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21 February 1980 =
USSR Report
PHYSICS AND MATF#EMATICS
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JPRS L18936
21 February 1980
- USSR REPORT -
- PHYSICS AND MATHEMATTCS
(FOUO 2/so) -
, This serial pu.blication contains articles, abstracts of articles and news
items from L1SSR scientific and technical journals on the specific subjects -
reflected in the table of contents.
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Requests should provide adequate identification both as to the source and
the individual article(s) desired.
CONTENTS PAGE
PHYSICS -
LASERS AND MASERS
:
The Gain at the 00�1-10�0 Transition of C02 in a Reacting
Flow of a Gas Mixture Containing CO and N20
(A. I. Didyukov, et al; KVANTOVAYA ELEKTRONIKA,
No 11, 1979) 1
The Devastation of the Lower Lasing Level of C02 Gas Dynamic Lasers Under Conditions of a Ch.emically Nonequilibrium
Med ium
(N. Ya. Vasilik, et al; KVANTOVAYA ELEKTRONIKA, No 11,
1979) E
On the Optical Excitation of a Molecular Laser in a Photo-
dissociation Wave Propagating in a Dense Gas
(I. A. Izmaylov, V. A. Kochelap; KVANTOVAYA _
ELERTRONIKA, No 11, 1979) 10
- The Effect of Thermal Chokin Suppression with the Resonance
Interaction Between High Fower Laser Radiation and a "
Gas Flow -
(A. A. Stepanov, V. A. Shcheglov; IVANTOVAYA
ELEKTRONIKA, No 11, 1979) 27
- a- [III - USSR - 21H S&T FOUO]
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CONTENTS (Continued)
Page
NUCLEAR PHYSICS
Interaction of a High-Intensity Relativistic Electrom Beam -
With Matter
(A. N. Didenko, et al; ATOMNAYA ENERGIYA No 5, 1979).... 32
Leningrad Institute of Nuclear Physics Imeni B. P. Konstanti-
nov Trends and Development Prospects Discussed
(VESTNIK AKADEMII NAUK SSSR No 7, 1979) 41
- OPTICS AND SPECTROSCUPY
The Color and Visual Contrast of an Ima~.;e on Thermochromic
Material Fitiros
(B. P. Zakharchenya, et al; ZHURNAL TEKHNICHESKOY FIZIKI
No 5, 1979) 53
PLASMA PHYSICS
P.elaxation of the Relativistic Electron Beam in a Gas, Taking
Account of the Radiation
(B. V. Alekseyev, et a1; DOKLADY AKADEMII NAUK SSSR No 1,
- 1979).................................................... 61 L
Features of the Heating of a Substance by Special-Form
Radiation
- (V. K. Ablekov, et al; DOKLADY AKADEMII NAUK SSR No 5,
1979) 66
MATHEMATICS
CYBERNETICS
The Polynomial Solvability of Convex Quadratic Programming '
(M. K. Kozlov, et al; DOKLADY AKADEMII NAUK SSSR No S,
1979) 71
A Polynomial Algorithm;in Linear Programming
(L. G. Khachiyan; DOKLADY AKADEMII NAUK SSSR No 5, 1979) 75
- b -
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PHYSICS
LASERS AND MASERS
- UDC 621.375.826+533.6�O11
THE GAIN AT THE 00�1-10�0 TRANSITTON OF C02 IN A REACTIIQG FLOW OF A GAS
MIXTURE CONTAINTNG CO AND N20
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 6 No 11, 1979 manuscript
received 18 Mar 78 pp 2439-2441
[Article by A.I. Didyukov, A.S. D'pakov, N.N. Ostroukhov, B.K. Tkachenko
and Ye.M. Cherkasov, Moscow Physics and Engineering Tnstitute]
[Text] A scheme for supersonic and subsonic blasts of
cold N20 into a heated mixture of gases containing CO is
studied. This scheme permizs a steady-state exothe_-mic
reaction with the formation of C02 molecules. It is found
- that the greatest gain 1%/cm) is rea7.ized when blowing
N20 into the subsonic portion of a fl.ow of N2-CO-He.
Replacing the He witfi Aydrogen or water vapors xeduces the
gain. Analysis indicates the possible contribution to the
- Sain of vibrationally excited C02 moieeules, formed as a
result of the reaction.
The possibility of using nonequilibrium chemical react3:ons to produce the
active medium of a C02--N2 laser was indicated in paper ji]. The results
of [2, 31 Which were subsequently achieved can be explained by tfie presence
of supplemental chemical pumping of the uppEr C02 lasitig 1eve1 as the "
result of an exothermal Qxidation reaction of CO in tfie critical cross-
- section region of the nozzle.
We studied the reaction of carbon monoxide with nitrous oxide, which is _
realized when cold N20 (To = 300� K) is b7.oWn into a heated mixture of
gases containing C0. This scheme makes it possible in principle, to re- _
alize a steady-state flow mode witfi nonequilibr;um exotfiermal reactions -
to form the active lasing medium. -
- We studied two blow-in variants: in the supersonic and the subsonic
channels of tfie nozzle. An advantage of the first is the bettar condi-
tions for freezing the vibrational energy, however, the initiation and
_ course of tfie chemical reactions in this case is made difficult of the
1uw density and onset temperature, which significantly increase the
1
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reaction delay time. In the case of blow-in into the suBsonic portion of
_ the flow, the conditions for mixing and the course of the reactions ar2
improved. Condsidering the fact that at the same density, the relaxation
- and reaction rates are basically determined Bq the onset and vibrational
temperatures respectively, and by a careful selection of the blow-in point,
one can assure the conditions for the nonequilibrium exothermal reaction
and assure effective freezing of the energy liberated in the expanding
flow.
Figure 1. The configurations of the nozzles used:
a. Nozzle 1 with injection into the
superconic section, h* = 0.35 mm, the
injection coordinate Xin = 2.2 mm, the
- C� - IOMH probe coordinate Xp = 25 mm; b. Nozzle
TI v:ith injection into the supersonic
section, h* = 0.5 mm, the aperture half-
- angle is 0= 5�, Xin = 0.5 mm , Xp m 70
mm; c. Nozzle III with injection in the
subsonic section, h* = 0.35 mm, Xin _
_ Q ao --13 mm, Xp = 3- mm.
~ - 6 bo
B Co
~z d.
d eo Figure 2. Oscilloscope traces of the intensity, regist--
e fo ered in the region 10.6 micrometers.
. ,w g o
SMC 5 msec r--+
/f, %%,+I
n,e
0, 6
0, 4 -
o, 2 -
n
Figure 3. The gain as a function of
the ratio of the rates of
flow min of the NZO (1) and
C02 (2) being blown in to
the overall flow rates mE
for the case of injection
into the helium containing
mixture (nozzle 3).
10 Za d0 (msa/mL)�>00
The experiments were performed on the set-up described in paper [4]. The
profiles of the nozzles used are depicted in Figure 1. The N20 was blown
in through holes in the nozzle wa11. I4i variants a and b, Roles with
2
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a diameter of 1 mm were spaced at interva9.s of 10 mm, in which case, the
series of holes in one half of the nozzle were shiPted by 5 mm with respect
_ to the series of the other ha1f. Tn variant e, the diameter of the holes
was 0.3 mm and the spacing between them was 5 mm; the gas was blown in from
one half of the nozzle. TRe ratio of the flow rates of the gas being blown
- in and the main f 1ow varied from 0.1 to l. ~
The eYperiments were carried out with mixtures of 40% CO + 40% N2 + 15% H2 +
+ 5% H20 and 40% CO + 20% N2 +40% He. For them, the radiation intensity
- of the gas flow in the region X = 10.6 mm was evaluated (in a band singled
out by a dispersion filter). In experiments without the blowing-in, the
oscilloscope traces of the radiation intensity of the flow, together with
the intensity of the probe laser and without it, are in agreement (Figure .
2a). The oscilloscope trace of the flow intensity wtth the N20 b1o4m-in
(Figure 2b) is similar to the first, however the maximum 1eve1 of the signal
is higher in this case.
Thus, signal amplification of the probe laser, recorded when the N20 is
blown-in, can be entirely explained by the formation of C02 in the chemical
- reactions.
We shall move on to a description of the results obtained with the blowing-
_ in of N20 in the case of the nozzle certfigurations whicfi we selected. Tn
experiments with nozzle I(see Figure 1a), no amplification araS recorded
over the entire length of the nozzle when working with both mixtu:es. This
negative result, apparently, is explained by the fact that the chemical
reaction delay time is greater than the flow ti:me of the gaseous mixture
_ from the blow-in point to the mozzle edge.
Nozzle II (see Figure lb) permited a reduction in the difference between
these times because of decrease in the flow rate and -7n increase in the ~
density and temperature. An oscilloscope trace of the trial when N20 was
blown into a mixture containing H2 and H20 is shown in Figure 2c. A gain
- of about 0.4%/cm was registered. For comparison, experiments were conducted
with C02 blown-in, other -conditions being the same (gigure 2d). Tfie maxi-
mum gain likewise reached about 0.4%/cm, however, the time curve was differ-
cnt. The gain when N20 is blown-in begins sharply somewhat earlier and
sharply terminates. when C02 is blown-in, absorption is initially observed,
which then smoothly goes over to amplifi:cation. The maximum in the gain is
achieved at that point in time when the gain for the case of N20 being
blown-in terminates. Even considering the fact that in the oxidation re-
action of C0, the N20 is completely expended and the partial quantities of
C02 in the former (see Figure 2c) and in the latter (see Figure 2d) cases .
are identical, a conclusion can be drawn concerning the cRemical pumping nf -
the upper lasing level. However, for a camplete and precise assessment of
the influence of the cl-emicall reactions, it is necessary to monitor the
- concentration of C02, which is formed as a result of the chemieal reactions
of CO with N20. This monitoring was not done in this work. In the ex- _
periments with the second mixture, no gain was registered. We believe that
3
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- this is related to a 1ower reaction rate in the absence of H2 and water
vapor in the mixture, sompthing which was ind:'tcated in 15].
- Tn exPeriments where nitrous oxide was blown-in ahead of the critical
cross-section of the nozzle (the profile of Figure lc), a gain was regts-
tered for both mixtures. For a hydrogen containing mixture, the gain
reached approximately 0.3%/cm (Figure 2e). This result is comparable to
that obtained when C02 is blown-in (Figure 2f). A significant increase
in the gain caas observed when N20 was blown into a mixture in which the
hydrogen was replaced by heli_um (Figure 2g). Tn these experiments, the
- maximum gain reached about 1%/cm. This is apparently due to the closer
to optimal conditions for the course of the reaction and to the effective
freezing of the liberated energy. It is necessary to note the difference
in the nature of the oscilloscope traces obtained for injection in the
_ supersonic and subsonic portions of the nozzle. Tn the oscilloscope
traces of Figures 2e-.and g, there is a valley in the intensity of the
- registered radiation, which is due to the specific features of the in-
_ jection process. The gas being blown in begins to get into the main
_ flow when the pressure in the main injection line (20-30 atm) and the
static pressure in the main flow are comparabte. The prPSSUre of the main
_ floca in this case varies from 45 atm to 0.
A curve aas obtained for the gain as a runction of the amount of N20
= blown-in (Figure 3), which was limited by the conditions ullder .:iich the
experiment was conducted. Gain appeared at minimal i.njection, and with
an increase in the injection, increases rapidly, r.eaching a maximum and
then falling off sliarPly. This nature of the funetion, in our opinion is
related to the critical conditions for the cour.se of the nonequilibriusn
reactions.
Tlius, the results obtained attest to the possibility of chemical pumping
of the upper lasing level of the C02 mnlecule as a resu7.t of the occurr-
ence of nonequilibrium exothermal reactions of CO with N20 in a steady-
state gas flocv. The results of tr:e studies a11ow for the hope thaC by a
careful selection of the injection point, the structural design oP the
nozzle and the composition of the mixture, one can significantly increase
the efficiency of the given scheme.
BIBLIOGRAPHY
l. I.S. Zaslonko, S.M. Kogarko, Yu.V. Chirilcov, ZHURN. PRIYI. MEKH. T
TFKHN. FI7_., [JOURNAI, OF APPLIED MECHANICS AND ENGINEERING PHYSICS],
No 2, p 48 (1373).
- 2. N.G. i3asov, V.V. Gromov, Ye.P. Markin, A.N. O-~:ayevskiy, A.K. Piskunov,
D.S. Shapovalov, KVAIVTQVAYA ELEKTRONIKEI, 3, 1154 (1976).
4
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- 3. N.N. Kudrysvtsev, S.S. Novikov, I.B. Svetlichnyy, DAN SSSR [REPORTS OF
TfiE USSR ACADEMY OF SCIENCES], 231, 1113 (1976).
4. A.S. D'yakov, A.I. Didyukov, B.K. Tkachenko, Ye.M. Cherkasov, KVANTOVAYA
ELEKTRONIKA, 5, 1166 (1978).
- 5. V.N. Kondrat'yev, Ye.Ye. Nikitin, "Kinetika i mekhanizm gazofaznykh
- reaktsiy" ["The Kinetics and Mechanism of Gas Phase Reactions"], Moscow,
Nauka Publishers, 1974.
COPYRIc=HT: Izdatel'stvo "Sovetskoye radio", "KVANTOVAYA ELEKTRONIKA", 1979.
[ 6'L-8225 ]
8225
C50: 1862
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LASERS AND MASERS
U'DC 621.375.82
THE DEVASTATION OF THE LOWER TASTNG LEVEL OF C02 GAS DYNAMIC LASERS UNDER
CONDITIONS OF A CHEMICALLY NONEQUILTBRI'(JM MEDI'UM
Moscow KVANTOVAYA ELEKTRONTKA in Russian Vol 6 No 11, 1979 manuscript
received 11 Jan 79 pp 2420-2421
[Article by N.Ya. Vasilik, A.D. Margolin and V.M. Shmelev, Institute of
Chemical Physics of the USSR Academy of. Sciences, Moscow]
[Text] Tt is experimentally demonstrated that in the
working medium of C02 gas dynamic lasers, which operate
on the combustion products of mixtures with an atomic
composition of C, 0, N, effective deactivation of the
lower lasing level occurs with the coll_ision of C02
molecules and NO molecules, which are formed in the decay
of the original substances, whi.le collisions with carbon
monoxide molecules do not provide gor effective deacti-
vation of the lower lasing level.
In GDL's [gas dynamic lasers], operating on the combustion porducts of
mixtures having an atomic composition of C, N, 0, H, water vapors are used
- to devastate the lower lasing level. However, during collisions with
- water molecules, a considerable portion of the vibrational energy is lost.
These losses are particularly pronounced when molecules of carbon monoxide
are used as the vehicle for the vibrational energy jlJ.
The purpose of this work is to study the deactivation of the lower lasing
- level of C02 GpT,'s for the case of collisions of C02 Tnolecules with CO
and NO molecules. High values are given in the literature [2 - 51 for the
probabilities of these ptocesses.
The experiments were carried out with a setup consisting of a combustion
chamber witii a volume of 0.5 liters, a chamber ahead of the nozzle (0.4
liters) and a supersonic nozzle. The critical section dfcnensions were
0.3 x 300 mm. The expanding section of the nozzle was formed by the
surface of a circular cylinder. The initial aperture half-angle of the
nozzle was 30�. In the case of an expansion factor of 100 for the gas
f1ow, the surface of the circular cylinder makes a tangential transition
6
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to a plane, and in this way, the expanding section of the nozzle is
coupled to a constanfi cross-aeetion. The optical gain (or absorption)
is determined by measuri'ng the increase (or decrease) in the radiation of
an electrical discharge laser in the constant cross-section channel at a
distance of 90 mm from the critical section of tRe nozzle. The following
mixtures were fed into the combustion chamber: C0:02:N2 =(3 + S):1,5:
_ :(7. 5-X) and CO:NZO:NZ =(3 + X) :3: (6 X), 0< X< 1.5. Comnercial grade
nitrogen and carbon monoxide, and medical grade oxygen and nitrous oxide
- were used in making the mxitures. The major equilibrium combustion pro-
- ducts of these mixtures are C02 (25 - 30% of the volume), CO (up to 15%)
and nitrogen.
The gas pressure in the constant cross-section supersonic channel and in
the pre-nozzle chamber was measured by induction transducers. The maximum
pressure values in the pre-nozzle chamber reached 40-50 atm, and in the
constant cross-section channel, 8-10 mm Hg.
- Experiments with the origina 1 CO-02-N2 mixture 5tlowed that in the case of
= collisions of the C02 molecules with carbon monoxide molecules, effective
relaxation of the lower lasing level does not occur, since the laser radi-
- ation is absorbed in the combustion products which contain up to 15%
carbon monoxide (the white experimental circles in Figure 1), while the
. introduction of an insigdificant amount of water vapor 1%) into the
composition of the work.ing medium assures a positive gain (the black ex-
perimental point in Figure 1).
The optical gain a for the g iven mixture, obtained by numerical integra-
tion of the system of kinetics equations for the viBrational relaxation
and gas dynamic equations, similar to t;:e system in [10], where the
_ presence of water vapors (curve 3 in Figure 1) is in quantitative agree-
ment with experimental data. The values of a for water free mixtures
cons isting of C02, N2 and CO were computed for two different functions of
the temperature for the constant K(T) of the deactivation rate of the
deformation type vibrations of the C02 molecules for the case of co11i-
sions with carbon monoxide molecules: curve 1 in Figure 1 corresponds to
_ values of K(T) = 104 - 105 (mm Hg � sec)-1 in a temperature range of 300-
1,000� K[2 - 5], and curve 2 was obtained assuming the equality of the
- probabilities of the deactivation of the lower lasing 1eve1 for the case
of collisions with nitrogen and carbon monoxide molecules [6, 111.
A comparison of the results of experiments and calculations allows for
the conclusion that the values of the deactivation constant K(T) in the
literature 12 - 51 are substantially overstated.
Experimental values of the optical gain are given in Figure 2 for the
combustion products of mixtures of CO-N20-N2 '(fhe sma11 wtiite circles), as
- we11 as in the combustion products of a control mixture of 2.$ CO + 0.1
C2H2 -h 3.4N20 + 5. 6N2 (the solid blacks circle). Tn this series of ex-
periments, the combustion products of mixtures wfiich do not contain water
vapors amplified radiation with a wavelength of 10.6 micrameters.
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Since the results of trials with CO-02-N2 and CO-N20-N2 'Miattures, having
the same atomic composition, and consequently, approximately the same
equilibrium r.ompesition of the major comBustion products, are different
qualitative7.y, one can conclude that in the combuetion producte of }lydrgen
free mixtures of (CO-N20-N2), deacCtvation of the lower lasing level
_ occurs with collisions with chemically nonequilibrium products.
Figure l. The optical gain as a function
QS 3 of the molar concentration of
carbon monoxide in the combus-
~ tion products.
~ 0,05 0,1 ~ca
-0,5 2
Figure 2. The optical gain as a func-
tion of the ratio of the
oL,M-1 ~ molar concentrations of
- a,s � � � ~ ~ ~ carbon monoxide and nitrous
oxide in the original mix-
0,25 ture.
019,75 1,0 1,zs [co]/[NZo]
The oxidation of carbon monoxide and the decay of nitrous oxide in the
CO + N20 at temperatures of 1,500-2,000� K, runs according to the follow-
ing scheme [7 - 9]:
~ N20+M-YN,+o,
N 20+O-�2NO,
N 0--0-OZ--N2,
Pda~--FCO-->COZ ,=N21
- O-}-CO-}= bt-�CO _+1%1.
The yield of nitric oxide in the mixture of N20 with CO at a temperature
of 2,000� K amounts to about 30% of the N20 191.
At a temperature of 2,000� K and a pressure of 10 atm, the nitric axide
has a characteristic lifetime T1, which exceeds the time T2 of the pre-
sence of the reaction products in the combustion chamber of a GDL under
~ the conditions of our experiments (T2 = 1 msec). A higfi value of the
probability P of the deactfivation of the deformation v3:brations of
carbon dioxide gas molecules is given in the literature [4, 51 for the
case of collisions with nitric oxide molecules (P = 4- 10'~) at room
temperature. On the basis of what has been presented I1ere, it can be
assumed that the devastation of the lower lasing level in experiments
- with N20 was assvred by the collisions of C02 moi,ecules witfl N0, and
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~ possibly, with other oxides of nitrogen. It is also possible that it is
specifically the presence of ND in the gaa discRarge plasma wfiich explains
_ the errors in the measurenent of K(T) in papers 12, 31.
- It is shown in this paper that in the working msdium of a carbon dioxid
GDL's, which operate on the combustion products of mixtures with an atomic
. compositi.on of C, 0, N, effective reactivation of the lower lasing level
occurs in the case of collisions of C02 molecules with NO molecules, and
~ possibly, with other oxides of nitrogen, formed in the decay of the orig-
inal substances, while collisions with carbon monoxide Tnolecules do not
- assure effective deactivation of the lower lasing level.
BIBLIOGRAPHY
~ 1. V.M. Shmelev, N.Ya. Vasilik, A.D. Margolin, KVANTOVAYA ELEKTRONTKA, 1,
~ 1711 (1974). _
2. P.K. Cheo, IEEE J. QE-4, 587 (1968).
- 3. M.C. Cower, A.I. Carswell, J. APPI,. PHYS., 45, 3922 (1974).
~ 4. I.M. Metter, PIIYSTKALTSCHE ZEITSCHRTFT SOWJETUNTON [PHYSICS JOURNAL OF
~ THE SOVTET UNION], 12, 233, (1937).
5. V.N. Kondrat'yev, "Ki.netika khimicheskikh gaznvykh reaktsiy" ["The
Kinetics of Gas Chemical Reactions"], Moscow, Nauka Publishers, 1958.
6. I. Soto, S. Tsuchiya, J. PHYS. SOC. JAP., 33, 1120 (1972).
7. M.S. Lin, S.H. Bauer, J. CHEM. PHYS.,50, 3377 (1968).
8. D. Milks, R. Matula, "14th Symp. on Combustion", 1972,
9. I.S. Zaslonko, Ye.V. Mozzhukhin, Yu.K. Mukoseyev, V.N. Smirnov,
FIZIKA GORENIYA I VZRYVA [^OMBUSTION AND EXPLOSTON PHYSTCS], 14, 101
(1978).
- 10. A.S. Biryukov, TRUDY FTAN [PROCEEDINGS OF THE USSR ACADEMY OF SCIENCES
. INSTITUTE OF PHYSICS TMENI P.N. LEBEDEV], 83, 13 (1975).
+ 11. M. Huetz-Aubert, G. Louis, J. Taine, PHYSICA, 93, No 2, 237, 1978.
COPYRIGHT: Izdatel'stvo "Sovetskoye radio "KVANTOVAYA ELEKTRONIKA", 1979.
- [62-8225J
- 8225
CSO: 1862 9
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LASERS AND MASERS
UDC 621.378.33
ON THE OPTICAL EXCITATION OF A MOLECULAR LASER TN A PHOTODISSOCIATION
- WAVE PROPAGATING IN A DENSE GAS
Moscow KVANTOVAYA ELEKTROIIIKA in Russian Vo1 6 No 11, 1979 manuscript
received 11 Feb 79 pp 2349-2360
[Article by I.A. Izmaylov and V.A. Kochelap, Institute of Semiconduetors
of the Ukrainian SSR Academy of Sciences, Kiev]
[Text] The photolysis of gaseous media wh3ch accompanies
- recambination reactions is studied. It is shown that
with the action of high power radiation, such media are -
completely or partially bleached into nonsteady-state photochemical waves. Intense exteraal radj_ation can _
produce lar e concentrations of atoms and radicals
(1018 - 101l cm-3) and initiates strongly nonequilibrium
reactions. The conditions for the formation of an in-
J verse popul.ation of the electror. states of the molecu].es -
- the recom3ination products - are studied for cases where the recombination reactions have a radition channel.
Inversion can occur both with lfnear light absorption and
in bleaching modes. The results are applied to a nuiaber -
- of specific mixtures, for which the conditions for the occurrence of inversion and the light gains which occur _
are calculated.
Optical pumping [1] is widely used at the present time to excite electronic
photo transition.molecular lasers. This kind of pumping is quite universal,
since it can be applied to various molecular systems, and is capable of
initiating and sustaining processes whicti lead to an inverse population
(direct population of the upper levels of the working photo transition,
- photodissociation with the formation of an excited moleeu7.e or atcrm, etc.).
Of particular interest is the photolysis of a gas with subsequent chemical
transformations which lead to excitation and an inverted population of the
chemical reaction products. Thus, lasing was realized for the first tine _
with the electron transiti:on of a molecule excited during the course of _
an exchange cilemical reaction 12, 3] (the lZg 3rg in the S2 moleeule
during the photolysis of COS).
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An inverse population and light amplification can also arrive with the -
_ recombination of atoms and radicals: thE products of photolysis. Such a
- possibility has been treated earlier in the literature 14, 51. These
and other studies have shown that when designing a recombination laser,
it is necessary to take the following factors into account:
l. It is necessary to produce nonequilibrium concentrations of atams and _
_ radicals of about 1018--1019 cm 3. This requires the application of high
power light fluxes of the pumping light and the utilization of gases with
high densities and absorption coefficients. Under these conditions,
photolysis at a considerable depth is possible only in photochemical
bleaching waves [6, 7].
_ 2. Recombination reactions are one og the main chemical processes, which
determine in many respects the nature of the photochemical waves which
_ prove to be nonsteady-state and decaying.
3. With high concentrations of atoms and radicals, fast chemical reactions
can also occur, which lead to the diminution of the active components,
- and which produce the molecules - the recombination products. These
parasitic processes make it difficult, and in some cases, impossible, to =
produce an inverted population and acliieve light gain.
4. In the case of absorption of the external light, considerable erergy is
liberated in the course of the subsequent chemical reactions, and the
temperature increases and the inversion existence time fa11s off.
- 5. The high radiation powers which are delivered, are liberated in
narrow spatial layers, lead to the appearance of large pressure gradients
i.n the gas and cause the motion of the medium, samething which complicates -
_ the photolysis pip,ture and leads to optical inhomogeneity of the medium.
6. We took the factors cited above into account when constructing the _
_ theory of the optical excitation of an inverse population and light gain - during the recombination reactions. The possibility of optical pumping
- of a recombination laser in a linear mode is treated (section 2), tRe
nature of the bleaching waves in the recombining gas is studied (sections _
3 and 4) and expressions are derived for the inverse population and light
gain criteria. The results of the theory are applied to specific gas
mixtures; the pressure and composition of the gas as we11 as the para-
= meters of the light sources needed to excite lasers of the type considered -
here are computed (section 5).
1. The Initial Equations _
The photolysis of a gas, which is accompanied by a bleaching wave and
chemical transformation, is described by radiation transfer and chemical
kinetics equations. These equations define the flux density of the
photons of the actual frequencies .T and the gas composition. The thermal
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balance equa~.ion determines the gas temperature T. When the motion of
~ the medium is taken into account, the gae density p and its velocity v -
are likewise to be determined. Theee cases wi11 be specified separately.
We shall assume that a11 quantities depend on one spatial coordinate x,
and the light propagates in a positive direction of x. Then the equation
for J is written in the form
t a.r ar - c ar + a.~ -WJ --xJ, (1)
where K is the light absorption coefficient, which depends on the -
composition and density of the gas. We sha11 assume that each act of
light absorption leads to photodissociation. Equation.(1) is applicable
in two very ir::teresting cases: for a monochromatic light source (laser
pumping), where K corresponds to Che frequency of this 1ight u.rL, and for _
r.adiation, the spectrum of which is considerably wider than the absorption
_ spectrum which leads to the photolysis (pumping by a source with a bright- -
ness temperature of tens of thousands of degrees). In the second case,
J is the flux of photons at frequencies which fa11 in the absorption
band 6wL; 3c _e~- f dwx (c~) ~ -
c, �WL
The kinetics equations can be written only for specific chemical pro-
cesses. We sha11 consider two types of gaseous mixtures, which consist
of donor molecules R and diluent moleculas M of the atoms.
- A. The mixture of homonucZear X2 and M moZecuZes. In this case, the
photolysis -
Xz-}-twL--r 2X
(2)
is accompanied by a single chemical process: the recombination reaction:
X -X -f- (M) = X, 4- (M) -f- W
IQI# (I) _
where Q1 is the process heat for (T). In reaction (I), the presence of
a radiation channe1 is assumed in addition to the tfiermal channel, where
the radiation from the radiation channel can be used in lasers.
The concentrations [X] aad [X2] are related by the relationship for the
material balance: [X2] _(p/pp)[X2]p - 0.5[X], where the "0" subscript
applies to the original gas, unperturbed by the light. The following
- equation is justiFied for jX]: -
d (X )ldt=2[V,-(WI-W 1
(3)
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where Wf A a[X2]J; W1 and Wl, correspond to the direct and inverse pro- cesses of (1). On1y thoae cases where the thermal diasociation processes ~
_ can be neglected (the inverse process of (T)) wi7.1 be treated below. ~
B. The mixture of heteromueZear AX cxnd M moZecuZes. Tn this case,
- besides tfie photolysis
AX-{-xwL--> A-{-X
(4)
recombination rea(~tions (I) also occur as we11 as the following pro-
- cesses, initiated by the external radiation:
A-I-X+(M)-IAX-I-(M)-f-Q2; (I'r)
AX-}-X.E A-}-Xa� (III)
here, Q2 is the process heafi of (IT).
Tt is assumed that the compounds A2, AM and XM do not exist. TAe cotagosi-
- tion of the gas i:s determined by the concentrations [AX], [A], jX], jX21
and [M]. They are interrelated by tAe relationships: [AXI +[A] _(p pp
_(P/PO)IAXIp, [AXI +[X] + 21X21 = 1(pIPO)AXJO� Taking them into accounfi,
- one can write the equations for any two concentrations, for example, for =
[AXI and [X]: '
- a [AX]=-WJ-f-Wa-=Wa, -
_ (5) -
_ at [X] = W, - Ina - Wl,
- (6) .
where WJ = a[AX]J; Wi (i = l, 2, 3) are tne rates of the forward processes ~
of (I) -(ITI). The quantities Wi have the fonn -
W1=k1 [Xl2[M], W2=k2(A) lX] lA1l, W3-k3 [AXI [Xl, (7)
where kl-k3 are the constants of the reactions rates for (T) -(IIT), -
which do not depend on T. The thermal balance equation is written in
= the conventional way. Thus, for the photolysis scheme of A, it has the
form:
dT
[M1RCM d1 - llI~)L- Qi)WJ + 2 Q!'~1,
(8)
where RcM is the heat capacity of the diluent.
The equations cited here should be suFplemented with the initial and
` boundary conditions. We sha11 asstune *hat at the point in t3me fi= 0,
raditiation falls on the boundary of the medium x= 0 having a constant photon fliix of J(x = O,t) = Jo, t> 0. For the points x< ct, the fo1-
- lowing intensity distribution is established by the point in t= x/c:
J (x, t)=Joe-x�x, sto=x (t=0), (9) -
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_ in which case, over these times, only an insignificant change in the concen-
- trations of the original components occurs. A further substanttal change
_ in J and the other characteristics of the system occurs after signifi-
cantly greater times (of pltotdlysis and the chemical reactions). For this
reason, the first term in equation (1) can be omitted, and the distribution
. o� (9) is referenced to the point in time t= 0. The initial conditions
for the chemical kinetics equations have the form:
- For photolysis scheme A: IXZ]-IX- ]o, [X]=0, t=0;
For photolysis scheme B: [AX]=IAXo], [A]=(X]=[X,)=0, t=0.
We assume: T(x,o) =To, p (.r, 0)=p0, ti (x, 0)=0, v(0, t)=J.
2. The Photolysis of Homonuclear Biatomic Molecules. The Linear Mode.
We shall begin the treatment of photolysis in accordance with scheme A
with the simplest case, for which fifie medium is not bleached. In this case,
- the distribution of J(x, t) does not depend on t and is determined by
Eormula (9). Neglecting gas dynamic perturbations (tfiey are estimated
_ below), we introduce the dimensionless parameters:
C1=[X1/2 lXZlo, S2=lX2]/lX2]0=1-Si, jW= J(x) Q 'neKo (10)
tvex=(4k1 LX.)o [M])-1, T=t/tPcs+ 6=T!T,), i1=1AX1o/1M1.
Itpek - trecl
Then we find Cl 3n simple form from kinetics equations (3):
= I (x) th (il/' I (x) � (11)
for 6, we find from (8):
ae . (A-B)1~ +B~i~ A A~Ln $ Q1~
- aT 2 - RcMro ~ - cMRTo ' (12)
Formulas (11) and (12) are justified in the absence of bleaching, i.e.,
for ~1 � 1. This condition is met for any T if T is sma11 (TT � 1)
anci for a11 T, if
1 (0)=fo�l.
(13)
An anaZysis of the inverted popuZation crtiterion. We sha11 employ the
inverted population criterion for the R2 molecules, formed in the process
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of recombination (1), which is given in [9]:
1X]3~1:-lX21 Ki (7) A co Ikr9 (14) '
where K1 (T) is the chemical reaction equilibrium constant for T; w is `
the frequency of the working photo transition. We shall assume tfiat K1(T) _
= KOe-Ql/RT. Using (11) and (12), this criterion is written in the form ~
1 th'- (T Y-I ) >M0 exp f(I
, - a) QIIRTO tih (T ~ ) I
1 -i- AIT - B
where , (15)
x�=K~�j~(4r~ lM]), S?=ho4i. Formula(15) , along with equation (9),
solves the problem of determining the spatial regions with an inverted -
population and their timewise evolution. Tt is convenient to study (15) in _
explicit form in the plane T, T, Our treatment is justified only for the
portion of the plane adjacent to the axes T= 0 and T= 0, and bounded by _
the curve C1(T, T) = 1. We shall partition this portion of the plane by
the line tTT = 1(curve 1 in F,i ure la). An inverted population appears
- below this line in the region T~I a< 1 under the condition g(To, St) = IfO� .
�exp[-Q1(1 - SZ)/E:Tp] � 1. The inversion curve, which separates the region
where (15) is observed, proves to be a hyperbola: TT =[F(TO, SZ)]1/2
- (curve 2). Tt follows from (15) for the inversion curve in the region
1/(I)1/2 � T� 1/I that I= const. a F(TO, SZ) (curve 3). Tfle line TT =
_ =(Q1/RTO)(1 - SZ)/A 1nKO (curve 4) is approximately obtained for IT � 1.
The strait line I= Tp is to be drawn for a specified incident radiation
intensity TO in Figure la, since in the working volume T< Io. Thus, the
inversion region in the variables T and T proves to be an island, the
boundaries of which depend substantially on the temperature TO: with an
_ increase in To, the island is reduced and when TD I (Q1/I)(1 - St)/ln(KO/Tp) i.
disappears. Tn this case, the intensity of the external light is insuf- =
ficient to produce the invers3on. For:
T~ Qt ln A�o )/R (16)
an inversion cannot form.
- Using the results presented, it is not difficult to describe the behavior '
of an inversion in the space-time variables x and T(Figure 1ii). The
most imporfiant conclusions from this treatment are the finite time of the
existence of an inverted population at each of the points in space and the
shift of the region in which the inversion is realized. -
If criterion (14) is observed, then the light gain can be represented in
the form:
_ a=u (w, T) lX]`, (17)
where a(w, T) depends on the type of molecules and was computed for
,vari:ous cases in [5, 9- 111. It is easy to compute a using the formulas
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given here. If a does not depend substantialI on T, tfien a reaches
a maximum in tAe region tFI > 1: amax = 4a1jX2] . For the latter case,
the qualitative course of the surves a(x, T) = 20nst is sfiown in Figure lb.
Tn conclusion, we sha11 give the expressions for gas dynamic perturbations
of the density:
- P-Po JocntC ( e-x�x [sh(t/tA)-t/tpJ, x>aot -
Po ~[x~lo -f- cn1j ao l - [t/tp e-'"�X ; ch (xox) e '/'n - 11, x
9� 10-'s [14]
1
285-375
3,4� 1029
0,4 [15]
57 [12]
1000 (3360
Clz
,
(14~
X\ T 1 eXp \ T/
A, = 1200 HM nRI
7, lQ-11s 1
7�10-4s� ~ X
5� 10-19 [14]
4
370-520
3�.1023
0,81151
45 (Z1J
3150)
1000
1/,
Brz
,
[14J
)
X(
eXp (
T )
.
X = 1320 xH tuq
7, tp-ai x
-11�
)
>
1,5� 10
5� 10-17 [16j"'
1
> 240-290
2,4� 102'
2,81171�')
100 [21]
3,900'
1000
Sa
,
(lg1
x( T exp (
T,
\ /
I= 450 HM mt
Key: 1. Jp, phot/(cm2 . sec);
2. kl � 1033, cm6/sec (T = 1,000� K); 3. Q3, Kcal/mo1e;
The value of a(a, T) is given for high pressures in the gas, when the
rotational structure in the radiation spectrun disappears. In other
cases, the value of a(a, T) corresponds to tfie doppler widening of the
electron-vibrational-rotational line and to the transition with the
maximally populated rotational level.
The measured value in [17] amounts to 27% of the total recombination
constant ki where T= 300� K[11]. A temperature dependence of
kl = 1,000� K/T was adopted. `
The mean value for the indicated band is given, which corresponds�to ~
transitions at the level v' = 10 - 26 S3(B32:-), which effectively decays as a result of spontaneous and induced predissociation colli-
sions [14].
The photoZysis of S2 gas. We shall consider a mixture of S2-N2 at Tp =
= 700� K, when a concentration of 1S21Q ~1018 cm-3 is achieved. From
Tab1e 1, when n= 0.25 we f.ind that trec � 22 microseconds, Ko1 = 0.07 cm
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and IQ = 80. A bleaching wave with a velocity of 4.7 km/sec is realized
(dp = 5.2, and the limiting velocity of (25) i:s equal to 1.8). The total
= penetration of the wave into the gas is 5.3 cm, and quasisteady-state flow
behind the wave front is possible when x< 4 cm. We sha11 consider the
- state of the gas when T= 0.9; tRe front is locared at x= 3,2 cm, and
I= 32; the extent of the nonsteady-state flow is 1.6 cm; behind the front,
the gas is accelerated up to v= 0.13 km/sec; T= 1,060� K; the compression
is p/po = 1.15; the cancentrations are ~g~= 1 and e = 0.03. For J~ = 450 nm,
the inversion layer amoiints to about 0.16 cm; inversion is disrupted when
_ T= 1,500� K. The gain right behind the front is equal to 1.2 � 10'2 cm 1
and at the moment inversion is broken off, 4. 10'3 cm-1. For X = 550 nm,
the inversion layer is about 0.66 mm, inversion is lost at T= 2,000� K
and the gain behind the front is 3- 10-3 cm, while at the moment of in-
version 1oss, it is 4.6 � 10-4 cm-l.
It can be seen that the levels of the gain are sufficient to realize
generation or recombination pumping. We wi11 note that in 1731, an S2
laser was optically pumped with direct optical excitation of the upper
lasing state of S2 (B).
- PhotoZysis of COS gas. Tn the photolysis of C195, sulfur atoms in the
1D2 and 1Sp excited states are formed in tiie spectral range indicated in
Table 2. We shall consider those pressures at wh3ch these states are
deactivated before the exchange chemical process of rype (TII) occurs. We
shall consider a gaseous mixture of COS-CO2, where [COS] = 2- 1018 cm-3
_ and n= 0.05. Using Table 2, we find t~;~ = 5 microseconds, K61 = 0.04 cm;
Ip = 28, S= 0.05 and S' = 0.1 (an exchange constant of k3 = 1.3 � 10-14
cm3/sec was used). The cor,ditions of (27) are met, i.e., maximum concen-
trations of [S] = 2- 1018 cm 3 are achieved in the wave front; the layer
. in which the recombination occurs is 1 cm thick. The wave penetration
depth is practically unlimited. Condition (29) leads to tfie criterion for
the occurrance of inversion, Tp < 1,320� K for a= 550 nm. Right behind
the wave front, T= 760� K, and as a result of establishing chemical equi-
_ librium, T= 1,020� K is established, i.e., the inversion is preserved
right up to the complete recombination of the S atoms. The maximum gain
of a= 10-3 cm-1 is realized immediately behind the wave front at the point
where half of a11 the atoms has reacted, a= 2. 10'4 cm'1.
Thus, the photolysis of COS can be accomplished practically any depth of
the gas, the inverted population at the SZ (B X) transition is preserved
in the extended layers of the gas and a gain is achieved wfiich is suffic-
ient to excite lasing.
PhotoZysis of CH3Br gas. Tn the case of photodissociation of CH3Br, the
following reactions occur: CH3Br + Ac,ul, CHg + Br, CH3 -i- Br CH3Br (TT),
2CH3 C2H6 (1), Br + Br + (M) Br2 + (M) (I' ) . As compared to photoly-
sis scheme B. this process has two recombination channels, T and V, in
which case, both reactions promote bleaching of the medium. Exchange
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reactions TII are slow because of
Che energy barrier. Reacrions TI and
T
are two-Frequency reactions and occur at greafier rates, and
process I'
is
- signif icantly lower, and for tfi is
reason, tRe res-ults of section 4 can
hP
applied to the entire process, if
we set A- Br and X- CH3
everywhere
(with the exception of the inversion criteria).
TABLE 2
A-'K I [1�14P.M ~ I Q� CM=
cro see '
I 4)OT/(CM'9C) I ki' CMg/C
KKan/wonb[121
phot. cm .~s
CO, I 105-115I 1,5� 10-17 [14]
I I 1,7� 10-34 [18]
127
_ COS I 140-180I 1,5� 10-17 [1]
I 4,3 I 2� 10-3") I
72
- CH3Br ( 140-260 i 7� t0-1e [14]
I 10 I 4,7� 10-11�o) I
67
10 -is:..)
k
The calculation is based
on the decay rate constant from [19]
and
the chemical equilibrium
constant of [12].
- The dual frequency reaction rate constant of CH3 +
CR3 + CZH6
[cm3/sec) [18].
~ The same, for CH3 + Lir
CH3Br.
_ By way of example, we sha11 con-cider the mixture CH3Br-CO2 with a concen-
tration of [CH3Br] = 4- 1018 cm'3 and n= 0.04. FoV the parameCers of
Table 2, we find Dp = 2.5 km/sec, treC = 5~ns and treC = 3 microseconds.
The Br atoms recombine over a length of ZreC = 0.8 cm, the temperature
behind the bleaching front is 700� K, and following recombination of the
Br atoms, it is 780� K. The inversion criterion is met right up to the
complete disappearance of the Br atoms, and the gain is amax = 1.2 � 10-4
cm-1.
6, Conclusion
We sha11 summarize the major results and conclusion of the paper. The
- photolysis of gaseous media fias been st-iidied, in wFiich some of the major
- chemical processes are recombination reactions. It is shown that with the
action of high power radiation, these media are completely or partially
bleached in nonsteady-state photochemical waves. At the maximum intensity,
a theory has been constructed for such waves. Tt is shown that a case
exists, of the greatest interest for lasers, for which quasisteady-state
flow, having the greatest homogeneity, is realized behind the photolysis
- wave front. Intense radition can produce large concentrations of atoms
, and radicals (1018 - 1019 cm-3) and initiates strongly nonequilibrium
recombination reactions. an inverted population og molecules--recombination
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_ y
FOR OFFICIAL USE ONLY = products was studied. Tnversion can occur both arltR linear absorption of
light and in bleaching modes. The degree of dilution oP the working gas
has a substanti:al influence on the inversion criteria.
_ The theory developed was used to calculate the photochemical wave, gas
dynamic parameters and inverted population which arise during the photo-
lysis of specific mixtures, for w$icR the effective population of the
excited molecular states in the recombination reaction are me11 known
from the literature. The optical pumping condifiions, under wRieR recombi-
nation laser operation is possible, are determined. TRe optical pumping -
of the lasers treated here is of the greatest interest, since consider- -
able excited particle densities should be acfiieved in tItem; large working
volumes can be used, and the broad dissociation spectra permit the effici- -
, ent utilization of the pumping energy. Optical pumping can also serve as
_ a simple approbation of the recombination mechanYSm of laser excitation, -
which can also be realized under other ("dark") conditions and are promis-
ing for applications in high power flow type chemical lasers using elec-
tron phototransitions [5, 20-221.
BTBLIOGRAPHY
_ 1. L.D. Mikheyev, KVANTOVAYA ELEKTRONIKA [QUANTUM ELECTRONTCS], 5, 1189
(1978).

2. V.S. Zuyev, S.B. Kormer, L.D. Mikheyev, M.V. Sinitsyn, T.T. Sobe1'man,
G.N. Startsev, PIS'MA V ZHETF [LETTERS TO THE JOURNAL OF EXPERIMENTAL
AND THEORETICAL PHYSICS], 16, 222, (1975).
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(1975).
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_ tation"], IP AN USSR [Institute of Semiconductors of the Ukrainian Acad-
- emy of Sciences], Kiev, 1970.
5. A.S. Bashkin, V.I. Igoshin, A.I. Nikitin, A.N. Orayevskiy, "Khimicheskiye
lazery. Ttogi nauki i tekhniki. Ser. Radiotekhnika" ["Chemical Lasers.
Progress in Science and Engineering. Radio Engineering Series"], Vol. 8,
Moscow, VINITI AN SSSR [Al1-Union Tnstitute of Scientific and Technical
- Information of the USSR Academy of Sciences], 1975, p 315. _
6. V.Ye. Khartsev, ZhETF [JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS],
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of Continuous Media"], Moscow, GTTT Publishers, 1953.
25
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- USSR Academy of Sciences Publishers, 1962, Vol 2.
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~ COPYRIGHT: Izdatel'stvo "Sovetskoye radio", "KVANTOVAYA ELEKTRONIKA", 1979
[62-8225]
8225
CSO: 1862
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LASERS AND MASERS
UDC 621.378.9 ~
THE EFFECT OF THERMA'L CHOKTNG SUPPRESSTON WTTH THE RESONANCE TNTERACTTON
BETWEEN HTGH POWER LASER RADIATTON AND AGAS FL'OW
_ Moscow KVANTOVAYA ELEKTRONTKA in Russian Vol 6 No 11, 1979 manuscript
received 23 May 79 pp 2476-2481
- [Article by A.A. Stepanov and V.A. Shcheglov, Phqsics Institute imeni P.N.
Lebedev of the USSR Academy of Sciences, Moscow] -
[Text] The phenomenon of thermal choking in a supersonic
flow of a chemically reacting gaseous mi'xture is ar.aiyzed.
- The conditions are found under which the choking situation
knowingly does not arise. Tfie possibilifiy of laser control _
_ of gas dynamic processes in such f1ows is demonstrated, wRi:ch permits suppression of the tfiermal choiting under
specific conditions. ,
1. It is well known (for example, see [1, 2]), that wfien heat is fed to
a supersonic or subsonic f1ow, the flow velocity in a constant cross-
section channel wi11 fa11 off (or increase) until a critical value is
reached, vcr (the Mach number is M= 1), after which, further forced
heat input proves to be impossiBle without changing the nature of the
- flow (the thermal choking phenomenon). Supercritical heat input can lead
- either to rearrangement of the steady-state floar (for example, to the
- formation of shock waves), or to the appearance of a nonsteady-sfiate mode
~ (in particular, surging).
2. In a typical situation, the heat source is a chemical reaction between
- a fuel and an appropriate oxidizer, or a discharge in tfie gas f1ow. It is
not difficult to establish the criteria under wfiich thermal choking know-
ingly begins in the system. For tliis, we make use of the conventional
- relationships which describe the gas flow in a cyl3ndrical channel with
heat input:
dT 1- y11I=-- dQ d;N2 1+ yM2 dQ ~
T- 1- M2 H+ M$ - 1- MZ N~
where T is the temperature; y is the adiabatic constant; Q is the heat
-
supplied and H is enthalpy. _
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Simple calculations make it possible to determ3ne the relationship between
the heat input and the Mach number grom (1):
Q a 1-- YM2 A92 -1 Mp - 1
cpTo - 2 (1- Mo / \ 1 ~-Y1N9 / \ I yMs -f' 1 +YMo ~ (2)
_ where Mp and Tp are the initial parameters of the f1ow; cP is the heat
capacity for the case of constant pressure. We wi1.l note tfiat in con-
trast to the estimating relationsfiips given in 13], expression (2) is
precise.
Setting M= 1 in (2), we obtain the maximum amount of heat, which cor-
responds to critical heating:
Qs=cuTu(Mu--MQ 1)s,.
_ (3)
where
c0=cp12(Y-f-1)= Ycv/2(Y-I- 1).
Taking (3) into account, the criterion for the occurrenee of thermal
- choking is written in the form:
(coTo14) (11'f o-Ma 1)Y