49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2011, Orlando, Florida
AIAA 2011-1150
Quenching of Excited Electronic States of Molecular
Nitrogen in Nanosecond Pulsed Discharges in Atmospheric
Pressure Air
Moon Soo Bak 1, Wookyung Kim2, and Mark A. Cappelli3
Mechanical Engineering Department, Stanford University, Stanford, California, 94305-3032
2
United Technologies Research Center, East Hartford, Connecticut, 06108
1,3
Time-resolved emission measurements for N2 (C-B) and N2 (B-A) transitions are carried
out in nanosecond pulsed discharges in both air and pure nitrogen to investigate the role of
dissociative quenching of excited electronic states of N2 (N2*) by O2 on producing atomic
oxygen (O). The emission curves both in air and nitrogen are found to be remarkably
similar. For quantitative analysis, 0-D kinetic simulations coupled with energy equation are
conducted to predict quenching rate coefficients of quenching of N2* by N2 and dissociative
quenching of N2* by O2 by matching the simulated emission curves to the corresponding
measurements. With the inferred quenching rate coefficients, the fractions of atomic oxygen
production for electron-impact dissociation of O2 and the dissociative quenching of N2* by O2
are calculated and compared. The dissociative quenching is found to be responsible for 82 %
of O production whereas the electron-impact dissociation is 5 %.
I. Introduction
H
igh repetition-rate nanosecond pulsed discharges to generate high pressure plasmas have been used in
combustion to reduce ignition delay times1 and to stabilize lean premixed flames2,3. These benefits have been
attributed to the production of reactive atomic oxygen (O), hydrogen (H), and hydroxyl (OH) radicals2,4 as a result of
either electron-impact dissociation or dissociative collisions with energetic heavy particles populated within
discharges. To understand O radical production mechanisms in detail, direct measurements of O radicals5,6 as well as
kinetic simulations7 have been carried out for short-pulsed discharges in air and air/fuel mixtures. Measurements in
air6 indicate that a rapid production of O radicals follows a fast decay of electronically excited states of molecular
nitrogen (N2*), suggesting that dissociative quenching of N2* by O2 may be the main O radical production channel,
expressed as:
N 2 ( A, B, a′, C ) + O2 → N 2 ( X ) + 2O
(1)
This finding is supported by previous kinetic experiments8-10 that suggest that ground-state molecular oxygen, O2,
quenches N2* more effectively than molecular nitrogen, N2. Unfortunately, most of these rate coefficients are
obtained at room temperature and low pressure (a few Torr), and their temperature or pressure dependence is not
well known. Therefore, the lesser role played by self quenching of N2* by N2 in these highly non-equilibrated
atmospheric pressure plasmas must be verified.
II. Experiment description
A schematic of the experiment is shown in Fig. 1. The discharge is generated between two tungsten electrodes (1
mm diameter, 1 mm separation) connected to a high repetition pulsed power supply (FID Technology F1112) that
generates Gaussian temporal voltage pulses of typically 8 kV peak, 10 ns duration, and 50 kHz repetition rate. The
light emitted from the center of the discharge is collected and transmitted through an optical fiber directly to a
photomultiplier tube (PMT, Hamamatsu R928, 2.2 ns rise-time, and PMT socket, Hamamatsu E717-63, designed for
1
Graduate Research Assistant, Mechanical Engineering, AIAA Student Member.
Senior Research Scientist.
3
Professor, Mechanical Engineering.
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
fast time response) equipped with band-pass filters (Thorlabs FB340-10 or FB760-10, depending on the N2* band of
interest), or is dispersed using a monochromator (Jarrell-Ash 82-020) with the PMT at its exit. The PMT signals
used in conjunction with the band-pass filters are directly recorded and averaged over several shots by an
oscilloscope (Tektronix TDS7104, 1GHz bandwidth), while the signals through the monochromator are gated and
integrated through a boxcar integrator (SRS SR250) with a gate width of 2 ns, triggered and synchronized with the
pulse generator using a delay generator (SRS DG535). The PMT/socket temporal response function is determined
through measuring emissions for single-photon event and scattered light of 5 ns pulse laser (Gemini PIV laser 20015). The detector is found to have an overall rise-time of 2 ns, with a fall time of about 5 ns. During the
measurements, either air or pure nitrogen flows through the discharge with a speed of about 4 m/s. During an
electron number density measurement, a little amount of methane (about 4 % in mole fraction) is added into air to
produce the hydrogen Balmer-β (Hβ) line.
Figure 1. Schematic of experimental setup.
III. Simulation description
We have developed 0-D kinetic simulations coupled with energy-equation for quantitative analysis of quenching
process of N2*. We consider ground state of N2(X), excited electronic states of N2(A, B, a’, and C), N, ground state
of O2(X), excited electronic states of O2(a, and b), O, NO, O3, N2+, N4+, O2+, and free electrons (e) in the analysis.
The reaction set provided in Table 1 includes electron impact excitation, dissociation and ionization of N2 and O2,
associative ionization, recombination of electrons and positive ions, ion conversion, direct quenching of N2* by N2,
dissociative quenching of N2* by O2, and chemical transformation of ground state species. The rate coefficients for
collisions between neutral species and ions are adapted from previous simulations of N2 and N2-O2 discharges.11-13
Since electron impact excitation, dissociation, ionization, and electron-ion recombination processes are coupled to
the electron energy distribution function, rate coefficients for these reactions are obtained through a solution of the
Boltzmann equation facilitated by the use of the commercially available software, BOLSIG14. Only a reduced set of
cross sections pertaining to elastic and inelastic collisions with the parent species (ground state N2 and O2) are
considered.15 The Gaussian temporal pulse of 10 ns width is used for the reduced electric field (E/n) in accordance
with a voltage measurement between the electrodes (shown later in the inset in Fig. 3). The peak E/n is determined
to be 285 (±4) Td by matching the temporal rise in the measured gas temperature (assumed to be equal to the
measured rotational temperature) to the simulated gas temperature. To predict the gas temperature and its affect on
the temperature dependence of the reaction rate coefficients, an energy equation is solved simultaneously with a set
of species conservation equations. In the energy equation, the energy deposited into Ohmic dissipation is set to be
equal to the summation of the enthalpy changes of the species as a result of reactions and gas heating in accordance
with the prescription provided by M. Uddi et al.16 The energy and species conservation equations are expressed in
detail as:
for each reaction,
∑ν n
i reac ,i
i
f

→ ∑ν i′n prod ,i ,
←

kb
k
i
2
American Institute of Aeronautics and Astronautics
(2)


ν i′
i
=
ν ′j −ν j )  k f  E n or Te or Tgas  ∏ nνreac
(
∑
,i − kb ∏ n prod ,i  for all species, j
 i
dt reactions
i
  tot

2
 d ( ene µe E ntot )
dTgas
dn 
1

=
− ∑ h j (Tgas ) j 
dt
dt
dt 
species j
∑ c p, j (Tgas ) n j 

species j
dn j
(3)
(4)
where nj is the number density of species j, νj is the stoichiometric coefficient of species j, kf and kb are forward and
reverse reaction rate coefficients, E is the electric field, Te is the electron temperature, μe is the electron mobility, Tgas
is the gas temperature, cp,j is the heat capacity of species j, and hj is the enthalpy of species j. The peak E/n used is
smaller than the nominal estimate based on the applied voltage and gap distance, a result attributed to sheath
formation across each electrodes.17 The calculation requires an initial estimate of the electron density between
Table 1. Reaction set used in kinetic simulations for discharges in air and nitrogen.
Reactions
Reactions
e
N2(X) + e → N2(A) + e
O2 + e → O2+ + e + e
+
a,e
N2(X) + e → N2(B) + e
O2 + e → O + O
+
a,e
N2(X) + e → N2(a') + e
e + N2 + O2 → N2 + O2
+
a,e
N2(X) + e → N2(C) + e
e + e + O2 → e + O2
+
a,e
N2 + e → N + N + e
e + O2 + N2 → O2 + N2
+
+
a,e
N2 + e → N2 + e + e
e + O2 + O2 → O2 + O2
+
a
N4 + e → N2 + N 2
N2(A) + O2 → N2(X) + 2O c,e
+
a
N2 + e → N + N
N2(B) + O2 → N2(X) + 2O c,e
d
+
a
k = 4×10-11 cm3s-1
e + e + N2 → e + N2
+
a
e + N2 + N2 → N2 + N2
N2(a’) + O2 → N2(X) + 2O c,e
+
c
N2(A) + N2(a') → N4 + e
N2(C) + O2 → N2(X) + 2O c,e
d
+
c
k = 10×10-11 cm3s-1
N2(a') + N2(a') → N4 + e
+
+
c
c,e
N2 + N 2 + N 2 → N4 + N 2
N2(A) + O → N2(X) + O
+
+
c
c,e
N4 + N 2 → N2 + N 2 + N 2
N2(A) + O → NO + N
c
c,e
N2(A) + N2 → N2(X) + N2
O2(a) + N2 → O2(X) + N2
c
c,e
N2(B) + N2 → N2(X) + N2
O2(a) + O2 → O2(X) + O2
-11
3 -1
d
c,e
k = 0.1×10 cm s
O2(a) + N → O2(X) + N
c
c,e
N2(B) + N2 → N2(A) + N2
O2(a) + O → O2(X) + O
-11
3 -1
d
c,e
k = 1.5×10 cm s
O2(b) + N2 → O2(a) + N2
a
c,e
N2(B) → N2(A) + hv
O2(b) + O2 → O2(a) + O2
c
c,e
N2(a') + N2 → N2(B) + N2
O2(b) + O → O2(a) + O
c
N2(C) + N2 → N2(a') + N2
N + N + O2 → N2(X) + O2 b,e
-11
3 -1
d
k = 2.5×10 cm s
N + N + O2 → N2(A) + O2 b,e
a
N2(C) → N2(B) + hv
N + N + O2 → N2(B) + O2 b,e
c
c,e
N2(A) + N2(A) → N2(B) + N2
O + O + N 2 → O2 + N 2
c
c,e
N2(A) + N2(A) → N2(C) + N2
O + O + O 2 → O2 + O 2
b
c,e
N + N + N2 → N2(X) + N2
N + O2 → NO + O
b
c,e
N + N + N2 → N2(A) + N2
N + O + N2 → NO + N2
b
c,e
N + N + N2 → N2(B) + N2
N + O + O2 → NO + O2
c
c,e
N2(A) + N → N2(X) + N
O + O2 + N2 → O3 + N2
e
c,e
O2(X) + e → O2(a) + e
O + O2 + O2 → O3 + O2
e
c,e
O2(X) + e → O2(b) + e
O + O3 → 2O2
e
O2 + e → O + O + e
a
The rate coefficient is from Ref. 11.
b
The rate coefficient is from Ref. 12.
c
The rate coefficient is from Ref. 13.
d
This is the rate coefficient proposed in the study.
e
This reaction should be excluded for discharges in nitrogen.
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discharge pulses, which we take to be the time-average electron density measured in similar experiments18, 1013 cm-3,
and the use of this value is partially validated through an electron number density measurement (discussed in detail
later). In evolving the kinetics, we assume a constant background number density of 5.6×1018 cm-3 (corresponding to
a value at 1 atm and an initial temperature of 1300 K) since the pulse time-scale is shorter than that of acoustic
expansion of the discharge volume.
IV. Results
A. Experimental results
Time-resolved emission intensities of the N2 (C-B) and N2 (B-A) transitions taken using the narrow band-pass
filters (10 nm windows, centered about 340 nm and 760 nm) for discharges in air and nitrogen are shown in Fig. 2(a)
and 2(b), respectively. The temporal characteristics are verified using the spectrally resolved emission taken with a
monochromator. The emission follows the general shape of the applied voltage but with slower overall decay. The
most surprising result is that we see little difference in the emission shapes (particularly the decay) between
measurements in air and in nitrogen, suggesting that the presence of oxygen has little effect on the emission decay
under these conditions. According to these results, any correlation between the temporal decay in the excited state
emission and the rise in measured O-atom concentrations may be coincidental and is not sufficient confirmation of
the importance of dissociative quenching by ground state O2.
Figure 2. Emission intensity curves of (a) N2 (C-B) and (b) N2 (B-A) for discharges in air (black) and
nitrogen (green). Symbols are measured, and dashed and dot-dashed lines are simulated using rate
coefficients proposed in this study and commonly-used ones, respectively.
B. Determination of simulation parameters
The peak E/n and initial discharge conditions (electron number density, gas temperature) are most critical
parameters in the simulations. To determine these parameters, we have conducted a time-resolved rotational and
vibrational temperature measurement of N2 (C) and an electron number density measurement. Figure 3 shows the
spectrum of the N2 (C-B) (0,2), (1,3) and (2,4) bands for discharges in air recorded at the time when the emission
intensity is highest with its spectral fit obtained using a spectral line simulation. The emission is well reproduced
using a spectrum synthesized with a Boltzmann distribution of rotational and vibrational states in accordance with a
temperature of Trot = 1900 K and Tvib = 4400 K, respectively. We measure the spectra with 2 ns gate-width during
the pulse, deduce rotational and vibrational temperatures (Trot and Tvib) of N2 (C), and include their temporal
evolutions in the inset in Fig. 3. Tvib is found to rise nearly immediately to a temperature of 4400 K while Trot
increases more gradually to 2200 K from 1300 K during the pulse. This rise in rotational temperature is indicative of
a slower, but still rapid energy cascade into translational energy of the background gas, since the high pressure
assures strong rotational-translational coupling. Assuming that the translational (i.e. gas) temperature is equal to the
rotational temperature, we determine the initial temperature to be 1300 K, a result of heating from previous
discharge pulses. With this initial temperature and atmospheric pressure, we also determine the peak E/n to be 285
(±4) Td by matching the measured rotational temperature to that from the simulation as also shown in the inset in
Fig. 3, given that the initial electron number density is 1013 cm-3.
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Figure 3. Normalized N2 (C-B) (0,2),(1,3),(2,4) emission spectrum measured in air (black) with its
spectral fit (green), and calculated rotational and vibrational temperatures of N2 (C) with simulated
gas temperature.
Figure 4 shows the hydrogen Balmer-β (Hβ) Stark-broadened line at the time when the emission intensity is
highest (the time when the electron number density is highest). Since hydrogen atoms in air are easily removed to
form NH3, and OH and H2O, we are able to measure a detectable level of signal near at the time when the intensity is
highest. We take the lineshape by measuring the spectrum near 486.13 nm for an air discharge both with and without
the addition of methane and then subtracting the former from the latter to establish a spectral baseline. The lineshape
present in Fig. 4 is averaged over several measurements. To account for instrumental broadening, we also measure a
slit function of the spectral line using a mercury line at 435.8 nm. The width of the Hβ line is strongly dependent on
electron number density, and its dependence is indicated as Eq. (5)19 based on a fit to the widths listed by Gigosos
and Cardeñoso20 for electron densities between 1014 cm-3 to 4×1017 cm-3. The fit in which the broadening is given as
the half width at half maximum (HWHM) in nm is expressed as:
∆λStark =
1.0 ×10−11 ( ne )
0.668
(5)
To deduce an electron number density, the Lorentzian lineshape with varying linewidth obtained from the formula is
convolved with the slit function and compared to the measurement as shown in Fig. 4. The peak electron number
density is determined to be 4.5(±1.2)×1015 cm-3, and it is very close to the value obtained from the simulations (as
shown in the inset in Fig. 4) with the discharge conditions of peak E/n of 285 Td, an initial electron density of 1013
cm-3, and an initial temperature of 1300 K.
Figure 4. Normalized Hβ emission line measured in air (black) with the convolved Lorentzian fit
(green), and simulated electron number density curve with measured electron density point.
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C. Simulation results
The simulated temporal emission curves of the N2 (C-B) and N2 (B-A) bands in air and nitrogen, which are
convolved with the temporal response function of the detector to account for the finite decay time of the detector,
are compared to the corresponding measurements as presented in Fig. 2(a) and 2(b), respectively. With commonlyused quenching rate coefficients13 for N2* by N2 (X) and by O2, we calculate a faster decay of N2 (C) and N2 (B) in
air than in nitrogen with notable differences between the simulated and corresponding measured curves. The
quenching of N2 (C) by N2 (X) is under-predicted while that of N2 (C) by O2 is over-predicted. For N2 (B),
quenching by N2 and O2 are both over-predicted, presumably because the commonly-used rate coefficients for N2
(B) quenching9,13 are weighted-averages over vibrational state-specific rates, which account for faster quenching of
higher vibrational states. This contrasts that used for N2 (C), which is based on quenching of the ground vibrational
level (v’ = 0). To model our temporal emission, the rate coefficients for these quenching reactions are adjusted to
obtain agreement between measured and simulated curves (black dashed lines for air and green dashed lines for
nitrogen). The resulting coefficients for quenching of N2 (C) by N2 and by O2 are found to be 2.5 (±0.3)×10-11 cm3s-1
and 10 (±0.3)×10-11 cm3s-1, respectively, whereas for N2 (B) by N2 and O2 are 1.6 (±0.3)×10-11 cm3s-1 and 4
(±0.3)×10-11 cm3s-1, respectively. For N2 (C) and N2 (B) quenching by N2, the rate coefficients needed to reproduce
experiments are between the state-specific coefficients for v’ = 0 and for v’ = 1, 2.21,22 This enhanced quenching is
not unexpected, as the high vibrational temperature will result in elevated populations of excited vibrational states.
In contrast, for the dissociative quenching of N2 (C) and N2 (B) by O2, the rate coefficients are smaller than those
commonly used by factors of 3 and 5, respectively. Since N2* is quenched faster in higher vibrational states by O28,9,
we surmise that the lower quenching rates needed may be due to a strong pressure or temperature dependence, for
which there is no experimental data.
Using the revised quenching rate coefficients of N2* by N2 and O2, we compute the evolution of O radicals
produced through the two dissociation channels (dissociative quenching or direct) for a single discharge pulse (see
Fig. 5.). We find that 82 % of O produced is the result of dissociative quenching while electron impact dissociation
is responsible for about 5 %. The revised rate coefficients decrease the fraction of O radicals produced by
dissociative quenching by 1 %, and dissociative quenching is still the dominant channel for producing O radicals, as
concluded from previous studies.5-7 The O radical concentration produced after a single discharge pulse is found to
be 2.5 (±0.5)×1017 cm-3 corresponding to a mole fraction of 4.4 (±0.4)×10-2.
Figure 5. Number densities of O radicals produced through electron-impact dissociation and dissociative
quenching of N2(A), N2(B), N2(a’), N2(C), and N-O2 collision as a function of time.
V. Conclusions
We observed that decay profile of N2 (C, B) are found to be remarkably similar in both air and pure nitrogen. We
therefore developed a 0-D kinetic simulation to study the quenching process of N2* and found that the rate of
dissociative quenching by O2 is larger than that of self quenching by N2, but not overwhelmingly larger as known by
the corresponding known rate coefficients under these discharge conditions. With the inferred rate coefficients, the
dissociative quenching by O2 is found to be still responsible for 82 % of atomic oxygen production. It indicates that
only consideration of electron-impact dissociation of O2 is not sufficient for estimation of O radical amount and for
evaluation of radical effect on flames in plasma-assisted combustion studies.
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American Institute of Aeronautics and Astronautics
Acknowledgments
This research was supported by the NSF/DOE Basic Plasma Initiative.
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