22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Kinetic processes initiated by pulsed nanosecond discharge in ambient air
N. Popov
Skobeltsyn Institute of Nuclear Physics, Moscow State University, Russia
Abstract: The results of a numerical study of kinetic processes initiated by pulsed
nanosecond discharge in high-pressure air are presented. The calculations of temporal
dynamics of electron concentration, density of atomic oxygen, vibrational distribution
function of nitrogen molecules, and gas temperature agree with the experimental data. It is
shown that the main gas heating and O atoms production occurs in the post-discharge stage
and is associated with the relaxation of non-equilibrium electronic excitation of atoms and
molecules.
Keywords: nanosecond discharge, fast gas heating, O atom production
1. Introduction
Recent increased interest in studying of powerful pulsed
nanosecond discharges arises from their application for
ignition of combustible mixtures [1], for solving plasmarelated problems in aerodynamics, etc. Gas-discharge
plasma affects the ignition via the production of
chemically active particles and gas heating. The energy
efficiency of chemically active particles production and
the fraction of discharge energy that goes into the fast gas
heating are higher at high values of the reduced electric
field E/N [1, 2]. An example of such a system with E/N
of about 200 - 400 Td is pulsed nanosecond discharges.
An optimal use of nanosecond discharges requires a
detailed investigation of the plasma-chemical processes
which are initiated by the discharge and which lead, in
particular, to efficient production of chemically active
particles and to fast gas heating.
Lo et al. [3] present the experimental results on the
temporal evolution of gas heating, O(3P) atoms number
density and vibrational temperature T 01 N2 of nitrogen
molecules in ambient air excited by pulsed nanosecond
discharge, τ imp ≈ 25 ns. The electrode configuration had a
point-to-plane geometry, with the interelectrode distance
of 6.5 mm. The positive high voltage pulse of 25 kV was
applied to the electrode tip at the repetition rate of 10 Hz.
Total input energy was about 20 mJ. The vibrational
energy distribution of molecules and gas heating during
the post-discharge phase was investigated by spontaneous
Raman scattering. The rotational temperature at the
discharge axis increased by ∆T = 550 K during t = 150 ns
after the current pulse, and the vibrational temperature
T 01 N2 reached 4000 K.
Montello et al. [4] present CARS data on rotational
temperature and vibrational distribution function in pulsed
nanosecond discharge (τ imp ≈ 100 ns) in nitrogen and dry
air at P = 100 Torr and ambient temperature, T 0 = 300 K.
The experiments were performed in a single filament
discharge with a pair of spherical copper electrodes of
7.5 mm in diameter. The electrode gap was equal to
1 cm, and the voltage amplitude was U max = 8 kV.
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Coherent Anti-Stokes Raman Spectroscopy (CARS) was
used to study N 2 (v) vibrational distribution function and
rotational temperature. Under the action of discharge
pulse the temperature increased by ∆T = 150 - 170 К
during t = 200 - 300 ns after the current pulse, and the
vibrational temperature T 01 N2 exceeded 1500 K.
The objective of the present paper is to describe the
parameters of a pulsed nanosecond discharge in air at
P = 100 - 760 Torr and to determine the main mechanisms
for the production and losses of atomic oxygen and of the
fast gas heating mechanism in such a discharge. The
results are compared with the experimental data [3, 4].
2. Model description
The problem of the evolution of a discharge channel
parameters was considered in one-dimensional axisymmetric formulation. This approach seems to be justified
because, under the conditions of [3, 4], the radial
gradients of the discharge parameters exceed the axial
gradients - in the direction between the electrodes.
Experimentally obtained dependence of conduction
current versus time [3, 4] was taken as initial data for the
numerical modelling. The initial radius R 0 of plasma
channel was equal to the measured value. For a given
discharge current I, the instantaneous electric field was
found from the equation
∞
E (τ ) = I (τ ) 2πe ∫ N e ( r ) m ( r ) rdr
0
where N e (r) is the radial electron density profile and m(r)
is the radial profile of the electron mobility, which
depends on E/N.
The kinetic model includes the processes responsible
for variation in the densities of the main charged and
neutral components of a nitrogen-oxygen mixture, as well
as the vibrational excitation of mixture molecules and gas
heating. Ten positive and negative ions were taken into
account: O 2 +, O 4 +, O 2 +⋅N 2 , N 2 +, N 4 +, NO+, O-, O 2 -, O 3 -,
and O 4 -. The set of reactions was based on the set of
1
3. Simulation results
Fig. 1 shows the temporal evolution of the dis-charge
current measured in [3] and the approximation I(t) used in
the numerical calculations. These results were used as a
basis for computing radial profiles of all the main neutral
and charged particles at different time instants. Fig. 1
also displays temporal evolutions of the specific energy
release at the axis of the plasma channel. In the discharge
under investigation, the energy is mainly deposited at
electric fields E/N = 80 - 120 Td, and the maximum
energy input amounts to W = 0.75 eV/mol. The
calculation result of a total input energy, 23 mJ, is close to
experimentally measured value of 20 mJ [3].
70
0,75
W
50
0,60
40
0,45
30
0,30
20
10
0,15
0
0,00
0
5
10
15
20
25
W, eV / mol.
Current, A
60
30
Time, ns
Fig. 1. Time evolution of the current pulse (experimental
data and approximation used in numerical simulations)
and the energy input at the discharge axis under the
conditions of [3]: P = 760 Torr, T 0 = 300 K.
The rate constants of the excitation of N 2 (X1Σ,v = 1 - 8)
vibrational levels by electron impact are calculated.
These data are used for the description of the temporal
evolution of vibrational distribution function of N 2
molecules during the discharge. The number density ratio
of N 2 (X1,v = 0) and N 2 (X1,v = 1) is used to determine the
2
first-level nitrogen vibrational temperature T 01 N2, as
follows:
T01N 2 =
hω
ln(N 2 ( v = 1) N 2 ( v = 0) )
where h ω = 3395 K is the energy difference between
0 - 1 vibrational levels.
Fig. 2 displays the time evolution of the first-level
nitrogen vibrational temperature T 01 N2. As it can be seen,
the calculated results at the end of the discharge for the
axial region (curve 1) and for the periphery (curve 2) are
consistent with the experimental data (indicated by
symbols in Fig. 2). This means, in particular, the
adequacy of the description of the magnitude and the
radial distribution of the specific input energy.
Vibrational temperature T01N2, K
ion-molecular reactions from [2, 5] and included reactions
involving the neutral particles O 2 (X3Σ), O 2 (a1∆ g ), O(3P),
O(1D), O(1S), N 2 (X1Σ g +), N 2 (A3Σ u +), N 2 (B3П g ),
N 2 (C3П u ), N 2 (a'1Σ u -), NO, NO 2 , N(4S), N(2D), N(2P), [2].
A detailed description of the plasma-chemical model and
the results of the test simulations are presented in [2, 5].
The radial expansion of a hot gas channel was modelled
by the set of one-dimensional time-dependent equations
with a heat source W R . The heat release source W R is
described by the fast gas heating model [2] with
allowance for the reactions of pre-dissociation of highly
excited electronic states of oxygen (populated via electron
impact or via the quenching of the electronically excited
states N 2 (A3Σ u +, B3П g , C3П u , a'1Σ u -) by oxygen
molecules, the reactions of quenching of excited O(1D)
atoms by nitrogen molecules, etc. The reactions of VT relaxation of N 2 (v) by O atoms and O 2 molecules are also
taken into account [2].
4500
4000
3500
1.
3000
2500
2.
2000
1500
1000
10-1
100
101
102
Time, ms
Fig. 2. Temporal evolution of the vibrational temperature
T 01 N2 of nitrogen molecules at the discharge axis (r = 0) –
curve 1, and at a distance of r = 0.7 mm from the axis –
curve 2. The symbols are for the experimental data from
[3], and the curves are for the numerical results.
The main relaxation of N 2 (v) vibrational excitation
occurs in collisions with O(3P) atoms. The increase of the
vibrational temperature T 01 N2 at the periphery of the
discharge at time scale t = 0.5 - 2 µs (curve 2) is
associated with the gas-dynamic expansion of the channel
and movement of vibrationally excited N 2 (v) molecules
from the axial region to the periphery. Concentration of
O(3P) atoms and gas temperature at the periphery is lower
than at the axis, so at the time t > 60 µs the vibrational
temperature T 01 N2 at the axis (curve 1) is lower than at a
distance r = 0.7 mm from the axis (curve 2).
Fig. 3 shows experimental data [3] and calculation
results of the time evolution of gas temperature and O(3P)
atom density at the discharge axis. Gas heating at the axis
for the first 200 ns is about ∆T = 550 K, followed by a
slight cooling of the channel associated with its gasdynamic expansion. Further increase of the temperature
during t > 2 µs is due to the VV - exchange processes and
VT - relaxation of N 2 (v) excitation on oxygen atoms.
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3
1200
O( P)
2,0
1000
Tg
1,5
800
1,0
600
0,5
Temperature, K
O(3P) density, 1018 cm-3
Concentration of O(3P) atoms at the discharge axis
exceeds 2∙1018 cm-3 and the dissociation degree of oxygen
molecules reaches 30%. Reduction of O(3P) density at
time scales of t = 0.1 µs - 2 µs is associated with
gas-dynamic expansion of the heated gas channel and
reduction of mass density in this region.
400
200
1
2
10
103
10
104
Time, ns
Fig. 3. Temporal evolution of O(3P) atoms density and
gas temperature at the discharge axis. The symbols are
for the experimental data from [3], and the curves are for
the numerical results.
Comparison between experimental [3] and calculated
radial profiles of gas pressure at time delay t = 150 ns and
1 µs after the discharge is shown in Fig. 4. The
simulation results adequately describe the evolution of the
spatial profiles of gas pressure and formation of shock
waves at times t > 1 µs. This indicates the adequacy of
the description of the fast gas heating occurring at
t ≤ 100 ns. For the time scale t > 6 µs, it can be assumed
that P ≈ Р 0 = 760 Torr and it is quite justified to use the
isobaric approximation.
At the axis, the fraction of discharge energy converted
to the fast gas heating is about 17%, about 27% of the
energy is spent on the dissociation of oxygen molecules
and the rest of 55% are used in the vibrational excitation
of nitrogen molecules. These data are consistent with the
results obtained in [3].
Measurements of the vibrational distribution function of
nitrogen molecules and rotational temperature in dry air,
excited by pulsed nanosecond discharge are presented in
[4]. The experiments were performed in a diffuse and
stable plasma filament discharge, approximately 4 mm in
diameter at P = 100 Tor, and T 0 = 300 K. The discharge
gap in a point-to-plane geometry had an inter-electrode
distance of 10 mm. The pulse repetition rate was equal to
f = 50 Hz, and the voltage amplitude was U max = 8 kV.
Picosecond CARS was used to study N 2 (v) vibrational
distribution function and evolution of rotational
temperature.
Fig. 5 displays the time evolution of the reduced
electric field E/N in the plasma channel. Here dots are the
results of the evaluation of the reduced electric field value
using the expression E = (U(t) - U c )/d, where U(t) is the
measured voltage [4], U c is a cathode fall voltage, d is an
inter-electrode distance. The numerical results correlate
with the E/N evaluation [4], an agreement showing that
the description of the ionization processes in the discharge
is adequate. Under given conditions, the energy is mainly
deposited at electric fields E/N = 70 - 150 Td, and the
maximum specific energy input at the discharge axis
amounts to W = 0.22 eV/mol. The calculation result of
total energy coupled per pulse is 13.5 mJ and close to
experimentally measured value of 15 mJ [4].
300
250
model
exp
E/N, Td
200
3,5
Pressure, atµ
3,0
- 150 ns
- 1.0 µs
2,5
150
100
50
P0 = 1 atµ
2,0
P = 100 Torr
0
0
1,5
20
40
60
80
100
120
Time, ns
1,0
0,0
0,3
0,6
0,9
1,2
1,5
R, µµ
Fig. 4. Comparison between experimental [3] and
predicted radial profiles of gas pressure. Time delays
after the beginning of the discharge are equal to t = 150 ns
and 1 µs. The symbols are for the experimental data from
[3], and the curves are for the numerical results.
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Fig. 5. Time evolution of the reduced electric field E/N
under the conditions of [4]. The solid curve is the
estimation of E/N based on the experimental data U(t)
from [4], and the dash curve is for the numerical results.
The comparison between experimental and predicted
N 2 (X1Σ,v) vibrational level population at the conditions
of [4] is presented in Fig. 6 for time delay after the
beginning of the discharge t = 50 ns and 100 ns. The
3
numerical results are in agreement with the experimental
data [4] (indicated by symbols in Fig. 5). Hence, the
specific input energy at the discharge axis is described
correctly.
Relative population
100
model
exp
-1
10
100 ns
-2
10
t = 50 ns
-3
10
0
2
4
6
8
Vibrational quantum number
Fig. 6. Comparison between experimental [4] and
predicted N 2 vibrational level population in air at
P = 100 Torr and time delay after the beginning of the
discharge t = 50 ns and 100 ns.
Fig. 7 shows the numerical results and measurements
[4] of temporal dynamics of gas temperature at the
discharge axis. At the axis, the fraction of discharge
energy converted to the fast gas heating is about 17%, that
corresponds to the effective value of reduced electric field
(E/N) eff ≈ 117 Td [2]. About 30% of the energy is spent
on the dissociation of oxygen molecules, the rest of 52%
are used in the vibrational excitation of nitrogen (about
0.4 of quantum per N 2 molecule).
Temperature, K
480
450
Air
420
390
360
model
exp
330
300
1
10
2
10
103
Time, ns
Fig. 7. Temporal dynamics of gas temperature at the
discharge axis under the conditions of [4]. The dots are
for the experimental data from [4], and the curve is for the
numerical results.
Fast gas heating leads to pressure increase and to
formation of acoustic and shock waves. The formation of
axisymmetric channel with a lowered gas density was
4
observed on Shlieren images [6]. It confirms the
assumption of a superiority of radial gradients of the
discharge parameters over the axial gradients - those in
the direction between the electrodes. Under given
conditions, the characteristic time of expansion of the
heated gas channel is τ g = 1 - 2 µs.
4. Conclusions
The results of a numerical study of kinetic processes
initiated by pulsed nanosecond discharge in atmosphericpressure air are presented. The calculations of discharge
parameters, as well as the temporal dynamics of O atoms
density, the evolution of vibrational distribution function
of nitrogen molecules, and gas heating under the
experimental conditions of [3, 4] were performed. The
results of modeling are consistent with the measured data.
Owing
to
the
high
O
atoms
density,
[O(3P)] max ≈ 1018 cm-3 [3], negative ions are efficiently
destroyed in the discharge afterglow. As a result, the
decay of plasma in the afterglow is determined by
electron-ion and ion-ion recombination, and the electron
density in the region of high O atoms density remains
relatively high between the pulses.
In air plasma at high dissociation degree of oxygen
molecules, relaxation of electronic energy of atoms and
molecules in reactions with O atoms becomes extremely
important. Active production of NO molecules and fast
gas heating in the discharge plasma due to the quenching
of electronically excited N 2 (B3П g , C3П u , a'1Σ u -)
molecules by oxygen atoms should be noted here [7, 8].
In the experiments [3], an increase of vibrational temperature of nitrogen molecules at the periphery of plasma
channel at time delay t = 1 - 30 µs after the discharge was
obtained. This is due to the intense gas heating and as a
result, gas-dynamic expansion of a hot gas channel.
Vibrationally excited N 2 (v) molecules produced near the
discharge axis move from the axial region to the
periphery. Consequently, at the periphery the vibrational
temperature of nitrogen molecules is increased.
5. Acknowledgements
The work was partially supported by PICS-RFBR
(grant 5745-11.02.91063-a/5745), RFBR (grant 12-0200637), AOARD AFOSR, FA2386-13-1-4064.
6. References
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Combustion Sci., 39, 61 (2013)
[2] N. Popov. J. Phys. D: Appl. Phys., 44, 285201
(2011)
[3] A. Lo, A. Cessou, P. Boubert and P. Vervisch.
J. Phys. D: Appl. Phys., 47, 115201 (2014)
[4] A. Montello, Z. Yin, D. Burnette, I. Adamovich and
W. Lempert. J. Phys. D: Appl. Phys., 46, 464002
(2013)
[5] N. Popov. Plasma Phys. Rep., 29, 695 (2003)
[6] A. Montello, D. Burnette, M. Nishihara,
W. Lempert and I. Adamovich. J. Fluid Sci.
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[7]
[8]
Technol., 8, 2147 (2013)
A. Klochko, J. Lemainque, N.A. Popov, J-P. Booth
and S.M. Starikovskaia. in: 51th AIAA Aerospace
Sciences Meeting. (Dallas, USA), AIAA-2013-0574
(2013)
I. Shkurenkov, D. Burnette, W. Lempert and
I. Adamovich. Plasma Sources Sci. Technol., 23,
065003 (2014)
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