV and a pulserepetition rate of 100 Hz, (a) ER dielectric, (b) PTFE dielectric. TheHV waveform is also plotted on the figures.

7


formed, which indicates the breakdown happens. This isaccompanied by the sudden rise of Ex at 2.5 mm and 5 mm,which happens later at a position further away from the HVelectrode, indicating the SIW propagation. These phenomenahappen during a time period roughly corresponding to theprimary SIW period indicated by the first peak of the currentwaveform in figure 5(a). However, due to the limited tem-poral resolution of the EFISH system, no exact matchingbetween the current waveform and the electric field evolutioncan be achieved. Afterwards, Ex near the HV increases againand reaches a second peak, while Ex at 2.5 mm and 5 mmkeeps increasing and reaches its positive maximum, whichalso happen in time sequence and correspond to the second-ary SIW.

On the voltage falling edge, Ex near the HV electrode andthat at 2.5 and 5 mm reverses and reaches their negativemaximum in time sequence, which is consistent with thenegative current shown in figure 5(a). This is explained by thefact that the residual positive charge on the dielectric surfacegenerates a negative horizontal electric field and a reversebreakdown process.

It is worth noticing that Ex at 7.5 mm, where the SIWreaches its maximum length, experiences a dull rise during thevoltage rising period, followed by a slow decay during thevoltage falling period and it presents no reverse process. Thisis explained by that this location is affected by the electricfield at the SIW front, which rises as the wave front of theSIW approaches and drops as the SIW decays, and no plasmaslide is formed across this location.

Comparing figures 7(a) and (b), it can be found that Exnear the HV electrode with the PTFE dielectric has only onepeak (without the two-peak feature in the ER case). With thePTFE dielectric, the peak Ex near the HV electrode is slightlylower than that with ER (23 kV with PTFE versus 26 kV withER). Even so, the time when the peak value is reached is later(−170 ns with PTFE versus −193 ns with ER), which is dueto a larger negative residual Ex with the PTFE dielectric(−18 kV with PTFE versus −14 kV with ER). With the PTFEdielectric, Ex also attenuates faster away from the HV elec-trode (for example, Ex at 2.5 mm is 15 kV cm

−1 with PTFE,while it is 24 kV cm−1 with ER). This feature is consistentwith its faster current attenuation during the SIW propagation(shown in figure 5).

Figures 8(a) and (b) show the temporal evolution of thehorizontal electric field at 2.5 mm with different PRRs usingthe ER dielectric and the PTFE dielectric, respectively.

It can be seen in figure 8(a) that with the ER dielectric,the absolute value of the residual Ex before the breakdowndeceases with the PRR, i.e. it decreases from −14.5 kV cm−1

with 500 Hz to −10.5 kV cm−1 with 10 Hz, which is alsoshown in figure 8(c). This indicates the decay of the residualsurface charges on the ER dielectric, as the pulse intervalincreases from 2 ms to 0.1 s. Other than this, the temporalevolution of Ex is almost the same with different PRRs.

In figure 8(b), when PRR changes from 10 to 500 Hz, theevolution process of Ex with PTFE coincides with each otherand the residual Ex before the breakdown remains the same.This indicates that the residual surface charges on the PTFE

dielectric hardly decay within a time period of 0.1 s. Indeed, ithas been verified the residual Ex with PTFE remainsunchanged for more than one hour after the HV generatoris turned off. This fact provides the possibility to perform an

Figure 8. The temporal evolution of the horizontal electric field at2.5 mm with different values of PRR and with a peak voltage of14 kV, (a) ER dielectric, (b) PTFE dielectric. (c) A summary of therelationship between the absolute value of the residual horizontalelectric field at 2.5 mm and the PRR with different dielectric materials.

8


off-line measurement on residual surface potential (as well asthe residual electric field) due to the surface charge accu-mulation using the Kelvin electrostatic probe, which will beshown in the next section.

Indeed, the characteristic time for the charge decay τVthrough the volume resistivity ρV is given by [42],

( )t e e r= . 5V r 0 VER has a volume resistivity on the order of 1010 Ωm(according to the datasheet of the dielectric material used) andits characteristic charge decay time is approximately 0.4 sobtained from equation (5), which can partially explain thedecay of the residual electric field when the pulse intervalincreases from 2 ms to 0.1 s. However, PTFE has a muchhigher ρV (>10

16 Ωm) and a much longer charge time(τV>2×10

5 s). Therefore, it is hard to observe a variationof the residual electric field within the pulse interval range inthis work (0.1 s). Other factors influencing the decay of thesurface charges include the electric conduction along the di-electric surface and the neutralization by the charge in the gasphase [42]. Currently, we do not perform a detailed analysison these effects, as it is already beyond the main topic ofthis work.

3.3. The residual surface potential distribution after thedischarge

As mentioned above, the residual electric field with the PTFEdielectric remains unchanged for a long time period (>1 h),which allows us to measure its residual surface potentialdistribution after the discharge using the Kelvin electrostaticprobe (shown in figure 9 with the contour-plot). From thegradient of the surface potential distribution, the electric fieldin x and z directions (Ex and Ez) can be obtained, which ispresented by the arrows, together with the surface potential in

figure 9. The HV electrode locates at 0 mm in the x directionand the middle point of the nozzle is set as the zeros point ofthe z axis.

It can be seen that the residual surface potential increasesaway from the HV electrode, which is due to the positiveresidual surface charges after the discharge and agrees withthat observed in [36]. Near the nozzle region, the contour-lineof the surface potential bulges away from the HV electrode,as the SIW mainly happens in the argon flow blown out fromthe nozzle. Two almost symmetric plateaus of the surfacepotential are formed at the coordinates of (x≈10 mm,z≈13 mm) and (x≈10 mm, z≈−13 mm). The electricfield is directed outside from these two plateaus and it isdirected toward the HV electrode. This verifies that the resi-dual Ex before the breakdown and the Ex during the SIWpropagation are in the opposite direction, the latter of which isdirected outward the HV electrode when a positive HV isapplied. Therefore, it is reasonable to perform an inversion ofthe measured Ex when it reaches a local minimum during boththe voltage rising and falling edges.

It worth to notice that the distance between the tip of theKelvin electrostatic probe and the dielectric surface (≈5 mm)limits the spatial resolution of the measured surface potentialand that of the electric field from its gradient, especially atlocations where their distribution is extremely non-uniform.For example, the residual Ex near the HV electrode is quitestrong (as shown in figure 7(b)), while Ex inside the HVelectrode, which is in parallel with the metal surface, shouldbe zero. However, Ex from the gradient of the surfacepotential will be smooth out this feature. Therefore, noquantitative agreement between the electric field from theEFISH method and that from the surface potential could beobtained in this work.

3.4. Analysis of EFISH signal accumulation along thebeam path

It is already known that the EFISH method detects a line-of-sight signal integration along the laser propagation path andformer investigations have prominently contributed to theinfluence of the measurement length [20, 33]. In this work,especially, as the SIW has an extremely non-uniform electricfield distribution and both the charge on the dielectric surfaceand that in the plasma slide will contribute to the EFISHsignal, it is desirable to analyze the distribution of the EFISHsignal along the laser beam path.

According to [43, 44], when both the external electricfield E0 and the electric field of the fundamental laser E1 havea non-uniform spatial profile, the electric field of the secondharmonic can be given as follows,

( ) ( ) ( )

( ) ( ) ( )

( )

/

òw c w wµ ¢´ + ¢ D ¢ ¢

-¥-

E z N E z E

i z b i kz z

2 , ,

1 2 exp d . 6

z

23

0 0 12

11

Here, b1 is the confocal parameter of the fundamental laserbeam, and b1/2 indicates the distance (along the laser path)between the focus to the position where the beam radius hasincreased by √2.

Figure 9. The contour-plot of the residual surface potentialdistribution on the PTFE dielectric after the discharge measuredusing the Kelvin electrostatic probe. The electric field in the x and zdirections is presented by the arrows.

9


The beam radius along the laser path w(z) is given by [45],

( ) [ ( ) ] ( )/= +w z w z b1 2 . 72 02 1 2

Here, w0 is the 1/e2 beam radius at the focus (w0≈130 μm). b1

can be obtained from,

· · ( ) ( )/p l l= =b w k w n2 81 02 1 02 1 1

and it is calculated to be about 10 cm.The spatial distribution of the laser intensity Ii(r, z) and

the relationship between the laser intensity and the electricfield are given by [45],

( ) ( ) ∣ ( )∣ ∣ ∣

( )⎛⎝⎜

⎞⎠⎟

l e= µ

´ -

I r z n c E r z Ew

w

r

w

, 0.5 ,

exp2

. 9

i i i i02 2 0

2

2

2

2

By moving the parallel-plate calibration electrodes alongthe laser path, the distribution of the square root of the EFISHsignal I(2ω)0.5 in the z direction is obtained, which is shownin figure 10. In the same figure, the calculated I(2ω)0.5 dis-tribution in the z direction corresponding to the uniformelectric field generated by the parallel-plate electrodes is alsoshown. It can be seen that the calculated I(2ω)0.5–z curveagrees well with the measured one, demonstrating the vali-dation of the analysis on the EFISH signal accumulationalong the beam path.

As for the SDBD, the analysis on the EFISH signalaccumulation is performed based on the residual electric fielddistribution in z direction on the PTFE dielectric (shown infigure 11(a)). As it is very challenging to obtain the real gascomponent in the discharge region in this work, a step wisemultiplicative factor accounting for the different hyperpolar-izabilities, χ(3), and wavevector mismatch, Δk, of argon andair is included, i.e. the gas component in the region with−3 mm

captures a line-of-sight integration of the electric field alongthe laser path, i.e. both the electric field around the mainstreamer channel in the argon flow region and that away fromthe main streamer will contribute to the EFISH signal. In fact,the effect of the laser-electric field interaction length L can betaken into account based on the relationship I(2ω)0.5∼E·Laccording to equation (1), i.e. there is an inverse relationshipbetween the electric field and the laser-electric field interac-tion length for the same EFISH signal. However, the choiceof the L value is somewhat arbitrary for an extremely inho-mogeneous SDBD, and the electric field distribution inferencemay be uncertain. Therefore, no attempt to infer the electricfield distribution in the discharge is performed. The line-of-sight integration may result in an underestimation of the peakelectric field during the SIW propagation, as the SIW in thiswork is quite filamentary and a strong electric field may existnear the wave front region (i.e. near the thin streamer head).On the other hand, the residual electric field near the HVelectrode may be overestimated, as it spans over the wholeHV electrode region (as shown in figures 9 and 11(a)).Indeed, the peak electric field in the nanosecond pulsed dis-charges obtained from the widely adapted line-ratio methodcan be much higher (up to 1000 Td, i.e. 260 kV cm−1 bar−1)[46–49]. This can be explained by the fact that the excitedspecies emitting optical light are mainly generated by theimpact of high energy electrons (> about 10 eV, dependingon the excitation threshold energy), which are concentrated inthe region where the electric field is the strongest[2, 26, 50, 51].

In this work, the temporal resolution of the EFISHmeasurement is limited by the laser pulse width (about7–9 ns), which could smear out the electric field evolution onthe shorter time scales, and reduce the peak electric fieldduring the SIW propagation. This effect could be significantespecially for the SIW propagating on the ER dielectric,which has a velocity VSIW of about 0.3 mm ns

−1. Consideringthe laser radius of about 130 μm around the focal point andthe characteristic length scale for atmospheric pressureplasma of the order of hundred micrometers, a sub-nano-second time resolution is needed to well resolve the electricfield evolution, i.e. a picosecond laser may be required in thefurther investigation. Note, however, that nanosecond EFISHmeasurements can provide a temporal resolution shorter thanthe laser pulse duration, by using a detector with a shorterresponse time [52]. Although the field reversal has beendetected, when the electric field at a certain position passesthough zero during the SIW propagation, only a local mini-mum value is obtained in the experiment. This is also due tothe limited temporal resolution of the EFISH system, whichinduces an averaging effect.

Only the horizontal electric field Ex are measured usingthe EFISH method in this work, as Ex is along the direction ofthe SIW propagation, in which we are more interested.Indeed, Ex alone could already demonstrate the effect of the

dielectric material and the PRR on the SIW propagation. Ahalf-wave plate can be introduced to rotate the polaritydirection of the laser in the further investigation and a mea-surement of the vertical electric field can be performed.However, this measurement is rather challenging in theSDBD. This is due to the fact that the SIW generates anextremely thin plasma slide with a thickness of the order of100 μm and the vertical electric field decays very fast abovethe dielectric surface. As a result, special effort is needed todistinguish the measured vertical electric field is in or abovethe thin plasma slide, as has been performed in [21].

In addition, it can be seen that there are a lot of surfacestreamers outside the area occupied by the argon flow. Thismeans that there is a contribution of the current of thesestreamers to the total current of the first ground strip. Even so,we speculate that this contribution may be minor, as the peakvalues of the current through the first and the second groundstrips are similar in both ER and PTFE dielectric cases, whilethese streamers do not reach the second ground strip.

5. Conclusions

In this work, the propagation of the SIW in the nanosecondpulsed SDBDs with different dielectric materials (ER andPTFE) and different PRRs (from 10 to 500 Hz) is investi-gated. With a specially designed ground strip array structure,the current waveform at different locations along the route ofthe SIW propagation is obtained. Using the EFISH method,the temporal evolution and spatial distribution of the hor-izontal electric field during the SIW propagation are measuredwith different dielectric materials and PRRs. The distributionof the residual surface potential after the discharge is mappedwith a Kelvin electrostatic probe, which verifies both theexistence and the direction of the residual electric field fromthe EFISH measurement.

By comparing the results using the dielectric materialswith different charge decay rates and by changing the PRR(i.e. the pulse interval), the effect of the residual surfacecharges on the SIW propagation is illustrated. It is found thatwith the ER dielectric, on which the residual surface chargesdecay faster, there are the well-pronounced primary andsecondary SIW propagation processes with a higher velocityon the voltage rising edge. Both the peak current and the peakelectric field during the SIW propagation on the ER dielectricare higher, with a less spatial attenuation of both parametersalong the SIW route. A higher PRR tends to smear out thefeature of the primary and secondary SIWs. The residualelectric field increases with the PRR in the ER dielectric case,which has a characteristic charge decay time comparable withthe pulse interval used in this work. However, when the PRRchanges, the residual electric field is nearly a constant withthe PTFE dielectric, whose characteristic charge decay timeis much longer than the pulse interval in this work. It is

11


demonstrated that the residual surface charges with the samepolarity as the HV pulse tend to suppress the development ofthe SIW.

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China under contracts 51777204, 51907190and 51911530118.

Professor Igor Adamovich from the Ohio State Uni-versity worked with the build-up of the EFISH system in June2018, supported by Chinese Academy of Sciences President’sInternational Fellowship Initiative under contract2018VEA0004.

Professor Yuri Akishev from the State Research Centerof Russian Federation TRINITI investigated the effect ofresidual charges on the SIW, supported by grant RFBR No.19-52-53003.

Appendix

According to [40, 41] and based on the Kirchhoff equations,the current in a SDBD is described as follows:

( ) · ( ) ( )òe e

=¶¶

I tW

d tU x t x, d . A1

r p

e

0

Here, U(x, t) describes the potential at different locationsalong the route of the SIW propagation and its temporalevolution. U(x, t) can be obtained combining the HV wave-form U(0, t) and the horizontal electric field Ex(x, t) from theEFISH measurement:

( ) ( ) ( ) ( )ò= - ¢ ¢U x t U t E x t x, 0, , d A2x

x0

which is shown in figures A1(a) and (b), corresponding to thecase with ER and PTFE dielectrics, respectively.

Combining equations (A1) and (A2), the current in aSDBD can be obtained, which is shown in figure A2, togetherwith the spatial integration of the potential ∫U(x, t)dx.

It can be seen in figure A1 that before the HV is applied,the potential rises away from the HV electrode, which is dueto the existence of the residual surface charges and thenegative residual Ex. This feature is consistent with themeasured surface potential distribution using the Kelvinelectrostatic probe. The SIW propagation process is accom-panied with a drop and a following fast rise of the potential ateach position. After the discharge, the potential recovers to asimilar value as that before the breakdown. Note that theovershot of U(x ≈ 5 mm) and U(x ≈ 7.5 mm) compared withthe peak value of HV waveform can be explained by theuncertainty of the absolute value of Ex from the EFISHmeasurement. This is due to the fact that the laser-plasmainteraction length has a strong impact on the EFISHsignal [21].

In figure A2, it can be seen that the current obtained fromequation (A1) has a negative dip before its main positive

peak, which is not observed in the measured current wave-form using the shunt resistor. Indeed, this dip is due to thenon-accuracy in the Ex measurement especially when Expasses through the zero point during the SIW propagation. Asmentioned above, Ex will be over-estimated due to thenanosecond pulse width of the laser used in this work. Thiseffect is even more obvious in the ER dielectric case, whenthe SIW has a much faster propagation velocity. Furthermore,the long laser pulse will also over-estimate the electric fieldafter the wave front of the SIW passes due to the averagingeffect, as a result of which, the voltage drop across the plasmaslide will also be over-estimated. Taking these factors intoconsideration, it is reasonable to argue that there is no fullagreement between the measured current waveform and thatobtained using equations (A1) and (A2). Based on an Exmeasurement with a better temporal resolution and perhaps adenser spatial sampling, one can expect a better agreementbetween the results from these methods.

Figure A1. The temporal evolution of the potential at differentlocations U(x, t) obtained using the HV waveform and the measuredhorizontal electric field Ex with the EFISH method. (a) ER dielectric,(b) PTFE dielectric.

12


ORCID iDs

Bangdou Huang https://orcid.org/0000-0002-1523-7380Cheng Zhang https://orcid.org/0000-0003-1512-2820Igor Adamovich https://orcid.org/0000-0001-6311-3940Yuri Akishev https://orcid.org/0000-0001-8379-5782Tao Shao https://orcid.org/0000-0002-5738-1241

References

[1] Starikovskiy A Y, Meehan K, Persikov N and Miles R 2019Static and dynamic stall control by NS SDBD actuatorsPlasma Sources Sci. Technol. 28 054001

[2] Zhang C, Huang B D, Luo Z B, Che X K, Yan P and Shao T2019 Atmospheric-pressure pulsed plasma actuators for flowcontrol: shock wave and vortex characteristics PlasmaSources Sci. Technol. 28 064001

[3] Zhu Y, Wu Y, Cui W, Li Y and Jia M 2013 Modelling ofplasma aerodynamic actuation driven by nanosecond SDBDdischarge J. Phys. D: Appl. Phys. 46 355205

[4] Peng B F, Jiang N, Yao X M, Ruan Y X, Wang D Y,Shang K F, Lu N, Namihira T, Li J and Wu Y 2019Experimental and numerical studies of primary andsecondary streamers in a pulsed surface dielectric barrierdischarge J. Phys. D: Appl. Phys. 52 325202

[5] Che X K, Nie W S, Zhou P H, He H B, Tian X H andZhou S Y 2013 Study on continuous vortices induced bysub-microsecond pulsed surface dielectric barrier dischargeplasma Acta Phys. Sin. 62 224702

[6] 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

[7] Ju Y and Sun W T 2015 Plasma assisted combustion: dynamicsand chemistry Prog. Energy Combust. 48 21e83

[8] Shao T, Wang R X, Zhang C and Yan P 2018 Atmosphericpressure pulsed discharges and plasmas: mechanism,characteristics and applications High Volt. 3 14

[9] Anokhin E M, Kuzmenko D N, Kindysheva S V,Soloviev V R and Aleksandrov N L 2015 Ignition ofhydrocarbon : air mixtures by a nanosecond surfacedielectric barrier discharge Plasma Sources Sci. Technol. 24045014

[10] Lagarkov A N and Rutkevich I M 1994 Ionization Waves inElectrical Breakdown of Gases (New York: Springer)(https://doi.org/10.1007/978-1-4612-4294-9)

[11] Bruggeman P J et al 2016 Plasma–liquid interactions: a reviewand roadmap Plasma Sources Sci. Technol. 25 053002

[12] Bogaerts A, Berthelot A, Heijkers S, Kolev S, Snoeckx R,Sun S, Trenchev G, Van Laer K and Wang W 2017 CO2conversion by plasma technology: insights from modelingthe plasma chemistry and plasma reactor design PlasmaSources Sci. Technol. 26 063001

[13] Kruszelnicki J, Engeling K W, Foster J F, Xiong Z M andKushner M J 2017 Propagation of negative electricaldischarges through 2-dimensional packed bed reactorsJ. Phys. D: Appl. Phys. 50 025203

[14] Ning W J, Dai D and Li L C 2018 Atmospheric pressureplasma jet impinging on a wavy dielectric surface: effects ofDC polarities Plasma Sources Sci. Technol. 27 08LT01

[15] Gibalov V I and Pietsch G J 2000 The development ofdielectric barrier discharges in gas gaps and on surfacesJ. Phys. D: Appl. Phys. 33 2618

[16] Sokolova M V, Voevodin V V, Malakhov J I,Aleksandrov N L, Anokhin E M and Soloviev V R 2019Barrier properties influence on the surface dielectric barrierdischarge driven by single voltage pulses of differentduration J. Phys. D: Appl. Phys. 52 324001

[17] Zemanek M, Pribyl R, Kelar J, Pazderka M, Stastny P,Kudelcik J, Trunec M and Cernak M 2019 Electricalproperties of alumina-based ceramic barrier layers fordielectric barrier discharge Plasma Sources Sci. Technol. 28075001

[18] Brandenburg R et al 2013 Novel insights into the developmentof barrier discharges by advanced volume and surfacediagnostics J. Phys. D: Appl. Phys. 46 464015

[19] Stollenwerk L, Laven J G and Purwins H-G 2007 Spatiallyresolved surface-charge measurement in a planar dielectric-barrier discharge system Phys. Rev. Lett. 98 255001

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

[21] Simeni M S, Tang Y, Frederickson K and Adamovich I V 2018Electric field distribution in a surface plasma flow actuatorpowered by ns discharge pulse trains Plasma Sources Sci.Technol. 27 104001

[22] Chng T L, Orel I S, Starikovskaia S M and Adamovich I V I V2019 Electric field induced second harmonic (E-FISH)

Figure A2. The temporal evolution of the spatial integration of thepotential ∫U(x, t)dx and the current obtained from equation (A1).(a) ER dielectric, (b) PTFE dielectric.

13


https://orcid.org/0000-0002-1523-7380https://orcid.org/0000-0002-1523-7380https://orcid.org/0000-0002-1523-7380https://orcid.org/0000-0002-1523-7380https://orcid.org/0000-0003-1512-2820https://orcid.org/0000-0003-1512-2820https://orcid.org/0000-0003-1512-2820https://orcid.org/0000-0003-1512-2820https://orcid.org/0000-0001-6311-3940https://orcid.org/0000-0001-6311-3940https://orcid.org/0000-0001-6311-3940https://orcid.org/0000-0001-6311-3940https://orcid.org/0000-0001-8379-5782https://orcid.org/0000-0001-8379-5782https://orcid.org/0000-0001-8379-5782https://orcid.org/0000-0001-8379-5782https://orcid.org/0000-0002-5738-1241https://orcid.org/0000-0002-5738-1241https://orcid.org/0000-0002-5738-1241https://orcid.org/0000-0002-5738-1241https://doi.org/10.1088/1361-6595/ab1461https://doi.org/10.1088/1361-6595/ab094chttps://doi.org/10.1088/0022-3727/46/35/355205https://doi.org/10.1088/1361-6463/ab16b7https://doi.org/10.7498/aps.62.224702https://doi.org/10.1088/0963-0252/23/4/045003https://doi.org/10.1016/j.pecs.2014.12.002https://doi.org/10.1049/hve.2016.0014https://doi.org/10.1088/0963-0252/24/4/045014https://doi.org/10.1088/0963-0252/24/4/045014https://doi.org/10.1007/978-1-4612-4294-9https://doi.org/10.1088/0963-0252/25/5/053002https://doi.org/10.1088/1361-6595/aa6adahttps://doi.org/10.1088/1361-6463/50/2/025203https://doi.org/10.1088/1361-6595/aacfe2https://doi.org/10.1088/0022-3727/33/20/315https://doi.org/10.1088/1361-6463/ab20efhttps://doi.org/10.1088/1361-6595/ab28fahttps://doi.org/10.1088/1361-6595/ab28fahttps://doi.org/10.1088/0022-3727/46/46/464015https://doi.org/10.1103/PhysRevLett.98.255001https://doi.org/10.1103/PhysRevApplied.7.024024https://doi.org/10.1088/1361-6595/aae1c8

generation for characterization of fast ionization wavedischarges at moderate and low pressures Plasma SourcesSci. Technol. 28 045004

[23] Chng T L, Brisset A, Jeanney P, Starikovskaia S M,Adamovich I V and Tardiveau P 2019 Electric fieldevolution in a diffuse ionization wave nanosecond pulsedischarge in atmospheric pressure air Plasma Sources Sci.Technol. 28 09LT02

[24] Goldberg B M, Reuter S, Dogariu A and Miles R B 2019 1Dtime evolving electric field profile measurements with sub-nsresolution using the E-FISH method Opt. Lett. 44 3853–6

[25] Lu X P and Ostrikov K K 2018 Guided ionization waves: thephysics of repeatability Appl. Phys. Rev. 5 031102

[26] Huang B D, Carbone E, Takashima K, Zhu X M,Czarnetzki U and Pu Y K 2018 The effect of the pulserepetition rate on the fast ionization wave discharge J. Phys.D: Appl. Phys. 51 225202

[27] Huang B D, Takashima K, Zhu X M and Pu Y K 2014 Theinfluence of the repetition rate on the nanosecond pulsed pin-to-pin microdischarges J. Phys. D: Appl. Phys. 47 422003

[28] Ye C Y, Huang B D, Zhang C, Chen G Y and Shao T 2019Study on the propagation characteristics of surfaceionization wave in surface dielectric barrier dischargesustained by the nanosecond pulse voltage Trans. ChinaElectrotech. Soc. accepted (https://doi.org/10.19595/j.cnki.1000-6753.tces.190616)

[29] Huang B D, Zhang C, Qiu J T, Zhang X, Ding Y J and Shao T2019 The dynamics of discharge propagation and x-raygeneration in nanosecond pulsed fast ionisation wave in 5mbar nitrogen Plasma Sources Sci. Technol. 28 095001

[30] Korolev Y D and Mesyats G A 1998 Physics of PulsedBreakdown in Gases (Yekaterinburg: URO)

[31] Huang B D, Takashima K, Zhu X M and Pu Y K 2015 Theinfluence of the voltage rise rate on the breakdown of anatmospheric pressure helium nanosecond parallel-platedischarge J. Phys. D: Appl. Phys. 48 125202

[32] Shelton D P and Rice J E 1994 Measurements and calculationsof the hyperpolarizabilities of atoms and small molecules inthe gas phase Chem. Rev. 94 3–29

[33] Retter J E and Elliott G S 2020 On the possibility ofsimultaneous temperature, species, and electric fieldmeasurements by coupled hybrid fs/ps CARS and EFISHGAppl. Opt. 58 2557

[34] Edlén B 1953 The dispersion of standard air J. Opt. Soc. Am.43 339

[35] Peck E R and Fisher D J 1964 Dispersion of argon J. Opt. Soc.Am. 54 1362

[36] Opaits D F, Shneider M N, Miles R B, Likhanskii A V andMacheret S O 2008 Surface charge in dielectric barrierdischarge plasma actuators Phys. Plasmas 15 073505

[37] Zhang C, Lin H, Zhang S, Xie Q, Ren C and Shao T 2017 Plasmasurface treatment to improve surface charge accumulation anddissipation of epoxy resin exposed to DC and nanosecond-pulse voltages J. Phys. D: Appl. Phys. 50 405203

[38] Shao T, Tarasenko V F, Zhang C, Burachenko A G,Rybka D V, Kostyrya I D, Lomaev M I, Baksht E K and

Yan P 2013 Application of dynamic displacement currentfor diagnostics of subnanosecond breakdowns in aninhomogeneous electric field Rev. Sci. Instrum. 84 053506

[39] Soloviev V R 2019 Analytical model of a surface barrierdischarge Dev. Plasma Phys. Rep. 45 264–76

[40] Akishev Y, Aponin G, Balakirev A, Grushin M, Karalnik V,Petryakov A and Trushkin N 2013 Spatial–temporaldevelopment of a plasma sheet in a surface dielectric barrierdischarge powered by a step voltage of moderate durationPlasma Sources Sci. Technol. 22 015004

[41] Akishev Y, Aponin G, Balakirev A, Grushin M, Karalnik V,Petryakov A and Trushkin N 2013 DBD surface streamerexpansion described using nonlinear diffusion of the electricpotential over the barrier J. Phys. D: Appl. Phys. 46 464014

[42] Kindersberger J and Lederle C L 2008 Surface charge decay oninsulators in air and sulfurhexafluorid: I. Simulation IEEETrans. Dielectr. Electr. Insul. 15 941

[43] Bigio I J, Finn R S and Ward J F 1975 Electric-field inducedharmonic generation as a probe of the focal region of a laserbeam Appl. Opt. 14 336

[44] Finn R S and Ward J F 1971 Dc-Induced optical second-harmonic generation in the inert gases Phys. Rev. Lett.26 285

[45] Demtröder W 2008 Laser Spectroscopy 4th edn (Berlin:Springer) (https://doi.org/10.1007/978-3-540-73418-5)

[46] Goekce S, Peschke P, Hollenstein C, Leyland P and Ott P 2016OES characterization of streamers in a nanosecond pulsedSDBD using N2 and Ar transitions Plasma Sources Sci.Technol. 25 045002

[47] 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

[48] Liu C, Dobrynin D and Fridman A 2014 Uniform and non-uniform modes of nanosecond-pulsed dielectric barrierdischarge in atmospheric air: fast imaging and spectroscopicmeasurements of electric fields J. Phys. D: Appl. Phys. 47252003

[49] Liu C, Fridman A and Dobrynin D 2019 Investigation of thetransition from streamer to uniform ‘overvoltage’ mode ofatmospheric air nanosecond-pulsed dielectric barrierdischarge J. Phys. D: Appl. Phys. 52 105205

[50] Bílek P, Šimek M and Bonaventura Z 2019 Electric fielddetermination from intensity ratio of N2

+ and N2 bands:nonequilibrium transient discharges in pure nitrogen PlasmaSources Sci. Technol. 28 115011

[51] Huang B D, Takashima K, Zhu X M and Pu Y K 2016 Thebreakdown process in an atmospheric pressure nanosecondparallel-plate helium/argon J. Phys. D: Appl. Phys. 49045202

[52] Adamovich I V, Butterworth T, Orriere T, Pai D Z,Lacoste D A and Cha M S 2020 Nanosecond secondharmonic generation for electric field measurements withtemporal resolution shorter than laser pulse duration J. Phys.D: Appl. Phys. 53 145201

14


https://doi.org/10.1088/1361-6595/ab0b22https://doi.org/10.1088/1361-6595/ab3cfchttps://doi.org/10.1364/OL.44.003853https://doi.org/10.1364/OL.44.003853https://doi.org/10.1364/OL.44.003853https://doi.org/10.1063/1.5031445https://doi.org/10.1088/1361-6463/aabf2dhttps://doi.org/10.1088/0022-3727/47/42/422003https://doi.org/10.19595/j.cnki.1000-6753.tces.190616https://doi.org/10.19595/j.cnki.1000-6753.tces.190616https://doi.org/10.1088/1361-6595/ab3939https://doi.org/10.1088/0022-3727/48/12/125202https://doi.org/10.1021/cr00025a001https://doi.org/10.1021/cr00025a001https://doi.org/10.1021/cr00025a001https://doi.org/10.1364/AO.58.002557https://doi.org/10.1364/JOSA.43.000339https://doi.org/10.1364/JOSA.54.001362https://doi.org/10.1063/1.2955767https://doi.org/10.1088/1361-6463/aa829bhttps://doi.org/10.1063/1.4807154https://doi.org/10.1134/S1063780X19020119https://doi.org/10.1134/S1063780X19020119https://doi.org/10.1134/S1063780X19020119https://doi.org/10.1088/0963-0252/22/1/015004https://doi.org/10.1088/0022-3727/46/46/464014https://doi.org/10.1109/TDEI.2008.4591214https://doi.org/10.1364/AO.14.000336https://doi.org/10.1103/PhysRevLett.26.285https://doi.org/10.1007/978-3-540-73418-5https://doi.org/10.1088/0963-0252/25/4/045002https://doi.org/10.1088/0963-0252/25/2/025017https://doi.org/10.1088/0022-3727/47/25/252003https://doi.org/10.1088/0022-3727/47/25/252003https://doi.org/10.1088/1361-6463/aaf8f0https://doi.org/10.1088/1361-6595/ab3936https://doi.org/10.1088/0022-3727/49/4/045202https://doi.org/10.1088/0022-3727/49/4/045202https://doi.org/10.1088/1361-6463/ab6790

1. Introduction2. Experimental methods3. Results and discussion3.1. The current flowing through the ground strip array3.2. The electric field: temporal evolution and spatial distribution3.3. The residual surface potential distribution after the discharge3.4. Analysis of EFISH signal accumulation along the beam path

4. Limitations5. ConclusionsAcknowledgmentsAppendixReferences

surface ionization wave propagation in the nanosecond ......oct 11, 2019 · sdbd using the er...

Documents