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Contrib. Plasma Phys.
35
(1995)
3,
273-296
Modeling
of
Plasma-Chemical Reactions in Gas Mixture
of
C02 lasers
11.
Theoretical Model and its Verification
A.
CENIAN
(a),
A.
CHERNUKHO
(b), and
V.
BORODIN
(b)
(a) Polish Academy
of
Sci.,
Institute
of
Fluid-Flow Machines,
80-952
Gdansk,
ul.
Fiszerd
14,
Poland;
(b)
Belarus Academy
of
Sci., A.
V.
Luikov Heat and Mass Transfer Institute,
220072
Minsk,
15
P. Brovka Str., Belarus
Abstract
In the paper we have modelled plasma-chemical reactions in the C02 low pressure, DC excited
lasers.
A
good agreement of theoretical and experimental results has been achieved. It has been proved
that neglect of reactions with electronic excited species or heterogeneous recombination leads to almost
50% overestimation of GO2 equilibrium conversion. The relation of
C02
equilibrium conversion to
the reduced field
E/N,
pressure and current density depends on discharge conditions and mainly on
the role played in discharge by ambipolar diffusion. This role decreases with an increase
of
the discharge
diameter and
of
the mixture convection velocity. The
CO,
equilibrium conversion increases with
growth of
E/N
and
j
and with decrease
of
pressure for discharges in small, sealed-off laser systems.
The
CO,
equilibrium conversion is not always
a
monotone function of
p
in large, convection cooled
lasers. It does not depend
so
much on
E/N
as the electron temperature alone if conversions in different
mixtures are compared.
1
Introduction
The kinetics of
CO,
dissociation was extensively studied due to its effect on performance
of
CO,
lasers
[l
-
111.
The laser power decrease was ascribed to fall of
CO,
concentration
[4-9] as well as to creation of chemical species
(O,,
O,,
NO,
N,O)
which effectively
deactivate vibrational excited states of
CO,
and
N,
molecules
[2,
4,
9,
121,
might also
degrade laser mixture
C02
:
N2
:
He and change the electric discharge conditions due to
their strong electron affinities [9,
131.
These effects are controlled and reduced in existing lasers by gas mixture additives
[13,
141,
thermal regeneration
of
a gas mixture
[6],
partial gas replenishment
[7,
151,
and different
catalyst placed either on the cathode
[16],
or
inside the cavity
[8,
121
or
in the gas duct
[17].
The efficiency of above listed methods can be increased by knowledge of laser chemistry
products and mechanisms of their production, e.g. it has been pointed out lately
[12]
that
the catalyst placed along the discharge tube does not only limit
CO,
conversion and oxygen
formation but it opens an additional channel of heat conduction to the wall in diffusion
cooled systems. The heterogeneous recombination of
CO
and
0
on the catalytic wall
contributes to energy transfer from the gas by delivery of dissociation energy. It increases
thermal conductivity leading to a power increase of about
50%
[12].
However, only the time evolution of
CO,,
CO
and
0
concentrations
[l,
3,
6,
7,
8,
101
was measured in the majority of published experimental works.
MACKEN
et al.
I181
and
FREUDENTHAL
[19]
have observed production
of
NO,
generally in the presence
of
H20.
The presence of small amounts of
NO,
N,O
and
NO,
has been predicted by
CARBONE
19
Contrib. Plasma Phys.
35
(1995)
3
274
Contrib. Plasma Phys.
35
(1995)
3
[20]. Ref. [2] presents the measured values of
NO
and
NO,
concentrations and steady-state
concentrations of positive ions:
Ni,
Ol,
COi,
NO’
and
0’.
DOERK et al. [lo] have measured spatial distribution of CO, dissociation products using
the CARS-spectroscopy method. They have not found any significant amount of nitrogen
oxides in the laser mixture after a long time laser operation.
TuRE~COVA
[I
11
has studied
the process of complete CO, decomposition in sealed-off systems. The only gas measured
in a mass spectrometer was He after more than
30
h
of
system operation.
However, the complete experimental analysis of plasma chemistry in CO, laser is still
absent even if it is possible. Therefore, it is our goal to develop a theoretical model which
allows us to study the time evolution and production mechanisms of different chemical
species present in DC discharges of CO, lasers.
Only few numerical models have been proposed to study plasma-chemical reactions in
CO,
lasers. Models which did not consider the CO, reconversion processes
[3,
51
have led
to the exponential decay of CO, concentration, [CO,], and could be applied only to sytems
with significant gas replenishment. In the case of sealed lasers these models describe properly
only the initial stage of mixture decomposition far from the steady-state value of CO,
conversion.
The model [21] based on the chemistry of neutral components in the electronic ground
states has described satisfactorily the initial power decrease of a
10
kW
CO, laser with a
gas duct volume of 6m3. However, it leads to the substantial overestimation of CO,
equilibrium conversion’) X,(CO,) in case of the MLT 1200 laser 1221. Moreover, it has
been concluded, that the vibrational excitation in a glow discharge influences the CO,
dissociation process slightly.
The model of HOKAZONO et al.
[9]
is up to date one of the most comprehensive models
of
plasma-chemistry in CO,
:
N,
:
He laser mixtures. It has been originally proposed for
analysis of processes in TEA CO, lasers. The high pressure, characteristic for TEA lasers,
allows authors to neglect some of the kinetic processes e.g. the heterogeneous recombination
and reactions with electronically excited molecules. Very high decomposition of CO,
-
90%
-
exceeding measured values for TEA lasers, has resulted from the calculations
[9].
The processes excluded in Ref.
[9]
can play an important role in case of low pressure
CO, DC excited lasers. They influence dissociation of CO, molecules and formation of
species which can efficiently quench vibrational excitation. It has been stated [27] that
heterogeneous recombination needs to be included for the correct description of CO,
decomposition at low pressures,
p
2 Torr. The significance of electronic excited states of
CO in the process of CO, formation has been pointed out in studies of glow discharge in
the low pressure CO
:
He
:
0,
gas mixture [28, 291.
In the first part of this work [24], referred to as paper
I,
we have modelled the kinetics
of plasma-chemical processes in pure
CO,
gas discharge of DC type. The important role
of heterogeneous recombination as well. as of reactions with ions and with the CO(u3n)
excited state in recombination of
CO
has been clearly stated. The calculated equilibrium
conversion of CO, into CO had strongly depended on the
E/N
ratio. It grew from a few
percent for
E/N
=
20 Td to more than 70% for
E/N
-
90
Td
(1
Td
=
lo”
V
cm’). The
X,(CO,) values were only slightly influenced by the change of electron density and
temperature. The time required to reach the steady-state concentrations of chemical species
in the system varied from a few seconds for high
E/N
values to hours for the low ones; it
’)
The often measured,
so
called
COz
equilibrium conversion XJCO,) 123) represents quasi-
equilibrium (steady-state) conversion of
COz
into CO established in non-isothermal plasma of a
discharge,
as
was mentioned in Ref. [24]. The value X,(C02)
=
[p’”(CO,)
-
pcq(CO,)]/pi”(CO,) differs
substantially from the quasi-equilibrium one measured after discharge turn-off, and even more from
chemical equilibrium value. The phenomenon of chemical quasi-equilibrium in non-isothermal plasmas
has been in detail described in Refs. [25] and I261
A.
CENIAN,
A.
CHERNUKHO, V. BORODIN,
C02
Lasers
I1
275
increased with the fall of discharge current. Satisfactory agreement with experimental data
was achieved.
In this paper we present a model of plasma-chemical reactions of
CO,
:
N,
:
He mixtures
of
DC
excited lasers. The model is verified taking an advantage of the published experimental
data
[l,
2,
6,
lo]
to check its reliability. The role of ion-molecular reactions, of reactions
with electronically excited species and of heterogeneous recombination in reconversion of
CO
into
CO,
is studied. The model will be applied (in part
111)
to analyze plasma-chemi-
cal processes taking place in an active medium of
CO, DC
transversely excited laser
of
MLT
1200
type (close-cycle, slow flow)
1151.
2
Kinetic
Model
The considered plasma chemical processes together with their rate constants are listed in
the Appendix i.e.
383
plasma-chemical reactions of
54
species: reactions of neutral atoms,
molecules and their basic electronic states, reactions with positive and negative ions,
heterogeneous
-
on wall
-
as well as homogeneous
-
in volume
-
recombination and
energy relaxation of electronic levels. In contrast to the model by
HOKAZONO
et al.
191:
-
we take into consideration more, relevant in our case, electronic states
of
molecule
N,
(Nz(A3C),
N2(B317),
N2(C3n)
and
Nz(aln))
as well as three states of oxygen
(0,(A3C),
O,(a'd), O,(b'Z))
and state
CO(a3n)
-
see processes M-T in the Appendix;
-
we take into account chemical processes with electronically excited atoms He(3S),
N('D),
N('P),
O('D),
O('S)
and above mentioned molecules, processes of electronic states
excitation as well as the processes of energy exchange between electronically excited
atoms and molecules
-
processes
I
-
L
in the Appendix;
-
we take into account spontaneous emission of
N2
which leads to suppression of its
electronic excitation
-
processes
N
in the Appendix;
-
we include heterogeneous recombination of
CO,
0
and
N
as well as relaxation processes
of electronic excited states
-
processes
P
in the Appendix;
-
we neglect reactions with hydrides considered in Ref.
[9]
and we postpone it up to the
analysis of influence of different additives on laser performance in the future
work.
In the present work we do not consider the vibrational relaxation processes due to the
complexity of the considered problem. These processes are important for determination
of
laser radiation characteristics but are of secondary importance for the laser plasma-
chemistry. It was concluded earlier
[21, 221
that e.g. the influence of vibrational excitation
on equilibrium conversion
XJCO,)
is practically negligible at the vibrational temperatures
(less or about
1500
K)
usually realized in
CO,
:
N,
:
He
DC
excited lasers.
The rate constants of reactions initiated by electron collision as a function of reduced
electric field
E/N
and laser mixture composition were calculated basing on the electron
energy distribution function
(EEDF')
and their cross sections. In the Boltzmann equation,
we took into account the processes of elastic collisions, electronic excitation, ionization and
dissociative attachment. Moreover, the effect of the
C02
and
Nz
vibrational excitation on
EEDF
is taken into account due to the importance of second kind electron collisions
[30].
The electron-electron collisions are neglected in Boltzmann equation, as in Refs.
[4]
and
[9]
because
NJN
N
lo-'
and therefore these processes influence
EEDF
only slightly. The
necessary cross section data of the processes are the same as in Refs.
[31, 321.
The reduced
electric field values
E/N
corresponding to experimental conditions were derived from
current-voltage characteristics and discharge goemetries. In our calculations we neglected
the influence of reagent vibrational excitation on the rate constants of plasma chemical
processes without electron participation.
19'
276
Contrib.
Plasma
Phys.
35
(1995)
3
The rate constants of heterogeneous processes were calculated using a well-known formula
(see
for
example
[33])
(for an effective rate, which describes a two stage process: species
diffusion to a surface and interaction with molecules adsorbed on the surface
where
S(V)
is the surface (volume) of discharge chamber,
k,
=
1/4y*c (2)
is the rate constant of the heterogeneous process (recombination
or
electronic energy
quenching),
k,'
=
A2/D
(3)
is the avarage time of the reagent species diffusion in the gas mixture. In the last equations
y
is the probability for the heterogeneous processes,
fi
is the average velocity
of
molecules
and atoms in the discharge,
D
denotes a diffusion coefficient and
A
=
rdc/2.4
for a cylindrical
geometry, where
rdc
is the discharge chamber radius. The same rate constants for
heterogeneous
CO(P1)
and
O(P2)
recombination processes were used as in Ref.
[24].
was
assumed basing on data of Refs.
[34,35].
For
the rate constants of
P8
-
P16
processes,
y
=
1
was supposed, as the electronic energy quenching coefficient, because practically every
collision of an excited molecule with a surface ends with an electronic energy being quenched.
The diffusion coefficients were taken from Ref.
[36].
The electron density is assumed constant in the discharge volume, as in paper I. Its value
depends on discharge excitation conditions. In the case
of
laser systems with gas convection
current is nullified as soon as gas leaves discharge region. The kinetic equations for chemical
processes in positive column
DC
plasma were solved under condition of constant gas
temperature and pressure.
The probability for the heterogeneous recombination of atomic nitrogen
y
=
3
Model
Verification
The presented model has been verified using existing experimental data
[l, 2,6, lo],
referring
mainly to the equilibrium conversion of
CO,
into
CO
and time characteristics of equilibra-
tion processes.
The first step in validation of the model has been done using the data of
CARS
displaying
CO,
dissociation in high power, transverse-flow laser
[lo].
The gas mixture CO,
:
N,
:
He
=
1
:
3
:
18
recycling in a gas-dynamic loop is periodically exposed to a glow discharge
under following conditions:
p
=
37.5
Torr;
T
-
350
K;
EIN
=
23
Td; period of cycle
-
2.6
s,
T~/T,~
-
0.004,
where
~~(5,~)
is the residence time in discharge (afterglow) region.
Two different regimes has been compared: with a without gas replenishment. The rate
of
replenishment was
y
=
g/G
=
0.015
where
G
-
gas flow rate,
g
-
flow rate of replenished
gas. The experimental and theoretical results for equilibrium conversion are put together
in Tab.
1.
A
good agreement both for the case with and without gas replenishment has
been achieved.
The high value of equilibrium conversion X,(CO,)
=
81%
has resulted from calculations
in the case of a continuous discharge,
T~/T,~
-
03.
In the case of a periodical discharge
interruption caused by gas convection through the gas-dynamic loop of transverse flow
laser, the X, drops about one third. It was stated that the X, value decreases with an
increase of the afterglow region and saturates as
Tag/Td
ratio reaches the value
1OOO.
A
similar behaviour has been reported for MLT
1200
laser
[22].
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN,
C02
Lasers
I1
277
Table
1
The equilibrium conversion
of
CO,
in high power, transverse-flow laser
[
101
G/%g
=
a3
0.01
0.001
0.004
o.Ooo1
o.oO01
theory
81%
58%
56% 56% 56%
8%
-
-
62%
-
11%
experiment
[lo]
-
The good agreement between measured and calculated values of the equilibrium quantity
(X,)
encouraged us to check the validity of the plasma-chemical time evolution. We compare
first the chemical relaxation time
TJ
the period of time needed to reach the quasi-equilibrium
of chemical composition) calculated in our model with estimated one for the same experiment
described in Ref.
[lo].
We take into account that in chemical quasi-equilibrium,
CO,
dissociation and flow of
the new molecules due to replenishment balance each other. It means the approximate
number of
CO,
molecules which dissociate in one gas-dynamic loop cycle is
N,
-
yXt(CO,),
"*"
denotes the case with gas replenishment. Next, the number of cycles needed for
equilibration can be estimated by the ratio
Xe/(YX,*)
=
350
3
(4)
when constant in time conversion rate is assumed. This value can be compared with results
of our calculations
-
Tab.
2.
If the conversion rate had been constant,
[CO,]
would have reached its quasi-equilibrium
value after less than
400
cycles. It corresponds very well with the ratio given in eq.
(4)
for
the experimental data.
Table
2
The calculated
C02
conversion as a function
of
time (in cycles)
time [cycles]
100
200
500
loo0
xc,,(t)/x,(coA
26%
45
yo
76% 96%
There is an even better agreement between our model and the experiment of KOZLOV
et al.
[6]
with respect to time evolution of
CO,
conversion
-
see Fig.
1
-
which confirms
the validity of the modelled plasma-chemical kinetics. In the experiment the dissociation
in high power, axial flow
C02
laser
161
was studied; glow discharge in a gas mixture
COz:
N,:
He
=
1
:
1.8:
5.6,
T
=
470
K,
p
=
20
Torr,
E/N
=
30
Td,
j
=
26
mA/cm2. The
small discrepancy in the initial stage
of
plasma-chemical interactions points probably to
underestimation of processes with electron collisions. These processes play a major role in
the initial, linear stage of
CO,
dissociation.
The pressure dependence of the
CO,
equilibrium conversion is the next step of our
verification. The good agreement between the modelled (paper
I)
and observed
[23]
values
of
Xe
=
X,(p)
has been achieved for a glow discharge in pure
C02.
The experimental data
for a glow discharge in the active mixture
CO,
:
N,
:
He
=
1
:
1.22: 5.65
of a sealed-off laser
have been published by TANNEN et al.
[2].
Discharges characterized by
E/N
=
30-60
Td
and
j
=
1.5
-20
mA/cmZ have been investigated in the pressure range
1
c
p
c
8
Torr.
The experimental dependence of
CO,
conversion versus pressure in a sealed-off laser
[2],
is presented in Fig.
2
together with calculated
Xe(CO2)
values. The gas kinetic tempera-
ture
T,
-
and important initial parameter
-
was estimated using a formula of KOZLOV
and KUZNIETSOV
[3]
for a cylindrical discharge chamber
T,
=
TO
+
W/~AA,,
278
Contrib.
Plasma
Phys.
35
(1995)
3
eo
s9
60
0"
u
X"
40
0
0.5
1.0 1.5
2.0
0~~"'~"""'"""'
t,
-
-
-
Fig.
1.
,Time evolution
of
C02
conversion basing
on
experiment
KOZLOV
et al.
[6]
and
X(r)
calculated for the same discharge conditions: gas mixture
COz
:
N2
:He
=
1
:
1.8:
5.6
under pressure
p
=
20 Torr.
where
To
is the measured temperature on the surface of the discharge chamber,
W
=
j*E
-
power per unit of discharge length,
A,
-
heat conductivity coefficient of the gas mixture.
The calculated temperature
T,
varies from
302
K
to
338
K for
1
<
p
<
8.07
Torr and
I
=
10
rnA
(it
corresponds to curve
1
in Fig.
2)
and from
371
K to
532
K
in the same
pressure range and
I
=
80
mA (curve
3).
loo
r------
**
m
A
A
A
A
'1
2
3
4
5
6
10
p
,
Torr
Fig. 2. The
C02
conversion versus pressure for laser mixture
COz
:
N,
:
He
=
1
:
1.22
:
5.65
measured
by
TANNEN et al. [2] together with
A',
calculated for the same conditions.
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN,
C02
Lasers
I1
279
Both experimental and theoretical data display the same character i.e. the
CO,
conversion
falls with increase of pressure
(E/N
decrease). It corresponds very well with our results
[24]
for a pure CO, discharge and the same
E/N
range. The dependence on the current density
(conversion increases with
J)
is
more evident here than in pure COz case however this
becomes less pronounced as one goes to higher
E/N
values (lower
p).
It seems that
X,
increases faster with current density as
E/N
value decreases.
Although the agreement between theory and experiment is satisfactory, the experimental
data are systematically smaller than theoretical values and a generally better coincidence
is achieved for the higher currents. One possible explanation is that experimental data
correspond to temporal, not yet equilibrated values of conversion. The chemical relaxation
time decreases with current density increase, which is why, values agree better for higher
values.
The high relative concentrations of
NO,
up to 0.23%
(I
=
80
mA) measured by TANNEN
et al.
[2]
have not been confirmed by our model
[NO,]
-
lo-'%.
In contrast, the calculated
relative concentration of
NO
(-0.033)
and the measured values
0.02
<
[NO]
<
0.03%
coincide very well especially for low current
(I
=
5
and 10mA) discharges. However,
the experimental values of
[NO]
exceed again the calculated ones for highest considered
currents
(I
=
80
mA). The large increase of
NO
concentration with the discharge current
growth measured
in
the experiment
-
6
times, going from
I
=
5
mA to
80
mA, is probably
related to the increase of
N,
vibrational temperature and vibration stimulated
N,
oxidation, as was discussed in Ref.
[37].
The vibrational excitation of molecules was not
fully considered' in the model with the exception of an
EEDF
evaluation.
It
could lead to
observed discrepancy between the measured and calculated
[NO]
values in the case of high
currents and related strong vibrational excitation. It stays somehow in contrast to the stated
negligible influence of vibrational excitation on
CO,
dissociation
[21].
The measured high
NOz
concentration can result from the efficient
NO
into
NO,
conversion
in
the afterglow
before spectrometer.
100
0
1
80
20
o~""~"l'"''''''l'''~'
5
10
15 20 25
p,Torr
Fig.
3.
The
calculated
(solid
line)
and
experimental
[l]
(filled circles)
CO,
conversion
for
the
mixture
CO,
:
N,
:
He
=
1
:
2
:
13.7
related
to
corresponding
equilibrium
conversion
X,
(dashed
line).
280
Contrib. Plasma Phys.
35
(1995)
3
On the other hand, reports of other experiments do not confirm the existence of high
N,O,
concentrations in laser mixtures [lo, 381 and may suggest further investigation of
that issue using sensitive, time-resolved techniques.
The higher pressure region was probed in dissociation analysis by Smith et al.
[l]
in the
gas mixture
CO,
:
N,
:
He
=
1
:
2
:
13.7 under glow discharge condition:
10
<
E/N
<
60
Td,
j
=
12.3 mA/cm2,
T
=
350
K,
p
c
22
Torr,
gas flow rate
G
=
2 l/s, discharge tube volume
V,
=
0.74 1. Fig. 3 presents calculated
-
continuous line
-
and experimental values
-
dots
-
of CO, conversion measured at the end of the discharge region. Unfortunately, they
represent equilibrium conversion only in the case of low pressure,
p
-
2 Torr. The residence
time in discharge
rd
-
V,/G
=
0.37
s
is much smaller than the calculated
rch
for
p
>
2 Torr.
Therefore, the above mentioned values differ significantly from equilibrium
CO,
conversion,
displayed
in
the same figure as a dashed line, especially at the higher end of the investigated
pressure region. One knows that the chemical relaxation time increases with pressure due
to decrease of
EjN
value in the system. It means that the ratio
of
rd/tch
decreases as the
pressure grows and the measured values of
CO,
conversion refer to an non-equilibrium
state of the considered system, as far as plasma-chemical composition is concerned. Although,
some uncertainty in discharge time estimation, the overall agreement between experimental
and related theoretical
CO,
(non-equilibrated) conversions is satisfactory. Once again
discrepancy at the higher end of the pressure range may evidence underestimation of
CO,
dissociation by electron collisions, the most important process at the initial (far from
equilibrium) stage of
CO,
decomposition in laser mixture.
Finally, we state that the equilibrium conversion and its relation to pressure is generally
well predicted by the presented model. However, some discrepancies are to be expected
at
the description of the initial (non-equilibrium) stage of plasma-chemistry in
CO,
lasers.
4
Equilibrium Conversion in Laser Systems
-
Results and Discussion
The above verified model is used to study chemical processes in different gas mixtures of
CO,
lasers. Preliminary calculations of
CO,
conversion in gas mixtures excited under
DC
discharge conditions of an MLT 1200 laser [15]
-
transverse flow, 1.2
kW,
CO,
laser
-
are presented in Tab. 3 and Fig.
4.
The reduced field
E/N
was estimated from voltage
-
current characteristics.
The equilibrium conversion does not depend significantly on the He relative concentration
in the presented model
for
mixtures CO,
:
He and
0
5
[He]
g
80%.
It varies from 54.0 up
to
56.6%
for
p
=
10
Torr and from 61.7 up to 62.0% for
p
=
40 Torr. This slight dependence
stays somehow in contrast to the rf discharge measurements done by DE BENEDICTIS et al.
[39]. The observed increase
of
CO, decomposition with the [He] growth is related to the
increase of electron mean energy in the
rf
discharge. One sees from Table 3 that the electron
temperature
T,
(calculated from the Boltzmann equation) is almost constant in our system
Table
3
The
C02
equilibrium conversion as a function
of
electron temperature
T,
p
=
10
40Torr
[Tdl
lev1
1
:0:4
1:o:o
I:l:O
1:4:0
56.6 61.7
34
3.1
54.0
62.0 90 3.4
41.9 51.5
87
2.6
38.0
34.2
19
1.8
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN,
CO,
Lasers
I1
28
1
65
I
1
60
x"
45
40
3s
30
0
10
20
30
40
50
p
,Tow
Fig.
4.
Pressure dependence
of
X,(CO,)
for
different gas mixtures circulating in gas-
dynamic
loop
of
MLT
1200
laser.
and the studied mixtures, although the reduced field varies significantly,
34
c
EjN
c
90
Td.
The difference in T,([He]) relations is probably due to various volume-surface ratio in our
case and the one described in Ref.
[39]
and to the role of heterogeneous processes as discussed
later in the paper.
The dependence of
X,(CO,)
on pressure is more significant in studied system but it is
also limited to
15%
in the considered range of
p.
One sees an appreciably different picture in the case
of
CO,
:
N,
mixtures i.e. equilibrium
conversion decreases with
[N,]
and there is a minimum in
X,
dependence on pressure
-
see Fig.4. The values of
EIN
decrease only slightly in the considered range of
[N,]
in
contrast to
T,
which almost halves.
In conclusion, the
EIN
value does not uniquely determine the conditions of glow
discharge in different
CO,
:
N,
:He mixtures however, it is worth noting the generally
monotone dependence of
X,
on
T,
for the investigated mixtures in the studied system.
Comparing the results for an MLT
1200
laser and other systems
[l, 2, 231
one sees
qualitative difference in
X,
=
X,(p)
relation. These relations for different glow discharge
systems are shown in Fig.
5.
The solid, dashed and dotted lines represent the calculated
values of
X,
for the discharge conditions: of the MLT
1200
laser and of the experiments
in Refs.
[2]
and
[23],
respectively. The data measured in experiments
[2,
231
and the related
calculations in paper
I
show that equilibrium conversion decreases with pressure growth.
At low pressure
p
<
15
Torr the
X,
values are generally high
(50%
-90%)
and fall rapidly
as pressure grows. In the middle region
20
c
p
c
40
Torr a kind of plateau is reached.
In contrast, discharge in the MLT
1200
system and the gas mixture
CO,:N,:
He
=
1
:
9
:
15
exposes the saturation character of
X,(p)
dependence but non-monotone function
or monotone increasing functions were also found for gas mixtures
(CO,
:
N,
:He
=
1
:
4:
0)
and
(CO,
:
N2
:He
=
1
:
1
:
0
or
1
:
0
:
x),
respectively
-
see Fig. 4.
The reason for the different
X,(p)
dependence is the role played by ambipolar diffusion
(AD) in these discharges and the relationship
of
AD to pressure. The ambipolar diffusion
can significantly influence sealed-off, small-diameter discharges but is negligible in large
20 Contrib.
Plasma
Phys.
35
(1995)
3
282
Contrib. Plasma Phys.
35
(1995)
3
80-0
60.0
s
-
-
N
40.0
-
XU
20,o
00
20
40
60
p
,Torr
Fig.
5. Pressure dependence
of
XJCO,)
in
gas
mixture
of
MLT
1200
laser and other
DC-discharge
systems
[I.
2,
231.
chambers
or
fast flowing discharge systems. Although
AD
does not appear in our calculation
explicitly, it come into consideration by assuming the experimental value of
EIN
and its
relationship to
p.
In small diameter discharges the effects of ambipolar diffusion decrease
with a pressure growth and
so
glow discharge can be supported by the electric field of a
lower
EjN
value. The decrease of
E/N
value leads to weaker mixture decomposition by
the electron scattering processes. We conclude that in sealed, small-diameter systems,
decomposition processes do not depend
so
much on pressure as on the connected
E/N
value.
The ambipolar diffusion is negligible in large chamber discharges
or
fast flowing systems.
Discharge in this case is controlled by processes of ionization, recombination, attachment
and detachment, which depend on pressure alike. The reduced field
E/N
does not depend
so
much on pressure
(if
at all) as on mixture composition. It means that due to
E/N(
p)
-
const decomposition processes controlled by scattering with electrons will only
slightly depend on pressure in these systems.
Due to pressure dependence of
E/N
=
E/N(p)
the equilibrium conversion of
C02
does not
exhibit saturation but falls to null in the case of small-diameter discharges.
As
soon as
E/N
comes close to its characteristic value (the majority of electrons having energy lower than the
threshold energy for
CO,
dissociation) the rate falls down rapidly with further decrease of
E/N
(increase
of
p).
This is why, the small-diameter discharges will lead
to
lower
COz
conversions for pressures higher than the one connected with characteristic
E/N
and a
threshold value
of
average electron energy. The opposite is true, when going to lower
pressures. Higher values
of
X,
are expected for the same mixtures, due to much higher
values of
E/N
-
see dotted line in Fig.
5.
Finally, the pressure dependence of
X,
is weaker in the case of large diameter discharges.
Moreover, one can decrease the
CO,
conversion by increasing the tube diameter for low
pressure discharges.
We have studied the influence of residence times
in
discharge
T~
(species decomposition
prevails) and in afterglow region
T~~
(recombination crucial). The quasi-equilibrium relative
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN, CO,
Lasers
I1
283
L
10
lo-’
1
o-’
t-=
02
I
NO
F
I
N
02
I
1
100
lob
‘ag
/‘d
Fig.
6.
Steady-stateconcentrations
of
the main species at thedischarge outlet
as
a function
of
T~~;
standard discharge conditions of MLT
1200
laser.
concentrations of neutral species as a function of
Tag/5d
ratio at constant
T~
value are
presented in Fig.
6.
The characteristic plateau for
T,&
>
1000 determines the afterglow
interval needed to finish all important relaxation (recombination) processes. For lower
values of
T,~/T*
<
100
the quasi-equilibrium concentrations vary significantly.
The
C02
concentration increases
-
Xe(C02)
decreases, when the afterglow zone grows.
It
is due to the prolonged
CO
+
0
recombination (both homogeneous
-
in volume, and
heterogeneous
-
on the wall). Simultaneously, the atomic species concentrations fall, because
the increased afterglow period allows the significant relaxation into molecular
form.
The
nitrogen oxides concentrations grow due to their decreased decomposition on lower
concentrations of atomic nitrogen in reaction
NO+N=N,+O.
(5)
Next, we have studied the role of ion-molecular reactions, reactions with electronic excited
species and heterogeneous recombination for the standard condition of an MLT 1200
system, i.e. gas mixture
C0,:N2:
He
=
1
:9:
15,
p
=
30
Torr,
E/N
-
45 Td,
j
=
20
mA/cm2,
T
=
350
K.
The neglect of reactions with electronic excited species or
heterogeneous recombination leads to almost
50%
overestimation of equilibrium
CO,
conversion. However, calculated in the model
X,(CO,)
=
42.9% decreases to
39%
when
CO(a37c)
state
is
not considered. It means that this state in contrast to other electronic
states
is
more efficient in
C02
dissociation than recombination. In the considered conditions,
the reactions with ions do not influence
C02
conversion significantly.
Fig.
7
presents the time evolution of the basic neutral (a) electronic excited (b) and ionized
(c-d) components of the considered mixture during the first gas circulation and after 100
and 500 cycles. After
100
cycles
50%
of
quasi-equilibrium value
of
[CO]
is
reached and the
chemical steady-state is established after about
500
periods.
20’
284
Contrib. Plasma Phys.
35
(1995)
3
10
I
m
lo'
1d3
10".
10'
I
I
I
10'
to3
Id
18
s
-
-
10
-5
>2-
I
-1
10
I
135
Fig.
7.
Time evolution
of
main neutral species at ground state (a), electronic excited states
(b),
negative
ions (c) and positive ions
(d)
at
glow
discharge outlet
for
the first cycle
-
I;
the 100th cycle
-
11;
and 500th cycle
-
111;
standard discharge conditons
of
MLT 1200 laser:
CO,:
N,
:
He
=
I
:
9
:
15,
T,,JT*
=
1O00,
p
=
30
Tor,
EjN
=
45
Td,
j
=
20
mA/cm2.
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN,
COz
Lasers
I1
285
Two different groups of components can be separated: (a) these whose concentration
does not vary much during a cycle but monotone increase (decrease) for two following
cycles is observed:
N,,
CO,,
CO;
0,
and
N,O;
(b) those whose concentration changes
(oscillates) rapidly during the cycle, usually growing fast in the discharge region and relaxing
efficiently in the afterglow e.g.
N,
0
or
NO.
The same oscillatory behaviour
is
observed in
case of
0,
with the opposite trend: concentration falls in the discharge region and grows
in the afterglow. There is
a
small
shift
in characteristic evolution of “fast” species when
comparing subsequent cycles connected with the monotone rise of the “slow” species
concentration.
The
NO
molecule
-
Fig. 7a, is produced in the discharge region mainly in reactions
with the electronically excited atomic nitrogen
N(D
or
P)
due to its relatively high
concentration
N(D,
P)
+
O,(X,
a)
*
NO
+
O(P,
D)
,
N(D)
+
CO,
*
NO
+
CO
.
(6)
(7)
Initially, when
[O,]
is small the reaction (7) constitutes the main channel.
As
soon as the
0,
concentration becomes considerable the other reaction prevails. In the afterglow region
the excited states of nitrogen decay much faster than their ground state is reconverted into
molecular
N,.
It
leads to rapid decomposition of
NO
in reaction (5). At the end of the
afterglow region the value of
NO
concentration reaches practically its value at the discharge
inlet of that cycle. This periodic evolution of
[NO]
is characteristic for most of considered
species despite the fact, that the amplitudes of “oscillations” may vary.
The opposite trend is observed in the evolution of the ozone concentration
-
Fig. 7a.
The
0,
molecule is efficiently decomposed in reaction with electronically excited species
in the discharge region
O(D,
S)
+
O3
3
0,
+
2
0,
O,(a,
b)
+
0,
202
+
0.
(8)
Outside that region the influence of electronic states diminishes and slow
[O,]
production
via a channel
(9)
0
+
0,
+
M*03
+
M
overcomes its initial decomposition. It does lead to the small increase of
[O,]
if compared
with the initial value in the considered cycle.
-
Fig. 7b emphasizes the main role played by the excited
N,(A)
molecule in the chemical
kinetics of CO,
:
N,
:
He mixture in the DC discharge. The relatively high concentrations
of electronic excited
0
and
N
result from the fast growth of
[O]
and
[N]
in the discharge
region
-
see Fig. 7a. The increasing in time
0,
concentration leads to significant values
of
[O,(a)]
and
[O,(b)].
These components characterized by low excitation energy
-
0.98
and 1.64eV, are the most long-lived, excited species in the mixture. In contrast to other
fast quenched electronic states the
O,(a)
excited state does not completely decay in the
afterglow region.
The basic negative ions in the system under consideration are COY and
0;
-
see
Fig. 7c. The role
of
the second one grows from cycle to cycle in accordance with increasing
[O,].
At the discharge outlet the negative ions concentration falls due to increased
concentrations of atoms and electronic excited species which strengthen the electron
detachment processes.
The role of positive ions changes during discharge period
T~
as well as when going from
the initial gas circulation to the later one
-
Fig.7d. During the initial cycles, the CO:
and C,O: ions are basic. Later, when the
0,
concentration increases
(t
2
100
cycles) the
0:
ions become crucial in the region near the discharge inlet and simultaneously
concentration of
NO+
ions prevails at the end of discharge region.
286
Contrib. Plasma
Phys.
35
(1995)
3
4
Conclusions
In this paper we have proposed the model
for
studying the plasma-chemical react'ions in
CO, low-pressure, DC-excited lasers. The verification
of
the model basing on existing
experimental data [1,2,6,10] has been done taking into account both the value
of
steady-state
composition
-
mainly X,(CO,), and the kinetics of equilibration process.
A
good agreement
of theoretical and experimental results convinces
us
about the validity
of
the model and its
assumptions for the considered range
of
parameters
p,
E/N
and
j.
The dependence
of
equilibrium conversion on the reduced field
EIN,
pressure and current
density differs for different discharge chambers, e.g. small radius tubes or large radius
containers. The equilibrium conversion increases with growth of
E/N
and
j
and with
decrease of pressure for discharges in small diameter tubes. The growth with
j
becomes less
significant
as
one goes to higher
E/N
values (lower
p).
In the case
of
large container discharge reduced field
E/N
does not depend on
p.
The
equilibrium conversion exhibits saturation character for standard
CO,
:
N,
:
He
=
1
:
9
:
15
gas mixture, is a growing function
of
p
for CO,
:
He mixtures and loses its monotone
character in
CO,:N,
gas. In this case
X,
is an almost monotone function of electron
temperature, even for different mixtures considered here.
The high relative concentrations of
NO2
up to
0.23%
(I
=
80
mA) measured by TANNEN
et al.
[2]
have not been confirmed by our model,
[NO,]
-
In
contrast, the calculated
WO]
-
0.023
agreed very well with the measured relative concentration of
NO,
0.02
<
[NO]
d
0.03%,
for low current
(I
=
5
and 10mA) discharges. The discrepancy
between theoretical and experimental
[NO]
values observed for the highest considered
currents
(I
=
80
mA) is probably related to strong vibrational
N,
excitation and its role
in nitrogen oxidation.
The role of ion-molecular reactions, reactions with electronic excited species and
heterogeneous recombination was studied for low pressure
(-
30
Torr) lasers. It has been
proved that neglect
of
reactions with electronic excited species
or
heterogeneous recombina-
tion leads to almost
50%
overestimation
of
equilibrium CO, conversion. It means the
heterogeneous recombination constitutes an important process in glow discharge even for
pressures higher than
2
Torr as in Ref. [27]. The
CO(a3n)
state, in contrast to other electronic
states, is more efficient in CO, dissociation than recombination.
The
CO,
and
NO
concentrations increase
-
X,(C02)
decreases, when the afterglow
zone
in convection-cooled laser grows.
Acknowledgements
This work has been partly sponsored by. Polish Academy
of
Sciences and the Committee
for Scientific Research under contract PB
599/8/91/KBN.
The authors would like to thank
Dr.
J.
STANCO
for
helpful discussions,
for
reading and commenting
on
the manuscript.
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984) (in
Russian).
Cimento
14
(1992)
1051.
Fiz.
18
(1992) 93.
XX
ICPIG, Contributed Papers, Pisa (1990) 1176.
Proc.
1810
(1993) 133.
(1994) 25.
(1980) (in Russian).
and MOLINARI, E., Gazetta Chim. Ital.
113
(1983)
615.
Russian).
Ion-molecular reactions in gases, Nauka, Moscow (1979) (in Russian).
288
Contrib. Plasma Phys.
35
(1995)
3
[47] The same as
for
0:.
[48] The same as for CO:.
[49] SMETANIN,
V. V.,
Theoretical investigations of heat transfer in supersonic flows with taking into
[50]
ATKINSON, R., BAULCH, D.
L.,
Cox,
R.
A,, HAMPSON,
R.
F.,
KERR,
J.
A.,
TROE,
J., J.
Phys. Chem.
[51]
KISLYUK, M.
U.,
Khim. Fizika
8
(1989) 59.
I521
POLAK, L.
S.,
SLOVETSKI, D.
I.,
and TODESAYTE, R.
D.,
Khimija
Vys.
Temp.
10
(1976)
64.
[53]
NIST
Standard Reference Database 17 (1990), distributed by
NIST
Standard Reference Data,
account excited particles, PhD dissertation, Moscow (1990) (in Russian).
Ref. Data
18
(1989) 881.
Gaithersburg, MD 20899,
USA.
Appendix
Rate constants for ion-molecular reactions;
T,(
T,)
is the gas kinetic (electron) temperature.
Ionization
Al.
A2.
A3.
A4.
A5
A6.
A7.
Dissociative attachment
B1.
B2.
B3.
B4.
B5.
B6.
B7.
Three-body attachment
C1. O+e-+M-+O-+M
C2.
CO,
+
e-
-+
CO:
+
2 e-
N,
+
e-
-
Ni.
+
2 e-
He
+
e-
-+
HeC
+
2 e-
CO
+
e-
-+
CO'
+
2e-
0,
+
e-
+
0:
+
2e-
N,(A)
+
e-
-+
N:
+
2 e-
He(3S)
+
e-
3
Hef
+
2e-
CO,
+
e-
-+
0-
+
CO
CO
+
e-
+
0-
+
C
0,
+
e-
-+
0-
+
0
NO,
+
e-
-+
0-
+
NO
N,O
+
e-
--t
0-
+
N,
0,
+
e-
-+
0;
+
0
0,
+
e-
-+
0-
+
0,
0,
+
e-
+
M
-0;
+
M
(23.
C4.
0,
+
e-
+
M
-+
0;
+
M
NO,
+
e-
+
M
+NO;
+
M
Associative detachment
D1.
0-
+
0
-+
0,
+
e-
D2. O-+N+NO+e-
D3.
0-
+
CO
--*
CO,
+
e-
D4.
0-
+
0,
+
O3
+
e-
Boltzmann equation
2.0.
lo-"
2.0
*
10-
lo
6.6. 10-9Tb.75
4.0
.
10-
1.0.10-3'
2.0
.
10-30
(M
=
0,)
2.0.10-30
(M
=
co)
3.0.10-30
(M
=
co,)
5.0.10-3l
1.6. 10-si
(M
=
0,)
1.6.10-3'
(M
=
co)
1.6.10-3l
(M
=
co,)
2.0. (M
=
He)
1.0. (M
=
N2)
8.2.
(M
=
He)
1.6. (M
=
N,)
2.0. 10-
lo
2.2
.
10-
lo
6.0
*
lo-''
1.0.
lo-',
See text
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN, C02
Laser
I1
D5.
0-
+
N,
-+
N,O
+
e-
D6.
0-
+
NO
-+
NO,
+
e-
D7..
0-
+
O,(a)
-+
0,
+
e-
D8.
0;
+
0
-+
0,
+
e-
D9.
0;
+
N
-+
NO,
+
e-
D10.
NO;
+
0
-+
NO,
+
e-
D11.
NO;
+
N
-+
N,
+
0,
+
e-
D12.
NO;
+
0
+
NO,
+
0,
+
e-
D13.
NO;
+
N
-+
N,
+
0,
+
e-
D14.
0;
+
0
-+
0,
+
0,
+
e-
D15.
0;
+
0,
-+
3
0,
+
e-
D16.
CO;
+
CO
-+
2C0,
+
e-
Collisional detachment
El.
0-
+
CO,
-+
CO,
+
0
+
e-
E2.
0-
+
O,(b)
-+
0,
+
0
+
e-
E3.
0-
+
N,(A)
-+
N,
+
0
+
e-
E4.
0-
+
N,(B),+
N,
+
0
+
e-
E5.
0;
+
0,
-+
0,
+
0,
+
e-
E6.
0;
+
O,(a)
-+
0,
+
0,
+
e-
E7.
0;
+
O,(b)
-+
0,
+
0,
+
e-
E8.
0;
+
N,(A)
-+
0,
+
N,
+
e-
E9.
0;
+
N,(B)
-+
0,
+
N,
+
e-
E10.
NO-
+
M
-+
NO
+
M
+
e-
Ell.
0;
+
0,
-+
0,
+
0,
+
e-
Neutral dissociation by electron impact
F1.
CO,
+
e-
-+
CO
+
0
+
e-
F2.
N,
+
e-
-+
N
+
N
+
e-
F3.
0,
+
e-
-+
0
+
0
+
e-
F4.
CO
+
e-
-+
C
+
0
+
e-
F5.
CO,
+
e-
-+
CO
+
O(D)
+
e-
F6.
CO,
+
e-
-+
CO(a)
+
0
+
e-
F7.
0,
+
e-
t
0
+
O(D)
+
e-
Ion-electron recombination
GI.
CO:
+
e-
-+
CO
+
0
G2.
0;
+
e-
-+
0
+
0
G3.
NO'
+
e-
-+
N
+
0
G4.
N:
+
e-
-+
N
+
N
G5.
NO:
+
e-
-+
0,
+
N
G6.
N,O+
+
e-
-+
N,
+
0
G7.
N,O:
+
e-
-+
N,
+
0,
G8.
N:
+
e-
-+
N,
+
N
G9.
N:
+
e-
-+
N,
+
N,
G10.
0:
+
e-
-+
0,
+
0,
G11.
C20:
+
e-
-+
CO
+
CO
G12.
CiOf
+
e-
-+
CO,
+
CO
G13.
C,O:
+
e-
-+
CO,
+
CO,
Two-body ion-molecule reactions
H1.
CO:
+
0
-+
0:
+
CO
H2.
CO;
+
0,
-+
0:
+
CO,
1.0.
lo-',
2.5
'
lo-''
3.0.
lo-''
3.3
.
10-l0
4.0.
lo-''
1.0.
lo-',
1.0.
lo-',
1.0.
lo-',
1.0.
lo-',
3.0.
lo-''
1.0.10-13
5.0.10-13
4.0.
lo-',
6.9.
lo-''
2.2. 10-9
1.9. 10-9
6.0
.
10-
lo
2.0.
10-'O
3.6.
lo-''
2.1.10-9
2.5
.
10-9
5.0
.
lo-''
2.3.
lo-"
Boltzmann equation
2.6.
lo-''
5.0.
lo-''
See text
290
Contrib.
Plasma
Phys.
35
(1995)
3
H3.
CO:
+
NO
-+
NO'
+
CO,
H4.
N;
+
0,
-+
0:
+
N,
H5.
N:
+
NO
-+
NO'
+
N,
H6.
N;
+
CO
+
CO'
+
N,
H7.
N:
+
CO,
-+
CO:
+
N,
H8. He'
+
N,
---t
N:
+
He
H9. He'
+
CO,
-+
CO'
+
He
+
0
H10.
Cot
+
CO,
-+
CO:
+
CO
H11.
CO'
+
0,
-+
0;
+
CO
H12.
0:
+
N
-+
NO'
+
0
H13.
0:
+
NO
-+
NO'
+
0,
H14.
0:
+
NO,
-+NO:
+
0,
H15.
0:
+
N205
-+NO:
+
NO,
H16.
NO'
+
0,
-+
NO:
+
0,
H17.
NO'
+
N205
-+NO:
+
NO,
H18.
NO:
+
NO
-+NO'
+
NO,
H19.
N20'
+
NO
-+
NO'
+
N,O
H20.
Nl
+
0,
--*
0:
+
N,
+
N
H21.
N:
+
0,
--*
NO'
+
N2
+
0
H22.
Nl
+
0,
-+
NO:
+
N,
H23.
N:
+
NO
-+
NO'
+
N,
+
N
H24.
Nl
+
NO
-+
N20t
+
N,
H25.
N,'
+
0,
-+
0:
+
N,
+
N,
H26.
N:
+
NO
-+
NO'
+
N,
+
N,
H27.
N,'
+
CO,
-+
CO:
+
N,
+
N,
H28.
N,'
+
He
-+
N:
+
N,
+
He
H29.
0,'
+
NO
-+
NO'
+
0,
+
0,
H30.
0,'
+
0
-+
0:
+
0,
H31.
N20i
+
0,
-+
0,'
+
N,
H32.
N,O,
+
N2
-+
0,'
+
N,
+
N,
H33.
N20i
+
He
-+
0,'
+
N,
+
He
H34.
C202
+
0,
-+
0:
+
CO
+
CO
H35.
C,O:
+
M
-+
CO'
+
CO
+
M
H36.
C20:
+
CO
-+
C201
+
CO,
H37.
C,O,f
+
CO
-+
C203
+
CO,
H38.
C20f
+
CO,
-+
CO:
+
CO,
+
02
+
NO2
+
co,
1.2
.
10-
lo
7.0.
lo-''
4.9.
lo-''
7.0.
lo-"
9.0.
lo-''
6.3
.
10-
''
1.0. 10-9
1.2. 10-9
2.0. 10-'O
1.9.
lo-"
7.0.
lo-''
6.6
*
10-
lo
8.8
.
lo-''
1.0. 10-l4
6.0.
lo-''
2.9
.
10-
''
2.9.
lo-''
2.3
.
10-
''
3.3.
lo-''
4.4
.
10-
7.0
.
10-
''
7.0.
lo-''
4.0.
lo-''
4.0.
lo-''
7.0.
lo-''
1.0. 10-
lo
3.0.
lo-''
5.0
.
10-
''
4.0.10-1'
2.4
.
10-
'
exp
(-
2785/T,)
9.0.
lo-*
exp (-2785/T,) [451
5.0.
lo-',
[461
1.0
.
10- [461
1.1. 10-9 [461
9.0
.
10-
''
[461
1.0- 10-l4 [461
H39. He(,S<+
CO,
-+
CO:
+
He
+
e-
5.0.
lo-''
H40. He(,S)
+
N,
-+
N;
+
He
+
e-
8.0.
lo-''
H41.
0-
+
034
0;
+
0
7.0.
lo-''
H42.
0-
+
NO,
-+
0;
+
NO
H43.
0-
+
NO,
-+
NO;
+
0
0-
+
N,O
-+
NO-
+
NO
H46.
0;
+
0,
--*
0;
+
0,
H47.
0;
+
NO,
-+
NO;
+
0,
1.0. 10-9
1.0. 10-9
H44.
H45.
0;
+
0
-+
0-
+
0,
2.0.
lo-''
3.0.
lo-''
3.5
.
10-
lo
2.0.10-9
1.0.
lo-"
5.0.
lo-''
2.5
.
lo-''
1.0.
10-
l1
H48.
H49.
0;
+
NO,
-+
NO;
+
0,
H50.
0;
+
0
--+
0;
+
0,
0;
+
N,O
-+
0;
+
N,
H51.
0;
+
NO
--*
NO;
+
0
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN,
CO,
Laser
11
29 1
H52.
0;
+
NO
-+
NO;
+
0,
H53.
0;
+
NO,
-+
NO;
+
0,
H54.
0;
+
NO,
+NO;
+
0,
H55.
0;
+
NO,
-+
NO;
+
0,
H56.
0;
+
CO,
+
CO;
+
0,
H57.
CO;
+
0
+
0;
+
CO,
H58.
COY
+
NO
-*
NO;
+
CO,
H59.
CO;
+
NO,
+
NO;
+
CO,
H60.
COT
+
0
-*
CO;
+
0,
H61.
COT
+
0,
-+
0;
+
0,
+
CO,
H62.
CO,
+
NO
.+
NO;
+
CO,
H63.
NO-
+
0,
+
0;
+
NO
H64.
NO;
+
0,3
NO;
+
0,
H65.
NO;
+
NO,
-+
NO;
+
NO
H66.
NO;
+
NO,
-+
NO;
+
NO,
H67.
NO;
+
NO
-+
NO;
+
NO,
H69.
0;
+
CO,
++
CO,
+
0,
Three-body ion-molecule reactions
J1.
0-
+
0,
+
M
--*
0;
+
M
52.
0-
+
CO,
+
M
-+COT
+
M
H68.
0,
+
NO
-+
NO;
+
02
53.
54.
J5.
0-
+
NO
+
M
-+NO;
+
M
0;
+
CO,
+
M
-+COT
+
M
0,'
+
0,
+
M
-+
0:
+
M
56.
5-7.
58.
0;
+
N,
+
M
-+
N,O,'
+
M
co:
+
CO,
+
CO,
-+
c20:
+
CO,
Ni
+
N,
+
M
-+
Nf
+
M
J9.
C20:
+
CO
+
CO,
J10.
C,Of
+
CO
+
C02
Ion-ion-recom bination
K1.
K2.
K3.
K4.
K6.
K7.
-+
c,o;
+
CO,
+
CO,
+
c20:
+
CO,
+
co,
CO,'
+
CO;
-,
CO,
+
CO,
+
0
CO:
+
CO,
-+
CO,
+
CO,
CO,'
+
NO,
-+
CO
+
NO,
+
0
CO,'
+
NO;
+
CO
+
NO,
+
0
NO'
+
CO;
--f
CO,
+
NO
+
0
NO'
+
CO,
-+
CO,
+
NO
+
02
K5.
CO;
+
0;
+
CO
+
02
+
0
+
02
2.6.
lo-',
7.0.
lo-''
2.8.
lo-''
5.0.
lo-''
4.0.
lo-''
8.0.
10-
9.0. 10-1,
1.0. 10-
lo
2.0. 10-1°
1.3
.
10-
lo
5.0.
lo-"
9.0.
10-
lo
1.8.
lo-''
4.0.
lo-',
3.0.
lo-''
2.0.
10-1'
2.5.
lo-''
4.8.
lo-''
3.0.
10-28T-1
2.0.
lo-,'
(k
=
He)
3.0.
lo-,'
(M
=
0,)
3.0.
lo-,'
(M
=
CO)
3.0
*
10-28Tq-'
1.5.
lo-,'
(M
=
He)
2.6.
lo-,'
(M
=
N2)
3.0.
lo-,'
(M
=
He)
8.0.
(M
=
N2)
3.0.
lo-"
1.0.10-29
(M
=
N,)
9.0.10-29
(M
=
co,)
1.0.10-29
2.0.10-30
(M
=
0,)
1.9.
(M
=
He)
8.0.
(M
=
N2)
2.6
'
4.2.
5.0.
10-7
5.0.
lo-'
6.0.10-7
5.0.10-7
6.0. 10-7
6.0. 10-7
6.0
.
10-7
(41
[41
[41
[41
[41
141
[41
292
Contrib.
Plasma Phys.
35
(1995)
3
K8.
NO'
+
NO;
+
NO,
+
N
+
0
K9.
NO'
+
NO;
-+
NO,
+
N
+
0
K10.
NO'
+
0;
+
0,
+
N
+
0
K11.
NO'
+
0-
+
NO
+
0
K12.
0;
+
COY
+
CO,
+
0,
+
0
K14.
0;
+
NO;
+
NO,
+
0
+
0
K15.
0;
+
NO;
+
NO,
+
0
+
0
K16.
0;
+
0;
+
0,
+
0
+
0
K17.
0;
+
0-
+
0,
+
0
K18.
Ni
+
CO;
-+
C02
+
N,
+
0
K20.
Ni
+
NO;
--r
NO,
+
N
+
N
K21.
Ni
+
NO;
+
NO,
+
N
+
N
K22.
N:
+
0;
-+
N2
+
0
+
0
K23.
N;
+
0-
+
N,
+
0
K24.
N20:
+
COY
+
N203
+
CO,
K25.
N2O;
+
CO;.+
N204
+
CO,
K26.
N20;
+
NO;
+
NO2
+
N2
K27.
N,O;
+
NO;
+NO3
+
N2
K28.
N201
+
0;
+
N,
+
0,
+
0,
K29.
N,O:
+
0-
--*
N,
+
O2
+
0
K30.
C20f
+
CO;
+
C02
+
CO,
K31.
C20:
+
COT
+
CO,
+
CO,
K32.
C,Of
+
NO;
-+
C02
+
CO,
K33.
C20f
+
NO;
+
CO,
+
CO,
K34.
C20f
+
0;
--+
CO,
+
CO,
+
0,
K35.
C20:
+
CO;
+
CO,
+
CO,
K36.
C20:
+
CO,
+
CO,
+
CO,
K37.
C201
+
NO;
--*
CO,
+
CO
K38.
C201
+
NO;
-+
CO,
+
CO
K39.
C20:
+
0;
-+
CO,
+
CO
K40.
C,Ol
+
CO;
+
CO
+
CO
K41.
C20;
+
COT
+
CO
+
CO
K42.
C201
+
NO;
-+
CO
+
CO
K43.
C,O;
+
NO;
+
CO
+
CO
K44.
C,O:
+
0;
+
CO
+
CO
+
0,
K13.
0;
+
CO;
+
C02
+
0,
+
02
K19.
N;
+
CO;
+
C02
+
N,
+
02
+
02
+ 02
+
co,
+
0
+
co,
+
0,
+
NO2
+
NO,
+
0
+co+o
+
co
+
0,
+
NO2
+
NO2
+
0
+
02
+
CO,
+
0
+
CO,
+
0,
+
NO2
+
NO2
+
0
5.1. 10-7
8.1. 10-7
5.8
.
10-7
4.9
'
10-7
3.0. 10-7
3.0. 10-7
4.1
,
10-7
1.3.10-7
4.2. 10-7
1.0
'
10-7
3.0. 10-7
3.0- 10-~
4.1. 10-~
1.3. 10-7
4.2. 10-7
1.0.
10-7
3.0.10-7
3.0. 10-7
4.1
.
10-7
1.3. 10-~
4.2. 10-7
1.0. 10-~
5.0.
10-~
5.0-
10-7
6.0
.
10-7
5.0.
10-7
6.0.10-7
5.0.
10-7
5.0.
10-~
6.0. 10-7
5.0
.
10-7
6.0. 10-~
5.0.10-7
5.0.
10-7
6.0. 10-7
5.0. 10-7
6.0
.
10-7
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN,
COz
Laser
I1
293
Electronic levels excitation
L1.
L2.
L3.
L4.
L5.
He
+
e-
-+
He(3S)
+
e- Boltzmann equation
L6.
L7.
L8.
L9.
N,
+
e- -+
N,(A)
+
e-
N,
+
e-
4
N,(B)
+
e-
N2
+
e-
3
N,(a)
+
e-
N,
+
e-
-+
N2(C)
+
e-
CO
+
e-
-+
CO(a)
+
e-
0,
+
e-
+
O,(a)
+
e-
0,
+
e-
3
O,(b)
+
e-
0,
+
e-
-+
02(A)
+
e-
See text
Reactions with electronically excited components and electronic levels relaxation
M1. N(D)
+
N
-+
N
+
N
M2. N(D)
+
0
+
N
+
0
M4. N(D)
+
O2
-+
NO
+
O(D)
M5. N(D)
+
N2
-+
N
+
N2
M6. N(D)
+
NO
+
N,
+
O(D)
M7. N(D)
+
O,(a)
-+
NO
+
O(D)
M8. N(D)
+
N20
--*
N,
+
NO
M9. N(D)
+
CO,
-+
NO
+
CO
M10. N(D)
'+
CO
-+
N
+
CO
M11. N(D)
+
He
-+
N
+
He
M12.
N(P)
+
N
N(D)
+
N
M13. N(P)
+
0
-+
N(D)
+
0
M14.
N(P)
+
0,
+
NO
+
0
M15. N(P)
+
0,
-+
NO
+
O(D)
M16.
N(P)
+
0,
+
NO
+
O(S)
M17. N(P)
+
N,
-+
N(D)
+
N,
M18. N(P)
+
NO
-+
NO
+
N(D)
M19. N(P)
+
He
-+
N(D)
+
He
M21. N(P)
+
O,(a)
-+
NO
+
0
M22.
O(D)
+
N
-+
0
+
N
M23.
O(D)
+
0
-+
0
+
0
M24.
O(D)
+
N2
-+
N,
+
0
M26.
O(D)
+
NO
-+
NO
+
0
M27.
O(D)
+
NO,
-+
NO
+
0,
M28.0(D)
+
O3
-+
0,
+
0,
M29.
O(D)
+
O3
+
0,
+
0
+
0
M30.
O(D)
+
CO,
-+
0
+
CO,
M31.
O(D)
+
N20
-+
N,
+
0,
M33.
O(D)
+
He
-+
0
+
He
M34.
O(D)
+
O,(a)
-+
0,
+
0
M35.
O(S)
+
N
-+
0
+
N(P)
M36.
O(S)
+
0
-+
O(D)
+
O(D)
M37.
O(S)
+
N,
-+
N2
+
O(D)
M38.
O(S)
+
O2
-+
02(A)
-t-
0
M39.
O(S)
+
NO
--*
NO
+
O(D)
M40.
O(S)
+
NO,
-+
NO
+
0,
M3. N(D)
+
02
+
NO
+
0
M20. N(P)
+
O,(U)
-+
O,(A)
+
N
M25.
O(D)
+
02
-+
02(b)
+
0
M32.
O(D)
+
N2O
-+
NO
+
NO
1.0.10-13
5.7.
lo-',
exp
(-505/T,)
7.5.
lo-',
exp
(-133/T,)
2.5
.
lo-',
exp
(-
133/T,)
9.4
. exp
(-510/T,)
5.4
.
10-
1.0.
lo-"
1.2.
lo-"
exp
(-570/T,)
2.5
*
lo-',
4.6
*
lo-''
1.8.
lo-',
1.0
*
lo-"
2.5.10-13
7.0.10-13
7.0.10-13
7.0.10-13
3.3
.
10-
l'
3.0
.
10-
'
4.2.
lo-''
5.0-
lo-"
5.0
*
10-
8.0.
lo-',
1.0.10-13
1.9
.
10-
l1
exp
(107/T,)
3.2
. 10-
l1
exp
(67/T,)
4.0.
lo-"
1.4.
lo-''
1.2
.
10-
lo
1.2
.
10-
lo
6.8
*
lo-"
exp (120/T,)
4.4.
lo-"
6.6.
lo-"
3.0.
3.0
.
10-
l1
1.0
.
10-
l3
2.0. 10-l4
5.0.10-17
4.9
.
lo-',
exp
(-
850/T,)
5.7
.
10-
lo
5.0.
lo-''
294
M41.
O(S)
+
O3
-+
0,
+
0
+
0
M43.
O(S)
+
O,(a)
-+
0
+
0
+
0
M44.
O(S)
+
O,(a)
+
O,(A)
+
0
M45.
O(S)
+
O,(a)
-+
O,(b)
+
O(D)
M46.
CO(a)
+
He
+
CO
+
He
M47.
CO(a)
+
N,
-+
CO
+
N,
M48.
CO(a)
+
0,
--*
CO
+
0,
M49.
CO(a)
+
0,
--*
CO
+
0
+
0
M50.
CO(a)
+
0,
--*
CO,
+
0
M51.
CO(a)
+
CO
-+
CO
+
CO
M52.
CO(a)
+
CO
3
CO,
+
C
M53.
CO(a)
+
CO,
-+
CO
+
CO,
M54.
CO(a)
+
CO,
+
CO
+
CO
+
0
M55. N,(A)
+
N
-+
N,
+
N(D)
M56. N,(A)
+
N
-+
N,
+
N(P)
M57. N,(A)
+
0
--*
N,
+
O(D)
M58. N,(A)
+
0
-+
N,
+
O(S)
M59. N,(A)
+
N2
--*
N,
+
N,
M60.
N,(A)
+
0,
-+
N,
+
0
+
0
M62.
N,(A)
+
0,
-+
N,O
+
0
M63.
N,(A)
+
NO
-+
N,
+
NO
M64. N,(A)
+
N,O
-+
N,
+
N,
+
0
M65.
N,(A)
+
CO
-+
N,
+
CO(a)
M66.
N,(A)
+
N,(A)
-+
N,(B)
+
N,
M67.
N,(A)
+
N,(A)
--t
N,(C)
+
N2
M68.
N,(A)
+
N,(B)
+
N2(C)
+
N,
M69. N,(B)
+
N,
-+
N,(A)
+
N2
M70.
N,(B)
+
0,
-+
N,(A)
+
O,(a)
M71.
N,(B)
+
0,
--$
N,(A)
+
0,
M72. N,(B)
+
He
-+
N2(A)
+
He
M73. N,(C)
+
N,
-+
N,(B)
+
N,
M75.
N2(C)
+
0,
+
N,(B)
+
0
+
0
M76. N,(a)
+
N2
-+
N,
+
N,
M77. N,(a)
+
0,
-+
N,
+
0,
M78. N,(a)
+
NO
-+
N,
+
NO
M79. N,(a)
+
N,O
-+
N,
+
N,O
M80.
O,(a)
+
N
--*
0,
+
N
M81.
O,(U)
+
0
+
0,
+
0
M42.
O(S)
+
CO,
-+
O(D)
+
C02
M61. N,(A)
+
0,
+
N,
+
O,(A)
M74. NZ(C)
+
02
--*
N,(B)
+
O,(b)
M82.
O,(U)
+
N2
-+
02
+
N2
M83.
O,(U)
+
02
-+
02
+
02
M84.
O,(a)
+
NO
-+
0,
+
NO
M85.
O,(a)
+
O3
-+
0,
+
0,
+
0
M86.
O,(b)
+
N
--t
O,(a)
+
N
M87.
O,(b)
+
0
-+
O,(a)
+
0
M88.
O,(b)
+
N,
+
O,(a)
+
N2
M89.
O,(b)
+
0,
-+
O,(a)
+
0,
M91.
O,(b)
+
N,O
--*
O,(a)
+
N,O
M92.
O,(b)
+
NO,
--t
O,(a)
+
NO,
M90.
O,(b)
+
NO
+
O,(U)
+
NO
5.8
.
lo-''
4.0.
lo-"
1.2.
lo-''
4.0.
lo-"
5.0.
lo-"
6.0.
lo-"
6.0
.
10-
l1
5.0.
lo-',
1.0
*
lo-''
1.2.
lo-',
1.5.
lo-"
1.5
.
lo-"
2.2.
lo-"
2.2.
lo-"
6.0.
lo-',
2.4.
lo-"
3.0.
lo-'*
1.6.
lo-"
3.6.10-13
1.0.10-14
8.0.10-13
5.0.10-14
6.5.
lo-"
6.2.
lo-"
1.6.
lo-',
8.0.
lo-"
1.5.
lo-''
1.0.10-11
3.0.
lo-"
1.5.
lo-''
1.5.
lo-''
3.0.
lo-''
1.5.
lo-"
1.5
.
lo-''
1.5.
lo-''
2.8.
lo-"
3.6
.
lo-''
1.7.
lo-''
7.0
.
.3.0.
lo-,'
1.7
*
lo-''
1.9.10-13
2.7 .10-15
4.5.10-17
4.0.10-15
1.0.10-13
8.0
.10
-
14
2.1 .lo45
4.6.10-17
3.7.10-14
1.0
'
10-13
2.8.10-14
A.
CENIAN,
A.
CHERNUKHO,
V.
BORODIN, C02
Laser
I1
M93.
O,(b)
+
O3
+
0,
+
0,
+
0
M95. O,(A)
+
N
+
02
+
N(P)
M96.
O,(A)
+
0
-+
02
+
O(S)
1.3.
lo-"
5.4
'
10-1,
1.3.
lo-"
1.3.
lo-"
M94.
O,(b)
+
O3
+
0,(4
+
O3
M97. O,(A)
+
N2
+
O,(b)
+
N2
M98.
O,(A)
+
02
+
O,(b)
+
02
N1.
N,(C)
+
N,(B)
+
hv
2.5
.
107
N2.
N,(B)
-+
N,(A)
+
hv
2.0
.
105
N3.
N2(4
-+
N,
+
hv
3.3
'
10'
9.3 .10-15
1.3.10-13
Radiation processes
Heterogeneous recombination and relaxation
P1.
P2.
P3.
P4.
P5.
P6.
P7.
P8.
P9.
P10.
Pll.
P12.
P13.
P14.
P15.
P16.
CO
+
0
+
wall
3
CO,
+
wall
0
+
0
+
wall
--f
0,
+
wall
N
+
N
+
wall
+
N,
+
wall
N
+
0
+
wall
-+
NO
+
wall
N,(A)
+
wall,'+ N2
+
wall
O,(a)
+
wall
-,
0,
+
wall
O,(b)
+
wall
-+
0,
+
wall
O(D)
+
wall
-+
0
+
wall
O(S)
+
wall
-,
0
+
wall
N(D)
+
wall
+
N
+
wall
N(P)
+
wall
-+
N
+
wall
N2(B)
+
wall
+
N,
+
wall
N2(C)
+
wall
-+
N,
+
wall
N2(4
+
wall
-+
N,
+
wall
O,(A)
+
wall
-+
0,
+
wall
CO(a)
+
wall
-+
CO
+
wall
Neutral molecule reactions
R1.
R2. N+O+M-+NO+M
N
+
N
+
M
+
N,(A)
+
M
R3.
N
+
0,eNO
+
0
R4.
N
+
NOeN,
+
0
R5.
N
+
NO,
$0
+
N,O
R6. N
+
NO,$NO
+
NO
R7. N
+
NO,+O
+
0
+
N,
R8.
N
+
NO,
e
N,
+
0,
R9.
N
+
O3
e
NO
+
0,
R10.
N
+
CO,
+
NO
+
CO
R11.
N
+
NO,
+
NO
+
NO,
R12.
0
+
0
+
Me0,
+
M
R13.
0
+
0,
+
Me03
+
M
keff
=
7.4
.10-17/rdc,
cm3/s
k,
=
5
.1016/[CO],
cm/s
=
10-3
=
10-3
y
=
3.10-~
=
4.10-5
y=2.10-2
y=l
y=l
y=l
y=l
y=l
y=l
y=l
y=l
y=l
8.3
.
exp
(500/T,)
1.1
.
lO-l4e;p
(-3150/T,)
1.9. 10-31~-0.5
1.1
.
10-12~,0.5
3.0.
lo-',
2.3.
lo-',
9.1.10-13
7.0.10-13
.2.0
'
10-16
1.0.10-19
5.7.10-13 [41
5.2
.
exp
(9OO/T,)
(M
=
He)
[34],
1.9
.
exp
(900/T,)
(M
=
N,)
1341,
5.2
.
exp
(900/T,) (M
=
0,)
[341,
5.2.
exp
(900/T,)
(M
=
CO)
[MI,
5.2
.
exp
(900/T,) (M
=
CO,)
[34],
(M
=
He)
[531
3.3. 10-317--1.20
(M
=
N2)
[531
(M
=
0,)
t531
(M
=
CO)
1531
1.7.10-30~:133 (M
=
co,)
[531
4.1
.
10-31T~l.20
5.5.
10-3lT5.20
5.5.
10-31TP1.20
296
Contrib.
Plasma
Phys.
35
(1995)
3
R14.
0
+
CO
+
MeCO,
+
M
R15.
0
+
N,
+
M
e
N,O
+
M
R16.
0
+
NO
+
M
-+
NO,
+
M
R17.
0
+
NO,
+
M
-+
NO,
+
M
R18.
0
+
0,
-+
0,
+
0,
R19.
0
+
NO,
-+
NO
+
0,
R20.
0
+
N,O
-+
N,
+
0,
R21.
0
+
N20
-+
NO
+
NO
R22.
0
+
CO,
e
CO
+
0,
R23.
0
+
NO,
-+
0,
+
NO,
R24.
0
+
C,O
-+
CO
+
CO
R25.
0
+
N203
-+
NO,
+
NO,
R26.
0
+
N204
-+
NO,
+
NO,
R27.
0
+
N205
-+
NO,
+
NO,
R28. C
+
CO
+
M
+
C,O
+
M
R29. C
+
O2
-+
CO
+
0
R30. C
+
CO,
-+
CO
+
CO
R31.
0,
+
C20
-+
CO,
+
CO
R32.
0,
+
NO3
-+
NO,
+
0,
R33. NO
+
0,
-+
0,
+
NO,
R34.
NO
+
NO,
+
M
-+
N,O,
+
M
R35.
NO
+
NO,
-+
NO,
+
NO,
R36. NO
+
N,0eN2
+
NO,
R37. NO
+
NO
+
NO+NO,
+
N20
R38. CO
+
NO,
-+
CO,
+
NO,
R39. NO,
+
NO,
-f
NO
+
NO
+
0,
R40. NO,
+
0,
NO,
+
0,
R41. NO,
+
NO,
+
M
-+
N204
+
M
R42.
NO,
+
NO,
-+
NO
+
NO,
+
0,
R43. NO,
+
NO,
-+
N,O,
R44.
NO,
+
NO3
+
M
--*
N,O,
+
M
R45.
NO3
+
M
-+
NO
+
0,
+
M
R46. NO,
+
NO,
+
NO,
+
NO,
R47.
N204
+
M
+
NO2
+
NO,
+
M
R48.
N205
+
M
+NO,
+
NO,
+
M
+
02
2.8 . exp
(-
1510/T,) P31
(M
=
He)
8.3 . exp
(-
1510/T,) [531
8.3
.
exp
(-
1510/T,)
[531
8.3 . exp
(-
1510/T,) [531
1.7
1
exp
(-
1510/T,) [531
1.8 .
lo-''
exp (480/T,)
(M
=
N,)
(M
=
NO,)
(M
=
CO)
(M
=
C02)
3.2
.
10-30~-1.25 e
XP
(-134OWT,) [341
8.0.
10-27~:2.0
3.1
.
10-14T,0.75 exp (-1575/T,)
3.3. 10-12T0.18
5.8
.
10-
''
exp
(-
11 986/T,)
1.8. lO-'Oexp (-14494/T,)
4.2. 10-l2 exp (-22043/7J
1.0.
lo-"
5.0.
lo-"
4.5.10-13
2.0
*
lo-',
3.0.
6.3.10-32
3.3 . 10-
1.0.10-15
3.3 . 10-
l3
1.0.10-17
2.0 . 10-
9.1 .10-33
1.6.
lo-"
exp (150/T,)
4.2 10-"exp (-25200/T,)
3.5. 10-38exp (-13588/T,)
3.3. 10-"exp (-13500/T,)
1.2.
lo-',
exp (-2450/T,)
8.2
. 10-
l4
e:p
(-
1480/T,)
9.5 . 10-
l4
exp
(-
1414/T,)
8.5
.
10-
l3
exp
(-
2450/T,)
3.3 . 104T,
3.8
exp
(-
6460/T,)
1.7 . 108T;4.4 exp
(-
11 080/T,)
exp
(-
1400/T,)
4.0.
3.5. 10-24T-3.8
2.6. 10-11T-0.5
9.6. 10-20TP4:3
Received December
14, 1994;
revised
manuscript
received
March
9. 1995
