Combustion and Flame 197 (2018) 254–264

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Combustion and Flame

journal homepage: www.elsevier.com/locate/combustflame

Electric field in Ns pulse and AC electric discharges in a hydrogen

diffusion flame

Marien Simeni Simeni a , Yong Tang

b , Yi-Chen Hung

a , Zakari Eckert a , Kraig Frederickson

a , Igor V. Adamovich

a , ∗

a Nonequilibrium Thermodynamics Laboratory, Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA b Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University,

Beijing 10 0 084, China

a r t i c l e i n f o

Article history:

Received 23 May 2018

Revised 14 August 2018

Accepted 14 August 2018

Keywords:

Electric field

Second harmonic generation

Diffusion flame

ns pulse discharge

Plasma-assisted combustion

Ion wind

a b s t r a c t

Time-resolved electric field is measured in ns pulse and AC sine wave dielectric barrier discharges sus-

tained in an atmospheric pressure hydrogen diffusion flame, using picosecond second harmonic genera-

tion. Individual electric field vector components are isolated by measuring the second harmonic signals

with different polarizations. Electric field measurements in a ns pulse discharge are self-calibrating, since

the field follows the applied voltage until breakdown. Electric field is measured in a ns pulse discharge

sustained both in the hydrogen flow below the flame and in the reaction zone of the flame. Peak electric

field in the reaction zone is lower compared to that in the near-room temperature hydrogen flow, due

to a significantly lower number density. In hydrogen, most of the energy is coupled to the plasma at

the reduced electric field of E / N ≈ 50–100 Td. In both cases, the electric field decreases to near zero after

breakdown, due to plasma self-shielding. The time scale for the electric field reduction in the plasma

is relatively long, several tens of ns, indicating that it may be controlled by a relatively slow propaga-

tion of the ionization wave over the dielectric surfaces. In the AC discharge, the electric field is put on

the absolute scale by measuring a Laplacian electric field between two parallel cylinder electrodes. The

measurement results demonstrate that a strong electric field in the plasma-enhanced flame is produced

during the entire AC voltage period, without correlation with the random micro-discharges detected in

the plasma images. The measurement results indicate consistently higher peak electric field during the

negative AC half-period, as well as a significant electric field offset. Both the asymmetry and the offset

of the electric field are likely responsible for the ion wind resulting in the flame distortion. The results

suggest that at the present conditions the ion wind is dominated by the transport of negative ions gen-

erated in the ambient air plasma near the flame. The results demonstrate a significant potential of ps

second harmonic generation diagnostics for non-intrusive measurements of the electric field in atmo-

spheric pressure flames enhanced by electric discharge plasmas.

© 2018 Published by Elsevier Inc. on behalf of The Combustion Institute.

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1. Introduction

Measurements of electric field in weakly ionized plasmas gen-

erated in reacting fuel–air mixtures and in flames are critical for

quantifying the effect of strong electric fields on kinetics of ex-

cited species and radicals produced in the plasma, ignition, flame-

holding, and flame stability, as well as for development of plasma

assisted combustion applications and combustion control meth-

ods [ 1 –3 ]. In electric discharges sustained in fuel–air mixtures,

the electric field waveform is well known to control the dis-

∗ Corresponding author.

E-mail address: adamovich.1@osu.edu (I.V. Adamovich).

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https://doi.org/10.1016/j.combustflame.2018.08.004

0010-2180/© 2018 Published by Elsevier Inc. on behalf of The Combustion Institute.

harge input energy partition among the internal energy modes

f molecules and atoms [1] , which determines the rates of pro-

uction of excited species and radicals by electron impact, as well

s the rates of plasma chemical reactions at low temperatures [2] .

n high-pressure chemically reacting plasmas, evaluating the elec-

ric field based on the applied voltage waveform, or predicting

t based on a semi-empirical estimate of the space charge dis-

ribution [4] may result in a significant uncertainty. The electric

eld distribution may be strongly perturbed by the plasma self-

hielding, which is controlled by ionization, electron-ion recom-

ination, ion-molecule reactions, electron and ion transport, elec-

ron emission from electrodes, and surface charge accumulation

n dielectric surfaces. In flames, externally applied electric field

M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264 255

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Fig. 1. Schematic of the burner, double dielectric barrier discharge electrode

assembly, and the laser beam (a–c). Flame spreader dimensions 0.5 mm ×45 mm, diameter of brass electrode rods D = 3.2 mm, electrode overlap L 0 = 45 mm,

non-overlapping electrode length L 1 = 5–20 mm, alumina ceramic tube thickness

�= 1.6 mm, electrode gap d = 12–15 mm (a) or d = 4–5 mm (b). Both the electrode

plane and the laser beam are 2 mm above the flame spreader exit.

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lso generates the ion wind entraining the flow of neutral species,

nd affects the ion-molecule reaction chemistry. This has a strong

ffect on flame stability [5,6] , flashback [7] , soot generation [8] ,

nd flow field in the reaction zone [9–11] . Understanding kinet-

cs of these processes and validation of high-fidelity modeling pre-

ictions require electric field measurements using accurate, non-

ntrusive experimental methods.

Two laser diagnostic techniques for electric field measurements

n high-pressure plasmas developed over the last decade are ns/ps

our-Wave Mixing (FWM) [12–16] and fs/ps Second Harmonic Gen-

ration (SHG) [17,18] . Both of these methods can provide sub-

s temporal resolution, limited by the coherence decay time of

olecules excited by the pump and probe beams (in the four-wave

ixing technique, which is similar to CARS), or by the duration of

he laser beam (in the second harmonic generation). Other advan-

ages include a straightforward absolute calibration and measure-

ent of individual components of the electric field vector with

ell-defined spatial resolution. Finally, the second harmonic gen-

ration is basically species independent [17] and can be used for

iagnostics in different gas mixtures, while the four-wave mixing

equires the use of different wavelength Stokes beams for differ-

nt probe species. In both methods, the spatial resolution along

he laser beams, determined by the Rayleigh range of the beams

nd by the coherence length, may vary from ∼1 mm [17] to sev-

ral cm [14] . The spatial resolution in the direction perpendicular

o the laser beam is of the order of the focused beam diameter,

100 μm.

In our previous work [16] , ps four-wave mixing was used for

he measurements of the electric field in ns pulse discharges in

mbient air and in a hydrogen diffusion flame, using molecular ni-

rogen as a probe species. The results have shown that the sen-

itivity of this diagnostic in the flame is significantly worse com-

ared to that in room-temperature air, ∼20 kV/cm vs. 3–4 kV/cm.

his occurs primarily due to the higher temperature and lower N 2

raction in the combustion product mixture, since the signal is pro-

ortional to the number density of the probe species squared. This

ifficulty limits the applicability of the four-wave mixing to the

lectric field measurements in high-pressure flames (several atm),

here plasma generation and control become more challenging.

owever, comparison of ps FWM and ps SHG measurements of the

lectric field in ambient air shows that the latter method is consid-

rably more sensitive, generating a much higher signal at a signif-

cantly lower laser power, and suggesting that it would be more

ffective for diagnostics of atmospheric pressure flames. Also, the

lectric field induced second harmonic signal is generated in the

isible part of the spectrum, instead of the IR signal obtained in

he four-wave mixing (4.3 μm if molecular nitrogen is used as a

robe species), such that it can be measured by photomultiplier

etectors and CCD cameras.

In the present work, ps second harmonic generation is used

or the electric field measurements in dielectric barrier discharges

DBD) sustained by ns pulse and AC sine wave waveforms in an at-

ospheric pressure hydrogen diffusion flame. The use of two dif-

erent voltage waveforms makes possible isolating two different ef-

ects of the applied electric field on the flame, (i) radical species

eneration in a ns pulse DBD plasma, and (ii) ion wind generated

n an AC DBD plasma. It is well known that the ion wind effect on

he flame in a ns pulse discharge is minimal, since it requires a sig-

ificant impulse of the Coulomb force, typical for AC and DC fields.

n the other hand, ns duration voltage pulses can produce a sig-

ificantly higher peak electric field during breakdown, compared

o DC or AC voltage waveforms [15] . The objective of this work

s to provide insight into ns pulse breakdown kinetics in reacting

ydrogen–air mixtures, which controls the discharge energy cou-

ling and energy partition, and to quantify charge transport pro-

esses in AC plasmas generating the ion wind in the flame.

. Experimental

Figure 1 shows a schematic of the burner, the flame, the dou-

le dielectric barrier discharge electrode assembly, and the location

f the laser beam. The burner used in the present work is a Bun-

en burner, in which the barrel with the air intake slots has been

emoved and replaced by a custom-made flame spreader made

f quartz, with the rectangular exit slot dimensions of 0.5 mm ×5 mm. The quartz wall thickness at the flame spreader exit is

.25 mm. Hydrogen flows through the burner at the flow rate of

–2 slm, maintaining a diffusion flame ≈ 50 mm long above the

ame spreader. The flame spreader provides ample access for the

ischarge electrodes applying the electric field across the flame,

n a simple rectangular geometry. Two parallel cylinder brass

lectrodes, inside alumina ceramic tubes, are placed parallel to

he flame spreader. The electrodes are located slightly above the

urner, as shown in Fig. 1 , such that their horizontal plane of sym-

etry is 2 mm above the flame spreader exit. The laser beam is

irected parallel to the electrodes, in the horizontal plane of sym-

etry and halfway between the electrodes (see Fig. 1 ).

The rectangular geometry of the flame and of the electrodes,

ather than the axisymmetric geometry used in Ref. [11] , is em-

loyed because of the relative simplicity of the data interpretation

t the conditions when the electric field vector is not expected to

hange direction over the Rayleigh range of the lens focusing the

aser beam. The diameter of the brass electrode rods is D = 3.2 mm,

he alumina ceramic tube wall thickness is �= 1.6 mm, the over-

apping electrode length is L 0 = 45 mm, and the gap between the

lectrodes is varied from d = 4 mm to d = 15 mm. For large elec-

rode gaps, d = 12–15 mm, the flame is attached to the flame

preader, while for smaller gaps, d = 4-5 mm, it is attached to the

op of the ceramic tubes, as shown schematically in Fig. 1 . The

lectrodes are powered by a custom-made high-voltage pulse gen-

rator producing alternating polarity pulses with peak voltage of

p to U peak = 16 kV and pulse repetition rate of 20 Hz, or by a Trek

odel 20/20A high-voltage AC amplifier driven by a sine wave

unction generator, at peak voltages of up to U peak = 14 kV and

requencies of f = 1–10 kHz. The discharge voltage and current

256 M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264

Fig. 2. Schematic of picosecond second harmonic generation diagnostics.

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waveforms are measured by the Tektronix P-6015 high voltage

probe (bandwidth 75 MHz) and Pearson 2877 current probe (band-

width 200 MHz). Plasma emission images are taken by the Prince-

ton Instruments PI-Max 3 ICCD camera with a UV lens.

Figure 2 shows a schematic of ps SHG laser diagnostics. The

fundamental (1064 nm), vertically polarized output beam of an Ek-

spla PL2143A Nd:YAG laser, with a pulse duration of 30 ps and

maximum pulse energy of 50 mJ, operating at 10 Hz, is focused

into a region where the electric field is applied, using a 100 cm fo-

cal distance lens. The laser beam diameter at the focal point, mea-

sured by traversing a razor blade across the beam, is approximately

200 μm, with the Rayleigh range of about z R ≈ 3 cm. The focal

point of the beam is placed at the center of the discharge electrode

assembly (see Fig. 1 ). In the present experiments, the laser is op-

erated at a pulse energy of 10 mJ/pulse. The advantage of the use

of the fundamental laser output, instead of the second harmonic,

is the absence of hydrogen flame emission and plasma emission

at the wavelength of the second harmonic signal (532 nm) gener-

ated in the presence of the external electric field. The second har-

monic signal beam is separated from the fundamental beam us-

ing a pair of dichroic mirrors and a dispersion prism, as shown in

Fig. 2 . The signal beam is recollimated and focused onto the en-

trance slit of a monochromator, followed by a narrowband pass fil-

ter (50% transmission at 532 nm, 10 nm band pass) to remove the

remaining 1064 nm signal, plasma emission, and stray light (see

Fig. 2 ), and detected by a photomultiplier tube (PMT). To further

reduce the noise due to stray light, the monochromator, the pass

filter, and the PMT are placed inside a dark enclosure with a ∼2 cm

diameter entrance aperture. Using a polarizer mounted on a ro-

tation stage before the focusing lens, as shown in Fig. 2 , allows

isolating the vertically and horizontally polarized second harmonic

signals, by rotating the polarizer over 90 °. The alignment of the

laser beam is done with the laser second harmonic crystal in place,

after which the crystal is removed. The timing and the pulse en-

ergy of the fundamental laser beam are monitored by a photodi-

ode.

The theory of second harmonic generation in the presence of

an external electric field is discussed in Ref. [17] . Briefly, the in-

tensity of the electric-field-enabled second-harmonic signal, I (2 ω) ,

scales with the electric field, E , number density, N , and pump laser

intensity, I ( ω) , as follows, I (2 ω ) = A • [ENI ( ω ] 2 . Here A is the calibra-

tion constant which depends on the electric field polarization and

the mixture composition, and which is determined by measuring

a known Laplacian field. At the present conditions, the estimated

ignal coherence length, L c ≈ 20 cm, is such that the region where

he second harmonic signal is generated is limited by the confocal

arameter of the lens, b = 2z R ≈ 6 cm. Measurements of the spa-

ial distribution of the signal, by translating a pair of electrodes

ith sub-breakdown DC voltage applied to them along the laser

eam, showed that the signal varies by only about 10% over a

cm distance. Therefore the present diagnostic measures the root

ean square value of the electric field, 〈 E (t) 2 〉 1 / 2 z , averaged nearly

niformly over the span of the overlapping electrodes in the z -

irection (see Fig. 1 ). The signal polarization is parallel to the di-

ection of the electric field. The spatial resolution in x and y di-

ections is of the order of the laser beam diameter, approximately

00 μm.

During the electric field measurements in a ns pulse discharge,

he laser is triggered externally, by the same delay generator that

riggers the high-voltage pulser. This results in the laser pulse jit-

er relative to the discharge voltage pulse of approximately 2 μs.

or the electric field measurements in the AC discharge, the laser is

riggered internally, and the AC voltage frequency is varied slightly

ff the nominal value, by �f ∼0.01 Hz, to slowly “scan” the laser

ulse along the voltage period. The value of �f is adjusted such

hat the scan time over one AC period would take approximately

00 s (3000 laser shots). The voltage waveform (ns pulse or AC),

he laser pulse waveform, and the second harmonic signal mea-

ured by the PMT are saved by a LeCroyWaverunner MXi-A dig-

tal oscilloscope with a 1 GHz sampling rate for each laser shot,

nd post-processed after the run. The time-integrated PMT sig-

als for each laser shot are placed into the “time bins”, 5 ns wide

or measurements in the ns pulse discharge, or equal to 1/100 of

he AC period (i.e. 3.33 μs wide for f = 3 kHz, 30 data points per

in), and averaged. Although ps SHG diagnostics can provide sub-

s time resolution limited only by the laser pulse duration, 30 ps,

uch high resolution is not necessary for the relatively long ns dis-

harge pulse, ∼100 ns, and for very slowly changing AC field.

Absolute calibration of the measurements is obtained from the

nown electrostatic electric field generated halfway between the

lectrodes during the ns pulse voltage rise, before breakdown, or

rom a separate measurement of the electrostatic field produced

y a lower peak voltage AC waveform, at the conditions when

he plasma is not generated. The electrostatic electric field distri-

ution is calculated by solving the Laplace equation for the elec-

ric potential, for the given electrode and burner geometry (two

arallel cylinder electrodes in alumina ceramic tubes, with the

uartz flame spreader placed below the electrode plane, as shown

M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264 257

Fig. 3. Photographs of a 2 slm hydrogen diffusion flame without the plasma (a,b) and with a 3 kHz, 11 kV peak voltage AC plasma (c,d). Panel (e) shows a 1 slm flame with

a 3 kHz, 14 kV peak voltage AC plasma. Electrodes are placed 2 mm above the flame spreader exit, electrode gap d = 15 mm. In panels (b–e), the grounded electrode is on the

left.

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Fig. 4. Photographs of a hydrogen diffusion flame for different gaps between

the electrodes: (a) d = 12 mm, flame is attached to the flame spreader exit; (b)

d = 4.5 mm, flame is attached to the top of the ceramic tubes. In both cases, the

ceramic tubes are placed 2 mm above the flame spreader exit. Hydrogen flow rate

1.5 slm, no plasma.

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chematically in Fig. 1 ). During the calibration and measurements

n the discharge, the PMT voltage is kept sufficiently low to avoid

ts saturation at high electric fields.

The temperature in the flame is measured by the broadband

s CARS, described in detail in our previous work [19] . The length

f the probe volume, defined as the region where 95% of the

ARS signal is generated, is approximately 4 mm. The rotational-

ranslational temperature is inferred by fitting the experimental

quare root intensity of the N 2 ( v = 0) band spectra with synthetic

ARSFT spectra [20] .

. Results and discussion

Figure 3 shows the photographs of the hydrogen diffusion flame

ithout (a,b) and with (c–e) the AC voltage applied. The estimated

eynolds number based on the width of the flame spreader and

oom temperature density and viscosity of hydrogen is very low,

e ≈ 6 at the hydrogen flow rate of 2 slm, indicating a laminar

iffusion flame. It can be seen that applying the AC voltage, when

he dielectric barrier discharge (DBD) plasma is generated in the

5 mm gap between the ceramic tubes, strongly distorts the flame,

hich always extends toward the grounded electrode, due to the

on wind (see Fig. 3 (c,d)). Since the effect of the ion wind on the

ame becomes stronger as the H 2 flow rate is reduced, the flame

xtending beyond the plasma at 2 slm becomes fully overlapped

ith the plasma at 1 slm (compare Fig. 3 (d) and (e)), such that

t becomes difficult to detect in the photograph. The effect of the

on wind on the flame is qualitatively similar to the one observed

n Ref. [11] in a hydrogen diffusion flame combined with an AC

BD plasma actuator in a cylindrical geometry, except that in Ref.

11] the flame extended toward the high-voltage electrode.

As discussed above, for the electrode gap of d = 12-15 mm, the

ame is attached to the flame spreader exit (see Fig. 4 (a)). When

he electrode gap is reduced to d = 4--5 mm, the flame becomes at-

ached to the top of the ceramic tubes ( Fig. 4 (b)). In the latter case,

he spacing between the ceramic tubes and the flame spreader be-

omes so small that the air flow between them is inhibited, such

hat the flow between the electrodes is mostly hydrogen (with an

dmixture of air), while the hydrogen–air mixing air and combus-

ion occur above the ceramic tubes. When the AC DBD plasma is

enerated in the 4--5 mm electrode gap, such that it is confined

o the region between the ceramic tubes below the flame, the ion

ind effect on the flame also becomes much weaker compared to

hat observed for the 12–15 mm gap.

When a ns pulse discharge is generated between the electrodes,

he ion wind effect on the flame is not detectable in the en-

ire range of electrode gaps tested, d = 4–15 mm, due to the ex-

remely low Coulomb force impulse and low discharge pulse rep-

tition rate, 20 Hz. Since the main focus of the present work is on

he measurements of the electric field in plasma-enhanced flames,

ather than on kinetics of plasma-assisted hydrogen combustion,

he ns pulse discharge was operated at 20 Hz, such that the repe-

ition rate of positive and negative polarity discharge pulses (10 Hz

ach) would match the laser pulse repetition rate.

The temperature in the flame, 2 mm above the flame spreader

xit, was measured at the H 2 flow rate of 1 slm for the electrode

ap of d = 12 mm, with the laser beams directed along the center-

ine between the electrodes (see Fig. 1 ) and focused near the cen-

er of the flame spreader. Although the CARS interaction region,

pproximately 4 mm long, is much shorter compared to the flame

ength, about 50 mm, a good fit with a single-temperature CARSFT

pectrum could not be obtained. This is most likely due to incom-

lete mixing of hydrogen, ambient air, and combustion products

n the reaction zone, resulting in the contributions of both low-

emperature and high-temperature regions into the CARS spec-

rum. The estimate of the upper bound temperature is obtained

rom the tail of the N 2 ( v = 0) vibrational band, T ≈ 1480 ± 180 K. Re-

ucing the gap to d = 4 mm reduces dramatically both the CARS

ignal intensity and the temperature inferred from the CARS spec-

rum, to T = 370 ± 40 K. As discussed above, at these conditions the

ame is attached to the top of the electrode tubes rather than the

ame spreader exit (see Fig. 4 (b)), such that the temperature is

easured in a hydrogen flow mixed with a small amount of ambi-

nt air, below the flame.

Figure 5 shows a collage of single-shot plasma emission im-

ges taken during the positive and negative polarity ns pulse dis-

harge generated in a 1.5 slm hydrogen flow below the flame, for

he electrode gap of d = 4.5 mm when the flame is attached to the

op of the ceramic tubes (see Fig. 4 (a)). In all these images, the

amera gate is 10 ns, and t = 0 corresponds to the moment when

258 M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264

Fig. 5. Collage of single-shot, 10-ns camera gate plasma emission images, and a 50-shot accumulation, 400-ns camera gate image taken during (a) positive polarity and (b)

negative polarity dielectric barrier discharge in a hydrogen flow below the flame. Hydrogen flow rate 1.5 slm, pulse repetition rate 20 Hz, discharge gap d = 4.5 mm. Top view,

the outline of the ceramic tubes is shown with dashed lines.

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the pulse voltage peaks. It can be seen that for both pulse polar-

ities, the plasma is first generated in the central region between

the ceramic tubes. The breakdown moment during the discharge

pulse is indicated clearly by a well-pronounced current spike and

a “kink” in the voltage waveforms, both reproducible shot-to-shot.

After breakdown, the plasma extends both along the discharge gap

and over the surface of the ceramic tubes, while the emission in

the central region between the electrodes decays, indicating elec-

tric field reduction due to the charge separation by the applied

electric field, and the resultant plasma self-shielding. The plasma

eventually extends to the ends of the ceramic tubes and the ex-

posed parts of the electrodes (see Fig. 1 ), generating bright local-

ized emission. At this moment, the applied voltage begins to de-

crease. The plasma between the electrodes remains fairly diffuse,

without well-pronounced isolated filaments, except near the ex-

posed electrodes. This is also evident from the 50-shot accumu-

lation, 400-ns camera gate images of the entire discharge pulse,

shown in Fig. 5 .

Increasing the discharge gap to d = 12 mm while keeping the H 2

flow rate the same, when the flame becomes attached to the exit

of the flame spreader (see Fig. 4 (b)), results in the ns pulse dis-

charge plasma becoming more filamentary. Figure 6 shows single-

shot 10 ns gate plasma emission images taken during the posi-

tive and negative polarity ns pulse discharge at these conditions,

as well as a 50-shot image with a 400 ns gate “wrapped around”

the entire applied voltage pulse. In this case, the plasma is sus-

tained in the flame as well as in the ambient air flow near the ce-

ramic tubes, on both sides of the flame. It can be seen that every

discharge pulse generates several fairly well pronounced stream-

ers. The 50-shot accumulation images shown in Fig. 6 indicate that

these streamers remain random, generating the quasi-diffuse time-

averaged emission. Note that at these conditions, the plasma does

not extend to the exposed parts of the electrodes, such that the

bright localized filaments detected for the shorter electrode gap

(see Fig. 5 ) are not observed.

Figure 7 (a) plots the electrostatic (Laplacian) electric field

distribution for the electrode gap of d = 4.5 mm, predicted by the

numerical solution of the Laplace equation for the electric poten-

tial. In the calculations, the dielectric constants of the alumina

eramic and quartz are ε = 9.1 and ε = 3.8, respectively, and the

ame spreader exit is placed symmetrically between the ceramic

ubes, 2 mm below the electrode plane. It can be seen that the

lectric field between the ceramic tubes and the flame spreader is

ignificantly enhanced. At these conditions, the horizontal electric

eld in the electrode plane, halfway between the ceramic tubes

s E x [kV/cm] = 1.94 cm

−1 • U [kV]. The uncertainty of the elec-

ric field obtained by solving the Laplace equation is due to the

ncertainty of the gap between the electrodes and the laser beam

osition between the electrodes, both estimated to be ± 0.5 mm.

t the conditions of Fig. 7 (a), this results in the combined un-

ertainty of the electric field of ± 5%. For larger electrode gaps of

= 12–15 mm, the combined uncertainty remains similar, ± 5%.

Figure 7 (b) plots the horizontal electric field measured at this

ocation during a positive polarity, near-electrostatic high-voltage

ulse (peak voltage 7 kV) in a 1.5 slm hydrogen flow below the

ame attached to the top of the ceramic tubes (see Figs. 1 (b), 4 ).

he electric field data are plotted together with the pulse volt-

ge and current waveforms. The electric field data points are put

n the absolute scale using the numerical solution of the Laplace

quation plotted in Fig. 7 (a). It is readily apparent that the elec-

ric field follows the applied voltage until about t ≈ 30 ns, when the

easured field becomes lower than the Laplacian field. From the

ow-amplitude current peak observed near this moment, it is clear

hat breakdown occurs somewhere between the electrodes during

he voltage reduction, resulting in the partial plasma self-shielding

ue to the charge separation and distortion of the electric field.

his demonstrates that the comparison of the electric field mea-

ured before breakdown with the electrostatic field calculated by

olving the Laplace equation can be used for the absolute calibra-

ion, i.e. the electric field data in the ns pulse discharge are self-

alibrated before breakdown. The combined uncertainty of the cali-

ration data points, including the uncertainty in the gap and in the

aser beam position and the signal-to-noise, is ± 6% at 14.3 kV/cm

nd ± 16% at 4.6 kV/cm, as indicated in Fig. 7 (b).

Figure 8 plots the horizontal electric field in a ns pulse, dielec-

ric barrier discharge at the same conditions as in Fig. 7 , but at a

ignificantly higher peak voltage, 15 kV. The electric field data mea-

ured during the positive and negative polarity pulses are plotted

M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264 259

Fig. 6. Collage of single-shot, 10-ns camera gate plasma emission images, and a 50-shot accumulation, 400-ns camera gate image, taken during (a) positive polarity and (b)

negative polarity dielectric barrier discharge in a hydrogen flame. Hydrogen flow rate 1.5 slm, pulse repetition rate 20 Hz, discharge gap d = 12 mm. Top view, the outline of

the ceramic tubes is shown with dashed lines.

Fig. 7. (a) Laplacian field distribution for the electrode gap of d = 4.5 mm, with the electric field halfway across the gap indicated; (b) Horizontal electric field in a positive

polarity, near-electrostatic high-voltage pulse in a hydrogen flow below the flame, plotted together with pulse voltage and current waveforms. Hydrogen flow rate 1.5 slm,

pulse repetition rate 20 Hz, electrode gap d = 4.5 mm. Weak breakdown occurring during the voltage reduction, resulting in electric field deviation from the electrostatic

value, is apparent.

Fig. 8. Horizontal electric field in a ns pulse, dielectric barrier discharge in a hydrogen flow below the flame, plotted together with pulse voltage and current waveforms,

during (a) positive polarity, and (b) negative polarity pulses. Hydrogen flow rate 1.5 slm, pulse repetition rate 20 Hz, discharge gap d = 4.5 mm. For the negative polarity

pulse, voltage, current, and electric field axes are inverted.

260 M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264

W

T

s

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d

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d

m

h

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p

m

d

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b

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fl

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1

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together with the pulse voltage and current waveforms. For differ-

ent pulse polarities, different electrodes play the role of the cath-

ode. Since the electrodes and the flow above the burner are not

exactly symmetric, electric field measurements for both pulse po-

larities, in the alternating polarity pulse train, and with the volt-

age pulse shapes before breakdown essentially identical, are neces-

sary to isolate the effect of the discharge asymmetry. Note that in

Fig. 8 (b), voltage, current, and electric field axes are inverted, to

make the comparison between different polarity pulses easier.

From Fig. 8 , it can be seen that the electric field follows the ap-

plied voltage pulse until breakdown, when the current increases

abruptly and the field decays rapidly due to the plasma self-

shielding. Breakdown field measured at the present conditions is

E br ≈ 19.0–19.5 kV/cm, significantly higher compared to DC break-

down field predicted by the Paschen law in hydrogen at P = 1 atm

and T = 370 K, E br, DC ≈ 13 kV/cm. On the other hand, the break-

down field predicted by a ns pulse discharge model [15,16] be-

tween two plane dielectric-covered electrodes for the same elec-

trode gap and dielectric parameters, is close to the experimental

results. For a Gaussian voltage pulse in hydrogen with the Half-

idth at Half-Maximum (HWHM) of τHWHM

= 40 ns, the value pre-

dicted by the model is E br = 19 kV/cm. As the pulse duration is in-

creased, the breakdown field predicted by the model approaches

the DC limit given by the Paschen law for the same ionization co-

efficient. The electric field reduction after the breakdown is consis-

tent with the plasma emission images shown in Fig. 5 , which in-

dicate the decay of the emission intensity between the electrodes

following breakdown. The plasma self-shielding occurs as the ion-

ization wave is propagating over the surface of the ceramic tubes

(see Fig. 5 ). When the wave reaches the exposed parts of the elec-

trodes, both the applied voltage and the electric field are gradually

reduced to near detection limit. No detectable electric field offset is

observed either before or after the discharge pulse, indicating that

the residual surface charge accumulation from the previous pulse,

as well the charge accumulation after the pulse, are insignificant.

The results plotted in Fig. 8 show that during the discharge

pulse, most of the energy is coupled to the hydrogen plasma at the

electric fields of E ≈ 9–19 kV (reduced electric field of E / N ≈ 50–100

Td, 1 Td = 10 −17 V cm

2 ). At these conditions, over 50% of the input

energy goes to H 2 electronic excitation and dissociation by elec-

tron impact [21] , generating H atoms. At the present conditions,

the time scale for the plasma self-shielding and the electric field

reduction after breakdown, several tens of ns, is much longer com-

pared to the predictions of the one-dimensional ns pulse discharge

model [15,16] , suggesting that it is controlled by a relatively slow

propagation of the surface ionization wave over the dielectrics (see

Fig. 5 ), not accounted for in the model. Finally, the present results

demonstrate that the main trends in the electric field evolution af-

ter the breakdown remain essentially the same for both pulse po-

larities, although the plasma self-shielding in the negative polar-

ity pulse occurs somewhat slower. The vertical component of the

electric field before, during, and after the discharge pulse was near

or below detection limit. Note that the present diagnostic is more

sensitive to the vertical electric field, since the laser beam is verti-

cally polarized [17] .

Figure 9 plots the electric field measured in the ns pulse dis-

charge between the ceramic tubes placed d = 12 mm apart, at the

same H 2 flow rate of 1.5 slm. As discussed above, at these condi-

tions, when the flame becomes attached to the exit of the flame

spreader, the plasma becomes more filamentary (see Fig. 6 ). Com-

paring Figs. 8 and 9 , it can be seen that in the discharge with

the larger electrode gap, breakdown occurs later during the pulse,

near the pulse voltage peak. Breakdown field, on the other hand,

is almost a factor of two lower compared to that in hydrogen be-

low the flame, E br ≈ 9.3–10.8 kV/cm, due to the much higher tem-

perature in the central part of the discharge gap, T = 1480 K vs.

= 370 K at the conditions of Fig. 8 . Also, the apparent plasma self-

hielding effect is significantly less pronounced. This occurs since

he present diagnostic measures the absolute value of the elec-

ric field averaged over the length of the flame and the overlap-

ing length of the electrodes, approximately 50 mm. Therefore the

eld is averaged over the regions where the plasma self-shielding

s strong (in the filaments) as well as over the regions between the

laments, where the self-shielding may be less significant. Similar

o the electric field measurements in the discharge with the gap of

= 4.5 mm gap, neither the electric field offset due to the surface

harge accumulation nor the vertical electric field were detected.

Figure 10 shows the plasma emission images in the AC dielec-

ric barrier discharge in a hydrogen flame, taken at the hydrogen

ow rate of 2 slm, AC frequency of 3 kHz, and electrode gap of

= 12 mm, at the conditions when the flame is attached to the

ame spreader. A 50-shot accumulation, full AC period (333 μs)

amera gate image exhibits a quasi-diffuse plasma, while single-

hot and 10-shot accumulation, 20 μs gate images taken during

he positive and negative AC half-periods clearly show the individ-

al well-defined filaments (micro-discharges) extending between

he ceramic tubes. The average number of micro-discharges gen-

rated during the positive polarity AC period exceeds that dur-

ng the negative polarity half-period (see Fig. 10 ). At these con-

itions, the discharge current waveforms also indicate multiple

icro-discharges generated during the positive and negative AC

alf-periods and separated by ∼10–20 μs, with the positive po-

arity current peaks significantly exceeding those of the negative

olarity (see Figs. 12 and 13 ). As expected, the 50-period accu-

ulation image illustrates that the micro-discharges are fairly ran-

om, generating the quasi-diffuse plasma emission. As discussed

n Section 2 , the second harmonic signal measured in the present

ork is accumulated over the entire distance between the overlap-

ing electrodes, such that the measured electric field represents a

oot mean square value averaged along the span of the electrodes,

ncluding both the field in the micro-discharges and in the regions

etween the micro-discharges.

Figure 11 plots the second harmonic signal calibration for the

orizontal component of the electrostatic field in the hydrogen

ame without the plasma. Unlike in ns pulse discharges, putting

he electric field measured in the AC discharge on the absolute

cale requires a separate calibration, due to the significant sur-

ace charge accumulation on the dielectric surfaces detected at

hese conditions. The data in Fig. 11 are taken at H 2 flow rates of

slm and 2 slm, AC frequency of 3 kHz, and the electrode gap of

= 12 mm. For the calibration, the AC peak voltage was approxi-

ately 6.5 kV, when the plasma was not generated between the

lectrodes. No evidence of breakdown or the effect of the ion wind

n the flame were detected during the calibration. Again, the elec-

rostatic electric field is calculated by solving the Laplace equation,

s discussed above. It can be seen that the square root of the sec-

nd harmonic signal follows the absolute value of the applied volt-

ge closely. Since the second harmonic signal is proportional to the

bsolute value of the electric field, the negative half-period of the

pplied voltage, when the electrostatic electric field clearly changes

irection (at t = 167–333 μs), is inverted.

Most of calibration data sets exhibit a slight negative shift rel-

tive to the applied AC voltage, by ≈ 0.5–1.0 kV/cm (i.e. the electric

eld measured during the negative half-period is slightly higher),

ndicating a weak offset electric field directed from the grounded

lectrode to the high-voltage electrode. This shift (never observed

uring the calibration in air) can only be due to the asymmetric

urface charge accumulation on the ceramic tubes. Since during

he calibration the applied voltage was significantly below break-

own threshold, the most likely source of the surface charge is

hemi-ionization in the flame. Although ion concentrations in pure

ydrogen flames are known to be very low [22] , and may be

M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264 261

Fig. 9. Horizontal electric field in a ns pulse, dielectric barrier discharge in a hydrogen flame, plotted together with pulse voltage and current waveforms, during (a) positive

polarity, and (b) negative polarity pulses. Hydrogen flow rate 1.5 slm, pulse repetition rate 20 Hz, discharge gap d = 12 mm. For the negative polarity pulse, voltage, current,

and electric field axes are inverted.

Fig. 10. Full AC period (333 μs) camera gate, 50-shot accumulation plasma emission image, two 20 μs gate, single-shot images, and two 20 μs gate, 10-shot accumulation

images taken during positive and negative half-periods of AC dielectric barrier discharge in a hydrogen flame. Hydrogen flow rate 2 slm, AC frequency 3 kHz, peak voltage

14 kV, electrode gap d = 12 mm. Top view, the outline of the ceramic tubes is shown with dashed lines.

Fig. 11. SHG signal calibration for the horizontal electric field in the hydrogen flame without the plasma. Electrode gap d = 12 mm, AC frequency 3 kHz, hydrogen flow rate

is (a) 1 slm and (b) 2 slm. The polarity of the negative voltage half-period, at t = 167–333 μs, is inverted.

a

g

t

t

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p

r

e

i

c

q

w

ffected by im purities, a chemi-ionization mechanism in hydro-

en flames has been determined, H + H + OH → H 3 O

+ + e [23] . Note

hat in very weakly ionized plasmas, the surface charge neutraliza-

ion time can be extremely long, such that the surface charge accu-

ulation may well be significant even if the chemi-ionization rate

s very low. The calibration data in Fig. 11 have been corrected for

his effect. Note that the electrostatic calibration such as shown in

ig. 11 assumes that the chemical composition of the combustion

roducts is not affected by the plasma and by the ion wind, which

emains an open question.

Figure 12 plots the root mean square value of the horizontal

lectric field, < E x 2 >

1/2 , averaged over the span of the electrodes,

n the AC dielectric barrier discharge in the hydrogen flame at the

onditions of Fig. 11 , H 2 flow rates of 1 slm and 2 slm, AC fre-

uency of 3 kHz, and the electrode gap of d = 12 mm. In the flame

ith the AC voltage applied, the hydrogen flow rate was varied

262 M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264

Fig. 12. Absolute value of the horizontal component of the electric field in the AC dielectric barrier discharge in the hydrogen flame, at the electrode gap of d = 12 mm.

Hydrogen flow rate is (a) 1 slm and (b) 2 slm. Electric field asymmetry and non-zero field offset resulting in ion wind is apparent in both cases. The polarity of the negative

voltage half-period, at t = 167–333 μs, is inverted.

Fig. 13. Absolute value of the horizontal component of the field in the AC dielectric barrier discharge in the flame, for the electrode gap of d = 15 mm. H 2 flow rate (a) 1 slm

and (b) 2 slm, AC frequency 3 kHz. Non-zero field offset resulting in ion wind is apparent. The polarity of the negative voltage half-period, at t = 167–333 μs, is inverted.

n

2

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to take a data set when the flame is strongly deformed by the

ion wind such that it is completely enclosed in the plasma (see

Fig. 3 (e)), and another data set when the ion wind is significantly

weaker but still detectable (see Fig. 3 (d)). At the conditions of

Fig. 12 , L 1 in Fig. 1 is approximately 5 mm, such that the exposed

parts of the electrodes are located fairly close to the flame (as can

be seen in Fig. 3 (d)). In this case, the plasma sometimes extends

to the exposed parts of the electrodes, producing sporadic local-

ized filaments. This effect establishes a conduction current path

removing the surface charges accumulated on the ceramic tubes.

From Fig. 12 , it can be seen that with the AC plasma turned on,

the electric field waveform becomes noticeably asymmetric and

reaches a higher peak value during the negative AC period, approx-

imately 4.5 kV/cm at 1 slm and 4 kV/cm at 2 slm. Also, a notice-

able offset in the second harmonic signal (i.e. the horizontal elec-

tric field offset) is detected, ≈ 1.5 kV/cm at 1 slm and ≈ 1 kV/cm at

2 slm.

Figure 13 plots the electric field data taken at the same H 2 flow

rates of 1 slm and 2 slm, but at larger electrode gap of d = 15 mm.

In the data shown in Fig. 13 , L 1 is increased to 20 mm, such that

the exposed parts of the electrodes are located further away from

the flame (as shown in Fig. 3 (e)). This forces the plasma to re-

main confined to the span of the overlapped electrodes and the

flame spreader, such that it no longer extends to the exposed parts

of the electrodes. At these conditions, the electric field asymme-

try becomes significantly less pronounced while the peak values,

still achieved during the negative voltage half-period, increase sig-

ificantly, to approximately 6 kV/cm at 1 slm and 5.5 kV/cm at

slm. Also, the horizontal field offset becomes higher, ≈ 2.5 kV/cm

t 1 slm and ≈ 1.5 kV/cm at 2 slm. Comparing Figs. 12 and 13 , it is

pparent that the increase in the peak value of the electric field

s largely due to the offset increase. This is most likely caused by

onfining the plasma to the overlapping electrodes and preventing

t from reaching the exposed parts of the electrodes, thus reducing

he surface charge “leak”. In all measurements at the conditions of

igs. 12 and 13 , the vertical component of the electric field is near

r below the detection limit.

Unlike the electric field in the ns pulse discharge, the interpre-

ation of the electric field data in the AC discharge is less straight-

orward. Comparison of the electric field measurements plotted

n Figs. 12 and 13 with the AC plasma emission images shown

n Fig. 10 suggests that at these conditions the net second har-

onic signal, averaged over the span of the electrodes, is due

o two different electric fields. The first is the AC field produced

y the applied voltage, E app , and the second is the electric field

ue to the surface charge accumulated on the dielectric tubes by

he micro-discharges, E surf , which appear random both spatially

nd temporally. Depending on whether these electric fields are

enerated over the same spatial region (e.g. in the same micro-

ischarge) or over different spatial regions (e.g. one between the

icro-discharges where E app is not fully shielded, and the other

n the micro-discharges where the plasma self-shielding is much

tronger), their contribution into the net second harmonic signal

ould be different.

M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264 263

Fig. 14. Qualitative illustration of second harmonic (SH) signal averaging over the span of the electrodes in the AC discharge plasma: (a) field due to applied voltage, E app ,

and its absolute value; (b) field due to surface charge on the dielectrics, E surf , and its absolute value; (c) net electric field and SH signal in the case when E app and E surf are

generated in the same spatial region, resulting in field superposition and no apparent offset (compare with Fig. 12 ); (d) net SH signal in the case when E app and E surf are

generated in different spatial regions, resulting in SH signal superposition and an apparent field offset (compare with Fig. 13 ).

t

t

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b

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e

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1

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This is illustrated qualitatively in Fig. 14 , where E surf is assumed

o be constant in time, for simplicity. Figure 14 (c) and (d) illustrate

wo extreme cases when the applied field and the field due to sur-

ace charges are produced in the same spatial region (c) and in

ifferent spatial regions (d). In the first case, the second harmonic

ignal is proportional to the square of the net field. In the second

ase, the line-of-sight averaged signal is the sum of two signals,

ach proportional to the square of the respective field. Therefore,

hen E app and E surf are generated over the same spatial region,

quare root of the signal generated by the net field would indi-

ate an asymmetric electric field waveform without an offset (com-

are Fig. 14 (c) with Fig. 12 ). On the other hand, when E app and E surf

re generated over different spatial regions, square root of the line-

f-sight averaged signal would indicate an apparent electric field

ffset (compare Fig. 14 (d) with Fig. 13 ). Both of the possibilities

hown schematically in Fig. 14 may be present in the same data

et. This shows that the apparent electric field offset and the asym-

etry observed in the present experiments are due to the same ef-

ect, surface charge accumulation on the dielectrics by an ensemble

f random micro-discharge filaments. Since the extent of the re-

ions where the field due to the surface charge accumulation and

he applied AC field are dominating is uncertain, estimating their

ndividual magnitudes from the present data is challenging. There-

ore Figs. 12 and 13 plot only the root mean square value of the net

orizontal electric field averaged over the length of the electrodes.

Both the electric field offset and its asymmetry during the AC

eriod contribute to the generation of the ion wind, which results

n the flame distortion and motion toward the grounded electrode,

ased on numerous visual observations (e.g. see Fig. 3 (c,d)). The

lectric field asymmetry indicates that the direction of the induced

lectric field, E surf , is from the grounded to the high-voltage elec-

rode (see Fig. 14 ). Since the direction of the ion wind remains

he same, both when the field asymmetry dominates (as in Fig.

2 ) and when the offset electric field dominates (as in Fig. 13 ), we

onclude that the direction of the offset electric field is also from

he grounded to the high-voltage electrode, as indicated schemat-

cally in Fig. 14 . This conjecture is consistent with the AC plasma

c

mission images (see Fig. 10 ) and with the discharge current wave-

orms plotted in Figs. 12 ,and 13 , which consistently exhibit more

icro-discharge pulses with the higher peak current during the

ositive AC half-period. This indicates a more significant net neg-

tive charge accumulation on the high-voltage electrode over the

ntire AC period, and therefore a net induced electric field directed

oward the high-voltage electrode, in spite of the symmetric elec-

rode geometry.

Thus, the direction of the net, time-averaged ion wind in the AC

lasma in the present experiments is always toward the grounded

lectrode. On the other hand, the analysis of the electric field data

ndicates that both the peak and the offset electric fields are di-

ected away from the grounded electrode. Since the net ion wind

s directed against the electric field, this leads us to conclude that

t is dominated by the transport of negative ions. Formation of

egative ions in the flame is unlikely, due to the high tempera-

ure resulting in electron detachment [24] . However, negative ions

ay well dominate the ion transport in the low-temperature am-

ient air plasma generated on both sides of the flame (see Fig. 3 (c–

)), where they are formed by rapid electron attachment to oxygen

olecules [25] .

. Summary

The present work demonstrates a significant potential of ps

econd Harmonic Generation diagnostics for straightforward, non-

ntrusive measurements of time-resolved and spatially-resolved

lectric field in atmospheric pressure flames enhanced by ns pulse

nd AC sine wave Dielectric Barrier (DBD) discharges. The co-

erent second harmonic signal is easily separated from the fun-

amental laser beam, and discriminated against the plasma and

ame emission. Individual electric field vector components are de-

ermined by isolating the second harmonic signals with different

olarizations. Electric field measurements in a ns pulse discharge

re self-calibrating, since the field follows the applied voltage until

reakdown. No additional calibration is necessary in this case, and

hemical composition of the reacting mixture does not need to be

264 M. Simeni Simeni et al. / Combustion and Flame 197 (2018) 254–264

A

M

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2

2

known. Time-resolved electric field is measured in a ns pulse dis-

charge sustained both in hydrogen flow below the flame and in

the hydrogen diffusion flame. In both cases, the electric field is re-

duced to near zero after breakdown, which is identified by a sud-

den rise in the discharge current, due to the plasma self-shielding.

Peak electric field measured in a near-room temperature hydro-

gen flow, E ≈ 19 kV, is close to the breakdown field in hydrogen

predicted by a ns pulse dielectric barrier discharge model [15,16] .

Peak electric field in the flame is significantly lower, E ≈ 9–11 kV,

due to the lower number density in the plasma at these condi-

tions. Most of the energy is coupled to the low-temperature hy-

drogen plasma at the reduced electric field of E / N ≈ 50–100 Td,

when over 50% of the input energy goes to H 2 electronic exci-

tation and dissociation by electron impact, generating H atoms.

The time scale for the electric field reduction after breakdown is

relatively long, several tens of ns, indicating that it may be con-

trolled by a relatively slow propagation of the ionization wave over

the dielectric surfaces. The present results can be used for val-

idation of predictive kinetic models of plasma-assisted combus-

tion and flameholding using ns pulse discharges. Correct evalua-

tion of the electric field variation during and after breakdown is

critical for predicting the energy partition in the plasma and the

number densities of excited species and radicals generated in the

plasma.

In the AC plasma, the electric field data are put on the ab-

solute scale by measuring an electrostatic electric field between

the parallel cylinder electrodes and comparing the results with the

numerical solution of the Laplace equation for the electric poten-

tial in this geometry. The accuracy of the calibration depends on

whether the AC plasma affects the chemical composition of the

flow at these conditions, which has not been studied in the present

work. The measurement results demonstrate that a strong electric

field in the plasma-enhanced flame is produced during the entire

AC voltage period, without any apparent correlation with the dis-

charge current waveform (i.e. with the random micro-discharges

detected in the plasma images). The electric field in the flame is

significantly lower compared to the Laplacian field at the same

voltage, due to significant surface charge accumulation on the di-

electric surfaces. The measurement results indicate a higher peak

electric field during the negative AC half-period, in spite of the

symmetric electrode geometry, as well as a significant electric field

offset. The asymmetry and the offset of the electric field are likely

responsible for the electrohydrodynamic (EHD) body force (“ion

wind”) resulting in the flame distortion, which is one of the domi-

nant effects of the electric field at these conditions. The analysis of

the electric field offset and asymmetry, along with the visual ob-

servations of the effect of the ion wind on the flame, suggest that

at the present conditions the ion wind is dominated by the trans-

port of negative ions, generated in the ambient air plasma on both

sides of the flame. The present results can be used for develop-

ment and validation of non-empirical, predictive kinetic models of

flame control by the ion wind.

Spatial resolution of the present diagnostic in the direction of

the laser beam can be improved significantly, from the present

value of several cm to ∼1 mm by using a shorter focal distance

focusing lens, producing a laser beam with a shorter confocal pa-

rameter [17] . However, measurements of the electric field averaged

along the laser beam (i.e. over the span of the electrodes) and over

the ensemble of the micro-discharges, are particularly relevant for

quantifying the effect of the ion wind. Since the impulse of the

body force produced by the individual micro-discharges (a few ns

duration) is very low, the ion wind and the flame motion are con-

trolled by the ensemble-averaged electric field, measured by the

present diagnostic. The present approach can also be used for mea-

surements of the electric field distribution across the laser beam,

if a PMT detector is replaced with an ICCD camera [26] .

cknowledgments

The support of US Department of Energy Center for Exascale

odeling of Plasma Assisted Combustion and US Department of

nergy Plasma Science Center “Predictive Control of Plasma Kinet-

cs: Multi-Phase and Bounded Systems” is gratefully acknowledged.

e would also like to thank Dr. Benjamin Goldberg (Princeton Uni-

ersity) for productive technical discussions.

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