Development of Fast Ionization Wave Discharges at High

ORI GIN AL PA PER

Development of Fast Ionization Wave Discharges at HighPulse Repetition Rates

Keisuke Takashima • Igor V. Adamovich • Uwe Czarnetzki •

Dirk Luggenholscher

Received: 15 July 2011 / Accepted: 5 April 2012 / Published online: 28 April 2012� Springer Science+Business Media, LLC 2012

Abstract Positive and negative polarity fast ionization wave discharges in nitrogen and

dry air are studied in a rectangular geometry channel over a wide range of time delays

between the discharge pulses, s = 10 ms to 25 ls (pulse repetition rates of m = 100 Hz–

40 kHz). The discharge is generated by alternating polarity high-voltage pulses (peak

voltage 18–23 kV, pulse duration 50–60 ns). Ionization wave speed and electric field

distributions in the discharge are measured by a calibrated capacitive probe. Plasma images

show that for long time delays between the pulses, above s * 1 ms (pulse repetition rate

up to m * 1 kHz), the positive polarity wave propagates along the channel walls and the

negative polarity wave tends to propagate along the centerline. For time delays below

s * 0.5–1.0 ms (above m * 1–2 kHz), both positive and negative polarity waves become

diffuse, while wave speed and peak electric field in the wave front become nearly inde-

pendent of the polarity. Wave speed remains nearly constant for s * 1–10 ms (up to

m * 1 kHz), 0.8–0.9 cm/ns, and decreases for shorter time delays, by 30–40 % at

s = 25 ls (m = 40 kHz). Peak electric field in the positive polarity wave decreases sig-

nificantly as the pulse repetition rate is increased, from 2.7–3.0 kV/cm to 1.2–1.5 kV/cm.

Comparison of experimental results in nitrogen with kinetic modeling calculations at high

pulse repetition rates, when the discharge is diffuse, shows good agreement. Calculation

results show that peak electric field reduction at high pulse repetition rates is mainly due to

higher electron density in the decaying plasma generated by the previous discharge pulse.

Reduction of wave speed and coupled energy at high repetition rates is primarily due to

slower voltage rise and lower pulse peak voltage, limited by the pulse generator. The

model shows that at high pulse repetition rates most of the discharge power is coupled to

the plasma behind the wave, at E/N * 200–300 Td. Discharge energy loading at

m = 1–40 kHz is 1–2 meV/molecule/pulse.

K. Takashima � I. V. Adamovich (&)Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus,OH, USAe-mail: [email protected]

U. Czarnetzki � D. LuggenholscherDepartment of Physics and Astronomy, Ruhr University Bochum, Bochum, Germany

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Plasma Chem Plasma Process (2012) 32:471–493DOI 10.1007/s11090-012-9377-9

Keywords Fast ionization wave � Nanosecond pulse � Electric field measurements �Kinetic modeling

Introduction

Fast ionization wave (FIW) discharges have been extensively studied over the last decades.

A review of experimental results in this field and theoretical models developed in 1980s

and 1990s can be found in [1, 2]. Since mid-1990s, fundamental kinetic processes in

nanosecond pulse discharges and their applications have been studied at Moscow Institute

of Physics and Technology (e.g. see [3–5] and references therein). At the present time, a

large body of experimental data is available on fast ionization wave speed and attenuation

coefficient in various gases over a wide range of pressures, as well as on wave front

dynamics, UV/visible emission from the wave, and generation of high-energy (runaway)

electrons in the wave front. Recently, numerical and analytic models of FIW discharge

have been developed and validated experimentally for wave speeds of *1 cm/ns [6].

The main difference between streamer discharges and FIW discharges is that the latter

demonstrate high spatial uniformity and reproducibility, thus allowing accurate measure-

ments of discharge parameters in a repetitively pulsed mode. Qualitative similarity

between these two types of discharges is due to the fact that key elementary processes

controlling discharge propagation are electron impact ionization in the discharge front and

photoionization. The transition between the streamer and the ionization wave discharge

modes is rather gradual, and requires high peak reduced electric fields and therefore high

pulse voltage rise rates, typically of the order of *1–10 kV/ns. At these conditions, the

ionization wave speed is of the order of *1–10 cm/ns [1]. Due to the high reduced electric

field in the discharge front, up to E/N * 103 Td (1 Td = 10-17 V cm2), the role of high-

energy electrons in ionization kinetics can be significant [7].

Current interest in characterization of FIW discharges is driven mainly by their potential

for applications such as plasma chemical fuel reforming [8], plasma-assisted combustion

[4, 5, 9, 10], pumping of electric discharge excited lasers [9], and generation of high-

energy electrons [7]. A unique capability of FIW discharges to generate significant ioni-

zation and to load a significant fraction of input energy into molecular dissociation and

electronic excitation at high pressures and over large distances, before ionization insta-

bilities have time to develop [3–5], is very attractive for these applications. Also, high peak

electron/ion and electronically excited species concentrations reached in near-surface FIW

discharges result in rapid energy thermalization on sub-microsecond time scale, which is

critical for high-speed flow control using nanosecond pulse surface plasma actuators [11–

13]. Most of these applications involve discharge operation at high pulse repetition rates,

from a few kHz up to *100 kHz, to maximize time-averaged electron density [9], number

densities of excited species and radicals [9, 10, 14], or to match flow instability frequencies

[13, 15]. Insight into FIW formation and propagation dynamics at high pulse repetition

rates requires the use of non-intrusive optical diagnostics with sub-nanosecond time res-

olution, as well as development of predictive kinetic models and their validation.

The main objectives of the present work are (i) measurements of wave speed, electric

field in the wave front, and coupled pulse energy in FIW discharges in nitrogen and dry air

operated at high pulse repetition rates, and (ii) comparison of the experimental results with

kinetic modeling calculations to obtain insight into wave propagation dynamics and energy

coupling kinetics. To reduce heating of the flow while producing significant pre-ionization

472 Plasma Chem Plasma Process (2012) 32:471–493

123

in the discharge channel typical for high pulse repetition rates, the discharge is operated in

repetitive burst mode, at a low burst repetition rate and short time delay between the pulses

in the burst (i.e. high pulse repetition rate in the burst).

Experimental

The experimental apparatus used in the present work and shown schematically in Fig. 1 is

essentially the same as described in our previous publication [6]. Briefly, the fast ionization

wave discharge is generated in a rectangular cross section quartz channel, between a high

voltage electrode on the left and a grounded electrode on the right. The high voltage

electrode is a 12 mm outside diameter hollow cylinder made of copper. The grounded

electrode is a square shape copper flange, with a circular port 25 mm in diameter. The

22 mm 9 13.5 mm outside dimension rectangular cross section, 20 cm long quartz

channel with 1.75 mm thick walls is fused to two quartz tube sections 14 cm long and

25 mm in diameter on both ends, as shown in Fig. 1. The grounded flange is connected to

two copper waveguide plates, mounted above and below the quartz channel 40 mm apart,

as shown in Fig. 1. The distance between the edge of the high voltage electrode and the

grounded flange is 28 cm. The high voltage electrode is connected to a high voltage

terminal of a custom-designed, high-voltage, nanosecond pulse generator. The grounded

terminal of the pulse generator is connected to the waveguide plates, thus forming a plane

geometry plasma waveguide. Pulse peak voltage and current are measured by a Tektronix

P6015 high voltage probe and a custom-designed current shunt probe [12].

A custom designed, capacitive voltage divider probe has been used to measure the

ionization wave speed and the electric field in the wave front. The capacitive probe is

mounted in a slot the top waveguide plate, with the tip extending into the waveguide, and

can be moved along the discharge channel. Details of the probe operation and its use for

the surface charge, electric potential, and electric field distribution measurements in

nanosecond pulse discharges are discussed in [16]. The design of the probe used in the

present experiments, as well as its time response and amplitude response calibration are

described in detail in Ref. [6]. Time-resolved electric potential on the discharge channel

wall at the location of the probe tip, as well as the axial electric field in the channel, have

been inferred from the probe signal.

Optical access to the discharge channel, for discharge imaging and emission measure-

ments, is available from the sides (see Fig. 1). Additional optical access is provided from the

ends of the discharge channel, through the quartz windows fused to the ends of 25 mm

diameter quartz endpieces, connected to flow inlet and exhaust tubes, made of glass (see

Fig. 1). Broadband images of the plasma have been taken using a PI-MAX ICCD camera. The

Fig. 1 Schematic of the fast ionization wave discharge apparatus

Plasma Chem Plasma Process (2012) 32:471–493 473

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present experiments have been conducted in nitrogen and in dry air at a pressure of

P = 10 Torr. The baseline nitrogen flow rate is 100 sccm, which corresponds to the flow

velocity through the discharge channel of approximately u = 0.7 m/s at P = 10 Torr. The

flow rate through the discharge section and the pressure are controlled by mass flow con-

trollers and by a shutoff valve between the test section and the vacuum pump.

The high-voltage nanosecond pulse generator [6], also used in the present experiments,

has been custom designed to generate alternating polarity pulses with peak voltage of 10–

30 kV, pulse duration 50–100 ns, and pulse repetition rate up to 50 kHz. In the present

work, the pulser is operated at repetition rates of 100 Hz–40 kHz. The pulse output voltage

is regulated by varying the voltage of a DC power supply providing input to the pulse

generator. Increasing input DC voltage also reduces the output pulse duration. Figure 2

shows typical positive and negative polarity pulse shapes generated in nitrogen at

P = 10 Torr at different pulse repetition rates. The experimental voltage waveforms

shown in Fig. 2 can be approximated by a Gaussian shape pulse,

U ¼ Upeak exp � t0 � t

s

� �2� �

; ð1Þ

with Upeak = 21–19 kV and s = 30–37 ns (FWHM of 50–61 ns) for UDC = 720 V and

pulse repetition rate in the range of m = 0.1–40 kHz. Pulse peak voltage reduction and

pulse duration increase at high pulse repetition rates (above m = 5 kHz, see Fig. 2) are due

to the relatively slow charging of capacitors in the DC power supply. Pulse voltage

waveforms taken in atmospheric pressure nitrogen, when no breakdown is detected in the

discharge channel, are almost the same as shown in Fig. 2.

Kinetic Model

To model the ionization wave propagation in the rectangular geometry channel, shown

schematically in Fig. 3, we used a quasi-one-dimensional hydrodynamic plasma model in

Fig. 2 Typical positive andnegative polarity voltage pulsewaveforms generated by thepulsed plasma generator fordifferent pulse repetition rates


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the drift–diffusion approximation. The model has been derived from a two-dimensional

plasma model assuming weak transverse nonuniformity of the FIW discharge, as discussed

in greater detail in Ref. [2] and in our previous paper [6]. In Fig. 3, the channel length and

half-height are L = 30 cm and a = 0.5 cm, respectively, the dielectric thickness is

h = 1.5 cm, and the dielectric constant is e = 1. The governing equations in the discharge

channel and the boundary conditions on the high-voltage electrode (at x = 0) and on the

grounded electrode (at x = L) are as follows,

onþotþ

o lþnþE� �

ox¼ mine � b nþne ð2Þ

one

ot� o leneEð Þ

ox� lenek2u ¼ mine � b nþne; ð3Þ

oEx

oxþ k2u ¼ e

e0

q; Ex ¼ �ouox

ð4Þ

nþðx ¼ 0Þ ¼ 0 one=oxðx ¼ 0Þ ¼ 0 neðx ¼ LÞ ¼ 0 onþ=oxðx ¼ LÞ ¼ 0 ð5Þ

uðx ¼ 0; tÞ ¼ UðtÞ uðx ¼ L; tÞ ¼ 0: ð6ÞInitial conditions for the electron and ion densities and for the potential in the discharge

channel are

ne ¼ nþ ¼ no; u ¼ 0: ð7ÞIn Eqs. (2)–(4), k is the wavenumber of a linear electrostatic wave formed in a weakly

pre-ionized, rectangular geometry waveguide (see Fig. 3) at the conditions when ionization

is negligible [2],

tanðkaÞ tanðkhÞ ¼ v ¼ e1þ r

e0f

¼ e

1þ eneleEx

e0f

; f ¼ 1

ududt: ð8Þ

For small wavenumbers (i.e. long wavelengths), a simple asymptotic expression for the

wavenumber can be used,

ka� 1; kh� 1 : k � vah

� �1=2

: ð9Þ

The rate of electron impact ionization is assumed to be controlled by the local electric

field. The expression for the ionization frequency, mi, used in Eqs. (2)–(4) is a fit to the

a

h Dielectric,

Grounded waveguide

High voltage electrode,

U(t) x

y

Pre-ionized plasma channel, n0

L

Fig. 3 Schematic of the plasma channel and the dielectric layer in simplified quasi-two-dimensionalgeometry


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experimental data on Townsend ionization coefficient in nitrogen as a function of the

reduced electric field, E/p [17],

ap

�

N2

¼900

Ep

� exp � 315Ep

� �cm�1 ; E

p \100 V/cm torr

12 � exp � 342Ep

� �cm�1 ; 100\ E

p \800 V/cm torr

8>><>>:

mi ¼ aleE: ð10Þ

This problem formulation does not incorporate photo-ionization and ionization in col-

lisions of excited species.

At relatively long delays after the previous voltage pulse, s = m-1 �[ne(t = 0)b]-1 * 1 ls, the initial electron density in nitrogen is nearly independent of the

peak electron density and can be approximated as follows,

n0 ¼ neðtÞ ¼neðt ¼ 0Þ

1þ neðt ¼ 0Þbt� m

b: ð11Þ

Here ne(t = 0) * 1012 cm-3 is the peak electron density achieved during the pulse [6]

and b = 2 9 10-6 cm3/s is the electron–ion dissociative recombination rate coefficient for

N4? ions, N4

? ? e- ? N2 ? N2, which are the dominant ions in nitrogen plasma at the

present conditions. Modeling calculations using an air plasma kinetic model [18] show that

the characteristic time for the primary N2? ions conversion reaction, N2

? ? e- ?

M ? N4? ? M, is *1 ls at P = 10 Torr.

The electron mobility is approximated as a function of the reduced electric field,

lep = 0.82 9 106�(E/P)-0.24 cm2 Torr/V s, based on the prediction of the Boltzmann

equation solver for electrons in a nitrogen plasma [19]. Since both electron–ion recombi-

nation and ion drift are extremely slow on the time scale of wave propagation (tens of

nanoseconds), the recombination rate coefficient, b = 2 9 10-6 cm3/s, and the ion mobility,

l ? p = 0.21 9 104 cm2 Torr/V s, have almost no effect on the results. Similarly, both

electron diffusion and ion diffusion are negligible on this time scale. The experimental pulse

voltage waveforms were approximated by a Gaussian shape pulse, given by Eq. (1).

The applicability of a quasi-one-dimensional model for modeling of FIW discharges at

the present conditions has been assessed in our previous work [6], where the present

model’s predictions have been compared to the results of two-dimensional FIW modeling,

showing good agreement. Two-dimensional modeling calculations in Ref. [6] have also

shown that transverse electric field nonuniformity at the present conditions is relatively

weak, thus justifying the use of a quasi-one-dimensional approach.

Results and Discussion

As discussed in our previous work [6], the electric potential at the probe location, u(t), has

been determined using the following relation,

uðtÞ ¼ A VðtÞ þ 1

s

Z t

0

Vðt0Þdt0

24

35; ð12Þ

where V(t) is the raw probe signal, and A = 3.45 9 103, s = 6.7 ns are the amplitude and

time response of the probe, determined using a calibration voltage pulse of known shape

[6]. The spatial resolution of the probe, also determined during calibration while translating

the probe along the channel, is approximately 1 cm (22 ± 3 mm FWHM) [6].


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Figure 4 shows a schematic of high-voltage pulse time sequence used in the present

experiments. The pulsed plasma generator operated in the ‘‘double-pulse’’ mode, with

‘‘bursts’’ of two opposite polarity pulses generated in rapid succession, with time delay

between the pulses of s = 10 ms–25 ls (corresponding to pulse repetition rate ranging from

0.1–40 kHz), and a low burst repetition rate of 20 Hz, thus keeping the flow at near room

temperature. This approach allowed isolating the effect of high residual electron density

remaining in the decaying plasma generated by the previous pulse from the gas temperature

rise, which would occur during continuous discharge operation at a high pulse repetition rate.

Figure 5a plots electric potentials measured in a positive polarity wave in nitrogen at

P = 10 Torr, time delay between the pulses of s = 10 ms (pulse repetition rate of

m = 100 Hz), and burst repetition rate of 20 Hz. The potentials at probe locations, u(t), are

inferred from the raw probe signals, V(t), using Eq. (12). The probe signals are taken for

multiple probe tip locations ranging from x = 5 to x = 25 cm from the high voltage

electrode, 1 cm apart. The traces in Fig. 5a are averaged over 200 positive polarity dis-

charge pulses (i.e. 10 s). It can be seen that the results are reproduced very well run-to-run,

with excellent signal-to-noise, which is critical for inference of the electric field from the

probe signals. Figure 5a illustrates that the wave of electric potential propagates to the

right, from the high voltage electrode to the grounded electrode. The potentials measured

by the probe start decreasing when the wave reaches the grounded electrode. Figure 5b

plots time-resolved axial electric field at midpoints between the probe locations, i.e. at

x = 5.5, 6.5, … 24.5 cm, determined from the potential difference at these locations. It can

be seen that the wave front initially steepens while peak electric field increases consid-

erably (from about 2 kV/cm to nearly 3 kV/cm), before reaching a quasi-steady-state shape

(at x & 12 cm). Behind the wave, the field remains low, in the range of E = 0.3–0.7 kV/

cm. Finally, Fig. 5c plots the wave front arrival time, as well as peak potential, peak

electric field, and potential at the moment when the field peaks, at different probe locations.

Fig. 4 Schematic of ‘‘double-pulse’’ operation of the pulsed plasma generator for a negative-positivepolarity, and b positive–negative polarity. Pulse repetition rate m = 0.1–40 kHz (time delay between pulses10 ms–25 ls), burst repetition rate 20 Hz


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The uncertainty of the capacitive probe tip location is ±0.5 mm, and the estimated

uncertainty of the wave speed inferred from the slope of the t–x diagram such as shown in

Fig. 5c is 2 %. From Fig. 5c, it can be seen that far from the high voltage electrode (at

x [ 12 cm), the wave speed becomes nearly constant, V = 0.89 cm/ns at x = 12–25 cm.

In this region, peak electric field in the wave front remains about the same,

E & 2.8–3.0 kV/cm. The potential at the location of peak field also remains approximately

the same, u = 6.5–7.0 kV, although the peak potential in the wave decreases by more than

a factor of two, from 19 to 9 kV as it propagates along the discharge channel (see Fig. 5c).

The results shown in Fig. 5 are similar to our previous measurements in a FIW dis-

charge in nitrogen operated at low pulse repetition rates of 10–20 Hz [6]. When time delay

between the pulses is reduced to s = 100 ls (pulse repetition rate increased to

m = 10 kHz), both peak field in the wave front and the wave speed are reduced signifi-

cantly, as shown in Fig. 6. This occurs in spite of rather modest peak pulse voltage

Fig. 5 a Time-resolved potentials; b time-resolved axial electric fields; c ionization wave front arrival time,peak potential, peak electric field, and potential at the moment when electric field peaks at different probelocations. Data obtained for 21 different locations of the capacitive probe 1 cm apart, ranging from 5 to25 cm from the high voltage electrode. Nitrogen, P = 10 Torr, m = 100 Hz, positive polarity wave (pulsesequence as shown in Fig. 4a


123

reduction, by approximately 1 kV (see Fig. 2). In this case, the peak field and the wave

speed remain nearly the same in the entire channel, E & 1.6 kV/cm (about a factor of two

lower than at m = 100 Hz) and V = 0.61 cm/ns (about 30 % lower than at m = 100 Hz).

Again, the potential at the location of the peak field remains approximately the same,

u & 4.0 kV, although the peak potential in the wave decreases considerably, 18–6 kV

(see Fig. 6).

Figure 7 summarizes the results of peak electric field and potential measurements in

positive and negative polarity ionization waves in nitrogen at P = 10 Torr and for different

time delay between the pulses (pulse repetition rates). It can be seen that for long time

delays between the pulses, s = 10 and 1 ms (low pulse repetition rates, m = 100 Hz and

1 kHz), the behavior of the positive polarity wave is significantly different from that of the

negative polarity wave. In particular, peak electric field and potential at the peak field

Fig. 6 a Time-resolved potentials; b time-resolved axial electric fields; c ionization wave front arrival time,peak potential, peak electric field, and potential at the moment when electric field peaks at different probelocations. Data obtained for 21 different locations of the capacitive probe 1 cm apart, ranging from 5 to25 cm from the high voltage electrode. Nitrogen, P = 10 Torr, m = 10 kHz, positive polarity wave (pulsesequence as shown in Fig. 4a)


123

location are considerably higher in the positive polarity wave (see Fig. 7). For long time

delays between the pulses, s = 100 and 50 ls (high pulse repetition rates, m = 10 and

20 kHz), the values of both these parameters in positive and negative polarity waves are

reduced significantly (especially for the positive polarity) and become rather close to each

other. Also, at high pulse repetition rates, peak electric field and potential at the peak field

location remain nearly the same along the entire discharge channel, for both polarities, i.e.

the initial wave steepening (e.g. see Fig. 5b is not observed. Basically, at these conditions

the ionization wave becomes nearly self-similar (e.g. see Fig. 6b), and opposite polarity

waves begin to ‘‘mirror image’’ each other. Similar behavior has been observed in FIW

discharges in dry air, also at P = 10 Torr (see Fig. 8).

Fig. 7 Peak electric field and potential at the moment when electric field peaks versus axial location, fordifferent pulse repetition rates: a,b positive polarity wave (see Fig. 4a); c,d negative polarity wave (seeFig. 4b. Nitrogen, P = 10 Torr


123

The results of wave speed measurements in nitrogen and dry air are shown in Fig. 9.

The wave speed has been determined from the slope of the t–x diagrams, such as shown in

Figs. 5 and 6, in the discharge channel region where the wave reaches quasi-steady-state

speed. From Fig. 9, it can be seen that for long time delays between the pulses, above

s * 1 ms (low pulse repetition rates, up to m * 1 kHz), the positive polarity wave speed

in nitrogen and air exceeds that of the negative polarity by 5–15 %, consistent with our

previous measurements in nitrogen [6]. For shorter time delays between the pulses, below

s * 1 ms (at higher pulse repetition rates, above m * 1 kHz), the wave speed begins to

decrease for both polarities, with the negative polarity wave speed becoming somewhat

higher. For s = 25 ls (m = 40 kHz), the wave speed is reduced by 30–40 % compared to

the baseline value at s = 10 ms (m = 100 Hz). Similar trend is observed in the discharge

Fig. 8 Peak electric field and potential at the moment when electric field peaks versus axial location, fordifferent pulse repetition rates: a,b positive polarity wave (see Fig. 4a); c,d negative polarity wave (seeFig. 4b). Dry air, P = 10 Torr


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pulse energy coupled to the plasma, plotted in Fig. 10. It can be seen that coupled pulse

energy in nitrogen and dry air decreases at high pulse repetition rates (above m * 1 kHz)

for both discharge pulse polarities, from 5 to 6 mJ/pulse at m = 100 Hz to 2.5 mJ/pulse at

m = 40 kHz (nitrogen) and from 6 to 7 mJ/pulse at m = 100 Hz to approximately 3 mJ/

pulse at m = 40 kHz (air).

Figure 11 shows broadband, single-shot ICCD images of positive polarity ionization

waves in nitrogen at P = 10 Torr and for different time delays between the pulses,

Fig. 9 Positive and negative polarity ionization wave speed versus pulse repetition rate. a Nitrogen; b Dryair. P = 10 Torr

Fig. 10 Coupled pulse energy in positive and negative polarity ionization wave discharges versus pulserepetition rate. a Nitrogen; b Dry air. P = 10 Torr


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s = 10 ms, 1 ms, and 100 ls (pulse repetition rates of m = 100 Hz, 1 kHz, and 10 kHz).

In the images, the wave propagates left to right. The camera gate is sgate = 4 ns, time delay

between the frames is 2 ns, and the field of view of the images is 4.6 cm by 3.1 cm. The

images are centered midway through the rectangular quartz channel (see Fig. 1), at

x = 15 cm. The camera was triggered externally, by a trigger pulse provided by the high-

voltage pulse generator, with jitter of about 1 ns. Pulse-to-pulse reproducibility of the

ionization wave launch timing and wave speed is very good, such that 4–8 shot averaged

images appear essentially identical to the single-shot images shown in Fig. 11. The wave

speed at these conditions is V & 0.9 cm/ns (at m = 100 Hz and 1 kHz) and V & 0.6 cm/

ns (at m = 10 kHz, see Fig. 9a), such that the 4 ns camera gate provides fairly low spatial

resolution in the axial direction, approximately Daxial * 2.5–4 cm. However, estimated

transverse resolution, Dtrans * w�sgate, where w * 5 9 107 cm/s is electron drift velocity

in nitrogen at the upper bound reduced electric field Eaxial/N * 103 Td (Etrans � Eaxial) is

Dtrans * 0.1 cm. Therefore the images in Fig. 11 resolve the transverse structure of the

ionization wave front fairly well. From Fig. 11, it can be seen that at m = 100 Hz

(s = 10 ms), the emission is brighter along the top and bottom walls of the channel rather

in the volume, i.e. the wave propagates ‘‘hugging the walls’’ adjacent to the waveguide

plates. At m = 1 kHz (s = 1 ms), bright emission also appears in the channel volume,

although a distinct near-wall structure is still detectable. Finally, at m = 10 kHz

(s = 100 ls), the plasma emission becomes diffuse, without clearly defined near-wall

Fig. 11 Single-shot ICCD camera images of positive polarity ionization wave front in nitrogen at differentpulse repetition rates: a 100 Hz; b 1 kHz; c 10 kHz. Nitrogen, P = 10 Torr, camera gate 4, 2 ns delaybetween frames


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regions, although emission intensity on the center of the channel is somewhat lower. UV/

visible emission spectra taken at the conditions of Fig. 11 show that plasma emission is

dominated by the nitrogen second positive bands.

Two-dimensional kinetic modeling of a single-pulse, positive polarity FIW discharge in

nitrogen conducted in Ref. [6] reproduced the wall hugging effect, observed at low pulse

repetition rates, qualitatively. These results have shown that higher electron density near

the channel walls adjacent to the waveguide plates is caused by the electric field

enhancement near the wall due to the jump in permittivity, as well as by secondary photo-

electron emission from the wall irradiated by the UV photons from the plasma. At the

present conditions (using alternating polarity pulses), electron accumulation on the channel

walls is caused by electron motion away from the high voltage electrode toward the walls

during the negative polarity pulse, preceding the positive pulse. Note that even at these

conditions the two-dimensional kinetic model [6] predicts fairly weak transverse electric

field nonuniformity. As the pulse repetition rate is increased, higher residual electron

density remaining from the previous pulse is expected to make volume electron impact

ionization more significant compared to ionization by secondary electrons emitted from

dielectric surfaces. This would reduce the wall hugging effect, as observed in the present

experiments (see Fig. 11). Also, transverse nonuniformity of the FIW discharge at low

pulse repetition rates is likely to be reduced by reducing high voltage pulse duration (i.e.

increasing the rate of voltage rise on the electrode, dU/dt) and pressure. As discussed in

Ref. [6], this would result in higher peak electric field in the wave, more rapid electron

impact ionization in the volume, and higher wave speed. For example, spatially uniform

FIW discharges in air have been obtained using voltage pulses with 5 ns rise time [20].

Figure 12 shows 4-shot averaged images of positive and negative polarity FIW front in

nitrogen at P = 10 Torr. One can see that, as the pulse repetition rate is increased, the

positive polarity wave gradually transitions from a ‘‘wall-hugging’’ mode to a volumetric

mode. As the pulse repetition rate increases from 100 Hz to 1 kHz, a diffuse luminous

structure appears in the volume of the discharge channel, which occupies nearly the entire

channel at m = 1–4 kHz. At m = 10 kHz, bright regions near the top and bottom walls of

the channel merge with the structure in the volume of the channel. Above 10 kHz, the FIW

discharge remains diffuse and fills the entire channel, while emission intensity near the

centerline appears to decrease. In negative polarity waves at low pulse repetition rates

(below m * 1 kHz, see Fig. 12b), a well-defined bright region can be identified along the

centerline of the discharge channel. Note that the effect of electron accumulation on the

walls is absent if the positive polarity pulse is generated first. In this case, discharge

propagation during the subsequent negative polarity pulse is primarily due to electron

motion in the direction of the wave, which produces pre-ionization ahead of the wave front.

The extent of electron penetration ahead of the wave strongly depends on the electron

energy in the wave front, i.e. on peak reduced electric field in the wave, which is primarily

controlled by the rate of voltage rise on the electrode, dU/dt, and discharge pressure [6].

Basically, high-energy electrons would penetrate further ahead at higher dU/dt and lower

pressures, thus enhancing discharge uniformity. At lower dU/dt and higher pressures, the

negative polarity wave is more likely to be ‘‘constricted’’ to the near-centerline region,

where breakdown near the electrode occurs first. At the present conditions,

dU/dt * 0.4 kV/ns at P = 10 Torr (see Fig. 2), which is significantly lower compared to

dU/dt * 2 kV/ns at P = 8 Torr in Ref. [20]. This may explain qualitatively greater

transverse nonuniformity of the negative polarity wave at the present conditions compared

to the results of Ref. [20]. Diffuse emission in the volume of the negative polarity dis-

charge gradually becomes brighter as the pulse repetition rate is increased, until the


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discharge becomes diffuse and volume-filling above m * 2 kHz (see Fig. 12b). Similar to

the positive polarity discharge, at high pulse repetition rates (4 kHz and above) emission

intensity near the centerline becomes somewhat lower than near the walls.

The results obtained at the same conditions in dry air, shown in Fig. 13, are consistent

with nitrogen results, although transverse nonuniformity of the wave front in this case is

noticeably reduced. Qualitative similarity between FIW discharge behavior in nitrogen and

Fig. 12 ICCD camera images (4-shot averages) of ionization wave front at different pulse repetition rates(indicated in the images), a positive polarity wave, b negative polarity wave. Nitrogen, P = 10 Torr, cameragate 4 ns


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in dry air, which can be seen in Figs. 7, 8, 9, 10 and 12, 13, suggests that electron

attachment and negative ions kinetics are not playing significant role in ionization wave

front development at the present conditions. Indeed, at high peak reduced electric fields

involved, E/N * 300–1,000 Td, electron impact ionization in air dominates dissociative

attachment, O2 ? e ? O ? O- [17]. Also, at low pressures the effect of three-body

attachment, O2 ? e ? M ? O2- ? M, on electron density decay in dry air between the

Fig. 13 ICCD camera images (8-shot averages) of ionization wave front at different pulse repetition rates(indicated in the images), a positive polarity wave, b negative polarity wave. Dry air, P = 10 Torr, cameragate 4 ns


123

discharge pulses is not very significant, with the characteristic time of satt *(katt�[O2]�[M])-1 * 100 ls, longer or comparable to the characteristic time for electron–

ion recombination, srec * (bne)-1 * 1–100 ls for ne = 1010–1012 cm-3.

Figure 14 compares experimental time-resolved axial electric field in positive and

negative polarity FIW discharges in nitrogen at P = 10 Torr and m = 10 kHz (a,b) with

kinetic model predictions (c,d). The results are shown at different distances from the high-

voltage electrode, ranging from x = 6.5 to 24.5 cm, with 2 cm increments. At these

conditions, both the positive and the negative polarity waves appear diffuse and volume

filling (see Fig. 12), which justifies the use of a quasi-one-dimensional kinetic model. For

comparison with the experimental data, the predicted electric field plotted in Fig. 14 has

been approximated as a difference between the potentials at two axial locations Dx = 1 cm

apart, i.e. Ei?1/2 & ui-ui?1. At the conditions of Fig. 14, this value is about 5 % lower

than the actual electric field, Ex = -du/dx, calculated by the model. Since Dx & 1/

2�DFWHM of the capacitive probe, this illustrates that at these conditions, the probe mea-

surements underestimate the peak electric field in the wave front by a few percent, due to

the finite spatial resolution of the probe. From Fig. 14, it can be seen that the model

reproduces peak electric field values as well as time dependence of the electric field fairly

well. Note that in the experiment, peak electric field remains nearly the same in the entire

range of distances covered by the capacitive probe, while the model predicts first a gradual

rise of peak electric field followed by a gradual reduction (see Fig. 14). The model also

overpredicts the electric field at long times after the wave arrival.

Figure 15 compares the experimental wave front arrival time, as well as peak potential,

peak electric field, and potential at the moment when the field peaks with the model

predictions, at the conditions of Fig. 14. It can be seen that the predicted peak electric field

and potential at the field peak are in good agreement with the experiment, although the

model somewhat overpredicts the wave amplitude attenuation and underpredicts the wave

speed. The predicted wave speed (i.e. the inverse slope of the wave trajectory in Fig. 15)

increases when the predicted peak electric field is increased, and decreases when the peak

field begins to decay (compare Figs. 14c,d, 15). In particular, significant wave speed

reduction is predicted by the model at large distances from the high voltage electrode (see

Fig. 15). Such wave speed reduction is not detected in the experiment, where both peak

field and the wave speed remain nearly constant throughout most of the discharge channel.

Note that at relatively long voltage pulse durations (*50 FWHM, see Fig. 2) and

relatively low peak discharge currents measured (*10 A), the discharge cell behaves

essentially as an electrostatic load. The estimated inductance of the discharge section,

approximated as a conducting wire of length l = 30 cm and radius of a = 0.5 cm placed

between two conducting planes, h = 3 cm apart from each plane (see Fig. 3), is

L * 0.2 lH. For the peak current through the discharge of I * 10 A, varying over

s * 25 ns, the upper bound estimate of the inductance e.m.f. is of the order of UL * LI/s * 80 V (induced electric field of EL * 3 V/cm), which is negligible compared to the

axial electric field behind the wave front measured in the experiment, a few hundred V/cm

(see Fig. 14).

Figure 16 plots the electron density and the discharge power distributions at the con-

ditions of Figs. 14 and 15. The results for positive and negative polarity waves are shown

by solid and dashed lines, respectively. The distributions are shown for every 5 ns, with the

last output time corresponding to the moment when the applied pulse voltage peaks,

t0 = 18 ns (see Fig. 2). From Fig. 16a, it can be seen that after the wave front has passed,

the electron density continues to increase, by up to an order of magnitude, although the

electric field behind the wave is reduced significantly compared to the peak value in the


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front, by a factor of 2–3 (see Fig. 14). Because of this significant additional ionization,

nearly all discharge power is coupled to the plasma behind the wave front (see Fig. 16b).

At m = 1 kHz, a local power maximum near the wave front becomes considerably more

pronounced and exceeds the discharge power behind the wave, but the fraction of the total

Fig. 14 Comparison of experimental and predicted time-resolved axial electric field at different distancesfrom the high-voltage electrode. Positive polarity wave: a experiment; c modeling calculations. Negativepolarity wave: b experiment; d modeling calculations. Nitrogen. P = 10 Torr, m = 10 kHz

Fig. 15 Comparison of experimental results with kinetic model predictions: ionization wave front arrivaltime, peak potential, peak electric field, and potential at the moment when electric field peaks at differentprobe locations. a positive polarity wave, b negative polarity wave. Nitrogen, P = 10 Torr, m = 10 kHz


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energy coupled in the front remains fairly insignificant. Also, in the entire range of time

delays between the pulses (pulse repetition rates), more than half of total pulse energy is

coupled to the plasma after the ionization wave reaches the grounded electrode. Thus, at

high pulse repetition rates most of the FIW discharge power is coupled to the plasma

behind the wave, at E * 0.5–1.0 kV/cm (E/N * 200–300 Td). This is different from

energy coupling to the plasma in a nanosecond pulse discharge in plane-to-plane geometry,

with dielectric barriers on the electrodes [14]. In that case, most of the energy is coupled

during breakdown at high peak E/N, followed by rapid plasma shielding due to charge

accumulation on the dielectric plates. The use of FIW discharge configuration, on the other

hand, makes possible energy coupling to the plasma over more extended periods of time,

using long duration high-voltage pulses (up to tens of nanoseconds).

Based on the present coupled pulse energy measurements (see Fig. 10), discharge

energy loading at m = 1–40 kHz is *1–2 meV/molecule/pulse. At the present experi-

mental conditions (burst repetition rate of 20 Hz and two discharge pulses per burst) this

Fig. 16 a Electron density, b reduced electric field, and c coupled discharge power distributions at theconditions of Figs. 14 and 15, predicted by the kinetic model. Solid lines, positive polarity wave; dashedlines, negative polarity wave. Nitrogen, P = 1 Torr, m = 10 kHz, results are plotted every 5 ns


123

corresponds to the temperature rise of a few degrees above room temperature, if all input

energy is thermalized. The estimated decay time of metastable N2(A3R) molecules gen-

erated in the discharge, mainly due to collisional energy pooling processes, is a few

hundred microseconds. This is approximately two orders of magnitude shorter than time

delay between the discharge bursts (50 ms), such that most of electronically excited

metastables decay between the bursts, suggesting that accumulation of excited species over

multiple bursts is a minor effect. Note that in the present experiments, varying burst

repetition rate from 10 Hz (20 pulses per second) to 40 Hz (80 pulses per second) did not

result in detectable difference in the measured wave speed or peak electric field.

Similarity between parameter distributions in positive and negative polarity waves at

high pulse repetition rates, when the wave does not exhibit significant transverse non-

uniformity (see Fig. 13), is apparent in Figs. 14, 15, 16. The present quasi-one-dimen-

sional, local ionization, hydrodynamic plasma model offers straightforward interpretation

of this behavior. At the present conditions, the ratio of electron drift velocity and wave

speed is fairly low, w/V * 0.05–0.1. Therefore swapping the electric field direction, such

that the electrons move either into the wave our out of the wave, does not affect the wave

dynamics. Indeed, it can be shown that in these two cases the electron density distribution

is a self-similar solution of the following ordinary differential equation [6],

dne

dn¼ mine

V � w; ð13Þ

where n = x?Vt for a wave propagating to the right, and the plus sign is used for the

positive polarity wave. From Eq. (13), it can be seen that changing the polarity would

change the electron density only by a few percent.

Figure 17 compares experimental wave speed, peak electric field, and coupled pulse

energy in nitrogen with the kinetic model predictions. It can be seen that the model

correctly reproduces the trends of reduction of these parameters as the pulse repetition rate

is increased. However, the model considerably underpredicts peak electric field at low

pulse repetition rates, i.e. at the conditions when the FIW discharge exhibits significant

transverse nonuniformity (see Figs. 12, 13). Analysis of the calculations results shows that

peak electric field reduction in the wave front at high pulse repetition rates is primarily due

to higher residual electron density in the discharge channel, which limits the electric field

by more rapid charge separation in the wave front. This effect is also predicted by the

analytic FIW discharge model developed in our previous work [6]. Reduction of wave

speed and coupled energy at pulse repetition rates higher than a few kHz is mainly due to

slower voltage rise on the electrode at these conditions (dU/dt, see Fig. 2), limited by the

nanosecond pulse generator performance.

Summary

In the present work, fast ionization wave (FIW) discharge propagating along a rectangular

geometry channel/plasma waveguide and operated for short time delays between the pulses

(i.e. at high pulse repetition rates) is studied experimentally and using kinetic modeling.

The repetitive nanosecond pulse discharge in the rectangular cross section channel is

generated using a custom built pulsed plasma generator (peak voltage 10–30 kV, pulse

duration 50–100 ns, rate of voltage rise up to *1 kV/ns), producing a sequence of

alternating polarity high-voltage pulses with time delay between the pulses of s = 10 ms


123

to 25 ls (pulse repetition rates of 100 Hz to 40 kHz). Both negative polarity and positive

polarity ionization waves have been studied. The experiments have been conducted in

nitrogen and dry air, at a pressure of 10 Torr. The ionization wave speed, as well as time-

resolved potential distributions and axial electric field distributions in the propagating FIW

discharge have been inferred from the capacitive probe data. The probe is calibrated using

voltage pulses of known pulse shape and amplitude.

For long time delays between the pulses, above s * 1 ms (pulse repetition rates up to

m * 1 kHz), both the wave speed and peak axial electric field in the positive polarity wave

front in nitrogen and air exceed those for the negative polarity wave, by 5–15 %. ICCD

camera images demonstrate that at these conditions, the positive polarity ionization wave

Fig. 17 Comparison of experimental results with kinetic model predictions: a wave speed, b peak electricfield, and c coupled pulse energy versus pulse repetition rate. Nitrogen, P = 10 Torr, positive and negativepolarity waves


123

in nitrogen and air propagates along the walls of the discharge channel adjacent to the

waveguide plates, while the negative polarity wave tends to propagate along the centerline

of the channel. For short time delays between the pulses, below s * 0.5–1.0 ms (pulse

repetition rates above m * 1–2 kHz), the positive and the negative polarity waves begin to

‘‘mirror image’’ each other, i.e. polarity dependence of the wave speed and peak field in the

wave front becomes weak. At these conditions, both peak field and electric potential at the

peak field location remains nearly constant along the entire discharge channel, in spite of

significant reduction of peak potential in the wave, by a factor of 2–3. Also, at these

conditions, both positive and negative polarity waves become diffuse and volume-filling,

although emission intensity near the walls of the discharge channel remains higher than

near the channel centerline, especially above *10 kHz.

Wave speed in nitrogen and air remains nearly constant for time delays between the

pulses above s * 1 ms (pulse repetition rate up to m * 1 kHz) and begins to decrease as

time delay between the pulses is reduced further, by up to 30–40 % at s = 25 ls

(m = 40 kHz). Peak electric field in the positive polarity wave front decreases significantly

as the pulse repetition rate is increased, both in nitrogen and in air. Peak electric field

reduction versus pulse repetition rate in negative polarity waves is not as pronounced,

especially in nitrogen. Both in nitrogen and in air, reducing time delay between the pulses

(increasing pulse repetition rate) results in significant reduction of discharge pulse energy

coupled to the plasma, by more than a factor of two.

Comparison of the experimental results in nitrogen with quasi-one-dimensional kinetic

modeling calculations at high pulse repetition rates, *5–40 kHz, shows good agreement,

both for positive and negative polarity waves. At lower pulse repetition rates, *100 Hz–

5 kHz, the model considerably overpredicts peak electric field in the wave front. Kinetic

modeling calculations show that peak electric field reduction as the pulse repetition rate is

increased is mainly due to higher residual electron density in the decaying plasma,

remaining from the previous discharge pulse. Reduction of wave speed and coupled energy

at high pulse repetition rates is primarily due to slower pulse voltage rise, limited by the

nanosecond pulse generator performance. The results of modeling calculations show that at

high pulse repetition rates most of the FIW discharge power is coupled to the plasma

behind the wave, at E/N * 200–300 Td. At these conditions, most of the input discharge

power in molecular gases is spent on electronic excitation and dissociation by electron

impact. This demonstrates significant potential of large volume, high pulse repetition rate

FIW discharges for novel plasma chemical applications.

Acknowledgments This work has been supported by the US Department of Energy Plasma ScienceCenter, by the Department of Physics and Astronomy of the Ruhr-University Bochum, and by the ResearchDepartment ‘‘Plasmas with Complex Interactions’’ of the Ruhr-University Bochum. We would also like tothank Svetalana Starikovskaia for numerous helpful discussions, and Bernd Becker, Frank Kremer, StefanWietholt, and Thomas Zierow for their help with the experimental apparatus.

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Documents

Development of Fast Ionization Wave Discharges at High