INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 34 (2001) 3456–3465
PII: S0022-3727(01)27166-6
Experimental study of discharge with
liquid non-metallic (tap-water)
electrodes in air at
atmospheric pressure
P Andre1 , Yu Barinov2 , G Faure1 , V Kaplan2 , A Lefort1 ,
S Shkol’nik2 and D Vacher1
1
Laboratoire Arc Electrique et Plasmas Thermiques CNRS UMR 6029, Univ. Blaise Pascal,
24, Av. des Landais, Clermont-Ferrand, France
2
A F Ioffe Phys. Techn. Inst. Rus. Acad. Sci., Politechnicheskaya 26, St Petersburg 194021,
Russia
Received 25 July 2001, in final form 15 October 2001
Published 5 December 2001
Online at stacks.iop.org/JPhysD/34/3456
Abstract
The discharge with liquid non-metallic electrodes (DLNME) was
investigated. The discharge burnt steadily with a DC power supply between
two streams of weakly conducting liquid (tap water) in open air at
atmospheric pressure. The metallic current leads were inserted into the
streams and were covered by a 5 mm thick water layer. The discharge burnt
in volumetric (diffuse) form with fairly high voltage (∼3 kV between leads)
and low current density (∼0.2–0.25 A cm−2 ). The plasma state in the
inter-electrode gap was studied by spectroscopy, microwave sounding and
electrical probe technique. The rotational and vibrational temperatures of
N2 electronically excited molecules were measured. The absolute radiation
values of different species were obtained as a function of position in the gap.
The electric field E and the concentration of charged particles were
obtained. The value of parameter E/Ng was estimated (Ng being the gas
concentration). The density of water vapour in the discharge column was
estimated. The results obtained show that DLNME generate molecular
plasma at high pressure but out of thermal equilibrium. The properties of
DLNME make it promising for various engineering applications, including
those in plasma chemistry.
1. Introduction
Electric discharges that use non-metallic liquids for electrodes,
e.g. aqueous solutions of various salts or bases, service or tap
water, possess unique properties. These are self-maintained
discharges, which can, under certain conditions with DC
supply, burn in volumetric (diffuse) form at high (atmospheric
and higher) pressures.
Unlike those of arc type, the discharges with liquid
non-metallic electrodes (DLNME) burn at a relatively
high voltage, U 103 V, and low current density, j ∼
10−1 –1 A cm−2 . Varying the electrolyte composition and
concentration provides a possibility of controlling the burning
0022-3727/01/243456+10$30.00
© 2001 IOP Publishing Ltd
mode over a wide range. Discharge burning duration, which
in the case of using metallic electrodes is limited by their
erosion, is actually unlimited for DLNME. Such a discharge
finds wide use in machining of metal surfaces, applying
coatings for various purposes, and so on [1]. However, the
above-listed properties of DLNME, as well as a number of
others (e.g. the presence in the discharge emission spectrum of
spectral lines of the elements, dissolved in a liquid electrode
[2], the highly non-equilibrium condition of the dischargegenerated plasma, including under the burning of the discharge
in the atmosphere of molecular gases at a high pressure [3])
make it promising also for various engineering applications in
plasma chemistry (in particular for waste gas flow treatment),
Printed in the UK
3456
Discharge with liquid non-metallic electrodes
spectral analytics [4], etc. One should note an advantageous
distinction of DLNME from a barrier discharge [5] that
recently aroused interest as a generator of high-pressure nonequilibrium plasma. To supply power for a barrier discharge,
one needs an AC source of frequency f ∼ 103 Hz and
higher, whereas the DLNME burn steadily under a DC power
supply as well. However, DLNME has not yet been studied
well. The main results relate to the discharge with one liquid
electrode—a cathode [6].
The present paper deals with the study of plasma in the
inter-electrode gap of the discharge burning in open air at
atmospheric pressure, which uses a weakly conducting liquid
(tap water) for both electrodes.
First, we will describe the experimental technique and
present the experimental results of spectroscopy, microwave
sounding and electrical probe diagnoses of the discharge
plasma. Second, we will estimate the characteristic lengths
and parameters of the discharge and discuss all these results.
Finally, we will present our conclusion.
2. Experimental technique and results
2.1. Experimental setup
The section view of the discharge assembly used in the
experiment is shown schematically in figure 1. The discharge
burns in the open air between two streams of tap water (water
electrodes), which flows along ceramic chutes making a small
angle with the vertical. The chute bottom is 15 mm wide, the
side walls are 5 mm high. Holes are opened opposite each
other in the chutes to pass metallic current leads of stainless
steel, 3 mm in diameter. The current leads are fixed with their
ends flushing with the water-covered bottom surface. The
water flow rate is stabilized and chosen so as to maintain a
high-voltage diffuse mode of a discharge burning at a minimal
flow rate. The experiments show that for the high-voltage
mode to be implemented it is necessary that thickness h of the
water layer, covering the metallic current leads, exceeds some
minimal value hmin . Otherwise, the water layer breaks down
and erosion-contracted attachments appear on the metallic
current leads. Discharge changes into an arc with low voltage
and high current density in a contracted channel, typical for an
arc. The inter-electrode gap (the air gap between two water
surfaces facing each other) could be as wide as L 10 mm.
To supply power to the discharge, a high-voltage source
is used supplying current I 2 A at voltage U0 10 kV
Figure 1. Section view of the discharge with liquid non-metallic
electrodes: 1—metallic current leads, 2—ceramics chutes,
3—tap-water streams, 4—moveable probe, 5—discharge plasma.
with stepwise-continuous adjustment. The source includes a
step-up transformer and a full-wave rectifier. A capacitance–
resistance filter is connected to the output to ensure a ripple
factor 1%. The positive terminal of the source is grounded.
The ballast resistor R0 is connected in series with the discharge
assembly to limit the circuit current in the case of water
electrode breakdown. Discharge ignition is performed by
interrupting the circuit after a short-time closing of the interelectrode gap with a special metallic conductor.
2.2. General characterization of the discharge
The experiments were carried out with current 40 I 100 mA and L ≈ 6 mm. The diffuse form of a discharge
was implemented by selecting voltage U0 , ballast resistor R0
and thickness h of the water layer, covering metallic current
leads. With U0 ≈ 4 kV, R0 = 10 k, the minimal thickness
of the water layer to protect against a breakdown amounted to
hmin ≈ 4 mm. Then, the water flow speed was estimated using
the results of flow rate measurements as ≈1 m s−1 . Due to a
rather high flow rate, the heating up of water during flowing
through the zone of the current passage was rather slight (for
details see section 3).
Under these conditions, the discharge burning voltage,
including the voltage drop across water electrodes, i.e. the
voltage between metallic current leads, amounted to U ≈ 3 kV
and depended very little on the current. The voltage drop
U consisted of that inside water electrodes U1 and that
in the plasma across the inter-electrode gap U2 . Quantity
U1 was measured in independent experiments without a
discharge. Thin disks were made of stainless steel, their
diameter equalling that of anode and cathode attachments of
the discharge to the surface of water electrodes. The diameters
of attachments were found by photographing the discharge.
The sizes of the cathode and anode attachments were found
to be close to one another. Attachment diameter d grew with
increased current. So the dependence of current density on
current is a weak one. With I ≈ 60–70 mA, a typical value
is d ≈ 0.6–0.7 cm. The disks were brought into contact
with the corresponding water electrodes, and the voltage drops
between current leads and the disks were measured in the
range of currents under study. As an example, the scheme
of measurement of the voltage drops inside the water cathode
is shown in figure 2. Experiments have shown that about a
half of the voltage U drops across the water electrodes. For
instance, with close values of the thickness of the water layer
to cover anode and cathode current leads, h ≈ 5 mm and
I ≈ 65 mA, the value U1 was ≈1.6 kV, with an approximately
Figure 2. Scheme of measurement of the voltage drops inside water
cathode: 1—metallic current leads, 2—ceramics chutes,
3—tap-water streams, 4—stainless steel disk.
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P Andre et al
equal voltage drop in each electrode. The value of U1 obtained
from these measurements is in accordance with the results of
inter-electrode gap potential distribution measurements, which
were done by electrical probe (see below).
The estimation of water electrode conductivity by the
results of U1 measurements yields σ ≈ 10−4 cm−1 , which is
about an order of magnitude higher than that of distilled water
[7]. This result indicates that there are no apparent distinctions
in the mechanism of current transfer inside the water electrodes
(partial discharges, etc), since the differences from the data of
[7] reduce to within what could be expected when tap water
without additional filtration is used.
The discharge under study was noisy. In the frequency
range f < 107 Hz, which was limited by the response time
of metering circuit, an amplitude of the noise high-frequency
component was well below the discharge voltage. We also observed low-frequency voltage oscillations with an amplitude up
to several dozen volts, the basic frequency, e.g. at L = 6 mm,
used in our measurements amounting to f ≈ 60 Hz.
The procedure of probe measurements is described later.
One should note here only that the measurements with the help
of auxiliary probes, located one above another at the centre of
the inter-electrode gap at the periphery of the current channel
(one under and the other below the channel), made it possible
to determine the cause of low-frequency voltage oscillations.
In the process of burning, the current channel appears to ‘float
up’, which causes it to lengthen a little and, accordingly, causes
the voltage to rise, and then return to the initial position. The
vertical displacement of the channel at the centre of the interelectrode gap amounts to <0.5 mm.
2.3. Spectroscopic measurements
The block diagram of spectroscopic measurements is shown
in figure 3. A quartz condenser was used to produce a reduced
image of the discharge at the monochromator (1.3 nm mm−1 )
entrance slit. The scanning of the image across the slit was
carried out using a plain-parallel quartz plate. A multichannel
optical analyser with linear photodetector was used to record
the radiation. The linear photodetector could record a spectrum
region ≈22 nm with spectral resolution (FWHM) ≈0.15 nm.
When measuring spectra, an auxiliary slit crossed with the
entrance slit was used to extract the near-axial region of the
discharge image. The spatial resolution along the discharge
axis was ≈0.5 mm. To measure the radial distribution of the
Figure 3. Block diagram of spectroscopic measurements:
1—discharge channel cross section, 2—mirror, 3—diaphragm,
4—lens (quartz), 5—plain-parallel plate (quartz),
6—monochromator, 7—multichannel optical analyser with linear
photodetector.
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radiation intensity, the linear photodetector was turned 90◦ and
the exit slit was set in front of it. Calibration of the apparatus
sensitivity used a band lamp with an Uviol glass window.
Each measurement was repeated ten times. The results were
summed up by a computer and cleaned of noise by cutting off
the high frequencies in the Fourier transform of the spectrum
and subsequent regularization procedure [8].
The discharge radiation spectrum shows emission lines of
oxygen and hydrogen atoms. Hydrogen radiation (Hα and Hβ )
was only observed near the cathode (z 2 mm, where z is the
distance from cathode). In the violet and ultraviolet spectral
regions, molecular bands of N2 , OH and N+2 were observed.
The radiation of N+2 was observed only near the electrodes,
with the intensity of corresponding bands near the cathode
being several times higher than that near the anode.
The radiation of the second positive system of the
N2 molecule in the spectral interval 363–385 nm (sequence
v = −2) was used to find the rotational (Trot ) and the
vibrational (Tvib ) temperatures of the molecules. The structure
of these spectra (the overlapping branches of the triplet
structure) and the resolution of the experimental spectra
cannot allow the use of the Boltzmann plot. Therefore,
we calculate the second positive system of N2 , especially
the sequence v = −2, and determine the rotational and
vibrational temperatures of C3 u state of N2 by comparison
between experimental and calculated spectra. The technique
of calculation and comparison to the experiments is described
in [9]. Figure 4(a) shows an example of a comparison of an
experimental spectrum with the calculated one after fitting the
calculation by way of variation of rotational and vibrational
temperatures of molecules. We would like to note that the
results of fitting are quite satisfactory for all vibrational–
rotational structures, which we registered in our experiment,
including those of high vibrational levels. The dependence of
relative populations of four vibrational levels (ν = 0, 1, 2, 3),
which was derived from experimental spectra, on the level
energy is shown in figure 4(b). It can be seen from this figure
that vibrational distribution of C3 u state of N2 in discharge
plasma is close to the Boltzmann distribution.
Figure 5 shows the axial distribution of the observed Tvib
and Trot . The vibrational temperature of C3 u state rises
up to 5000 K. (This value is higher than that in [9] because
incorrect band strength data were used. The available values
are given in table 1 for the sequence ν = −2.) We assume
that the rotational temperature is equal to the gas temperature
Tg . The gas in the middle region of the inter-electrode gap is
heated by the discharge up to Tg ≈ 2000 K. The maximum
of the curve is somewhat shifted to the cathode. In a close
neighbourhood of water electrodes, at a distance of the order
of the free path length, the gas temperature differs, but little,
from that of the water surface (∼3×102 K). This explains the
observed decrease of the gas temperature when approaching
the electrodes. The results given below enable us to estimate
the current density and potential distribution, hence the specific
energy input along the discharge axis. This distribution
quantitatively agrees with the temperature distribution shown
in figure 5.
Figure 6 shows examples of the measurement results
for radial distributions of radiation intensity in the band of
molecule N2 and radical OH, subjected to the Abel inversion.
Discharge with liquid non-metallic electrodes
Table 1. Band strengths of the second positive system of N2 , in D2
for the sequence (v = −2). (1D = 1 Debye = 3.33564
×10−30 C m.)
Sv v (D2 )
(0–2)
3.7398
(1–3)
4.9857
(2–4)
3.9456
(3–5)
2.2389
(4–6)
0.9543
Figure 6. Band-head intensities radial distribution at I ≈ 65 mA,
z ≈ 2 mm.
Figure 4. A comparison between experimental and calculated
spectra. (a) I—experimental spectrum (I ≈ 65 mA, z ≈ 1.3 mm),
II—result of calculated spectrum fitting (FWHM = 0.15 nm,
Trot = 1800 K,Tvib = 3900 K). (b) Relative population of vibrational
levels (Nν /Nν=0 ) of C3 u state of N2 as a function of levels energy
(G). 1, 2 and 3 are obtained from experimental spectra at
z ≈ 1.3 mm, z ≈ 3.0 mm and z ≈ 5.0 mm, respectively. 1 , 2 and 3
are obtained from calculations after fitting to experiment.
Figure 5. Axial distribution of the rotational (gas) and vibrational
temperatures at I = 65 mA, L = 6 mm obtained by comparison of
experimental with calculated spectra of the second positive system
of N2 , sequence ν = −2: 1—water cathode, 2—water anode.
The intensities are seen to attain the maximum values at the
discharge axis. The width (full width at half maximum) of
radiation intensity distribution for OH is far greater than for N2 .
The reason for this is a considerable difference in excitation
energies for A2 + state of radical OH (≈4 eV) and C3 u
Figure 7. The dependence of on z at I ≈ 65 mA.
state of N2 molecule (≈11 eV), where the transitions originate,
producing the radiation recorded in the present experiment.
Figure 7 shows the dependence of on the distance from
the cathode, which indicates that, with the distance from the
cathode growing, the discharge first narrows a little and then
expands again when approaching the anode. The position of
the rotational (gas) temperature maximum coincides with that
of narrowing (z ∼ 2 mm). increases with current growth
approximately linearly in investigated current interval.
Figures 8 and 9 show the axial distributions of radiation
intensity for an oxygen atom (the sum of intensities of lines
with λ ≈ 777.2, 777.4 and 777.5 nm), and for bands of OH and
N2 , integrated over some spectral intervals: 306.4–307.0 nm
and 376–380 nm correspondingly. The absolute values of
radiation intensities were measured. We did not take into
account a possible self-absorption of OH radiation. It is
difficult at the present time to estimate self-absorption due to
poor knowledge of OH concentration in the discharge. The
intensity of hydrogen atom radiation (Hα ) near the cathode
amounts to ∼10−6 W cm−3 , i.e. of the same order of magnitude
as that of the most sensitive lines of atomic oxygen in this
region. But toward the anode, intensity of Hα decreases sharply
and at z ≈ 2 mm can be evaluated as ∼2×10−8 W cm−3 . This
is the lowest signal level to pick out from the noise under
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P Andre et al
Figure 8. Oxygen atomic lines (λ = 777.2, 777.4 and 777.5 nm)
summarized and radical OH band integrated (306.4–307 nm)
intensities axial distribution.
concentration as ne ∼ 1012 cm−3 in our estimates. In a
plasma with such parameters, the frequency ν of collisions
of electrons with gas molecules far exceeds that of electron–
electron collisions and amounts to ν ∼ 102 GHz, while the
plasma frequency is f0 ∼ 10 GHz.
The characteristic dimension of the plasma formation is
∼5 mm. In order to ensure spatial resolution and meet the
condition of applicability of open space technique [10], the
plasma must be sounded with radiation of wavelength λmicro ≈
10−1 cm or shorter. In this case, the frequency of MW probe
radiation F will be almost two orders of magnitude higher than
f0 . With this frequency ratio, the absorption of MW radiation
in the plasma will be extremely weak. The attenuation of MW
radiation caused by this absorption is described by
P
≈ 1 − 2βX,
P0
(1)
where P and P0 are the powers of the accepted MW radiation
X
with and without the plasma, respectively, βX = 0 β dx,
X being the distance which MW travels in the plasma, and β
is the attenuation constant defined by [10]
2
2 1/2
ω02
ω02
1 ω2
ν2
2
+ 2
1− 2
β =
2 c2
ω + ν2
ω
ω2 + ν 2
ω2
− 1− 2 0 2
,
(2)
ω +ν
Figure 9. N2 band (376–380 nm) integrated intensity axial
distribution (second positive system, v = −2).
our experimental conditions. The most intense among band
heads of molecular ion N+2 is the one with λ = 391.4 nm. Its
intensity, integrated over interval 390.9–391.4 nm, amounts to
∼10−5 W cm−3 in cathode plasma.
2.4. Measurements of microwave radiation absorption
Microwave (MW) sounding is a non-contact diagnostic
technique, which is an advantage over the electric probes
technique. Still, MW sounding fails to ensure locality
and to allow determining the plasma potential, which
requires using electric probes. Under the conditions of the
present experiments, as is shown subsequently, the electric
probe measurements are difficult to interpret. Therefore,
a comparison of the results of contact and non-contact
techniques is advisable, although MW sounding of the
discharge under study also runs into certain difficulties (high
gas pressure, relatively low electron concentration, small size
and spatial non-homogeneity of plasma).
Let us examine the experimental conditions and carry
out some estimates that were needed to select the sounding
radiation frequency and to determine the absorption expected.
The gas temperature in the middle region of the inter-electrode
gap Tg ≈ 1500–2000 K, so the molecules concentration at
the atmospheric pressure Ng ≈ (4–5)×1018 cm−3 . The
characteristic energy, or ‘temperature’, of electrons was
estimated in [3] as Te ≈ 4 × 103 K. We take the electron
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where ω = 2π F , ω0 = 2πf0 = (4π ne e2 /me )1/2 , me is
electron mass, e is charge and c is light velocity.
The coefficient of absorption of λmicro ≈ 10−1 cm MW
radiation, estimated using formulas (1) and (2), is so small for
our conditions 2βX 10−3 that the measurements become
technically difficult. The design of the discharge unit makes
it almost impossible to use cavity methods, which can give
high sensitivity. Thus, it is advisable to use longer-wavelength
MW radiation λmicro ≈ 1 cm. In this case, the attenuation of
MW radiation is substantially greater, being a few per cent.
For MW power, with this wavelength, to be localized in the
discharge plasma with a characteristic dimension of about
5 mm, a two-conductor transmission line can be used.
A waveguide channel, consisting of fixed and moving
parts, was used. The moving part contained a two-conductor
transmission line. The line was formed by two parallel copper
wires, which were connected electrically to the pointed ends
of the matching joints of the waveguide channel. The signal
from the detector, which is proportional to the MW radiation
power transmitted by the channel, was recorded using a storage
oscilloscope (for details of experimental technique see [11]).
The measurements were made as follows. After the discharge
had been ignited, the two-conductor line was inserted into
the discharge gap midway between the electrodes so that the
discharge channel was included between the wires (figure 10).
Two series of measurements were made at F = 29.6
and 35.2 GHz. The results were then averaged in each series.
Measurements at I = 60 mA yielded the following values
of the absorption coefficient of the MW probe radiation:
2βX = 0.056 (mean square deviation (msd) = 0.004)
at F = 29.6 GHz and 2βX = 0.034 (msd = 0.003) at
F = 35.2 GHz.
Discharge with liquid non-metallic electrodes
Figure 10. Section view of the plasma channel with two-conductor
transmission line: 1—two-conductor transmission line, 2—area of
microwave power localization.
Figure 11. Block diagram of probe measurements circuit:
1—moveable probe, 2—electronic switch, 3—probe power supply
(−2.5–0) kV, 4—high-voltage galvanic isolation device, 5—digital
voltmeter, 6—multichannel ADC.
2.5. Electrical probe measurements
The measurements were performed using a cylindrical probe
of diameter 0.3 mm and length 1.5 mm and a flat probe of size
0.33 × 1.2 mm2 . The non-working surfaces of the probes were
insulated with BeO ceramics. The working surface of the flat
probe was oriented perpendicular to the discharge axis and
faced both the cathode and anode. To avoid considerable
heating and oxidation, the probe was introduced into the
discharge for a short time. The duration of the probe presence
in the plasma was restricted to the time t 0.5 s. The
probe was introduced into the discharge from above (figure 1).
A short-time immersion of the probe into the plasma to a
controllable depth was performed using an electromagnet or
manually. The probe working surface was cleaned periodically
to avoid distortion of the measurement results [12] (for details,
see [13]).
Figure 11 shows the block diagram of probe measurements. To supply the probe circuit with power, a stabilized
DC source was used, which provided the possibility of continuous adjustment of output voltage between 0 and −2.5 kV.
Resistors R1, R2 and R3 = 150 M (as well as limiting
resistor R4 = 100 k) were connected in series with the
probe. Rating values of R1 and R2 were chosen depending
on the range of currents, which the measurements were to be
made in. The performance of probe measurements in the conditions described is complicated by the necessity to measure
small currents (down to fractions of microampere) at a high
probe voltage (1 kV and higher), and also by repulsion of the
discharge from the probe and the above-said discharge ‘floatup’. Therefore, a device was produced to measure the probe
Figure 12. Distribution of the floating probe potential (plasma
potential) in the inter-electrode gap at I ≈ 65 mA, U ≈ 2.95 kV,
L ≈ 6 mm (cylindrical probe): 1—water cathode, 2—water anode.
current, which ensured the galvanic isolation of measuring circuits from the recording instruments. The measurements of the
probe current and its floating potential were made at close intervals in time. This was accomplished by switching the resistor
R3 (and also R2), using an electronic switch. The switch was
controlled by a periodic signal of rectangular shape (meander)
with period ≈1 ms. The output of high-voltage galvanic isolation device, along with signals proportional to the voltage of
probe circuit supply and that across discharge, was digitized
and entered into a computer using a multi-channel 11-bit ADC.
The record duration was chosen to be about 0.5 s. The measurements were repeated many times. During this process, it
was visually checked whether the probe was in the discharge
channel. Then the supply voltage of the probe circuit was
changed, and a new series of measurements was launched. In
actual fact, the measurements were held at a distance <1 mm
from the discharge axis as, with the probe at the axis, the discharge was repelled from the probe.
Subsequent to the measurements, a special software
program was used to select from the whole data array those
consecutive values (at least two in succession) of the probe
current and its floating potential which differed by less than
10% and were in correspondence to close values of the
discharge voltage U ±6 V. The data thus selected were
subjected to statistical processing and averaging.
The probe measurements were performed at I =
65–70 mA and L ≈ 6 mm. Figure 12 shows the results of
measurements of the floating probe potential Uf . Solid circles
marking those obtained with the probe submerged in the water
near the surface of the water electrodes. Note that the results
of these measurements are not far from those described for
voltage drop in water when disk electrodes were used.
As seen from figure 12, the discharge can be distinctly separated into near-electrode regions and a discharge column with
roughly constant strength of the electric field. It is the discharge
column that the present paper pays most attention to. The floating probe potential in the column is shown below to be identifiable with plasma potential within an accuracy of ∼kTe /e.
Figure 13 shows current–voltage characteristics (CVC) of
a flat probe near the cathode and anode ends of the column
(potential UP was counted from that of the floating probe).
The appearance of the probe characteristic makes it possible
to conclude that most of the carriers of the electric current in
the discharge under study are electrons. A distinctive feature
of CVC is the linear dependence of the current on the probe
potential on a transition branch of CVC at UP 10 V. The
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P Andre et al
Figure 13. Probe characteristics at I ≈ 65 mA; L ≈ 6 mm (flat
probe facing the cathode): 1—z ≈ 2.5 mm, 2—z ≈ 4.5 mm.
Figure 14. Ion branches of probe characteristics at I ≈ 65 mA;
L ≈ 6 mm (flat probe facing the cathode): 1—z ≈ 2.5 mm,
2—z ≈ 4.5 mm.
linear plot on the probe CVC was observed previously in
different experiments in slightly ionized plasma at atmospheric
pressure [14–16].
The measurement results for the ion branches of CVC with
increased rating values of R1 and R2 are given in figure 14.
From the figures both ion and electron currents to the probe
are seen to depend on the position of the probe in the column.
When the probe is located at the cathode end of the column,
no dependence on the probe orientation is observed within
the spread in values. At the anode end of the column, no
measurements with a probe facing the anode seem advisable,
as the anode–probe spacing is close to the probe size and the
probe perturbs the plasma up to the very electrode.
3. Results of treatment and discussion
Spectroscopic measurements provide the possibility of
determining the gas temperature in the discharge. Combining
these results with electric probe measurements will allow us
to obtain the value of such significant parameters as E/Ng
(see below). From these measurements, one can also draw
another substantial conclusion: the plasma in discharge is
out of thermal equilibrium. As a matter of fact, rotational
and vibrational temperatures differ significantly. Electron
characteristic energy or ‘temperature’, by our preliminary
estimation [3], is also significantly higher than gas temperature.
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Now let us discuss and treat the results of sounding of the
discharge column by MW radiation. In order to determine the
average electron concentration using formulas (1) and (2), we
need to know ν and the distance X which MW travels in plasma.
In our experiments this distance is about d—the diameter of
the discharge. Calculations using ν in the range 100 < ν <
200 GHz, which corresponds to the dry air at temperature
2000 K > Tg > 1000 K, show that the indeterminacy of ν in
this range gives an error of at most 30% in the determination
of ne . The inaccuracy in estimating d from the results of
spectroscopic measurements gives approximately the same
contribution to the error. Taking into account these sources of
error, the average value of ne in a discharge with I = 60 mA
can be estimated as 4 × 1011 < ne < 7 × 1011 cm−3 . These
data will be corrected below taking into account air humidity.
Let us now consider the electric probe measurements.
The data in figure 12 enable us to estimate the electric
field in the column as Ec ≈ 7–8 × 102 V cm−1 . Taking
gas temperature distribution (figure 5) into account, one can
estimate parameter E/Ng changes from ≈20 Td in the cathode
side of the column to ≈15 Td in the anode side. Note that
both visual observations and photographs of the discharge and
the results of spectroscopic studies indicate that the column is
not quite uniform: it somewhat narrows at the joint with the
cathode region and expands towards the anode.
The near-cathode region is approximately 1.5–2 mm in
length and the voltage drop in it is of about 600 V. The nearanode region is approximately 1–1.5 mm in length and the
voltage drop in it is of about 400 V. The mean values of
the electric field strength in near-electrode regions are close
to one another (∼3–4 × 103 V cm−1 ). The mean value of
parameter E/Ng in the near-cathode region is approximately
1.5 times higher than that in the near-anode one due to higher
gas temperature (figure 5) and may be estimated as E/Ng ≈
60–80 Td.
To treat the probe characteristic, it is necessary to
consider the conditions of the current collection by the probe.
Let us remember and summarize what is known about the
discharge plasma parameters due to spectroscopic and MW
measurements. The gas temperature is Tgc ≈ 2000 K in the
cathode end of the column and Tga ≈ 1400 K in the anode one;
the molecular concentration is Ngc ≈ 3.7 × 1018 cm−3 and
Nga ≈ 5.3 × 1018 cm−3 , respectively. The average electron
concentration in the column is ne ≈ 5 × 1011 cm−3 . In
order to carry out estimations near the axis, we assumed ne =
1012 cm−3 . The characteristic electron energy or ‘temperature’
Te ≈ 4 × 103 K and varies slightly along the column. The
majority carrier of the positive charge in the plasma is NO+ .
The concentration of negative ions is small against that of
electrons [3]. So, one can write ne ≈ ni = n, where ni and n
are the positive ion or charged particle concentrations.
An important parameter is the water vapour concentration
in the discharge column, because the electron drift velocity
and characteristic energy in the water vapour and in the air at
E/Ng < 20 Td differ by more than an order of magnitude
[17]. Depending on the air temperature and humidity, the
atmosphere can hold up to a few per cent of the water
vapour. The sputtering of the water cathode can increase
humidity but not substantially, because of the relatively low
ion current density (∼10−1 A cm−2 ) and ion energy (∼102 eV).
Discharge with liquid non-metallic electrodes
The humidity can also be increased by heating up the water
flowing through the zone of the current passage between the
plasma and a metallic current lead.
The water is heated up by Joule (volumetric) heat
release and the heat flux to the surface through the discharge
attachment. In view of the water flow rate ≈102 cm s−1 and
the typical size of the electrode attachment d ≈ 0.7 cm, the
action time of the heat sources is evaluated at t0 ≈ 7 × 10−3 s.
Joule heating during this time was estimated to be only a
few degrees. To estimate the warm-up of the surface, let
us consider the cathode attachment with the highest energy
density. Assume all energy W that is released in the cathode
region of the plasma, where ≈600 V drops (figure 12) at
current density ≈0.20–0.25 A cm−2 , to be brought to the water
electrode, and leave out the cooling of the water surface. Since
l ∼ (at0 )1/2 ≈ 3 × 10−3 cm d (here a = //(Cp ρ),
where / is thermal conductivity, Cp is specific heat, ρ is
water density), the warm-up of the surface is estimated using
expression [18]: Ts = T0 + (2W//)(at0 /π)1/2 , where T0
is the water temperature in the flow prior to the discharge
action. At T0 = 285–290 K, the result is Ts ≈ 320–330 K.
This is the maximum Ts attainable by the water surface at the
exit from the zone of the current passage. The temperature
is in correspondence with saturated water vapour pressure
pw 2 × 10−1 atm [7]. The discharge produces fine drops,
which are warmed up in the plasma and can enlarge the
water vapour concentration (this is yet to be studied). So,
the water vapour concentration in discharge may substantially
exceed the value corresponding to the humidity of the
environment.
At first we will estimate the characteristic lengths of the
probe region for the dry air and then take into consideration
air humidity. At the above values of concentration and
temperature, Debye length lD ≈ 3 × 10−4 cm. The gas
temperature near the probe is close to that at its surface,
Tg ≈ 500 K. At this temperature the ion mean free path is
λi ∼ 10−5 cm and the electron mean free path is λe ∼ 10−4 cm.
The relaxation length of electron energy λε = δ −1/2 λe ∼
10−3 cm (δ is the parameter which characterizes the energy
exchange efficiency). So, we obtain the following relation:
λε Ec e ∼ 1 eV > kTe ∼ 0.35 eV. However, allowing for
relatively high humidity causes a change of the λe estimate
and the reversal of the inequality sign. Therefore, the electron
distribution function can be considered to be not too different
from the Maxwell distribution. The main recombination
mechanism under these conditions is the dissociative one. The
recombination length of NO+ ions is Lr = [Da /(αn)]1/2 ≈
4 × 10−3 cm (here Da = Di (1 + Te /Ti ) is the ambipolar
diffusion, where Di is the diffusion and α is the recombination
coefficient). Values of Di and α are taken from [19].
The results of the estimation show the following
inequalities to hold: λi lD ∼ λe λε ∼ Lr b
(here b is the characteristic size of the probe). Under these
conditions, the main contribution to the total probe–plasma
potential difference on the transition branch of CVC is in the
region of size ∼b, where the spreading of the probe current
takes place. In this region the plasma is in the state of ionization
equilibrium. The potential of the floating probe coincides with
that of the plasma within accuracy of ∼kTe /e. The current to
the probe is described by the following expression [14]:
IP = 4πχσ∞ UP ,
(3)
where χ is the probe capacitance, σ∞ is the unperturbed plasma
conductance.
The ion current to the flat probe is described by [20]
1/2
(1 + µi /µe )S0 ,
IP = 3−1/2 en3/2
∞ (Da α)
(4)
where n∞ is the unperturbed concentration of charged particles
in plasma, µi , µe are the ion and electron mobilities, and S0 is
the surface of the space charge layer.
Theories [14, 20] are developed under the assumption of
the external field being small compared to the ambipolar one.
The opposite case was treated in [21] and it was concluded that
the probe CVC has no linear section. The dependence of the
current on the probe potential is controlled by the probe shape.
For instance, the current to a spherical probe grows as square
of the increasing potential. The estimations of the ambipolar
field Ea under the conditions of the present experiment yield
Ea ∼ 103 Vcm−1 ∼ Ec . The suitability of relevant theories
at Ea ∼ Ec will be seen from a comparison with the results
of non-contact measurements. The applicability of equation
(3) also calls for the electric field in the unperturbed plasma
to be small compared to that produced by the probe in the
region of the current spreading. The estimates show the field
of the probe at UP 20 V to exceed that in the unperturbed
plasma.
Note also that equation (4) gives the value of the current to
the probe, provided that the density and temperature of neutral
particles in the probe region are constant. In our experiments,
the temperature of the probe is below that of the gas and there
are temperature and density gradients in the probe region. This
can be taken into account in the case of a flat probe, as shown
in [22], by way of introducing a correction to the probe current
of the order of the ratio of the probe and gas temperatures.
The charged particle concentration n was found by the
ion branch of the CVC in accordance with equation (4) and
corrected by taking into account the difference in probe and
gas temperatures. The ion current was found by extrapolation
to UP ≈ 0 (figure 14). The following estimates were found for
the concentration: nc ≈ 1.5–2.0 × 1012 cm−3 at the cathode
end and na ≈ 0.9–1.2 × 1012 cm−3 at the anode end of the
column.
The plasma conductance was found from the linear plot of
the transition branch of the CVC with the help of equation (3).
It was estimated to be σ ≈ 2–3 × 10−4 cm−1 at the cathode
end and σ ∼ 1 × 10−4 cm−1 at the anode end of the column.
The probe capacitance was determined as that of a one-sided
flat disk of the same area (χ ≈ 10−2 cm). Equation (3)
was also derived on the assumption that in the major part
of the probe current spreading region, the gas temperature is
constant and equal to that of unperturbed plasma. So, the
conductance values obtained in this way are somewhat lower
than the conductance of unperturbed plasma.
The estimation of charged particle concentration by the
results of conductance measurements and its comparison to the
values obtained by the ion current makes it possible to estimate
the concentration of water vapour in the column. Indeed, the
difference in the ion mobility in the dry air and in presence of
water vapour is not so large as that in the mobility of electrons.
Besides, the charged particle concentration dependence on ion
diffusion coefficient is found, through equation (4), to be weak
(cubic root). At the cathode end of the column, a satisfactory
3463
P Andre et al
agreement between the results of the estimation of charged
particle concentration by ion current and by conductance is
obtained, if the discharge is assumed to contain ∼30–40% of
water vapour. The data [23] were used for electron mobility
estimation. The mobility of electrons at such a concentration of
water vapour is controlled mostly by the latter. In water vapour,
the mobility of electrons is constant with satisfactory accuracy,
up to E/Ng ∼ 30 Td [17]. This justifies the use of equation (3)
derived under the assumption about independence of transport
coefficients on the electric field, and also the use of relationship
ne = σ/eµe to estimate the electron concentration. Note
that these estimations of the water vapour concentration are
rough estimations due to insufficient data on electrons and ions
transport coefficients at relatively high temperatures in the air–
water vapour mixture and also due to significant uncertainty in
the experimental results. This seems to be an overestimation.
It is of great interest to estimate the water vapour density in
another way and more correctly.
If we take into account the presence of ≈30% water
vapour, the estimation of the average electron concentration
obtained from the probing MW radiation absorption (see
section 2.4) will grow about twofold. Thus the agreement
with the results of probe measurements will become
satisfactory.
4. Conclusions
The investigations carried out show that DC discharge in
open air between two tap-water streams can burn steadily
in volumetric (diffuse) form at high voltage and low current
density (∼2 × 10−1 A cm−2 ).
The gas in the inter-electrode gap is heated up to the
temperature ≈1500–2000 K.
The discharge can be distinctly separated into three
regions: the near-cathode and near-anode regions and the
column.
The discharge column is not quite uniform. It somewhat
narrows at the joint with the near-cathode region and expands
toward the anode. The column electric field is approximately
constant Ec ≈ 7–8 × 102 V cm−1 , but the gas temperature
falls down from Tgc ≈ 2000 K in the cathode side up to
Tga ≈ 1400 K in the anode side. So, the parameter E/Ng
changes from ≈20 to ≈15 Td. The mean value of the charged
particle concentration n is about 1012 cm−3 . The concentration
decreases at the anode end of the column 1.5–2 times as much
as against the cathode one. The water vapour concentration
considerably exceeds that in the surrounding atmosphere.
The near-electrodes regions are greatly non-uniform. The
mean value of E/Ng was estimated to be of the order of 102 Td.
The emission of discharge is mainly in the violet and
ultraviolet range. Molecular bands of N2 , OH and N+2 were
observed. The emission of oxygen and hydrogen atoms is
also registered. Emission intensities of all species in the nearcathode region were much higher than in the column and in the
near-anode region, except N2 . Emission of nitrogen molecules
in the near-cathode and the near-anode regions is of the same
order of magnitude. The sensitivity of our experimental
equipment provides possibility of registering hydrogen atom
emission in the near-cathode region only. The absolute values
of emission intensities were measured.
3464
The results obtained show that the discharge under study
generates the plasma out of thermal equilibrium.
Acknowledgment
We express our gratitude to Prof. F G Baksht for his attention
to our work and for many productive discussions that we had
with him.
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