JPRS ID: 9937 TRANSLATION CHEMICAL LASERS BY V.K. ABLEKOV, Y.N. DENISOV AND V.V. PROSHKIN

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JPRS L/9~37
25 August 1981
T~anslation
CHEMICAL LASERS
~ By
V.K. Ablekov, Y.N. Denisov and V.V. Proshkin
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JPRS L/9937
25 August 1981
CHEMICAL LASERS
Moscow KHIMICHESKIYE LAZERY in Russian 1980 (signed to press 5 Sep 80)
pg 1-224
, [Book "Chemical Lasers", by Valeriy Konstantinovich Ablekov, Yuriy
Nikiforovich Denisov and Viktor Vasil'yevich Proshkin, Atomizdat,
2,850 copies, 224 pages, UDC 621.375.826]
CONTENTS
Introduction 1
References 4
Chapter 1. Principles of Kinetics of Gas-Phase Chemical Reactions 7
1.1. Law of Effective Masses 7
1.2. Mechanisms of Simple Reactions 9
1.3. Chemical Equilibrium 11
- 1.4. Complex Reactions 14
1.5. Chain Reactions 17
1.6. Elementary Processes of Excitation of Systems in Chemical Reactions 21
1.7. Chemical Reactions in a Closed Space and in a Stream 28
References 36
Chapter 2. Formation of Excited Particles in the Process of a Nonequilibrium
Chemical Reaction 41
2.1. The Recombin;~.tion Mechanism of Excitation 41
2.2. Nonequilibrium Excitation of Particles in Volumetric Reactions 46
References 48
Chapter 3. Basic Equations of Processes in Chemical Lasers 51
3.1. General Conditions of Lasing Onset 51
3.2. Equations of Motion of a Chemically Reacting Gas With Consideration of
Nonequilibrium Effects and Emission 53
3.3. Principal Characteristics af Chemical Lasers 54
3.4. Kinetics of Chemical Pumping and Lasing in the Pulsed Mode 57
3.5. Principal Equations of the cw Chemical Laser 59
3.6. Laser Kineti~s Under Conditions of Cooperative Spontaneous Emission 63
3.7. The Optical Cavity 66
References 68
- a - [I - USSR - L FOUO]
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Chapter 4. Gas-Static Chemical Lasers ~1
4.1. Photochemical Gas-Static Lasers ~1
4.2. Electric-Discharge Gas-Static Chemical Lasers 81
" 4.3. Gas-Static Chemical Lasers With Initiation of the Reaction by an
Electron Beam 85
4.4. ~;xcimer Gas-Static Chemical Lasers 88
References 92
Chapter Subsonic Chemical Lasers 98
5.1. Chemical Lasers With Circulation of Premixed Components 98
5.2. Chemical Lasers With Subsonic Mixing of Components 106
5.3. F1ane Lasers 125
5.4. Svbsonic Lasers Based on Metal Vapor 130
Refere~nces 132
Chapter 6. Supersonic Chemical Lasers 138
6.1. Diffusion Chemical Lasers With Thermal Initiation of the Reaction 138
6.2. Supersonic Chemical Lasers With Energy Transfer 148
6.3. Chemical Gas-Dynamic Lasers 151
6.4. Analysis of the Efficiency of Diffusion Chemical Lasers 152
6.5. Open-Cycle Chemical Lasers With Pressure Recovery in the Diffuser 161
References 165
Chapter 7. Chemical Detonation Lasers 169
7.1. General Information on Detonation Processes 169
7.2. "Optical" Pr~perties of Detonation Waves, and the Phase Nature of Their
- Propagation 175
7.3. Overdriven Deto.iation 186
7.4. Mechanisms of Populution Inversion in Chemical Detonation Lasers 188
7.5. Experimental Stimulation of Emission in Chemical Detonation Lasers 200
References 211
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UDC 621.375.826
~ CHEMICAL LASERS
Moscow KHIMICHESKIYE LAZERY in Russtan 1980 (signed to press 5 Sep 80) pp 1-224
[Book "Chemical Lasers", by Valeriy Konstantinovich Ablekov, Yuriy Nikiforovich
Denisov and Viktor Vasil'yevich Proshkin, Atomizdat, 2850 copies, 224 pages]
[Text] The book presents the principles of gas-phase reactions typical of chemical
lasers, gives fundamentals of the quantum mechanical description of molecular sys-
tems, and outlines processes of formation of excited particles in the course of
nonequilibrium chemical reactions. An examination is made of the kinetics of pro-
cesses in chemical lasers classified according to their hydrogasdynamic character-
~ istics into devices with a stationary medium, with subsonic and supersonic flow,
_ and with detonation processes in the medium. Designs and working principles of
present-day chemical lasers are described.
For engineers and scientists working in laser research and development. May be
of use to undergraduate and graduate students ma~oring in physics and in engineer-
ing physics.
Tables 7, figures 100, references 475.
INTRODUCTION
Lusers, or opticaZ quantum generators as they are called in the Soviet literature,
are more and more widely used each year ii~ industrial technology, medicine, commu-
nications, geodesy and other areas of science and enbineering. Quantum-mechanical
engineering is used in holography, in locating remote ob~ects and the measurement
of great distances in astronomy, in research on transmitting telel-ision images
by light beam and so on. Results have been promising in the use of quantum gener-
ators for solving the problem of nuclear fusion [Ref. 1].
The expansion of areas of use of quantum generators i.s accompanied by improvement
of the systems that have been produced and by development of quantum generators
based on new active media, and on new physical and chemical principles. Industry
has now mastered production of solid-state, gas-discharge, semiconductor and dye
lasers.
The development of generators and amplifiers of stimulated emission in the visible
and infrared bands of electromagnetic waveforms iRef. 2-7J is the outcome of funda-
mental research by N. G. Basov, A. M. Prokhorov, and by Townes et al., who achieved
coherent radiation [Ref. 8, 9] in the microwave band on the basis of the phenomenon
of amplification of electromagnetic waves [Ref. 10, llJ.
1
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In addition to pumping of quantum generators by optical or electrical energy, other
methods have been developed as well. The most promising among these have been
thermal and chemical pumping techniques. In the former method, heat energy is
converted to coherent stimulated radiation, while the transformed energy in the
latter case is that released during exothermal reactions with the formation of
ato~es and molecules in excited states [Ref. 12-15].
The chemicaZ Zaser is a dewice in which p~pulation inversion and la.sing are ~chieved
either directly as a resul~ of a chemical reaction, or after the reaction in the
exchange of energy between components of the medium, at least one of which is a
product of this reaction.
The branch of science on chemical lasers includes divisions of quantum mechanics,
physics, chemical kinetics, o~tics, hydrodynamics, gas dynamics and plasma dynamics.
With respect to the particulars of chemical energy transformations of reagents
A, B, C, D, G, we can represent the ma~or processes in chemical lasers graphically
in the following diagram [Ref. 16):
~ ~ ` ~ ~ _ ~ ~ ~ ~ w
hV
Chemical
, ~ A" + t3 ~ ~ photodissociation
l~ laser
~
�---AIS
~ Chemical laser
~~v ~ i ~ +cu
e- ~T A+13--.~C� U -.Ar, ' hv=~ ~aith purely
cY~emical reaction
Chemical laser
+ ,~c; + hv~-~with energy transfer
~ (hybrid)
Most chemical reactic~ns take place comparatively slowly, and therefore they are
not suitable for population. inversion. Before they have time to accumulate, the
excited particles (indicated by an asterisk) make a transition to the ground state,
- and quantum-mechanical emission is not stimulated. Therefore, chemical lasers
can operate only on fast reactions: photodissociation or other chemical reactions
initiated by the action of light (hv), combustion, explosion (~T), electric dis-
charge (e-) or chemical reaction between atoms or molecules, e. g. in colliding
beams of~atoms or molecules of various substances.
In principle,. the chemical method of population inversion permits creation of quan-
tum generators with high efficiency and output power. Especially large power can
be obtained from quantum generators with explosive chemical reaction. '
~ Chemical energy is directly converted to optical emission in quantum generators
with chemical pumping. We should add to the advantages of chemical lasers over
other known quantum ~enerators the fact that they have a wide spectrum of lasing
wavelengths from 2 um [Ref. 17, 18] to 100 um [Ref. 19]. The development of chemical
laser research extends the range into the ultraviolet and millimeter regions of
the spectrum.
N
2 ~
~
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The spectra of coherent emission of chemical lasers coincide with the region of
vibrational frequencies of many molecules, and this enables the u~e of chemical
lasers for directed selective stimulation of chemical reactions by the action of
radiation on selected vibrztional degrees of freedom [Ref. 20J.
Chemical lasers can be used to study the distribution and transfer of energy in
chemical reactions and to get information on the nature of excited particles with
respect to wavelength. Methods have been developed for measuring the cross sections
of relaxational and other chemical-kinetic pr~cesses, based on using the radiation
_ of chemical lasers and the pecuiiarities of their spectral--temporal characteristics.
- Chemical lasers utilize exothermal processes during which excited inverse-population
products are produc.ed. Therefore the features of chemical lasers enumerated above
include the fact that the energy required for excitation is produced by the chemical
reaction proper rather than by an external source as in solid-state and gas quantum
generators. However, further developments of the field of chemical lasers in sci-
ence and engineering have shown that they sho~~d cover a wider class of quantum
mechanical systems, including with external sources of energy (such as y-quanta,
electrons and the like) that are used as initiators of a chemical reaction since
these reactions may be photolytic and radiolytic. ExcimQr lasers can also be in-
cluded in tbe clase of chemical lasers with co~sideration of the kinetics of con-
versions of substances during a reaction. Inversion can also be obtained in plasma
chemical reactions under the influence of nuclear fission products in fuel elements
--evels [Ref. 21].
Ref. 22 presents still another qualitatively new possibility of pumping quantum
~ generators. It is proposed that quantum generat~rs utilize phototransitions that
arise upon collision of two molecules that are capable of exothermal conversion.
Such phototransitions correspond to the change of chemical bonds in molecules,
i. e. they are identical to elementary chemical acts. Optical stimulation o� a
phototransition leads to photostimulation of the chemical process itself.
Ref. 23 also includes with chemicallasers detonation quantum generators in which
the active medium is provided by detonation products.
In this boc,k, chapters 1 and 2 are devoted to exposition of the principles of gas-
phase chemicdl reactions typical of chemical lasers under various conditions, the
fundamentals of the quantum-mechanical description of molecular systems, some pro-
cesses of formation of excited particles in the course of nonequilibrium chemical
reactions. These chapters explain the concepts and processes utilized in subse-
quent presentation of the material. Chapter 3 gives the kinetics of processes
in chemical lasers.
The subsequent presentation develops the classification of quantum generators as
given in Ref. 23, 24 in accordance with hydrogasdynamic characteristics that char-
acterize both the construction of chemical laser systems and their operating prin-
ciples. Therefore chapter 4 singles out chemical lasers with a stationary working
medium (gas-static lasers). Chemical lasers with subsonic circul.ation of the medium
are considered in chapter 5, while chapter 6 examines lasers with diffusion of
components in a supersonic flow. Chapter 7 is devoted to chemical detonation
lasers.
3
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The considerable num~er of papers that have now been published on chemical lasers,
and the limited scope of this book have precluded a more exhaustive presentation.
The reader can fill in this gap by acquainting himself with the monographs of Ref.
16 and 25, the surveys of Ref. 23, 24, 26-42 and the sp~cific articles of Ref. 43.
Ref. 44 presents an analysis of different areas in the field of chemical lasera
and the history of their development.
This book uses the SI system of units. The principal units of this system and
their derivatives (N, W, J, Hz, V, F, S2 and so on), including prefixes to designate
multiple and fractional values havP been introduced by CEMA Standard 1052-78 and
will be familiar to the reader, with the ~xception of the recently introduced pres-
sure unit Pa [pascal]. Therefore we will give here the conversion of this unit
to the previously widely used nonstandard units of physical and technical atmos-
pheres, and millimeters of inercury: 1 Pa = 9.8692�10-6 atm (physical) = 10.1972�10-6
at (technical) = 7.5006�10-3 mm Hg.
For approximate calculations it is convenient to use the relations 1 MPa ~ 10 atm (at),
1kPa~7.5mmHg.
REFERENCES
1. Basov, N. G., Krokhin, 0. N., "Conditions of Plasma Heating by Laser Emission",
ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 46, 1964, p 171;
Pashinin, P. P., Prokhorc,v, A. M., "Production of a P.~~?~e High-Temperature
Plasma With Laser Heating of a Special Gas Target", Preprint No 160, Lebedev
Physics Institute [FIAN], i~ioscow, 1970; ZHURNAL EKSPERIMENTAL'NOY I TEORETI-
CHESKOY FIZIKI, Vol 60, 1971, p 1630;
Velikhov, Ye. P., Filyukov, A. A., "New Approach to Using Lasers for Controlled
Fusion" in: "Problemy lazernogo termoyadernogo sinteza" [Problems of Laser-
Driven Nuclear Fusion], Moscow, 1976, pp 3-14.
2. "Moiecular Amplifier and Oscillator on Submillimeter Waves", ZHURNAL EKSPERIMEN-
TAL'NOY I TEORETICHESKOY FIZIKI, Vol 34, No 6, 1958, p 1658.
3. Basov, N. G., Krokhin, 0. N., Popov, Yu. M., "Generation, Amplification and
- Display of Infrared and Optical Radiation Using Quantum Systems", USPEKHI FI-
ZICHESKIKH NAUK, Vol 72, No 2, 1960, pp 161-209;
Basov, N. G., Vul, B. M., Popov, Yu. M., "Quantum-Mechanical Semiconductor
Generators and Amplifiers of Electromagnetic Waveforms", ZHURNAL EKSPERIMENTAL'NOY
I TEORETICHESKOY FIZIKI, Vol 37, No 2, 1959, pp 587-588.
4. Shawlow, A. L., Townes, C. H., "Infrared and Optical Masers", PH1S. R~V.,
Vol 112, No 6, 1958, pp 1940-1949.
5. Maiman, T. H., "Stimulated Optical Radiation in Ruby", NATURE, Vol 187, No 4736,
1960, pp 493-494.
6. Ablekov, V. K., Pesin, M. S., Fabelinskiy, I. L., "Realization of a Medium
With Negative Absorption Coefficient", ZHURNAL EKSPERIMENTAL'NOY I TEORETI-
CHESKOY FIZIKI, Vol 39, No 3, 1960, pp 892-893.
4
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- 7. Javan, A., Bennett, W. R., Harriott, D. R., Jr., "Population Inversion and
Continuous Optical Maser Oscillation in a Gas Discharge Containing an He-Ne
Mixture", PHYS. REV. LETT., Vol 6, No 3, 1961, pp 106-110.
8. Basov, N. G., Prokhorov, A. M., "Using Molecular Beams for Radiospectroscopic
Investigation of Rotational Spectra of Molecules", ZHURNAL EKSPERIMENTAL'NOY
~ I TEORETICHESKOY FIZIKI, Vol 27, No 4, 1954, pp 431-438; "Molecular Oscillator
and Amplifier", USPEKHI FIZICHESKIKH NAUK, Vol 57, No 3, 1955, pp 481-501.
9. Gordon, J. P., Zeiger, ii. J., Tcwnes, C. H., "Molecular Microwave Oscillator
and New Hyperfine Structure in the Microwave Spectrum of NH3", PHYS. REV.,
Vol 95, No 1, 1954, pp 282-284.
10. Fabrikant, V. A., "Radiation Mechanism of a Gas Discharge", TRUDY VSESOYUZNOGO
ORDENA LENINA ELEI~TROTEKI~TICHESKOGO INSTITUTA IMENI V. I. LENINA, No 41, 1940,
p 236.
11. Fabrikant, V. A., Vudynskiy, M. M., Butayeva, F. A., "A Method of Amplifying
Electromagnetic Emissions", USSR Patent No 123209 (filing No 5767491,
18 Jun 51), BYULLETEN' IZOBRETENIY No 20, 1959, p 29; "Phenomenon of Amplifi-
cation of Electromagnetic Waves", Certificate of Discavery No 12, 18 Jun 51,
BYULLETEN' IZOBRETENiY No 8, 1962.
12. Polanyi, J. C., "Proposal for an Infrared Maser Dependent on Vibrational Exci-
� tation", J. CHEM. PHYS., Vol 34, No 1, 1961, pp 347-348.
13. Orayevskiy, A. N., "Arisal of Sub-Zero Temperatures in Chemical Reactions",
Z,HURNAL EK~PERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 45, No 2, 1963, p 177.
14. Tal'roze, V. L., "The Problem of Generation of Coherent Induced Radiation in
Chemical Reactions", KINETIKA I KATALIZ, Vol 5, No 1, 1964, pp 11-27.
~ 15. Kasper, J. V. V., Pimentel, G. C., "HC1 Chemical Laser", PHYS. REV. LETT.,
Vol 14, No 10, 1965, pp 352-354.
16. Kompa, K. L., "Chemi~al Lasers", ~3erlin, Springer V~rlag, 1973.
17. Suchard, S. N., Pimental, G. C., "Dueterium Fluoride Overtone Chemical Laser",
APPL. PHYS. LETT., Vol 18, 1971, pp 530-531.
18. Sadie, F. G., Btiger, P. A., Malan, 0. G., "Continuous-Wave Overtone Bands in
a CS2-02 Chemical Laser", J. APPL. PHYS., Vol 43, 1972, pp 2906-2907.
19. Skribanowitz, N., Herman, I. P., Osgoot, R. M., Jr., et al., "Anisotropic Ultra-
high Gain Emission Observed in Rotational Translations in Optically Pumped
HF Gas", APPL. PHYS. LETT., Vol 20, 1972, pp 428-432.
20. Tal'roze, V. L., Barashev, P. P., "Chemical Action of Laser Emission", ZHURNAL
VSESOYUZNOGO KHIMICHESKOGO OBSHCHESTVA IMENI D. I. MENDELEYEVA, Vol 8, No 1,
1973, p S.
21. Gudzenko, L. I., Yakovlenko, S. I., ~'Plazmennyye lazery" [Plasma Lasers], Moscow,
Atomizdat, 1978.
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22. Pekar, S. I., "High-Pressure Chemical Lasers and Light-Stimulated Chemical
Reactions", DOKLADY AKADEMII NAUK SSSR, Vol 187, No 3, 1969, pp 555-557.
23. Warren, W. R., Jr., "Chemical Lasers", ASTRON. AND AERON. Vol 13, No 4, 1975.
24. Christiansen, W. H., Russel, D. A., Hertzberg, A., "Flow Lasers", ANNUAL REV.
FLUID MECH., Vol 7, 1975, pp 115-139.
25. Bashkin, A. S. et al., "Chemical Lasers" in: "Itogi nauki i tekhniki. Radio-
tekhnika" [Advances in Science and Technology. Radio Engineering], Vol 8,
Moscow, VINITI, 1975, p 382.
26. Orayevskiy, A. N., "Chemical Lasers", KHIMIYA VYSOKIKH ENERGIY, Vol 8, No 1,
' 1974, pp 3-20.
27. Solimetio, S., "Che~rical Lasers", PHYS. BULL., Nav 74, pp 517-520.
28. Dzhidhoyev, M. S., Platonenko, V. T., Khokhlov, R. V., "Chemical Lasers",
USPEKHI FIZICHESKIKH NAUK, Vol 100, No 4, 1970, pp 641-679.
29. Heavens, Q. S., "Some Recent Developments in Gas Lasers", CONTEMP. PHYS.,
Vol 17, No 6, 1976, pp 529-552.
30. Cool, T. A., "The Transfer Chemical Lasers: a Review of Recent Research",
IEEE J. OF QUANTUM ELECTRONICS, Vol QE-1, No 1, 1973, pp 72-83.
31. Karnyushin, V. N., Soloukhin, R. I., Using Gasdynamic Flows in Laser Tech-
nology", FIZIKA GORENIYA I VZRYVA, No 2, 1972, pp 163-202.
32. Jones, C. R., Broida, H. P., "Chemical Lasers in the Visible", LASER FOCUS,
Vol 10, No 3, 1974, pp 37-47.
33. Basov, N. G. et al., "Dynamics of Chemical Lasers (Survey)", KVANTOVAYA ELEK-
TROHIKA, No 2, 1971, pp 3-24.
34. Chester, A. N., "Chemical Lasers: A Survey of Current Research", PROC. IEEE,
Vol 61, No 4, 1973, pp 414-422; '
Chester, A. N., Hess, L. D., "Study of the HF Chemical Laser by Pulse-Delay
Measurements", IEEE J. OF QUANTUM ELECTRONICS, Vol QE-8, No 1, 1972, pp 3-13.
35. Gross, R. W. F., Bott, J. F., ed., "Handbook of Chemical Lasers", a Wiley
Interscience Publication, New York, 1976.
36. Ewing, J. J., "New Laser Sources" in: "Chemical and Biochemical Applications
of Lasers", Vol II, edited by C. S. Moore, N. Y.-San Francisco-London, A~a-
demic Press, 1977, pp 241-278. .
37. Soloukhin, R. I., "State of the Art and Outlook for Gasdynamic Combustion
- Lasers" in: "Goreniye i vzryv" [Combustion and Explosion], Moscow, Nauka,
1977, pp 30-49.
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38. Orayevskiy, A. N., "Chemical Lasers" in: "Spravochnik po lazeram" [Laser
Handbook], edited by A. M. Prokhorov, Vol 1, Moscow, Sovetskoye radio, 1978,
pp 158-183.
39. "Chemical and Molecular Lasers", J. OPT. SOC. AMER., 1978, Vol 68, No 5,
pp 651-656.
40. Yeletskiy, A. V., "Excimer Lasers", USPEKHI FIZICHESKIKH NAUK, Vol 125, No 2,
1978, pp 279-314.
41. "W and Excimer Lasers. I", J. OPT. SOC. AMER., Vol 68, No 5, 1978, pp 702-706;
II, Ibid., pp 711-7i8.
42. Knyazev, I. N., Letokhov, V. S., "Gas Lasers in the W and XW Regions of
the Spectrum" in: "Spravochnik po lazeram", edited by A. M. Prokhorov,
' Vol 1, Moscow, Sovetskoye radio, 1978, pp 197-220.
43. Bashkin, A. S., Kupriyanov, N. L., Orayevskiy, A. N., "Chain-Reaction Chemical
Lasers in the Optical Band", KVANTOVAYA ELEKTRONIKA, Vol 5, No 12, 1978,
pp 2611-1619; "Use of Excited Atoms in Optical-Band Chemical Lasers with
Thermal Initiation", Ibid., pp 2567-2576.
44, Dunskaya, I. M., "Lazery i khimiya" [Lasers and Chemistry], Moscow, Nauka,
- 1978, 164 pages.
CHAPTER 1: PRINCIPLES OF KINETICS OF GAS-PHASE CHEMICAL REACTIONS
�1.1. Law of Effective Masses
In che;nical lasers, processes take place chiefly in the gas phase, and to get an
idea of the chemical reactions in these lasers it is necessary to know the rates
and proportions of reactions of the initial gases, and the composition of inter-
" mediate and final product.;. Therefore we will consider the principles that govern
chemical reactions in gaseous media.
Reaction Rate. Rate Constant. Consider a gas made up in the general case of chemi-
cal. components Ai (i = 1, 2,..., n), i. e. of N1 molecules of component A1, N2 mole-
cules of component A2, N3 molecules of component A3 and so on. Then a chemical
reaction that converts initial components A1, A2,..., A~ into reaction products
Ai, A~,..., A~ can be recorded by the stoichiometric equation
N N
~,'rr1lt--r J`riAr~ (1.1)
- r=i r-i
where ri and r~ are the stoichiometric coefficients of the reaction for the i-th
substance that is in the state of an initial reagent and a reaction product re-
spectively.
For a system with fixed volume V and fixed composition, the relation between changes
of concentration of any two substances i and j taking part in the reaction is ex-
pressed on the basis of relation (1.1) as
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~~l~~i-~~) -~1/~r1-r~)� (1.2)
Here w= V-10N/~t mole/ (cm3 � s) is the change in mole concentration c= N/V of the
substance in time ~t, i. e. the average rate of the chemical reaction.
The chemical reaction rate w in the general case is a function of the concentrations
of the reacting substances, pressure and temperature [Ref. 1]. The dependence
of the reaction rate on concentrations of the reagents ci is defined bv the law
of effective masses: the reaction rate is proportionaZ to the product of eoncen-
trations of the reacting substances. Thus for a reaction of general form (1.1)
N
k~l, -k (j c 3>
ja ~
where k is the rate constant or specific reaction rate. The value of k usually
increases rapidly with rising temperature.
Simple Reaction. Order of a Reaction. Molecularity. According to the derivation
of *he Zazu of effective masses from the kinetic theory of gases, the number of
simultaneous collisions when rl molecu~es of substance A1 (of concentration ;_1)
interact with r2 molecules of substance A2 (of concentration c2) and so on, is
protortional to the product c~lc~2... Or vice versa: the rate of single-stage
reactions that involve the simultaneous interaction of rl+ r2+ r molecules
must be expressed by the law of effective masses [Ref. 2]. Reactions that meet .
this condition are called simpZe reaetions.
By def inition
dclldl = rc~t, i= l, N, (1.4)
and in the elementary stage of the reaction
~i = (ri - r~) (1. 5)
With consideration of relations (1.3) and (1.5), we get for the i-th and ~-th sub-
stances instead of equation (1.4)
N
dcild~==(~r~ -r~~k~ n ci~, ~ (1.6)
/OI
where (ri - r�)k is constant for isothermal systems. Usually measurements of the
quantity dci~dt in isothermal systems lead to ~
N
dcj/dt Il ci~~ (1.7)
i
8
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where exponents n~ are constants. In such cases, the number ni is called the order
N
of the reacttion with respect to the i-th substance, and n~~ nt is called the
t-i
resuZtant order, or si~nply the order of the reaction.
We can see from formulas (1.6) and (1.7) that if the reaction is simple, ni = ri.
Then the quantity ni is the molecularity of the reaction with respect to substance
i, and n is the total molecularity of the reaction. Thus the moZecuZar2tr~ of a
reaction is deteYmined by the number of molecules participating in the process:
at r= 1, the reaction i.s of the first order, or monomolecular; when r= 2, the reac-
tion is of the second order and so on.
A relation of form (1.7) often holds even when equation (1.6) is invalid, i. e.
when the reaction consists of several stages. In such cases the relation between
the order of a reaction and molecularities becomes complicated, and ni may take
on non-integer values [Ref. 3].
- �1.2. Mechanisms of Simple Reactions
,
First-Order Reaction. When the rate of change in concentration is proportional
to concentration, it is said that a ~irst-order reaction is taking place. Such
a reaction is the simplest chemical process. According to the law of effective
masses (1.3), the reaction rate of a first-order reaction for reagent A1 (i=1)
is
u~ _ dcl/dt = kcl, (1. 8)
where
Jz [c-l1 > 0.
After integration of equation (1.8), we get at concentration ci known at the initial
instant t = 0:
c, = c~ exp ht) = c~ exp !/i). (1. 9)
From (1.9) we get an expression for the reaction rate constant
Jt = (I/t) itt (c~/cl). (1.10)
At t= T, the concentration of reagent A1 decreases by a iactor of e. The quantity
Te = 1/k is called the characteristic reaetion time. We can also ~udge the rate
of the chemical reaction from the haZf-Zife or haZf-period of the reaction T
the time during which the initial concentration ci decreases to one-half: T~~~-- ln 2/k.
The simplest type of reaction that conforms to equation (1.8) is the monomolecular
reaction of dissociation of a substance
AB A -f-~ B. (1.11)
9
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[Note: Hereafter in addition to the purely numerical designations of reagents
Ai and reaction products Ai, we will also use letter combinations: A, B, C,
AB, BC,
- It is assumed that molecule AB is stable and w{11 not spontaneously dissociate
into reaction products. What then is the mechanism of the monomolecular process?
It is assumed that not all molecules are subject to dissociation, but rather only
- the especially activated molecules that have internal energy exceeding the activa-
tion energy Ea. Such molecules are callPd active. According to Ref. 4, many
monomolecular reactions occur in tWO atages
AB-}-M~ AB*-}-M; (1.12)
� k~
AB* ~ AB~ A B, (1.13)
The first of which is activation ;kl) and deactivation (k2) of the molecuies, while
the second is dissociation (.k3). In (1.12), (1.13), M denotes an arbitrary mole-
cule, the asterisk after AB means that the molecule is in the excited (in this
case unstable) state, and the rate constants kl, k2, k3 for elementary stages of
the reaction are indicated above and below the arrows. '
On the second stage (1.13), monomolecular transformation takes place due to intra-
molecular redistribution of energy. Since such transformation requires that the
energy of the active particle be concentrated on c~rtain degrees of freedom, we
introduce the concept of the activated moZecuZe AB that is the instantaneous state
of the molecule through which the reaction is terminated.
First-order reactions and the second-order reactions described below play an essen-
tial part in chemical kinetics since most elementary stages are monomolecular or
bimolecular reactions. ,
Reactions of Second and Higher Orders. When molecules A1 and A2 form molecules
of type A' in reaction (1.1), and when the reaction rate in this case~is propor-
tional to the concentrations of both initial substances, it is said that a second-
order reaction is taking place.
The kinetics of a second-order chemical reaction for reagents A1, A2 is descr.ibed
by the equation ,
_ c~~l dc, ~ hc~ cz, (1.14)
dl ~ ` dt
where k has the dimensionality of cm3/(mole�s). �
After integration of equation (1.14) like (I.9), (1.10), we get under known initial ,
conditions cl = ci and c2 = c2 :
- exp[-(c2-c?)ktJ. (1.15) ,
c, e;
10
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whence the expression for ttie reaction rate constant will be
0
k=-~ - ~ ]n ~'~l . (1.16)
t c;-ci c=c1
, Examples of second-order reactions are bimolecular reactions of dissociation of
hydrogen iodide 2HI-} H2 + I2, and thermal dissociation of chlorine oxide ,
2 C120-~ 2C12 + 02 .
Consider the n-th order reaction
A+ B+ C+...-~ reaction products.
If ci = c2 = c�, the reaction rate will be
- f,~CI[~t lzC". (1.17)
Integrating (1.17), we get an expression for the reaction rate constant
1 r 1 l (1.18)
k - t (n _ I ) \ ~(n- I ) ~Cp)(n- I 1 .
,
with dimensionality of (cm3/mole)~n-l~.s-1.
For c= c~ /2, t= T~,
~
k = .
~~~2(n-I) ~~�~v~-i) ~1.19)
and
_ ~2~"r~~ - 1) 1
~~/2 k(n-1) ~~~(n-~~ ' (1.20)
Thus, for the general case of an n-th order reaction
~~~2 (~~-(n-I>~ (1.21)
i. e. the way that thP half-period of the reaction depends on the initial concen-
tration characterizes the actual order of the reaction. It is taken as unlikely
that chemical reactions with molecularity of more than three will play a role in
chemical processes, since reactions with higher molecularity take place extremely
slowly.
�1.3. Chemical Equilibrium
Equilibrium Conditions and Equilibrium Constant. Since chemical reactions go in
both directions, equation (l.l) should be rewritten as
11
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N k~ N
J' ri 11i ~ ri !~i, (1.22)
r=i kn
i. e., side by side with forward reaetion (1.1) is its reverse reaetion.
If the equilibrium concentrations are denoied by cie and c~e, then the condition
of equilibrium of the forward and reverse reactions will be
N N ~
k~ t1 ~i~` kt, II c;~ . (1. 23)
c= i 1= ~
Whence we get the equiZibrium constant -
N , N
~ K-- h~ n I ~ ~ 0, branchings arise from time to time on individual sections of the chain,
and the additional active centers give rise to secondary branched chains (see
Fig. 1.3b). When S~ = 1(e~= 2), branching takes place on every link of the chain
(see Fig. 1.3c). Chains that arise in this way are called continuousZy branched.
Let us calculate the length of a branched chain Z~, i. e. the number of elementary
reactions caused by the appearance of. a single primary active cQnter. The effec-
tive chain breaking probability will be equal to the difference - d~. Conse-
quently with consideration of (1.41):
- 1/~~~ g~) /~/(1 - - l~~i~); (1. 49)
c~v c,~ l~ = ~R ~~l~l - l~ Ti~). ~ 1.50)
Since s~ and d~ are functions of temperature and pressure, under certain conditions
it may happen that S~ - d~= 0, and then the length of the chain Z~->W~ This means
that if at least one branching takes place on the length of a simple chain, i. e.
Z~d~ = 1, an explosive process arises.
Limiting Phenomena. At a certain vapor pressure of phosphorus in a mixture with
oxygen, the region of ignition is bounded by two limiting oxygen pressures (pp~)1
and (p~2)2. Outside this region, phosphorus vapor does not ignite. Quantitative
investigations of this process together with a study of ignition of a stoichiometric
mixture of hydrogen with oxygen [Ref. 26-28] have yielded fundamental results for
the theoretical description of the effect by N. N. Semenov [Ref. 21, 29].
The existence of such limiting pressures--lower and upper limits of ignition of sub-
stances--can be explained by peculiarities of kinetics and the mechanism of the
branched chain reaction. In a simple chain reaction (e~a~ < 1) the rate of a c~m-
paratively sl.ow steady-state reaction is w= wQa~/(1- e~a~). In the case of a
branched chair. reaction (e~a~ > 1), the reaction rate (1.40) is
. r.�~ = ra~d �L` (exp q~t-1), (1. 51)
e~ a~ -1
where
q~= - T =(v;~ vp~~(e~a~- 1). (1.52)
For ~t~l from (1.51) and (1.52) with consideration of the fact that rz~ Pl va~/(va~
v~~~), we get Semenov's Zau~:
J u~o vac
~ ---1 e,cp ~pl. (1.53)
~P
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When e~a~~ 1 the reaction becomes rapid and self-accelerating, terminating in an
explosion. Transition from the steady to the unsteady state is d~~termined by the
condition
f~ a~ 1 � (1. 54)
From this, considering (1.48) and the relation for the chain continuarion proba-
bility a~ = vr~/~v~r ti~i~~~ we get
S~vi` -v9~� . (1.55~
The pressure dependences of va~ and v2~ can be written as
v~~=up and v;~-bpa-~-b', ~1.56)
where v2~ is expressed as the sum of terms, of which the first characterizes the
volumetric breaking of chains by the triple collision mechanism, while the second
term characterizes breaking of chains on the walls in the kinetic region of the
reaction.
Expressions (1.55) and (1.56) imply
pa = 8ap/b G'lG = 0, (1.57)
with a solution that gives the pressures on the lower (pl) and upper (p2) limits
of ignition:
P1= Sa/26 -YBaua/46~-b'/b, ~1.58)
Pz = Sa/2b �-~-YB' aa/4b' G'/b� (1.59)
The graph of the temperature dependence of pl and
p2 (Fig. 1.4) is conventionally called the "ig- ip
nition peninsula" and p= pM is called the "cape ~
of the ignition peninsula." ~
s
�1.6. Elementary Processes of Excitation of p,
Systems in Chemical Reactions p2
Pn P?
Principles of Quantum-Mechanical Description of ~.4p0 4B0 5,20 T,�C
Molecular Systems. Quantum mechanics describes
the relation between the structure of atoms and Fig. 1.4. Ignition penin-
molecules and their spectra, gives a represen- sula of a mixture of 2H2/OZ
tation of the energy distribution in a molecular
system, its excitation, relaxation and chemical reactivity. Transition of the
system from one state to another is accompanied by absorption or radiation of
energy:
. /iv EZ - E,, (1. 60)
where h is Planck's constant, v= c/a is the frequency of a quantum, a is wavelength,
c is the speed of light. Or, replacing v with the wave number w= v/c [cm 1], we get
21
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_ w = (EZ - El)/cit. (1.61)
When the molecular system absorbs light quanta, the energy of the system changes de-
pending on the energy of the absorbed quanta: rotational motion of the molecul.e
(R) when the energy of the absorbe3 quanta is 0.125-1.25 kJ/mole; vibration of
nuclei (V) at 1.25-50 kJ/mole; electron motion (E) at energies of the order of
tens and hundreds of kJ/mole.
J
J�4 ~~3
_ J
w2
J~J
J
V� 1
v-4
J=2 V~ 3
J�3 y. 2
J`2 V~ 1
~ V-0
J=0 '
a b c
A, cn f0 i J�10. Z 1,8�10 5.~8�10 S t~ s 10 ~o
v~ ~ G1 ~ I t~ m ~
'd . .O ~P~' .O f,~j~~ ~ cd
H rl ~
H N~ V~ r~.{ w v ,rl ~ ~-~I rOl ~ k ~O'
w {"'i rl vi H ,y "ti '7 }
d
Rotational ibrational Electron
spectrum spectrum spectrum
(R) (V) (E)
Fig. 1.5. Diagrams of energy levels and transitions R(a),
V-R (b), E-V-R (c) of spectra, and their corresponding re-
gions of electromagnetic radiation (d)
Corresponding to such changes of energy are the schemes of energy levels and tran-
sitions shown in Fig. 1.5a-c, and also regions of the spectrum of electromagnetic
radiation (Fig. 1.5d). Here the far infrared, microwave and millimeter regions
correspond to rotation R-spectra (a), the IR-region corresponds to vibrational-
rotational spectra V-R (b), and the visible and ultraviolet correspond to electron
(E) or electronic-vibrational-rotational (E-V-R) spectra (c).
22 ~
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A molecule can be represented as a harmonic oscillator with energy
Eo = hcwR (v 1/2), (1.62)
where v= 0, 1, 2, 3. is the vibrationaZ quantum number that defines the level
of vibrational energy, we corresponds to the ground state v= 0 with energy Ep ~hcwe,
that exists even at the zero of temperature. For the harmonic oscillator the dif-
ference of energies of ad~acent states is
Eo+l - ED = h~rue. (1. 63)
From (1.61) we have
Eo+i - Eo = hcw, (1.64)
i, e. w= we.
However, the model of a real molecule is an anharmonic oscillator, and w must dif-
fer from we, but this difference is small at low values of the vibrational quantum
number v.
Because of anharmonicity, the V-levels of energy with increasing v gradually get
closer together, and (1.62) is replaced by the two-term formula
Lo = hcw, (v 1 /2) - hcc~,xe (a 1 /2)~ (1. 65 )
with constant xe~l characterizing anharmonicity. In this case, transitions with
~v > 1 become possible--overtones. Upon a further increase in v, the energy of
the molecule reaches the value E~X, and when Emax ' Eo= Do the molecule d:~ssociates.
The R-structure of the vibrational band is determined by the change in r~otational
energy EJ = BJ(J + 1) in the V-transition:
- E~ - Ei = B' J' (J' 1) - B"J" (J" 1), (1. 6 6)
where J= 0, 1, 2, is the rotationaZ quantum nwnber, B is the rotationaZ con-
stant.
For dipole radiation ~J = J'- J"= 0, �1 respectively we get the three branches of
the spectrum But since transitions ~J = 0 are forbidden in the ground
electronic state for most diatomic molecules, only the positive ,I~- and negative
`.~-branches are observed.
The E-energy or E-V-R-energy of molecules depends in a complicated way on their
structure, and the electronic energy states of molecules are classified by sym-
metry types. For example the electronic states or terms of diatomic and axially
symmetric linear polyatomic molecules are classif ied according to:
a) quantum numbers ll characterizing the absolute value of the projection of the
complete orbital moment ~ on the axis of the molecule (in units of h/2~r). The
quantum number /1 can take on values of 11= 0, 1, 2, 3, L denoted by E, II,
~ respectively.
23
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b) multiplicity 2S+ l, where S is the quantum number of the resultant spin of all
electrons in the molecule. Multiplicity is placed to the upper left in the symbol
of etate, e. g. 3E;
c) total orbital moment characterized by a figure at the lower right for terma
different from E, e. g. 3II2;
d) the property of symmetry of the electronic eigenfunction of the molecule sym-
bolized by the sign or for state E to the upper right. In any plane that
passes through the line connecting the nuclei, the electronic eigenfunction either
remains unchanged (E+) or changes sign (E-);
e) evenness (g) or oddness (u) of the state for molecules in which the nuclei have
the same charge, e. g. lEg, lEu.
In the potential energy surface system the electronic state with the minimum that
lies lowest is called the ground state and is denoted by the symbol X placed before
the symbol of state (X1Eg), and the letters A, B, C,... are used for the character-
istics of a sequence of excited electron states. For light molecules, a sequence
of excited states that differ in multiplicity from the ground state is symbolized
by the letters a, b, c,..., while states that are the same in multiplicity are
denoted by A, B, C,... The state with the greatest possible value of S and the
greatest possible value of L(at the given S) has the lowest energy for a given
electron configuration (Hund's ruZe).
Since the energies of electrons, vibrations of nuclei and rotations of molecules
are quantized, the total energy is also quantized
E = Ee1+ Evib+ Erot� (1.67)
The quantity ~Eil/hc for each i-th level is called a term. The corresponding term
_ can be represented in the form of a sum of three terms:
T = Ei/hc = Tel + G(v) + F (J) , (1.68)
where Tel, G(v), F(J) are the electronic, vibrational and rotational terms respec-
tively.
At E-transitions in molecules, as can be seen from the diagram of Fig. 1.Sd, a �
quantum of light is emitted in the UV and visible regions of the spectrum, or more
rarely in the near-IR region. Superposition of V- and R-transitions on electron
transitions produces a f ine structure of the electron spectrum (see Fig. 1.5c).
The system of V-R levels (see Fig. l.Sb) can be obtained by solving the Schrddinger
equation for a molecule in the nonrigid rotator approximation--the anharmonic vi- .
brator. In doing this, the value of the potential energy is substituted in the
SchrtSdinger equation in the form of some function of the internuclear distance r.
In Ref. 30, the convenient empirical equation
EQ (r) = Do {1 - exp I- a(r - re)1}a (1.69)
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is proposed as the potential energy curve for diatomic molecules, where Do is the
energy of dissociation, re is equilibrium distance, a is a constant for the molecule.
Also used is the forni of the Lennard-Jones potential close to the real form:
er~ ~r) 4f. [(~/r)'z (v/~�)�1. (1.70)
where e is the force constant, and Q is the average diameter of the colliding
spheres.
Energy Distribution of Products of Chemical Reactions. The energy released in
elementary chemical processes is distributed over different energy levels or degrees
of freedom of the ultimate reaction products [Ref. 13, 31-33]. The nature of this
distribution determines for example the nonequilibrium luminescence in the course
of the reaction in the visible or UV regions of cool flames of hydrocarbons and
- CS2 [Ref. 14, 34, 35]. In combustion reactions, nonequilibrium luminescence is
observed in the IR r~gion of the spectrum [Ref. 36] corresponding to V-transitions.
Reactions can be divided into two types: those that take place within the limits
of a single potential energy surface, and are usually accc~mpanied by V-excitation--
adiabatic reactions [Ref. 77]--and those that include more than one potential energy
surface and are frequently accompanied by E-excitation--nonadiabatic reactions.
The concept of a reaction in the form of a curve or potential energy surface is
particularly useful in cases where the relation between E- and V-motions is weak.
- If we know the potential energy, we can get the electronic energy of the system
for arbitrary fixed positions of nuclei. The potential energy surface is either
- calculated or determined from experimental data [Ref. 38]. In doing this, two
problems are solved: finding the surface, and using it to describe the experi-
mental results.
However, one need not know the complete structure of the surfaces to interpret
experimental data. The energy distribution of reaction products can be determined
even by such qualitative characteristics of the surfaces as the radius of action
of forces, the relative slope of parts of the potential energy surface that corre-
spond to the initial reagents and products, and energy parameters [Ref. 39]. Let
us consider the energy distribution of products [Ref. 40-44] based on the example
of a substitution reaction of the type
A-}- BC ~ A B-I- C (1. 71)
that is typical of chemical lasers.
This reaction can be divided into three stages: first--approach of atom A to com-
plex BC; second--an intermediate stage where the B-C bond is stretched out in the
course of the continuing approach; third--separation of reaction products AB and C.
Let E1, E2, E3 be the energies released in these three stages of the process.
The relation between E1, E2, E3 is considerably dependent on the type of potential
energy En(r~, rB~). The major portion of E1 is released as vibrational energy,
E3--in the form of kinetic energy, and the percentage of E2 converted to the Evib
of the molecules is higher, the heavier the atom A as compared with B and C[Ref.
41]. For example, in the case of the interaction H+ C12, most of the energy is
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released on the second and third stages [Ref. 40, 41J. Of interest for chemical
lasers are reactions with high ratios of Evib~Ekin� Large values of Evib~Ekin
can be attained in reactions in which a hydrogen atom is replaced by a heavier
' atom such as deuterium or a metal, and also in the reactions F+ H2, Cl + HI and
so on.
~jl ~~I
~III II~I
~ec rec
~ ,
~
~
~ X
_ _ -
\ - ~ ~
_ x ~ ~
p ~~e 0 ~~e
b c
~ec
A
~ ~ ~
~ A�8C M
~ l
u~ 1
~ ,i
R
~ ~
~
a~
_ ~
~ p AB�C
w
0 ~,,e 0 t, relative units
a d
Fig. 1.6. The potential energy surfaces of a system of atoms in phases of attrac-
tion (a), repulsion (b), and mixed energy release (c), and a graph of the reaction
The potential energy surfaces of a system of atoms are shown in Fig. 1.6 in phases
of attraction (a), repulsion (b) and mixed energy release (c). The solid curves
- show lines of constant energy, the dot-and-dash curves indicate the coordinate
of the reaction (the potential energy increases to both sides of this line), and
the broken curves show the possible trajectory of motion of the system during the
26
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reaction (1.71). If the energy of the system is slightly greater than the activa-
tion energy of the reaction, these tra3ectories pass close to the saddle point on
the potential energy surface indicated by the cross.
If the form of the function En(r~, rB~) corresponds to Fig. 1.6a, then the most
probable trajectories are those with energy release on the stage of approach of
A and BC since after the system has passed the potential barrier, rAg decreases,
and rB~ changes but little, i. e. here we have energy release in the attraction
phase.
For the reaction corresponding to Fig. 1.6b, after the system has passed the po-
tential barrier there is little change in r~, while rB~ increases, i. e. energy
release takes place on the stage of dispersal, or in other words on the repulsion
phase.
In the intermediate case of Fig. 1.6c, we have mixed energy release in region M
of the graph of the reaction in Fig. 6.1d, where the phases of attraction and re-
pulsion are indicated by the letters A and R respectively. With energy release
in region M, the nature of the most probable tra~ectories depends to a great extent
on the ratio between masses of particles.
Adiabatic and Nonadiabatic Interactions, Energy Resonance. If two or more col-
liding particles have relative velocities that are small compared with the orbital
velocities of electrons, then the electrons will have time for rearrangement in
accordance with the instantaneous positions of the nuclei, and as a result their
energy will depend only on the relative positioi.s of the nuclei af the atoms. This
simplification is known as the Borm-Oppenheimer approximation. It ls applicable
not only to slow molecular collisions, but also to rotational and vibrational mo-
tions of nuclei in a single molecule. According to this approximation, the nuclei
have certain potentials relative to one another, the approximate form of which
for two different initial E-states is shown by the solid curves AB and A'B' in
Fig. 1.7 [Ref. 45]. Such a slow collision without E-transitions is called adia-
batic (B-A). Obviously, adiabatic collisions between two atoms will be elastic,
i. e. the atoms will fly apart, if the energy is not expended on a third particle
or on radiation. Adiabatic collisions of polyatomic molecules may be accompanied
by rotational or vibrational excitation or a chemical reaction. On the other hand,
A,
~ B'
R
~ ~
` 8
~ ~ w
~ �
~ ~ /
~ q v ~ B
~
a1
~
� ~ dr~
C
W
~ ~ t, relative units
Fig. 1.7. Potential curves of collision of nuclei:
B-A--adiabatic process; B-A'--nonadiabatic process
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in collisions that are fast enough the electrons will not have time to rearrange,
and the nuclei will follow the broken curve B-A'--a nonadiabatic collision. If
the relative velocity u is still high upon separation of the nuclei, then the nu-
clei following this curve will again enter state B, and the collision will again
be elastic.
To achieve the E-transition from B to B', the nuclei in converging must move along
the solid curve, and in diverging--along the broken curve, or vice versa. Conse-
quently, the excitation cross section has a maximum at certain intermediate veloci-
ties where the probabilities of following the solid or broken curves are equal.
Quantum-mechanical analysis shows that this occurs if the time in the crossing
region ~r~/u is approximately equal to the characteristic time of energy exchange
h/(2~r~E~) (see Fig. 1.7). Under such conditions, the cross section may be nearly
equal to the gas-kinetic value.
The potential curves may come together at very low ~E~, i. e. when there is energy
resonance between the initial and final states. However, in the thermal energy
range the existence of resonance is neither a necessary nor a sufficient condition
for a large excitation cross section. Potential curves that are far apart at great
internuclear distances may get much closer together when these distances decrease.
The reverse situation may also be realized. This is confirmed by careful measure-
ments in exothermic reactions and "quenching" reactions [Ref. 46-48].
In the process of electronic excitation, a molecule makes a transition from the
ground electron state to an excited state. The Franek-Condon principle answers
the question of just what is the vibrational state to which the molecule will make
its transition, and whether it will remain intact or be dissociated. According
to this principle, the change in state of the electron shell of a molecule takes
place so much more rapidly than vibrations of the atomic nuclei that there is not
time for a change in either the velocity of motion nor the position of the nuclei
in an E-transition [Ref. 49]. For many important transitions the relative proba-
bilities of vibrational levels, called Franck-Condon factors, have been calculated
' ~see for example Fcei. :iu j.
In nonadiabatic transitions a transitional complex A-B-C may form, which may also
radiate. Such a mechanism is more preferential for converting the energy of the
chemical bond to the energy of radiation since it does not involve competing pro-
cesses of energy dissipation. From the potential energy surface (see Fig. 1.6)
it is also clear that the lower potential curves of AB and C may have a dispersive
nature, and this means that complex A-B-C does not have a lower level in the usual
sense of the word, and exists only in the excited state.
Such complexes made up of elements from groups I and VII of the periodic table
were observed in Ref. 51. An investigation was made of chemiluminescence spectra
arising in a circulating system of Na and halides X. The spectra of Na + F(0.6-
0.81 um), and Na + C12 (0.42-0.55 um) have a vibrational structure. It was concluded
that the band carrier is the NaX2 molecule formed in the reaction in the electron-
ically excited state.
- �1.7. Chemical Reactions in a Closed Space and in a Stream
Exothermic Reactions in a Closed Space. Heat of Reaction. In contrast to the
rarely observed isothermic chain explosion [Ref. 52], the cause of thermal explosion
28 ~
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of a gas mixture in a closed volume V is a rise in temperature when the rate of heat
release q+ exceed5 the rate of heat removal q-. A general representation of such
a process is given in the quantitative theory of Ref. 53 with consideration of tem-
perature leveling within the volume.
The conditions of the explosion are characterized by the balance c~f q+ and q-
(,~t�~ (TZ) aq (S/I/) (TZ To) (1.72)
and by equality of temperature derivatives at point T2
Q(dta~lclT) a~(S/V), (1.73)
where T2 is the temperature of the combustion zone corresponding to explosion, aQ
is the heat transfer coefficient, S is the area of the wall surface.
For the fast processes that take place in chemical lasers it is of interest to examine
the adiabatic conditions of occurrence of an incipient reaction in a closed volume
[Ref. 2]. Under such conditions, all the heat released by the reaction goes to
raising the temperature of the mixture, i. e.
c~~ dT = l,~dc, (1. 74)
where cp is the specific heat of the mixture for constant volume.
Introducing Tmax~ the temperature of complete combustion, we can get
dT/dt ko (cv~Q)"'1 (Tm~ - T)" exp li/RT). (1.75)
The solution of this equation shows thatfor a certain time interval--the ignition
induction period--the gas temperature rises slowly, and then the reaction takes place
with rapid consumption of the reagent and a rapid rise in temperature.
The heat released in the closed system is equal to the heat of reaction -Q- -I dQ.
Tde know from thermodynamics that dQ = dHe - V dp, whence for isobaric processes
Q=! dHe = OHe --the enthalpy increment of the system during the reaction. For any
reaction in ideal gases, the heat released can be calculated by the formula
N
-~~H~ - - (ri -rj) A/l~.t, (1. 76)
t, i
where ~H~~i are the tabular values of the heats of formation of molecules i.
Exothermic Reactions in a S~tream. For a reacting mixture of ideal gases of density
p moving at mass velocity u, the following equations are satisfied [Rei. 3]:
the equation of continuity
a~?iar + v c~u) - o; c i.�>
the equation of conservation of momentum with consideration of the external force ~i
acting on a unit mass of component fraction Yi, and stress tensor P
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N (1.78)
c~u/~3f ~ uVu --VP/p Yt fi ;
~
_ the equation of conservation of ener~ including specific internal energy ue and with
consideration of the diffusion rate u~ of the i-th component
N
paue~at + r~ (uv~ - - ~vq~- r~: !~u~ ~ ~ Y~ (f? c i . ~9)
~
[the colon denotes a double convoluted tensorJ;
the equation of continuity of chemical components
vr,~dc + (u a) ~~~ir? - ~r~) (v~ Y~uo~ ~ i . so>
The stress tensor P is def ined by the formula
P = [p -f- (2r~/3 - r~') (V u)1 U r~ [(V u) (V u)TI, (1.81)
where n and n' are the coefficients of shear and volumetric viscosity respectively;
U is a unit tensor, T denotes transposition of the tensor.
The heat flux density vector q in equation (1.79), disregarding radiative heat trans-
fer, is determined by the formula
` x D u (1.82)
q = -~,Q VT -?-P ~ ~he)r Y~ u� RT ` ( pt~t l ( ~-11~),
r~~ J_1j ` ~
where aQ is the coefficient of heat conduction, (he)i and �i are the specific enthalpy
and molar mass respectively of the i-th component, X~ is the mole fraction of the j-th
component,_Di~ is the coefficient of binary diffusion of components.
The quantity uA in equations (1.79) and (1.80) for i= 1, 2,..., N components is de-
fined by the formula
N r
~X r X~X~ l~Uj - U~~ . I_ ~}~l - X i~ I~~
~ ~ t/ 1 ~
1 1 ~ ! - 1 ~ +
\P/ L.~Y f f (U~~ l(nYlf DYtt/J\ T~. (1.83)
J~ 1 1 ~
External forces ~i are taken as given, wi in equation (1.80) in accordance with the
law of chemical kinetics (1.3) with consideration of (1.27) and (1.38) is defined
by the expression
cc~~ (r!, k- rt, k) Qi~ T~`'' eXP Cn/R7~ II ~X~ P/RT)'!, k ~1.84)
k- 1 ~
(M is the total number of chemical reactions).
~
The quantities Yi, p, T and u can be the variables defined in equations (1.77)-(1.80).
Then the other variables can be expressed through them by the equation of state of
an ideal gas
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N Yt
~~=~R~' ~ (i.s5)
i- ~ t+r .
the expression for the specific internal energy of the gas mixture
N
ue v (l1~)t Yt-P/P, (1.86)
r- i
, the caloric equation of state, including the specific heat of formation (h~)i of
component i at temperature To
r
~he~t ~~11~t ~ Cp~t L~T ~ 1 .87~
(cp,i) is the specific heat of component i at constant pressure) and the relation
N -1
X t=1'i �i ~ Y~ . (1. 88)
~ Q ~ �l
In the case of a homogeneous inviscid steady-state flow without mass forces, equations
(1.77)-(1.83) are vastly simplified.
From (1.77) we get
pu = const. (1.89)
Equation (1.78) is converted to
puduldx dpldx = 0, (1. 90)
in which the integral puZ+ p= const. Equation (1.79) gives
pu (h~ u2/2) -I- g= consl (1. 91)
and from (1.80) we have
d 1
dx ~PYt (cc-{- ur�~1= r~~ � (1.92)
If we disregard conductive heat transfer and take q= 0, then for steady-state flow
of an inviscid medium equations (1.90)-(1.92) respectively take the form
udu ~ ~P .
- ~X - -dX ~ (1. 93)
dx (11e ~ -~2 ) ` n; (1.94)
udY~ldx c~i~P� (1. 95)
For a channel of variable cross section S(x) the equation of continuity takes the
Eorm
d (~~~tS)ldx = 0. (1. 96)
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The equation of state (1.85) and equations (1.86), (1.87) together with expression
he = ue + p/p relate the thermodynamic parameters he and p to the quantities p, T,
} N). Then equations (1.93)-(1.96) are a system of N+ 3 ordinary
u, Yi (i= 1, 2,...,
differential equations of first order for the N+ 3 unknowns Yi, T, p and u. If we
assign all the parameters of the flow and the area S in some cross section as a func--
tion of x, we can get the flow characteristics at any other point of the channel
by integrating equations (1.93)-(1.96) with consideration of relations (1.84)-(1.88).
_ More exact calculation should account for the boundary layer on the wall of the
_ channel, the ratio of the thickness of displacement of the inviscid flow to the thick-
ness of loss of momentum, and the local coefficient of friction on the wall with
flow of a relaxing gas [Ref. 54). In this case we can use as an approximation the
dimensionless numbers obtained for laminar or turbulent flow around a flat plate
[Ref. 55].
Photochemical Reactions. As pointed out in �1.2, it is only the activated molecule
that undergo chemical transformation. If molecules are activated by redistribution
of energy during collisions in thermal processes such as those described above, the
necessary activation energy of a molecule in photochemical processes is provided
by absorption of radiation from an external source with intensity I~.
In this case the Stark-Einstein Zam of photochemicaZ equivaZence is satisfied: in
a photosensitive system subjected to the action of radiation with frequency v, there
is one activated molecule for every absorbed quantum of energy hv.
Thus the kinetics of photochemical reactions is dependent on the laws of absorption
of light by the substance, and is associated with the quantum yieZd of t12e reaetion
~ defined as the ratio of the number of reacting molecules to the number of quanta
absorbed by the molecules. When one absorbed quantum causes conversion of a single
molecule, 1. In reality, due to deactivation 1, and vice versa, in the case
of photoinitiation of secondary exothermic chain reactions ~~1. In the case of st3.anu-
lated emission with photolytic or some other kind of initiation of a chemical reaction,
the quantum z~ieZd of stimuZated emission ~Se is defined as the ratio of the number
of quanta of the medium participating in stimulated emission in a unit volume of
_ the medium to the concentration na of active centers produced by the initiation:
Ese~h~se
se - n (1.97)
a
(eSe and vSe are respectively the specific energy and frequency of the stimulated
emission).
Kinetic effects are characteristic of many reactions with pulsed photoinitiation:
depending on initial conditions (initiation energy, temperature, concentration of
reagents, total pressure of the mixture), an explosive state is realized with al-
most total chemical conversion, or a state with fairly weak conversion of the reagents.
There is a threshold of transition from one state to the other. A quantitative de-
scription of such threshold phenomena and of the kinetics of the photoinitiated reac-
tion F~+ Dz(H2) inhibited by Oz is given in Ref. 56, 67 using concepts of the theory
of thermal acceleration of the reaction that are the basis of the theory of thermal
explosion [Ref. 21).
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The regime of the photoinitiated chain reaction is considered in Ref. 57 in the adia-
batic approximation in the absence of gradients of temperature and concentrations
of active particles. It is assumed that the reaction goes through a single active
center, and the nucleation of active centers is realized by volumetrically uniform
photoinitiation. The solution of equations for the concentration of active particles
and reaction heat balance implies that the kinetic nature of the curves changes
sharply with a slight change in heating near its critical value. The branched re-
action is typified by a sharp rise in the curves, associated with a sharply expressed
reaction induction period.
The existence of the critical condition is due to competition between processes of
thermal acceleration of the reaction and the deceleration due to annihilation of
active centers. Such a course of pulse-photoinitiated chemical reaction under con-
ditions of progressive self-acceleration due to the accumulation of heat or active
cneters in the system is a photothermal explosion [Ref. 57].
Nonequilibrium Effects in Chemical Reactions. Chemical Reactions in an Electric
Discharge. Real chemical reactions take place under appreciably nonequilibrium con-
ditions, i. e. with deviation from the Maxwell-Boltzman distribution function of
particles with respect to velocities and internal states. Such a deviation stems
naturally from the fact that molecules with energies higher than Ea are reactive,
and consequently the distribution function is continuously depleted in the high-
energy region due to disappearance of reacting molecules.
The solution of equations that describe the behavior of the distribution function
in nonequilibrium chemical processes and that comprise a system of nonlinear inte-
gral equations presents mathematical difficulties, and therefore recourse is taken
to various simplifications of the problem in analyzing relaxation processes. For
example the system is broken down into subsystems: equilibrium,~ "f rozen" and relaxing.
In some cases we restrict ourselves to examining the distribution function for the
number of particles n with respect to energies nA(E) dE, i. e. the probability in
a system with a surplus of molecules B of detecting relaxing molecules A in states
with energies close to E in an interval dE. Then the rate of change in population is
dnA (E)
--cs f p(E~ E~)nA(E)dE~ -F cs SP(E~, E)nn(E')dE'~ (1.98)
dt
where P(E, E') is the probability of a transition in a unit of time at unit concen-
trations of A and B for a molecule of A from energy level E to levels in the energy
range E', E'+ dE' at unit concentration of molecules of B. These probabilities
satisfy the relation
P(E, E')= p(E') E'-E
p(E~ . E) P(E) eXp k~ T ' (1. 99)
which includes the density p(E) of energy levels of the relaxing degrees of freedom
of molecules of A.
In cases where reaction and relaxation overlap, the kinetic equations expressed in
terms of concentrations are in general invalid, although even in this case the problem
33
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can be reduced to macroscopic equations that describe the behavior of both the con-
centrations and other parameters of the nonequilibrium distribution function such
as the temperatures corresponding to different types of degrees of freedom [Ref.
58-63].
Indeed it is the chemical reactions with sharply nonequilibrium parameters of the
reaction products that are responsible for processes in chemical lasers. For example
if the distribution of the products with respect to energy levels both during the
reaction and after its completion is nonequilibrium, or if during the chemical reac-
tion the rate of formation of products in upper energy states exceeds the rate of
formation of products on lower levels, we have popuZation inversion of energy levels.
The same thing can be accomplished in redistribution of energy with respect to dif-
ferent degrees of freedom of a molecular system.
Excitation of reaction products to electronic, rotational and vibrational nonequi-
librium states is possible in reactions of the following types:
photodissociation
ABC hv AB'" -I- C; (1.100)
exothermic exchange
A-I- BC AB* C, A-}- BC AB C*; (1.101)
dissociative energy transfer
AB -I- M* A* E. -I- M; (1.102)
the recombination process that is inverse to dissociation
A-}- M-~ AB* M, A-I- B-}- M-~ AB -I- M*. (1.103)
The next chapter deals with the excitation of products in a number of such nonequi-
librium chemical reactions.
In the present section we will briefly take up appreciably nonequilibrium processes
in chemical reactions that occur in an electric discharge plasma.
The electromagnetic gas dynamics of plasma flow in external electric and magnetic
fields is considered for example in Ref. 64. The quantitative picture of distribu-
tion of these fields in the discharge region can be found by numerical methods such
as those in Ref. 65, 66. An even more difficult problem is accounting for the chemi-
cal reaction in an appreciably nonequilibrium electric-discharge plasma.
In discharges, and especially in pulse discharges, the energy distribution of elec-
trons is nonequilibrium, whereas the energy of translational motion of heavy particles
conforms to quasiequilibrium distribution.
The approximate method of numerical calculation of the kinetic characteristics of
nonequilibrium reactions in electric discharges without consideration of hydrodynamic
processes (e. g. see Ref. 67) includes simultaneous consideration of:
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equations of chemical kinetics
an~ ku n~ ~ kita n~ nk (1.104)
ar ~ k
(n~ are the concentrations of components participating in the reaction: electrons,
ions, neutral and excited particles; ki~, ki~k are rate constants of ionization,
recombination, dissociation and cther processes);
Maxwell's equations
curl H _ dD
ar '
div D=pe;
curl E = - aB � (1.105)
ac '
div B = 0;
D = e' E,
}
where E and are respectively the intensity and induction of the electric field;
}H and ~ are the intensity and induction of the magnetic field, j and pe are the
current and charge densities of the external sources.
In this system of equations the properties of the fluid are expressed in terms of
the complex Permittivity that depends on the specific conductivity of the plasma
and the electromagnetic f ield frequency.
From (1.105) with satisfaction of the inequalities [Ref. 68]
ae' aE , d~ E a' e' a~ E
E � e (1.106)
I ar ac I K( e aa, I~ a~~ , ac'
we get a steady-state wave equation that together with (1.104) forms a nonlinear
system. In thi~s ~system the reaction rate constants ki~, kijk depend on electric
field strength E(r), and the complex permittivity e' depends on the time-variable
electron concentration ne obtained from the solution of equation (1.104), and on
the effective frequen~y of sollisions of these electrons with heavy particles, which
depends in turn on E(r) and on ne.
Nonstationary equation (1.104) and the steady-state wave equation with boundary con-
ditions determined in the course of numerical solution by a method of iterations
were integrated in Ref. 68 for reactions in an appreciably nonequilibrium nitrogen
plasma produced in a pulsed microwave discharge.
As an example of examination of a chemical reaction in an electric discharge we can
also cite the analysis in Ref. 69, 70 of the reaction of dissociation of carbon di-
oxide in a low-pressure discharge.
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REFERENCES
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2. Kondrat'yev, V. N., Nikitin, Ye. Ye., "Kinetika i mekhanizm gazofaznykh reaktsiy"
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pp 769-776.
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16. Ostwald, W., "Uber Oxydationen mittels freien Sauerstoffs", Z. PHYS. CH~M.,
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20. Semenov, N. N., "Types of Kinetic Curves of Chain Reactions", DOKLADY AKADEMII
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21. Semenof, N. N., "Tsepnyye reaktsii" [Chain ReactionsJ, Leningrad, GKhTI, 1934,
555 pages.
22. Frank-Kamenetskiy, D. A., "Diffuziya i teploperedacha v khimicheskoy k~netike"
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- grad, Nauka, 1967, 491 pages.
'l3. Khariton, Yu. B., Walta, Z. F., "Oxydation von Phosphordampfen bei niedrigen
Drucken", Z. PHYS., Vol 39, 1926, pp 547-556.
24. Semenov, N. N., "Die Oxyda~.ion des Phosphordampfes bei niedrigen Drucken",
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25. Kovalskii, A. A., "Kindling of Phosphorus Vapor in Oxygen", Z. PHYS. CHEM.,
Vol 4, 1929, pp 288-298.
26. Zagulin, A. V. et al., "Limits of Ignition of Mixtures of 2H2+ 02 and 2C0 + 02",
ZHURNAL FIZICHESKOY KHIMII, Vol Vol 1, 1930, pp 263-280; Entzundungsgrenze des
Gemisches 2H2 + 02 und 2C0 + 02", Z. PHYS. CHEM., Vol 6, 1930, pp 307-329,
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sures", Z. PHYS. CHEM., Vol 1, 1928, pp 275-291.
28. Thompson, H. W., Hinshelwood, C. N., "The Mechanism of the Homogeneous Combi-
nation of Hydrogen and Oxygen", PROC. ROY. SOC., Vol A 122, 1929, p E10.
29. Semenov, N. N., "0 nekotorykh problemakh khimicheskoy kinetiki i reaktsionnoy
sposobnosti" [Some Problems of Chemical Kinetics and Reactivity], Moscow,
Izdatel'stvo Akademii nauk SSSR, 1958, 686 pages.
30. Morse, P. M., "Diatomic Molecules According to the Wave Mechanics. II. Vibra-
tional Levels", PHYS. REV., Vol 34, 1929, pp 57-64.
31. Dzhidzhoyev, M. S., Platonenko, V. T., Khokhlov, R. V., "Chemical Lasers",
USPEKHI FIZICHESKIKH NAUK, Vol 100, No 4, 1970, pp 641-679.
37
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32. Kondrat'yev, V. N., Nikitin, Ye. Ye., Reznikov, A. I. et al., "Termicheskiye
bimolekulyarnyye reaktsii v gazakh" [Thermal Bimolecular Reactions in Gases],
Moscow, Nauka, 1976, 191 pages.
33. Carrington, T., Gravin, D., "Formation of Excited Particles in Chemical Reac-
tions" in: "Vozbuzhdenny}~e chastitsy v khimicheskoy kinetike" [Excited Parti-
cles in Chemical Kinetics]: translated from English, edited by A. A. Borisavi,
*~oscow, Mir, 1973, pp 123-213.
34. Kondrat'yev, V. N., "Emission of a Low-Temperature Hydrogen Sulfide Flame",
ZHURNAL FIZICHESKOY KHIMII, Vol Vol 14, 1940, pp 281-286.
35. Geydon, A. G., Wolfhard, H. G., "Plamya, yego struktura, izlucheniye i tempera-
tura [The Flame, its Structure, Radiation and Temperature]: translated from
English by N. S. Chernetskiy, edited by S. A. Gol'denberg, Moscow, Metallurg-
izdat, 1959, 333 pages.
36. Geydon, A. G., "Spektroskopiya plamen" [Flame Spectroscopy]: translated from
English by I. V. Veyts and L. V. Gurvich, edited by Academician V. N. Kondrat'yev,
Moscoia, Izdatel'stvo inostrannoy literatury, 1959.
37. London, F., "Probleme der modernen Physik", Berlin, Sommerfeld Festschrift,
1928, p 104; "Quantenmechanische Deutung des Vorgangs der Aktivierung",
Z. ELEKTROCHEM., Vol 35, 1929, pp 552-555.
38. Bunker, D. L., Blais, N. C., "Monte Carlo Calculations. V. Three-Dimensional
Study of a General Bimolecular Interaction Potential", J. CHEM. PHYS., Vol 41,
1964, pp 2377-2386.
39. Polanyi, J. C., "Dynamics oF Chemical Reactions", DISCUSS. FARADAY SOC., Vol 44,
1967, pp 293-307.
40. Airey, J. R. et al., "Absolute Efficiency of Con~~ersion of Heat of the Reaction
H+ C1 Into Vibration", J. CHEM. PHYS., Vol 41, 1964, pp 3255-3256.
41. Kuntz, P. J., Nemeth, E. M., Polanyi, J. C. et al., "Energy Distribution Among
Products of Exothermic Reactions. II. Repulsive Mixed and Attractive Energy
Release", J. CHEM. PHYS., Vol 44, 1965, pp 1168-1184.
42. Anlauf, K. J. et al., "Vibrational Population Inversion and Stimulated Emission
From the Continuous Mixing of Chemical Reagents", PHYS. LETT., Vol 24A, 1967,
pp 208-210.
43. Rankin, C. C., Light, J. C., "Quantum Solution of Collinear Reactive Systems:
H+C12-~HCl+Cl*", J. CHEM. PHYS., Vol 51, 1969, pp 1701-1719.
44. Russell, D., Light, J. C., "Classical Calculations of Linear Reactive Systems:
H+ C12->HCl+Cl*", J. CHEM. PHYS., Vol 51, 1969, pp 1720-1723.
45. Gilmore, F. R., Bauer, E., McGowan, J. W., "A Review of Atomic and Molecular
Excitation Mechanisms in Nonequilibrium Gases to 20,000 K", J. QUANT. SPECTROSC.
AND RADIAT. TRANSFER, Vol 9, No 2, 1969, pp 157-183.
38
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46. Herschbach, D. R., "Molecular Beams", edited by J. Ross, Chapter 9, N.Y.,
Interscience Pub., 1966.
47. Karl., G., Kruus, P., Polanyi, J. C., "Infrared-Emission Studies of Electronic-
to-Vibrational Energy Transfer. II. Hg* + CO", J. CHEM. PHYS., Vol 46, 1967,
pp 224-243.
48. Karl, G. et al., "Infrared-Emission Studies of Electronic-to-Vibrational
Energy Transfer. III. Hg* + CO", J. CHEM. PHYS., Vol 46, 1967, pp 244-253.
49. Vol'kenshteyn, M. V., "Stroyeniye i fizicheskiye svoystva molekul" [Structure
and Physical Properties of Molecules", Moscow-Leningrad, Izdatel'stvo Akademii
nauk SSSR, 1955, 638 pages.
50. Nicholls, R. W., "Transition Probabilities of Aeronomically Important Spectra",
ANN. GEOPHYS., Vol 20, 1964, pp 144-181.
51. Ham, David Q., Chang, H. W., ""Chemoluminescence Spectra of the New Molecules
NaF2 and NaC12 and Their Implications for Reaction Dynamics", CHEM. PHYS.
LETT., Vol 24, 1974, pp 579-583.
52. Kovalskii, A. A., "Die Verbrennungskinetik von Wasserstoff", PHYS. Z. SOW.,
Vol 4, 1933, pp 723-734.
53. Semenov, N. N., "Zur Theorie des Verbrennungsprozesses", Z. PHYS., Vol 48,
1928, pp 571-582.
54. Losev, C. A., "Gazodinamicheskiye lazery" [Gasdynamic Lasers], Moscow, Nauka,
1977.
55. Avduyevskiy, V. S., Danilov, Yu. I., Koshkin, V. K. et al., "Osnovy teplo-
peredachi v aviatsionnoy i raketnoy tekhnike" [Principles of Heat Exchange
in Aerospace TechnologyJ, Moscow, Oborongiz, 1960;
Lapin, Yu. V., "Turbulentnyy pogranichenyy sloy v sverkhzvukovykh potokakh
gaza" [Turbulent Boundary Layer in Supersonic Gas Flows], Moscow, Nauka,
1970.
56. Vasil'yev, G. K., Vizhin, V. V. et al., "Flash Photolysis of Mixtures of
F2+ DZ+ O2+ He", KHIMIYA VYSOKIKH ENERGIY, Vol 9, No 2, 1975, pp 154-159;
Vasil'yev, G. K., Makarov, Ye. F., Chernyshev, Yu. A., "Measurement of Chain
Continuation and Breaking Rate Constants in the Reaction F2 + H2(D2) Inhibited
by 02", KINETIKA I KATALIZ, Vol 16, No 2, 1975, pp 320-324.
57. Vasil'yev, G. K., Makarov, Ye. F., Chernyshev, Yu. A., "Regimes of Chain Re-
actions With Pulsed Photoinitiation", FIZIKA GORENIYA I V'LRYVA, Vol 12, No 6,
19%b, pp 896-906.
58. Nikitin, Ye. Ye., "Teoriya elementarnykh atomno-molekulyarnykh protsessov
v gazakh" [Theory of Elementary Atomic-Molecular Processes in Gases", Moscow
KHIMIYA, 1970, 455 pages.
39
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t'uR uN'b'~l'1:~1. l'~1~ l)~~ t
59. Ceneralov, N. A. et a1., "Simultaneous Analysis of Processes of Vibrational
Relaxation and Thermal Dissociation of Diatomic Molecules", TEORETICHESKAYA
I EKSPERIMENTAL'NAYA KHIMIYA, Vol 4, 1968, pp 311-315.
60. Kuznetsov, N. M., "Kinetics of Dissociation of Polyatomic Molecules in the
Case of Nonuniform Distribution of Vibrational Energy", DOKLADY AKADEMII NAUK
SSSR, Vol 202, 1972, pp 1367-1370; "Kinetics of Dissociation of Molecules
in a Molecular Gas", TEORETICHESKAYA I EKSPERIMENTAL'NAYA KHIMIYA, Vol 7,
1971, pp 22-33.
61. Kuksenko, B. V., Losev, S. A., "Kinetics of Excited Oscillations, and Disso-
ciation of Diatomic Molecules at Atomic-Molecular Collisions in a High-Tem-
perature Gas", TEORETICHESKAYA I EKSPERIMENTAL'NAYA KHIMIYA, Vol 5, 1969,
pp 475-483.
62. Osipov, A. I., "Relaxational Processes in Gases: I. Nonequilibrium Energy
Distribtuion With Respect to Translational Degrees of Freedom", FIZIKA GORENIYA
I VZRYVA, Vol 4, 1966, pp 42-61.
63. Polak, L. S., Khatchoian, A. V., "Rate Coefficient (Constant) of Nonequilib-
rium Chemical Reactions", TRANS. FARADAY SOC., Vol 67, 1971, pp 1980-1994.
64. Pai Shih-I, "Magnitnaya gazodinamika i dinamika plazmy" [Magnetogasdynamics
and Plasma Dynamics]: translated from English by V. P. Korobeynikov and
P. I. Chushkin, edited by A. G. Kulikovskiy, Moscow, Mir, 1964, 301 pages.
65. Coleman, R. L., Hudson, H. A., Garcia, B., "Potential and Current Distribution
in MHD Plasma Ares", RAKETNAYA TEKHNIKA I KOSMONAVTIKA, Vol 5, No 12, 1967,
pp 144-148.
66. Denisov, Yu. N., Kirelenko, N. I., Kirilkin, V. S. et al., "Potential and
Current Distribution in MEID Channel With External Azimuthal Magnetic Field",
MAGNITNAYA GIDRODINAMIKA, No 3, 1975, pp 75-79.
67. Polak, L. S., "Plasmochemical Kinetics" in: "Ocherki fiziki i khimii nizko-
temperaturnoy plazmy" [Notes on the Physics and Chemistry of Low-Temperature
Plasma], Moscow, Nauka, 1971, pp 302-380.
68. Vurzel', F. B., Lysov, G. V., Polak, L. S. et al., "Kinetics of Nonequilibrium
Chemical Reactions in a Pulsed Microwave Discharge. I. Method of Computer
Calculation of Kinetic Characteristics of Nonequilibrium Chemical Reactions
in a Pulsed Microwave Discharge", KHIMIYA VYSOKIKH ENERGIY, Vol 5, 1971,
pp 105-111.
69. Corvin, K. K., Corrigan S. J. R., "Dissociation of Carbon Dioxide in the Posi-
tive Column of a Glow Discharge", J. CHEM. PHYS., Vol S0, 1969, p 2570.
70. Ivanov, Yu. A., Polak, L. S., Slovetskiy, D. I., "Kinetics of Dissociation
of Carbon Dioxide in a Glow Discharge", KHIMIYA VYSOKIKH ENERGIY, Vol 5, 1971,
PP 382-387.
40
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f~l)Fi Ol~F~i('1:11. I~~h: ONI.1
CHAPTER 2: FORMATION OF ~XCIT~D PARTICLES IN THE PROCESS OF A NONEQUILIBRIUM
CHEMICAL REACTION
�2.1. The Recombination Mechanism of Excitation
E:ccitation of Electronic States of Atoms and Molecules. Theoretical analysis of
quantum state distributions that arise as a result of chemical interaction is
fairly complicated as a rule, even when simple models are used, and such analysis
enables prediction of energy distributions only in simple cases [Ref. 1, 2].
Population kinetics is appreciably influenced by processes of energy exchange be-
tween reagents and reaction products, including intermediate products. Six dif-
ferent kinds of energy can be distinguished in reactions of excitation and energy
exchange: T--translational; Te--translational for the electron; R--~.otational;
V-vibrational; E--electronic; X--chemical, and accordingly 36 different methods
of energy transfer: T-R, T-V, V-R, [Ref. 3]. The principal experimental re-
sults on energy distribution in chemical reaction products have been obtained by
flasY~. photolysis, investigation of luminescence in discharge tubes and crossed
molecular beams [Ref. 2, 4-8].
From general theoretical considerations we can expect that during a chemical re-
action, electronic population inversion on which chemical lasers must operate in
the visible range occurs only rarely since E-transitions require large excitation
energies. Besides, the interrelation between reagents and reaction products is
limited by symmetry exclusions [Ref. 9]. However, the last decade has witnessed
an increase in the number of reports on observation of inverse population of elec-
tronic states of chemical reaction products, and on E-transition chemical lasers
(see for example Ref. 10-20).
Electronic excitation upon radiative recombination of atoms. At a ther-
mal velocity of particles of the order of vT = 105 cm/s and particle size of the
order of d= 10'e cm, the duration of collisions is T~ d/vT = 10-13 s. The radia-
tive lifetime of the excited particle formed in the collision is about 10-~ s,
and therefore the probability of radiative recombination is of the order of 10-6.
This probability gets even lower with a reduction in the moment of radiative tran-
sition as a result of increasing intermolecular distance, which is typical o� re-
combining atoms in the ground or metastable state. As a consequence, radiative
recombination in direct collisions of two reacting molecules is improbable, but
its probability increases appreciably when a third particle participates. For
example, radiative recombination of oxygen atoms is caused by the reactions [Ref.
13)
O-}-O-}-M--~~z(61E~)~I-M~
O M--rO, A~~~ ~_~M, } (2.1)
O -4- -I- 1(
Both excited states of 02 correlate with atoms in the ground state (rig. 2.1),
and are stabilized upon collision with a third particle or on the surface of inetal-
lic nickel [Ref. 14). In ttie case of radiative recombination of atoms, for example
behind a shock wave (T = 2500-3800 K, 230-451.1 nm), the 02 molecules that are
formed make a transition from the initially repulsive potential energy curve to
state B3Eu, and then make a tra*~sition with radiation to the ground state [Ref. 15].
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1'l1R clt'~'i(', ~ 1 ~ ~r r ~ \
-
E eV E~ O~~D~~ O~~S)
'
10 ` , ~ D~JP)+O~~S)
1 ~0 _ _ _
\
g \ 0(~D1'0('D)
~ 0~'~P)+0(~0)
\
B'E~
6 J 9 sEu .rE~ t~9
n ~ ~ ~
~2 D~ ~_r.=~- __a~~ 1 U ~
AJEu ~ p (~P)+0 ( P1
~ ~
4 C'du ` j e ~3= -
/ 0 ~~P)+0 ( ?P
1 B\ �s~/~ ~ ~ at
U 49 ~
/ /
o x'~9 ~/txt~9
"Z 4
aq q8 ~~2 1,6 2,0 2,4 2,9 3,Z 3,6 r~ lp- um
Fig. 2.1. Diagram of potential energy of 02
In the reaction
~N+N~~Na+p (2.2)
The intensity of afterglow emission drops off rapidly at a< 191.5 nm, which is
due to the energy of dissociation of NO (6.49 eV) [Ref. 16].
There are many data on recombination of nitrogen atoms. The principal radiation
from a mixture with N2 content of the order of one percent is due to the B state,
and the remainder of the r~diation is caused by states bl and a[Ref. 17].
Transferof electronic recombination excitation to third particles.
The possible mechanisms of electronic excitation of atom C upon recombination of
_ atoms A and B are:
A-I- B-F- C--~ AB -i- (2. 3)
A-}- C-}- C-~ AC C~; ( 2. 3a)
_ A_}.. g-{- M-} AB -I- 1~4~' ~ ( 2. 3b)
M* C--r M-~- G~ ~ ( 2. 3c)
where M is the third particle.
Taking equation (2.3) as a collision of particle C with complex A-B, we can con-
clude that reaction (2.3b) is more preferntial from the standpoint of excitation
rate if M* has a longer lifetime than complex A-B. Besides, in this reaction the
42
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excited particles Ce may have a wider energy spectrum than those formed in reaction
(2.3) if M* is vibrationally excited and relaxes in multistep collisions. These
reactions can be interpreted either as reactions in a triple collision, or as re-
actions in which double collisions form intermediate complexes that then interact
with a third body.
Atoms of alkali metals that have low-lying electronic states are excited with ex-
penditure of only a part of the heat of reaction. The following reaction has been
suggested [Ref. 18] to explain the radiation of flames with additives of salts
of alkali metals to the initial medium in the presence of hydrogen:
H-}- H-I- Na Ha -I- Na~ ~P)� (2.4)
Calculations of potential energy surfaces for linear arrangement of the atoms
H+ H+Na [Ref . 19 ] show that the products of the reaction H+ H+ Na (2s) are H2 + Na
in the ground state or the excited 2p-state. As a consequence, reaction (2.4)
may take place adiabatically. Chemiluminescence of some metals occurs in recom-
bination reactions H+ H or H+ OH [Ref. 20]. For example, atoms of thallium are
excited mainly in reaction H+ H, while lead atoms are excited mainly in reaction
H+ OH.
Oxygen may be excited as a result of the reactions [Ref. 21]
0-f- 0-4- O-} Os -I- ~~'S); (2.5)
- p-{- IV N--~ N a-~- O('s)� ( 2. 5a)
The following reactions have been suggested for superequilibrium radiation of OH
[Ref. 22J:
H-}- OH OH H,O OH ('E+) (2.6)
and
H-}- O~ -I- Ha-~� H90 OH ('E+). (2.6a)
The principal long-lived particles in active nitrogen are N, NZ(A3Eu), N~ and
N2(5E~). It is the energy of these particles that leads to excitation of such
ad~itlves as C2N2, C1CN, CHC13, CZH2, C302, Ni(CO)y, (C2H5)2Zn, I2, PbI2, SF6 and
SeC14.
Radiation of CN takes place both due to vibrational and rotational excitation
and due to electronic excitation of CN and subsequent transitions: B2E+-}X2~-~
for the violet band, and A21I-~X2E+ for the red band [Ref. 23].
Excitation of electronic states upon recombination of an atom with a
diato mic mole cule. Among the reactions of radiative recombination of an atom
with a diatomic molecule, the most widely studied is
O -I- NU NO~,. (2 � 7)
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As in many other recombination reactions, the temperature coefficient of the rate
of this reaction k(T + lOK)/k(T) is negative, and the rate constant of the reaction
at T= 270 K accompanied by radiation in the vicinity of a= 0.4-1.4 ~an is equal
to 3.9�10~ cm3/(mole�s), i. e. radiation results in about one collision out of
_ 106 [Ref. 24]:
NO (X'Il) -f- O (3P) -f- M N02 (C) -I- 1b1~ ~2.8)
NO's (C) N02 (B) (nonradiative transition) ; ~2 � 4)
N02 (B) NO, (A) -I- /iv. (2.10)
Here A is the ground state, B and C are excited intersecting states.
Less well studied is the process of radiative recombinaeion in the reaction
O CO CO; . ( 2 .11)
The emission spectrum of C02 in flames and ares consists of diffuse bands superim-
posed on a continuous spectrum. In atomic flames at low pressure and room tem-
perature, the spectrum is only discrete in the range of wavelengths of 0.3-0.6 um.
It is significant here that the ~round state of C02 correlates with the ground state
of CO and with the excited atom 0(1D) [Ref. 25]. In contrast to the reaction N+ N0,
correlation with ground states CO(lE+) + 0(3p) is forbidden by the rule of conser-
vation of spin momentum. Consequently, the ground state cannot be immediately
realized as a result of reaction CO + 0(3p), and high-intensity radiation occurs.
According to the results of Ref. 26, the chemiluminescent reaction
O SO = SO�, (2.12)
has second order with respect to pressure, and the temperature dependence of the
rate constant of the reaction can be represented as
k=1,5�108( ~81-1 cm3/(mole�s) (2.12a)
~ 1
The radiation spectrum is bounded by the value ~min - 224 nm, and does not reach
the value a= 218.3 nm determined by the heat of reaction.
A typical chemiluminescent reaction [Ref. 27] resulting from triple collisions is
~-I NO M-> I-INO� M, v> (2.13)
The following mechanism of transitions leads to chemiluminescence:
y (2S) NO (Xali) M HNO~ (X'/l~, ~/1",'A~,'/1~) -I- 1~'~. (2.13a)
HNO (~A") I-INO (lA") (nonradiative transition) ; (2. 13b)
HNO (lA") I-INO (X~A') --I- /tv. (2.13c)
Excitation of Vibrational Degrees of Freedom Upon Recombination of Atoms and Mole-
cules. Recombination reactions due to triple collisions may lead to vibrational
44
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excitation of reaction products that are in the ground electronic state. Ttie reac-
tion rate depends on the partial pressure of the third particles since a newly
- produced particle necessarily decays if upon collisions with a third particle its
energy does not fall to excitation energy below the dissociation energy. Vibra-
tional-vibrational V-V relaxation on reaction products appreciably accelerates
the process of energy redistribution.
Molecules such as methylene H2C participate effectively in recombination reactions
with formation of vibrationally excited molecules. Vibrationally excited products
of reaction are formed when atoms of H attach to olefins. For propene, this reaction
can be written as [Ref. 28J
M yCs H~
H-}-C3He~C9H~~CH9+CaH4 (2.14)
The vibrationally excited intermediate product C3H~ may dissociate into H and
C 3H 6, or into CH3 and C ZH 4, and may also be stabilized in collisions with an inter-
mediate particle.
Of interest from the standpoint of chemiexcitation is a reaction in which the ex-
cited product that is formed takes part in processes that differ from deactivation
or decay into the initial products. Among such reactions is the formation of poly-
atomic molecules that have a weaker bond than the one that arises in recombination,
for example
CH s-I- CH aF CaHbF� ( 2.15 )
with liberation of excess energy of -380 J/mole [Ref. 5].
Rotational Excitation. Excitation of rotational degrees of freedom is restricted
not only by the conservation of energy, as is the case in excitation of vibrational
and electronic states, b~it also by conservation of total angular momentum. The
total angular momentum of the transitional complex consists of the orbital angular
momentum of the two reagents, which is associated with their transZational motion
relative to the co~non center of mass, and the internal rotational momenta of the
reagents. Upon dissociation of the complex, the total momentum is divided into
orbital and rotational components, the ratio between these components being asso-
ciated with the characteristics of the potential energy surface. In second-order
radiative recombination reactions the angular momentum consists of the total angular
momentum of the reagents, including the rotational and orbital components.
In collisions with participation of a third particle, the excess energy or excess
angular momentum of the reaction products is transferred to the third neutral par-
ticle, and in this event excess rotational excitation is improbable. When inter-
mediate complexes are formed in the reaction
~+BC-~(A-R-C)*-~~R-~-c
the rotational angular momentum of product AB may considerably surpass the tota.l
momentum of the complex since particle C carries off a large orbital angular momentum
45
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approximately equal in magnitude and opposite in direction to the momentum of
particle AB. The maximum momentum is approximately equal to the orbital angular
momentum of the departing particle C and is determined by the product of the mo-
mentum and impact parameter of separation, which is equal to the radius of action
of forces between C and AB. For example in the case of photodissociation of H20
[Ref. 29), the initial complex H2Oe has a small angular momentum 3h/2~r, while the
angular momentum of the dissociation product OHe is greater than 20h/2~r.
�2.2. Nonequilibrium Excitation of Particles in Volumetric Reactions
Excitation of Electronic Transitions. Exchange reactions of the type
A-{-BC-} AB~-}-C
AB C~
in pure form are nearly never realized, and may be considered as elementary stages
of a complex chemical reaction with formation of intermediate product A-B-C, which
requiras that the energy of bond AB b'~ much greater than that of BC. The proba-
bility of excitation increases when there is a lower-lying electronic state AB
in the case where formation of AB in the ground state is forbidden by the rule
of spin conservation. Considered quite probable is the reaction
H-I- H I--~ H a-{- I(aP ~~2) � ( 2.16)
In this reaction, only a few percent of the iodine atoms are formed in the excited
state [Ref. 30].
An example of an exchange reaction with participation of more than three atoms is
Br CIO, BrCI~ -i- p~, (2.17)
although in reality it is more complicated than mere exchange of the C1 atom.
In the reaction
O, NO Oa NO~~ ~-217. 7 kJ/mole) , (2.18)
- approximately 10% of the collisions lead to formation of N02 (2B1), only a few of
the lower V-levels of this state being populated (Ref. 31). The reaction
O, SO OZ -f- SOa (2.19)
has considerably higher exothermicity (-446.3 kJ/mole). The rate constants of
formation of the three possible E-states [Ref. 32] [in cm3/(mole�s)] are:
k (X lAl) =1,5 � lOla exp (-2100/R7');
k(A 1B1) = 1011 exp (-4200/R7~)~ (2. 20)
k (,z'f31) = 3 ~ 10t0 exp ( -3900/R7')�
Vibrational Excitation in Exchange Reactions. Flash photolysis of 03, N02, C102
- produces vibrationally excited oxygen molecules. Since the process takes place
46
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t~c~x c~t~~~~c~t t~~~~ citii ~
aua1~~;~u51y fur all tlirte substances, we may limit ourselves to examining the
formation of excited oxygen in photolysis of 03. We have the following significant
reactions that take place with the formation of atomic oxygen [Ref. 2]:
O9 ftv O (3P) 02;
O;~ hv O (1D) ~'D);
p(3 p) p~.-> p9 -}-Qa (-389 . 4 kJ/mole) ( 2. 21)
~(1D) -F Os ~a + Da (-745 . 2 kJ/mole)
Excited oxygen molecules in state X3E-g are observed up to levels v~ 29. A maximum
in the distribution of excited molecules occurs on v= 12, 13 and 14, and the popu-
lations of other levels decrease monotonically. Atoms of 0(3P) play an appreciable
part in the formation of vibrationally excited oxygen molecules. This applies
to thermal dissociation of ozone in shock waves and flash photolysis of N02. As
a result of the reactions considered above, the formation of the oxygen molecule
takes place on high V-levels and is not accompanied by chemiluminescence since
vibrational-rotational V-R transitions are forbidden for homonuclear molecules.
Of greatest interest among reactions with halide derivatives are
H-I- Cl - CI HCI� Cl (-188.4 k.T/mole) , ~2.22~
Cl H- I--~ HCI I(-310 k,T/mole) ,
in which population inversion takes place at low pressures. In the case of C1+H-I
the inversion is considerable, and quantum-mechanical stimulated emission is ob-
served. More than half the heat of reaction is converted to vibrational excitation.
The remainder goes to rotational energy, and as a consequence the energy of trans-
lational motion of the products is comparable to the energy of the initial reaction
products.
The distributions of populations of vibrationally excited oxygen molecules and
hydrogen chloride molecules are basically similar. The distribution maxi.mum falls
to levels that correspond to half the reaction energy. The distribution with re-
spect to V-levels of both molecules is quite close to the initial distribution
due to the reaction. This distribution may be distorted due to the high rate of
R-relaxation in collisions.
Vibrational-translational V-T relaxation takes place at a rate that is considerably
lower than rotational-translational R-T relaxation, and it differs appreciably
for HCl and O1, since for 02 the gas-kinetic number of collisions is Zo = 8�105,
while for HC1 'Lo =(0.5-1..5)�103. Radiative transitions are forbidden for oxygen,
and the radiative lifetime for HCl lies in a range of 10-2-10-`` s. Thus it can
be expected that the original distribution at high pressures is retained much longer
for O2 than for HC1. However, as a result of V-V energy exchange this distribution
may be considerably changed. For example in experiments with HCl and OH (reaction
H+ 03-~OH~ + 02) at p= 13.33 Pa nearly Maxwell-Boltzmann distribution was observed
with respect to V-levels, but the vibrational temperature was much higher than
the translational, and amounted to several thousand de~rees. This shows that by
47
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I~(1R HCl (v = 2) I ~ 2� 25~
nearly all the difference between the heat of reaction and the energy necessary
for excitation of level v= 2 goes to rotational excitation.
Strongly nonequilibrium rotational distributions are usually observed in chemi-
luminescent reactions that lead to formation of electronically excited molecules
in ordinary atomic flames in a discharge. In these cases R-relaxation is impeded
by the short lifetime of E-states.
REFERENCES
1. Nikitin, Ye. Ye., "Nonequilibrium Chemical Reactions" in: "Problemy kinetiki
elementarnykh khimicheskikh reaktsiy" [Problems of Kinetics of Elementary
Chemical Reactions], Moscow, Nauka, 1973, pp 5-50.
48
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~ox oN'F'~c't:�. t ~~t~ c~~i.~
2. Harrington, G., Gravin, D., "Formation of Excited Particles in Cheml.cal Re-
actions" in: "Vozbuzhdennyye chastitsy v khimicheskoy kinetike" [Excited
Particles in Chemical Kinetics]: translated from English, edited by A. A.
Borisov, Moscow, Mir, 1973, pp 123-213.
3. Gilmore, F. R., Bauer, E., McCowan, J. W., "A Review of Atomic and Molecular
Excitation Mechanisms in Nonequilibrium Gases up to 20,000 K", J. QUANT. SPECTR.
AND RAD. TRANSFER, Vol 9, No 2, 1969, pp 157-183.
4. Rabinovich, B. S., Flauers, M. S., "Chemical Activation" in "Khimicheskaya
Kinetika i tsepnyye reaktsii" [Chemical Kinetics and Chain Reactions]:
edited by V. N. Kondrat'yev, Moscow, Nauka, 1966, pp 61-144.
5. Kondrat'yev, V. N., "Kinetika khimicheskikh gazovykh reaktsiy" [Kinetics of
Chemical Gas Reactions], Moscow, Nauka, 1974, 558 pages.
6. "Fizicheskaya khimiya bystrykh reaktsiy" [Physical Chemistry of Fast Reactions]:
translated from English by Ye. V. Mozzhukhin and Yu. P. Petrov, edited by
I. S. Zaslonko, Moscow, Mir, 1976, 394 pages.
7. Kondrat'yev, V. N., "Konstanty skorostey gazofaznykh reaktsiy" [Rate Constants
of Gas-Phase Reactions], Moscow, Nauka, 1970.
8. McCowan, J. W., ed., "Advances in Chemical Physics, Vol 28. The Excited State
in Chemical Physics", N. Y.-London, Interscience Publ., 1976.
9. Thrush, B.. A., "Gas Reactions Yielding Electronically Excited Spectra", ANN.
REV. PHYS. CHEM., Vol 19, 1968, pp 371-388.
10. Zuyev, V. S., Kormer, S. B., Mikheyev, L. D. et al., "Arisal of Inversion on
the Transition lE+g-~3E-g of Molecular Sulfur Upon Photodissociation of COS",
PIS'MA V ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 16, No 4, 1972,
PP 222-224.
11. Jones, C. R., Broida, H. P., "Chemical Lasers in the Visible", LASER FOCUS,
Vol 10, No 3, 1974, pp 37-47.
- 12. "Electronic Transition Lasers", Cambridge, Massachusetts-London, MIT Press,
1976.
13. Young, R. A., Sharpless, J. L., "Chemiluminescent Reactions Involving Atomic
Oxygen and Nitrogen", J. CHEM. PHYS., Vol 39, No 4, 1963, pp 1071-1102.
14. Gilmore, F. R., "Potential Energy Curves for N2, N0, 02 and Corresponding Ions",
J. QUANT. SPECTR. AND RAD. TRANSFER, Vol 5, No 2, 1969, pp 369-390.
15. Mayers, B. F., Bartle, R., "Shock-Tube Study of the Radioactive Combination
of Oxygen Atoms by Inverse Predissociation", J. CHEM. PHYS., Vol 48, No 9,
1968, pp 3935-3934.
16. Tanaka, Y., "Emission Bands of NO in the Vacuum Ultraviolet Region Excited
in the NO Afterglow", J. CHEM. PHYS., Vol 22, No 12, 1954, pp 2045-2048.
49
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1~(1N O1~1~1('1,11 I'til~ c1'VI 1
17. Gross, R. W. F, Cohen, H., "Temperature Dependence of Chemiluminescent Reactions.
II. Nitric Oxide Afterglow", J. CHEM. PHYS., Vol 48, No 6, 1968, pp 2582-2588.
18. Sugden, T. M., "Excited Species in Flames", ANN. REV. PHYS. CHEM., Vol 13,
1963, pp 369-390.
19. Magee, J. L., Ri, T., "The Mechanism of Reaction Involving Excited Electronic
States", J. CHEM. PHYS., Vol 9, No 8, 1944, pp 638-644
20. Padley, P. J., Sugden, T. M., "Chemiluminescence and Radical Recombination
in Hydrogen Flames" in: Symp. Combustion 7th Lond., Butterworth, Publ. for
the Combustion Institute, 1959, pp 235-244.
21. Kaplan, J. et al., "Atomic Reactions in the Upper Atmosphere", CANAD. J. CHEM.,
Vol 38, No 10, 1960, pp 1688-1692.
22. Geydon, A. G., "Spektroskopiya plamen" [Flame Spectroscopy]: translated from
English by M. V. Veyts and L. V. Gurvich, edited by Academician V. N. Kon-
drat'yev, Moscow, Izdatel'stvo inostrannoy literatury, 1959, 382 pages.
23. Kiess, N. H., Broida, H. P., Emission Spectra From Mixtures of Atomic Nitrogen
and Orgatiic Substances" in: Symp. Combustion 7th Lond., Butterworth, Publ.
for the Combustion Institute, 1959, pp 207-214.
24. Fontijn, A., Meyer, C. B., Schiff, H. J., "Absolute Quantum Yield Measurements
of the NO-0 Reaction and its Use as Stanciard for Chemiluminescent Reactions",
J. CHEM. PHYS., Vol 40, No 1, 1964, pp 64-70.
25. Laidler, K. J., "The Chemical Kinetics of Excited States", Clarendon, Oxford
University Press, 1955, p 180.
26. Fletcher, S. R., Levitt, B. P., "0 + SO Recombination Emission at 3500 K",
TRANS. FARADAY SOC., Vol 65, No 558, part 6, 1969, pp 1544-1549.
27. Clune, M. A. A., Thrush, B. A., "Mechanism of Che*niluminescent Reaction In-
volving Nitric Oxide--the H+ NO Reaction", DISCUSS. FARADAY SOC., No 33, 1962,
pp 139-148.
28. Thrush, B. A., "The Reaction of Hydrogen Atoms", PROGR. REACTION KINETICS,
Vol 3, 1965, pp 65-95.
29. Carrington, T., "Angular Momentum Distribution and Emission Spectrum of
OH(ZE+) in the Photodissociation of H~0", J. CHEM. PHYS., Vol 41, No 7, 1964,
pp 2012-2018.
30. Cadman, P., Polanyi, J. C., "Production of Electronically Excited ~:toms. II.
H+ HI } H2 + I* (P 2)", J. PHYS. CHEM. , Vol 72, No 11, 1968, pp 3715-3724.
31. Clough, P. N., Thrush, B. A., "Mechanism of Chemiluminescent Reaction Between
Nitric O:cide and Ozone", TRANS. FARADAY SOC., Vol 63, No 532, part 4, 1967,
pp 915-925.
32. Halstead, C. J., Thrush, B. A., "The Kir.etics of Elementary Reactions Involv-
ing the Oxide of Sulf.ur. III. The Chemiluminescent Reaction Between Sulfur
Monoxide and Ozone", PROC. ROY. SUC. (Lond.), Vol A295, No 1443, 1966,
pp 38U-398
50
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~oR o~ric~~~i~. ~~~N: c~~i.v
- t;Ei~~Y1'ER 3: BASII; k:~Ur~'1' L~NS OF PROCESS~:S 1N (;Hr;M1CAL Lr1SERS
�3.1. General Conditions of Lasing Onset
The main purpose of investigations of processes in chemical lasers is to study
different chemical reactions in which atoms or molecules may be formed with energy
level distribution such that at least one optical transition satisfies conditions
that lead to synchronization of the individual emitters both in the case of inverse
population of levels, and in the case of phase correlation of the emitters. Setting
up nonequilibrium excitation of atoms with respect to internal degrees of freedom
is a necessary but insufficient condition for stimulation of coherent emission
during a chemical reaction. It is also necessary to have a reserve of inversion
that would compensate for losses in the resonant system. These losses determine
the limiting value of the diff erence in the concentration of populations. In
lasers whose operation is determined by phas? correlation of the radiating particles
there is a threshold of absolute concentration of these particles.
For lasers based on using the inversion effect, the critical density of inversion
of populations of energy levels is determined by the probability of a given induced
optical transition, the relative width of the emission line (4v/v), and also by
the properties of the excited modes in the resonator. If the radiation line width
is determined by Doppler broadening, which is usually the case at pressures of
- the order of a few millimeters of inercury, the kinetics of atoms and molecules
in the quantum-mechanical process of stimulated emission will show little dif-
ference. At high pres~ures in photostimulated chemical reactions the ratio ~v/v
is a significant factor in both the process of chemical reaction and the conditions
of stimulation of coherent radiation.
Calculations of radiation probabilities are based on the Born-Oppenheimer approxi-
mation that enables proper evaluation of the E-transition probability. The total
probability of the E-transition for an allowed molecular transition has the same
order as f or atoms (~10~ s-1). However, when the interaction of V- and R-levels
is considered, the probability of an individual allowed E-transition is several
orders less than the total probability of all transitions from the level. This
circumstance increases the threshold values of the critical density of inversior~
and absolute values of concentrations of radiating centers.
The critical density of population inversion of levels is det�~rmined both by the
_ oscillatory properties of the resonator and by nonoptical transitians that lead
either to further excitation or to relaxation processes that restore the system
to the equilibrium state. Chemical processes of excitation usually lead to an
increase in population over a fairly wide region of V- and R-levels. Thanks to
the small distance between R-levels, they are easily excited or relax on thermal
molecules that have energy of ~0.1 eV. These relaxational processes are an impor-
tant factor in the kinetics of the pro~ess of energy redistribution among molecules,
~ahich takes p~lace in only a few collisions in weakly bound molecules like I2, and
in up to ~10 collisions in strongly bound molecules .like N~.
Rel.axational processes within the limits of each degree of freedom determine the
corresponding temperature whose behavior is responsible for a given energy tran-
sition. As a rule, the temperature settles rapidly within a single degree of free-
dom, and then. energy E is e:{changed between degrees of freedom. For example, if
51
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FOR OFFICIAL USF: ON1..1'
a system is in the inverse state with respect to V-levels, rapid R-relaxation may
raise the population of the upper energy level of stimulated emission due to ad-
jacent R-levels, and accordingly may reduce the population of the lower energy
level of stimulated emission due to rapid transitions to adjacent R-levels in col-
lisions.
Besides, the different times of relaxation of V- and R-levels enable inversion
of the individual V-R levels even when both the vibrational and rotational distribu-
tions are characterized by normal law with temperatures T~ and TR.
According to �1.6, the energy of the V-R level of a molecule in the harmonic oscil-
lator approximation can be represented as
E(V, J)=E(V)-}-B(J-}-1)J, (3.1)
_ where V(vl, v2, vn) is the spectrum of vibrational quantum numbers.
For complete (vibrational) inversion, we have the relation
n - ~b' ~v~) it ~~2)~b' ~~2)1 > 0. (3.2)
Writing out the equilibrium distribution of V-levels
n~v) = fb' ('?)~zvil~ eXp ~v~ h`'~~k� T t), ,
7vib-~ [1-exp(-hv~~~� Ti)1-g~, (3.3)
where the vZ are numbers from the set V(vl, v2, vn), vZ, gZ, TZ are the fre-
quency, degree of degeneracy and temperature of the Z-th mode of vibrations, g(V)
is the statistical weight of V, we get the condition of existence of inversion
between levels Vl vi+~, v~, and Va vi, oi+l,
T~IT~ > v.!lvj > 1. (3.4)
Satisfaction of this condition necessitates comparatively small values of TZ/TZ
since the ratio v.L/vZ is small in cases of practical importance.
In the case of partia] inversion with Boltzmann distribution of rotational levels
~t(Vl, J)-b'(vi~ ~)n~~~s~ ~-I-~) (3.5)
bI?a, !-{-1)
and for inversion between v+ 1, J and v, J+ 1 we must have
R n� u~~ eXp f F~ k~T' E~v~T 1~ 1 (3.6)
( ) I. � J
or
~vih > hv/[2 (J ~{-1 } B~ ~B~-BU+~) ~ 1)l >1. (3. 7)
T
The latter colidition enables us to estimate the maximum population inversion
5'Z
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1~c1R ctt~l~lc'?:~1 ~ ~`1�~ c)\I ~
t Jm I i! ~~~it ~nt I~)
tlrtmax Z ~t (a 1) exp I- ko T I X
rot L
X~~-QXp~ -2B~?m-I-1)-I-~Bko~ v+~)~mt~m-~-~)J~ ~ (3.8)
vib
where
Jm N J0+ 1 k~T 2.l0-}-1 , .
2Jm~-3 B 2J,,,-~-1
a ((1 + hv~~�-en+~l T 1~~2-11=1.
Jo N
(Bo-eo+~) � B' Tvibl .l
The exchange exothermic reaction
A BC AB' C
_ AB C'
under conditions of an optical wave field may take the following short path with
emission of light
A-I- BC (A - B- C)* AB C-}- hv,
where (A-B-C)* is a complex that contains a chemical energy bond.
Chemical lasers based on reactions of this type are capable of converting chemical
energy to luminous energy with high efficiency by the shortest path since in a
number of these reactions the (A-B-C)* complex, as pointed out in �1.6, does not
have the usual lower state, i. e. it is always inversely populated. The concen-
tration of the complexes increases with increasing pressure up to levels where
triple collisions begin to play a significant part.
As the concentration of radiating particles increases, they can no longer be treated
as isolated emitters. In this case, as a result of collective interaction spon-
taneous emission becomes coherent with a considerable increase in intensity [Ref. 1].
It can be shown that for some conditions the rate of a chemical reaction due to
synchronization of emitters becomes comparable to the rate of the chemical reac-
tion due to induced transitions. In both cases, the reaction rate is proportional
to the square of the concentration of initial reagents, and this means that both
mechanisms may compete with one another, depending on the absolute values of the
radiating transitioz~s and the volume of phase correlation.
For the threshold of concentrations of radiating particles (Nth) in the case of
phase correlation we have the estimate [Ref. 1]
VNth/4 > 1. (3.9)
where V= a3 and a?/L respectively depending on the method of carrying out the
chemical reaction. Here ~ is the radiated wavelength, L is the length of the
resonator.
�3.2. Equations of Motion of a Chemically Reacting Gas With Consideration of
Nonequilibrium Effects and Emission
Equations f.or describing a multicomponent interacting mixture of gases in the pres-
ence of radiation are rather complicated for solving practical problems. With
53
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FOR OFFICIAI. USI~: ON1.1'
r~~ii~i~l~�i�:~t.lu~i .~C ~1.77)-(l.ti~) we ~lvt t~trr. a 51utp.litlc~cl 5y~~~m ol equaCiuns b~sed
on using the phenomeciological approach to problems of energy exchange and diffusion
of components.
~
The equation of continuity in Euler variables (p, u) remains valid in the presence
of chemical reactions and radiation, and has the usu~al form
dpldt p div (u) = 0. (3.10)
In the presence of chemical interaction and diffusion this equation for component
i can be written as
ap,~at t~~U) _~,t - a~~ n~, c3.~~>
where Dt = pt (ut - u) is the cliffusion flow of mass; wi is the change in mass of
the i-th component due to chemical reaction (or ionization).
The equation of momentum disregarding radiation pressure in accordance with (1.78):
~du/dt OP = 0. (3.12)
The equation of energy takes the form
~dheldt = div (Pu) - div q. (3.13)
The conservation equations for the i-th component can be written out, taking as
the component a particle that is in a definite chemLcal and quantum state. It
is convenient to convert to concentrations of particles in a unit of volume, n.
As an example, for a molecule of type m that is in vibrational state v, we can
write in place of (3.11) the equation
tfn~/df K~'. (3.14)
Here Kv is the change in number of particles of type m on vibrational level v as
a result of chemical reactions, collisions with other particles, or radiation.
The equation for the density of quanta q~ takes the form
dq /dl - a/~ -f- ca~~, (3.15)
where I~ is the intensity of resonant emission with frequency v, w~ is the pumping
rate, a is the coefficient of absorption (or amplification) of light.
�3.3. Principal Characteristics of Chemical Lasers
The major characteristics of chemical lasers and the fundamental quantitative cri-
teria of lasing onset may be found on the basis of the mathematical models of Ref.
2-5.
Let us consider the kinetics of chemical pumping and stimulated emission of chemical
lasers on the basis of the simples~ two-levei model that includes chemical pumping
of two working l.evels with populatio.i nl, n2, relaxation, aiid stimulated emission.
54
, ,
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FOR OF'~~I('1:1E. l~til~: ON1.1'
The equation of balance for the density of photons in the resonator in this case
is written as
dq~/dt = A~,ani -I- Bl.~n~q~ - B~,ln~qv - 9vk~� (3.16)
Here A1~2 is the coefficient of spontaneous radiation; B1~2 and B2~1 are the coef-
ficients of induced radiation for transitions 1-2 and 2-1 respectively, nl, n2 are
the number of particles on levels 1 and 2 respectively, T~ is the lifetime of a
photon in the resonator.
- Considering that Al,z = Bl.a 8 nv�%'+ Bl,sqv,i = 9v,aB9,i and introducing Q= o'l.a = Bi,a 9~~Ovc,
~n = n2- nnl, where cr1~2 is the cross section of the stimulated transition, we get
dq~ldt = A~,:ni ac~n9y - 9y~~~� (3.17)
Analogously for nl and n2 we have
dnl/dt = P,u~ n,~Tp vcy�~n, (3.18)
dn,ldt = P,uv - n~/Tp - vcq�~n, (3.19)
where Tp is the time of relaxation of the level, P1, P2 are the probabilities of
formation of populations nl, n2.
The limiting energy of radiation, defined as
~
~ ~ ~ (hvq~/~v) dt~
will be '
~
E,~x -(1/2)hv(P,-P,)S r~(i)dt. (3.20)
0
The limiting (maximum) efficiency is the ratio of the maximum energy of coherent
_ radiation to the reaction energy, and is called the chemicaZ efficiency nX, which
is independent of the reaction rate [Ref. 2-5]:
1 hv(Pz-Pl) (3.21)
~lmax = ~lx = 2 ~ --dHe ~ ~
Lasing arises at the initial instant if the rate of the chemical reaction satis-
f ie,~ the condition
ra> >~h= I/~rp trct~, = L1/tp, (3. 22)
where 0=(~cY,~,)-1 is the threshold density of inversion.
During steady-state chemical pumping, a time arrives when lasing stops due to re-
laxation on reaction products. This is the critical time of lasing cutoff
~~r = (pa - p~~TQ, ~3.23)
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~~c~u c~~~N'~c ~t i ~~t~ c~~~ ~
When inversion is created in molecules by etiergy transfer with probability P from
other molecules excited by the chemical reaction, the system of equations is sup-
plemented by the equation for the density of excited particles a* that arise as
a result of the chemical reaction
dn� _ ~ pp ~ -4- pa) ~i~ ~Pn ~ t = ~ ~ i = l, 2)., (3. 24)
dt '~p, t
Considering the creation of inversion due to energy transfer from excited particles,
we have for n2
dnaldt = Pgn* - Pv:ana - vcqv ~na - n~)- (3.25)
Also valid is equation (3.17) without the first term.
Lasing ensues under the condition
t�~th pn,z ~ni ~pv.~ -F- Ps)~Ps, (3.26)
where n$ is the equilibrium population of the lower working level.
Let us consider amplification of radiation under conditions of an unsteady three-
dimensional medium [Ref. 4]. In the case of partial inversion with unsteady chemi-
cal pumping of vibrational levels of a diatomic molecule, the gain on the R-V tran-
sition (v+ 1, J- 1) (v, J) for the~;~-branch with equilibrium distribution of ro-
tational levels is written as
o-F-~~r-~ o-~-t..?-~( P(- 2r~ (3.27)
an = ao, r = Qo. J `no+l-~p ex `
�+~'~r~ is the cross section
Here Ar is the characteristic rotational temperature, av,r
of induced transitions.
In the harmonic approximation
~-~~.r-~ _~~..~1)vo;?-~~ ~3.28)
~o, r
- i.r-~ i`~_~' Ao;.i-~ (2J-1)-T 8~~)eXP(- T J(J-1)~, (3.28a)
ao, ~ G ~
SJt ~YO. J
where vo; ,~i-~ is the f requency of the transition, g(0) is the form factor, Ao; is
the Einstein coefficient. From (3.27) and (3.28), (3.28a) we get
a=~an=QI9~-e~N1~ (3.29)
~
where e~ _(exp (20r J/T)-1)-'; N= Eno;
~ Q= Qo: i- ~(1-exp (-20~J1~)~ 9~ vno.
, ~
Using expression (3.15) as the equation of the medium, we get
dQv v
- -aly + ~ ~i ~i ~x~ (3. 30)
dt t~ i
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N'OR OFFI('IAL ~.;sN, oN~.v
where ~i and wi(x,t) are respectively the average number of excitation quanta and
the rate of excitation due to the i-th channel of the chemical reaction. For exam-
ple, for pumping in the process of a chain chemical reaction
A Bg Plo k' ~B ~L~ B A~ pfv k' ~B ~0~ ~
with probabilities of formation of reaction products on the v-th vibrational level
Plv and P2V at p= 2 we have
~i = ~+vpio~ ~9 = ~i vpao~ wi = ki ~A~ f B9~~ ~s = ks ~B~ ~Az~�
0 0
Using (3.29) and (3.30), we get the equation of the medium:
aa/d t=- val� K(x, t) ~ ( 3. 31)
where 1( (x, t) = a (ta~ (z, t) - ~t (e~ N)l .
L ~
In the case of complete inversion for molecules in which the upper and lower laser
levels belong to different modes (v3, vl), the expression for the gain on transition
00�1} 10�0 can be taken as
a=Q(9v.s-9v, (3.32)
Q=tQio~i~ /�~1-f-9v~i/N)-:~1-4-9v.~/N)-'(1-I-9v,3/N)''�
Here q~~i is the density of vibrational quanta of the i-th mode.
�3.4. Kinetics of Chemical Pumping and Lasing in the Pulsed Mode
Since high pumping powers and low energy losses can be achieved in pulsed operation
without difficulty, lasing in this mode is realized in many more active media and
on a considerably greater number of transitions over a wider spectral range than
in cw operation [Ref. 6].
Reactions with branched chains are the fastest. This includes reactions such as
oxidation of H2, PH3, SiH,,, CS2, C0, P, dissociation of NC13, some reactions of
molecular fluorine with H2i CH3, I, HI and several others. Taking survey Ref. 7
as our guide, let us present the patterns of occurrence of branched chain reactions
with inverse excitation of products based on the well studied reaction of hydrogen
oxidation [Ref. 8], for example when hydrogen reacts with fluorine.
It is shown in Ref. 9-11 that this is a branched chain reaction with energetic
branching in accordance with the scheme
inception of chains F2-~F + F; (3.33a)
continuation of chains F+ H2 HF (v < 3) + H; (3. 33b)
continuation of chains H+ F2 HF (v~ 6) + F; (3.33c)
branching of chains HF (v> 4) + F2 HF (v' < 4) + F+ F; (3.33d)
annihilation of chains H+ 02 + M-> HOZ + M, H02 wall; (3.33e)
annihilation of chains H-}wall, F->wall; (3.33f)
V-V relaxation and deactivation of vibrations of HF. (3.33g)
57
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In the lo�w-temperature region, collisions are rare, continuation and branching
of chains takes place at low rates, whereas the probability of annihilation of
' active centers H, F, HF (v > 4) on the walls is high. Thus at low pressures the
mixture is stable and does not self-ignite. The mix-
ture is also stable in the high-pressure region since
~ there is an appreciable increase in the probability
~~~j of annihilation of active atoms of hydrogen in triple
~ 1~1 collisions (3.33e). Self-ignition of the mixture
~ ~
takes place with progressive development and predomi-
~ nance of processes (3.33b), (3.33c) and (3.33d) in
~ some intermediate pressure region that is a function
~ a of the temperature of the mixture.
Such behavior of a chemical reaction in coordinates
~ T, p is described by graphing the region of the ig-
~ T, rel. units
nition peninsula (Fig. 3.1) typical of the branched
Fig. 3.1. Lasing limits chain reactions described in �1.5. The boundaries
for branched chain reac- of this peninsula (solid line) are the lower and upper
tions ignition limits, or to say it another way, the first
and second limits of ignition. For reactions H02+ F2->
HF + 0?+ F there is even a third limit of ignition (shown by the broken line in
Fig. 3.1).
Let us set up equations for the concentrations of particles nH, nF, nHF(v)'
- dnFi /df = - (k,nFa -I- h6no,nM -I- ke~~iH 'I' ka~1H~ nF~ (3.34)
dnFldt = k, nF, nH-(ks n~~. -F~ k~) nF -I- n~. o~'i~ ka, o ntiF co~ -f- ( 3. 35)
- dnHF ~o~ Idt --k3 ko nr�, rtF~-k4, o nF. nHr coi -F-~ (3. 36)
where SZ(t) is a term that describes relaxation and annihilation on the walls;
k2i k3, k4,~, ks are the rate constants of the corresponding processes (kq,v>4= 0);
w(t) is the rate of the reaction of chain initiation (3.33a); k6, k~ are certain
averaged constants that take consideration of the size, conf iguration and material
of the walls of the reaction space in the case of linearity of equations (3.34)-
(3.36).
Let us consider the initial period of the reaction, assuming that w(t) is a deltoid
function. In this case, the solution of linear system (3.34)-(3.36) will be the
sum of exponential terms
nHF = no exp (st),
where s is the largest of the determinants of system (3.34)-(3.36) [Ref. 2, 12].
The ignition peninsula is defined by the condition s> 0. The initial stage of
the reaction is typified by an exponential rise in the concentration of reaction
products and the reaction rate.
The distribiition of n~ for exponential growth of concentration without V-V relaxa-
tion is constant at large st, and is determined by the expression n= sk/(s + b).
Corresponding to the assigned quantities b and k~ is a minimum value smin at
which inversion still exists in the system of vibrational levels. Let k~ 0,
kv+l ~ 0, b be assigned in the form of a harmonic approximation. Then for large
st we have
58
, ~ .
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~'OR OFFt(7A1. t'SE Otil,~'
nt fto stp ll - eKEi hv~h1 j)-1 STP� ~3. 3/)
This implies that the condition of existence cf inversion in the given case will
be sTP> 1. The region of satisfaction of condition sTP~ 1 is located inside the
ignition peninsula (dot-and-dash line on Fig. 3.1) or is absent entirely.
The initial mixture has temperature and pressure far from the ignition region.
External factors typical of the given chemical lasers design such as the fast ac-
tion of an exothermic discharge, photolysis, transfer the mixture to the ignition
region, and when the energy of this action is sufficient, into the inversion re-
gion [Ref. 13].
From (3.34)-(3.36) we can make a qualitative estimate of the influence that V-V
relaxations have on the course of the reaction. If processes (3.33e) take place
very rapidly, relaxation will cause population of level v= 4 due to transitions
from the third level. In this case the reaction rate may increase somewhat. On
the other hand if processes (3.33e) are slow, relaxation leads to establishment
of Boltzmann distribution nV, and the reaction rate decreases.
Accounting for V-V relaxation within the framework of the linearized problem for
the case of radical chains was included in Ref. 8, 13 for a two-level model with
estimates of the possible efficiency of a laser based on a branched chain reaction.
�3.5. Principal Equations of the cw Chemical Laser
Theoretical analysis of the characteristics of the cw chemical lasers presents
considerable difficulties due to the necessity of simultaneously accounting for
the influence of diffusion, chemical reactions and radiation [Ref. 14].
In theoretical models the n~nequilibrium nature of energy distribution can be taken
into consider.ation by considering the gas as a mixture of several components in
analogy with gas reactions, each long-lived V-level of the active molecule being
taken as an individual gas component. It is assumed that the formation ot active
_ molecules in mixing and combustion of the fuel and oxidant is determined by dif-
fusion, while combustion takes place along the flame front [Ref. 15J. Collisional
deactivation of each vibrational level of the active molecule by resonant V-V and
V-T energy transfer is taken into consideration by expansion ic~ ~ series with re-
spect to powers of the ratio of the axial distance to the charactaristic deactiva-
tion length.
Fuel H2 + diluent '
u~,
R~~ T~
y
- nNZ ~HFIVI
~ x
Stream
,;n~ ~ ` Flame front
~F
p~ ~ T~
Oxidant F + diluent
Fig. 3.2. Flow diagram in diffusional chemical laser
59
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FOR nFN'I('lAi. t'til�: (1111
The flow scheme is shown in Fig. 3.2. Two homogeneous semi-infinite parallel gas
flows (one consisting of oxidant and diluent, the other of fuel and diluent) begin
mixing and burning at point x= y= 0. Here x is the coordinate in the direction
af flow, y is the coordinate in the direction perpendicular to x, the positive
direction of y corresponding to the fuel-filled region.
Such a conf iguration is an idealization of the f low in the channel of the chemical
laser, and is analogous to flow in a boundary layer with velocity components u
along the x-axis and v along the y-axis.
System of equations (3.10)-(3.14) with consideration of boundary layer theory
implies [Ref. 14]:
X (Pu) -t- ay (Pv) = 0; (3 . 38)
au au a/ au 1; (3. 39)
l" ax ay 1 ay ay 1
a~~o anp v aho aull (3.40)
p(tt -{-v-1=- f -{-(Pt-1)u a IJ- ~~'ao.rfo.r;
~ Jx � ~y l ay P~ ~ dy 9 0. .l
dYt dYt \ ~ / d~'~ I~HF ~~av. J lo. J a,u. J~o~ J ~3.41~
U - U D l ~-~t"~' ~t~o - ~
n( ax ~ ay J= ay I P t! a9 / a hNA ? vo~ ? yv, ?
~
~ o. _ aU, r 10, r, ( 3 . 4 2)
ay
where Pr= ncP/aQ; n is the coefficient of viscosity~ Cp=F~Cp,iYt;
P = PR7'E ~Yr~l~i)~ ho = lte -{-1I2u~;
T
he=~'Y~ ~S~p,tdT-~-h~,t~ .
~ ~o
Superscript v, J denotes transitions of the branch from level v, J to level
v- 1, J+ 1, while the subscript denotes transitions from level v+ 1, J- 1 to
level v, J.
The last term in the second member of equation (3.40) is the energy loss per unit
of volume due to stimulated radiation and absorption. It is equal to zero for
all i~ v. Term wi characterizes the arisal of the i-th component as a result of
the chemical reaction. The optical gain a~~J corresponds to its value in the center
of the line, and is defined by the formula
CCu,! = A ~Yo+l fC}rv~, (3.43)
where
s/~N Iy~+~ I'!p p
8n A o o..? exp(-E(v-F-1, J-!)lh�7'1~
3(2k�HF)~~~ RJ(o-}-l, J-1)7'~~z
_ ~
l2r (U~ = ~ (2J -}-1) exp [ (v, J)!k~ T'J;
a r-o
R~(u-}-1, J-1)
x= exp {-[E(v, J)-E (u-}-1, J-1)]/h" T}.
R~ (u, J)
60
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Here Y~ is ~he mass Erac[iuii oC excited mulecutes, NA is Avo~;~.idro's number, R~
is internal energy for rotational degrees of freedom. The term ~H~-~~~1 accounts
for the contribution of vibrational degrees of freedom to the electrical dipole
moment, and FV~J is the parameter of interaction of vibrationa]. and rotational
- degrees of freedom.
To describe the process of amplification of radiation in a premi:ced moving gas
stream in cw operation we have the system of equations [Ref. 4J:
al�lax - al~; rx3a/d~ aat� -I- K(x, J), (3.44)
where v is the velocity of gas flow along the y-axis.
Cross section y= 0 is the left-hand limit of the reference signal propagating along
the x-axis. The boundary condition is written as
0 , 0 1. (3.7Q
�3.7. The Optical ~avity
The resonator cavity is one of the main components of any quantum generator, as
it forms the radiation pattern. A cavity made up of two plane-parallel mirrors
(Ref. 18J was the first to enable attainment of directional coherent radiation
in the optical range. Cavities based on interferometers with spherical, para-
- bolic and other surfaces have come into extensive use [Ref. 19]. Unstable resonators
to some ex.tent resolve th~ problem of more complete filling of the active medium
with radiation [Ref. 20], but in these the ratio between aperture and cavity length
does not permit development of a compact laser. Resonators of periodic modes have
been developed thanks to the creation of a theory of cavity resonators with the
use of concepts of the theory of linear systems. Different types of cavities and
their theory are presented for example in Ref. 22, and their peculiarities in oper-
ation with chemical lasers are described in detail in Ref. 23. Let us consider
as an example of a resonator of periodic modes a system with mirrors with surfaces
determined by radii of curvature R1, RZ. The space-frequency characteristic of
such a system takes the form
Ho _ [1 - Ni ~~)1-1, (3.71)
66
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where ~ is a variable that describes er.citation of the electromagnetic field in
the cavity; H1(~) is the space-frequency characteristic that corresponds to one
p
As a result of reaction (4.6) , the level with v= 5(kl:k2:k3:k4:k5:k6 = 0.2:0.75:
0.6:0.7:1.0:0.95) is populated at the maximum rate. Most intensely populated as
a result of reaction (4.7) is the level with v= 2(kl:k2:k3 = 0.29:1.U:0.47) [Ref.
16J. The behavior of populations of the levels of the HF molecule as a function
- of quantum number v as a result of reactions (4.6) and (4.7) takes the form of
a smooth curve with two maxima, the chief one corresponding to level v= 2, and
the other--to v = 5.
Experimental results unambiguously confirm the chain nature of this chemical reac-
tion. Actually, the intensity of the radiation remains constant or increases after
the cessation of pumping. The main influence on the formation of HF is from the
reaction of vanishing of F atoms as a result of reaction with HZ, the damping con-
stant being Tp < 3 us, and the formation of H with Tg 5 8 us. The influence of other
reactions such as recombination of atoms or thermal dissociation of F2 and H2 at
T< 1200 K is several orders of magnitude weaker. Therefore the existence of lasing
over a duration of a few tens of microseconds after termination of pumping in mix-
tures that are rich in hydrogen presupposes the presence of a chain mechanism of
reaction. In this case we can readily explain the existence of lasing with a re-
duction in pumping power (or even total cessation), since the rate of a chain re-
action may increase with time due to self-heating of the mixture through the re-
lease of chemical energy. When the possibility of a chain reaction has been elimi-
nated, e. g. by replacing F2 with MoF6i lasing duration has not exceeded the dura-
tion of the pumping pulse.
In parametric analysis of a photochemical laser based on reaction H2+ F2 [Ref. 21],
the following expression is obtained for specific energy output from a unit volume:
~
ey= hv ~ 1- kNN ~
~n ~ ~ (4.10)
where hv is the energy of a lasing quantum, hn = 2/t�~~x-a and krv = k~1l~x-1 are the
effective model constants oE relaxation of vibrationally excited molecules of HF
on molecules of HF and F2 respectively; X=(w2 - wl) /(2Stn) ;~_(ni - n2) /2n;
ti2= (1/n)dn/dt; n2i nl are the respective populations of the upper and lower lasing
levels.
10
To find the effective model constants, a
graph ii ~lotted (Fig. 4.4) in coordinates
~EVex~th)~ vs. NS?t~, where subscripts "ex" ~~U 5 ~ s
and "th" denote the experimental and theo-
retical quantities respectively. It can
be seen that the aggregate of the results W'~ ~
is described by a linear relationship.
O
From this we get hvkn1= 0.8�10-e J/(cm3�s), 0 2 4 6 8
kN = 1.5�10-13 cm3/s and e~ = 0.8�10-8 lz 3
SZ (1 - 1. 5� 10-1 3 N/Sl) J/cm3 . ~N/S2th) , 10 mol cm- � s
Fig. 4.4. Parametric de-
pendence
77
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Comparative analysis of tne effectiveness of using different photolytic sources
of fluorine atoms shows that the greatest gain on HF molecules is realized on a
mixture of WF6/H2 [Ref. 22]. However, work with F~F6 is made difficult by the poor
reproducibility of results and the complexity of getting pure WF6�
The CO molecuLe~ is of interest as a working molecule of photo~.hemical g~s-static
laser~. Many reactions that lead to the formation of CO have high exothermicity,
enabling relatively easy excitation of CO to high vibrational levels (v ~ 17). This
results in low rates of relaxation of the CO molecule in collision with unexcited
particles.
The first photochemical gas-static CO laser was based on the reaction of oxidation
of carbon disulfide [Ref. 23]. The working chamber was a quartz tube with KC1
Brewster windows 7 mm in diameter placed in a resonator 1 m long. The CS2/OZ/He
mixtures were pumped by a xenon lamp 50 cm long. Emission power increased with
increasing He pressure, and at the optimum pressure p= 20 kPa He, the energy of
excitation reached about 0.5 W.
Lasing was observed on 31 transitions of the ~'-branch. Another 270 transitions
have been detected on the :1~- and~R-branches of the CO molecule [Ref. 24]. A common
pattern is that lasing on transitions with low values of J shows up earlier than
on transitions with high values of J.
Lasing with a= 4.7-5.7 u~ is observed over a wide range of mixture compositions,
initiating energies (from 0.5 to 4 kJ) and pressures (from 0.066.to 13.3 kPa) (Ref.
25]. The pressure corresponding to maximum power increases approximately as EI,
where EI is the initiation ener~y, and the maximum power first increases very rapidly,
and then in proportion to E}'S .
The lasing process is unaffected by vibrational relaxation of CO molecules, and
the characteristics of this process are determined only by chemical reactions [Ref.
26]. Most important of these are the following:
0) CS, hv (l~ < 220 nm) CS S;
1) S -I-O�k+SO-{- O (-27,1 kJ/mole) ;
2) O-}-CSa~?CS O (-96kJ/mole); (4.11)
3) O -I-CS~`? CO* -f-S (-313 kJ/mole) ;
4) S-{- CSak?CS3-f-M.
According to data of Ref. 27, 28, k1= 2�10-1Z cm3/s, which is three orders of mag-
nitude greater than the value assumed in Ref. 25 (at T= 300 K). In this case,
not only reaction 4), but also any trimolecular reaction of disappearance of active
particles (such as SO + 0+ M-~ S02+ M) cannot be compared in rate to bimolecular
reactions 1)-3) at low pressures of CS2 (p~g2~ 0.1 kPa) at which there is a drop
in lasing energy and power. Therefore, in order to analyze the observed contra-
diction between the decisive role of trimolecular chain termination and the low
calculated rate of such a reaction as compared with bimolecular reactions, special
78
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N~c~~ c~~~~~~~~:tt. t;~r: c~tit.~
experi.ments were done. The working tube of a chemical laser, made of optical
quartz (with transmission to 200 nm), 50 cm long and 20 m in diameter, was closed
on both sides with calcium fluoride (or barium fluoride) windows. The cavity was
120 cm long. ~nitiation was by two series-connected xenon lamps (pXe = 0.266 kPa).
The lamps and the tube were placed inside a cylindrical reflector of aluminum L-oil.
An investigation was made of the way that the energy E of stimulated emission de-
pends on the partial pr.essure of CS2 with dilution by gases He, Ar, Xe. The in-
fluence of dilution at high CS2 pressures is evidence in favor of the hypothesis
ef trimolecular nature of the chemical process that limits energy ar,~ power of
lasing.
The dependence of E and W on pressure of the components C02, N20, OCS is quali-
tatively the same as for dilution by inert gases. The effectiveness of C02 is
close to that of helium (1c~0-C02 ~ 10-14 cm3/s), and relaxation on N20 is more ef-
fective (kC0-N20 ~ 1~-13 ~m3/s). The strongest resonant exchange a~th vibrational
lavels of CO (4 DF (v - n) D (-129,5kJ/mole) ; (5.12)
D Fz DF (v = n) -E- P (-414 kJ/mole) ; ~5.13)
D ONF-> DF (v n) -E- NO (-326 kJ/mole) ; ~ (5.14)
D(=(v-n)-}-llF(v-m)~DF(v--l~-1)-I-
DF (u = nt 1); (5.15)
- DF(a=n)-f-M~DF(a--~i-1)-}-M; (5.16)
DF(v= n) -{-COa(00�0)~DF(v=-n- I)-I-
COZ (40� 1); j ( 5 .17 )
COz (00�1) M~ COa (~unt U)-~- M; (5.18)
COZ (10�0) COZ (00� 0) +
' 2C02 (01'0); (5.19)
C02 (O 1' 0) M~ COZ (0~�0) 1~9, ( S. 20 )
107
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FOR ONb'I('IA1. Util�: ONf.l'
where M= DF, N0, Iie, F~, Dz, ONF, COZ, F or D. When deuterium is replaced by hydro-
gen, equation (5.9) must be substituted for (5.17).
To illustrate how energy is transferred from vibrationally excited HC1, HF, DF,
HI or HBr to C02 (00�1), Fig. 5.11 shows a diagram of the vibrational levels of
v~_o
CDi ~z_~ .
4 242ch ~ ~4_~
+ - ~ - -
- HF
~ ~Zo~ - -
3 55BCn-~
U
~ o ~.00�16 DF(HCU
r+ ~ P -
^ 2 T,. - 10000 K
x rt T,.- 500 K
w Tt= 4 00 K
complete vibrational-resonance defects
~ D F= 558 cn''
NCt= 537 Cn''
~~-0 NBr~ 210 Cn-'
HI =-rr9 cn"'
�9 00�0 '
0
Fig. 5.11. Diagram of vibrational levels of molecules of
C02 and hydrogen halides
these molecules. The left part of the diagram shows the levels (00�0), (00�1),
(10�1) and (02�1) of CO2. The right-hand part shows the energies corresponding
to V-R tran.-itions of DF (very close to HC1) and HF in bands 1-~0, 2-~1, 3-~2 and
- 4-~ 3. For t:� assumed values of vibrational and rotational temperatures, Fig. 5.11
shows the qualitative relative distribution of molecules with respect to V-R states
as a function of the defects of resonances, whose values are indicated for the
band 1-~ 0.
Fig. 5.12. Diagram of subsonic chemical
laser with reagent mixing and energy ~ ,a�oo,a,
transfer: 1--F2 and He in~jectors; 2-- -2
C02 and NO injectors; 3--DZ or H2 in-
jectors; 4--NaCl Brewster windows; 5--
spherical mirror (radius of curvature 3 4���~��~~~~ ~
10 m); 6, 7--flat mirrors; 8--semi- - 6
~ ~ io
transparent spherical mirror (radius 15~M �B
of curvature 10 m); 9--section for blow- g__ j j~ 4
ing nitrogen over the mirrors; 10--
output emission of chemical laser; 11--
_ flow channel
� 108
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F'OR O~~H'1C'I:iL i:51�: ()til.l
_ Fig. 5.12 shows a diagram of a chemical laser that works on reactions (5.10)-(5.20)
under transverse flow conditions [Ref. 38~.
The operation of this laser is as follows. Premixed F2 with He and NO with C0~
are admitted to the upper part of flow channel 11 with cross section of. lx 15 cm
through two sets of gas-mixing in~ector tubes 1 and 2. The gases enter the tubes
through lines f.astened in the upper part of channel 11. The gases are mixed rapidly
(within about 50 us), and then the necessary concentration of fluorine atoms is
set up ia the reacti.ons (5.10) and (5.11). Deuterium or hydrogen is injected into
the flow through tubes 3 that are analogous to the tubes in the first two rows
of injectors, except for the fact that the gas from tubes 3 exits at a right angle
to the flow through staggered orifices.
_ A five-pass optical cavity with axis directed across the flow ensures selection
and extraction of energy from a region situated at a distance of from 0.5 to 6 cm
" from injectors 3. To eliminate the possibi~ity of parasitic lasin.g directly on
flat mirrors 6, 7, these mirrors are slightly misaligned. Streams of dry nitrogen
are directed along the side walls of channel 11 to prevent the mirrors from coming
_ into contact with the chemically active components of the flow. The NaCl Brewster
windows are installed ta enable use of external spherical mirrors. All mirrors
are water-cooled. The ~paque mirrors that are not intended for transmitting radia-
tion are covered with metal-dielectric coatings with reflectivity of 99.4%. The
output mirrors are made on a Ge substrate 3 mm thick with dielectric coating, and
have reflectivity from 10 to 50%. The optical path between mirrors with radius
o` curvature of 10 m is 1.8 m.
The specific construction of the described chemical laser design requires a study
of the mutual relations between all parameters, and optimization of these relations.
For example, selection of the evacuation system involves the optimum pressure in
the cavity, chemical efficiency is related to the specific consumption of reagents,
the dimensions of the chemical laser are related to optimization of the structure
and composition of the working gas mixture. It is desirable to maxi.mize the pressure
in the cavity, as this simplifies the construction of the evacuating system. In-
- creasing the chemical efficiency involves a reduction in the expenditure of reagents
per unit of emission power. Optimizing the composition and flowrate of the mixture
to maximize power leads to the pcssibility of reducing the dimensions of the cavity
and of the entire chemical l.aser.
i,J
Fig. 5.13. Relative output power of
subsonic chemical laser with energy
~ O,B transfer (DF-C02) as a function of
u static pressure in the cavity ps at
* different flowrate concentrations of
~ ~ N0, mole/s: 0--0.011; 0--0.007;
� 0,6 0.002. Enveloping curve--change in
~
v + lasing power with change of pr.essure
in the cavity at the optimum NO con-
~ 0~4 ~ centration
+ +
0, 2
2 4
~s, kPa
109
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Fig. 5.13 shows the typical dependence of output emission power W on the pressure
of the mixture in the cavity pS [Ref. 40]. Here the change in output power with
change in total pressure of the mixture in the cavity depends on the molar concen-
tration of radicals NO introduced into the mixture. It can be seen that the opti-
mum total pressure of reagents in the cavity that corresponds to maximum lasing
power depends on the NO concentration. Increasing the pressure of the mixtu2e
leads to a reduction in molar concentration of NO in inverse proportion to ps.
Fig. 5.13 also shows that there is an optimum pressure of the mixture (2.26 kPa)
and an optimum flowrate of NO (7 mole/s) that maximize the output power of stimu-
lated emission.
The nature of the distribution of the relative population nv/n of the upper level
of C02 (00�1) in the vicinity of the cavity x~ and beyond this region in the x-
direction downstream beginning with the H2 (D2) injector is shown in Fig. 5.14.
0 ~00 100 300 400 t~ u S
n~in
I
- I
o,g - ----f-- - -
I
I
qs -i -
I
0,9 -
xv
D, 2 - -
x~
p g g 11 15 18 x, cn
Fig. 5.14. Distribution along the x-axis of the relative
population of the uppe.r, level of C02(00�1) n~/n
Increasing the flowrate of NO accelerated the chain reaction, intensified 4.3 um
radiation and reduced xp--the distance to the peak of the relative population, and
accordingly the maximum emission intensity.
By way of example, let us cite some data on lasing powers W and chemical efficien-
cies rlX of purely chemical subsonic lasers with transverse circulation (Table 5.1).
TABLE 5.1
Systems of purely chemical subsonic lasers have
also been developed with longitudinal pumping Values of W and r~X according to
[Ref. 42, 43]. A diagram of such a chemical various references
laser is shown in Fig. 5.15 [Ref. 43]. Reac-
~ tions (5.12), (5.13) and (5.17) were carried RefPr_~Pn~
Parameter ~40~ ,I ~38~ ~ ~4i~
out in Teflon tube 1. The length of the tube
_ was 150 mm, and inside diameter was 8 mm. Re- W, watts I 5GU I IGO I 19
action (5.10) took place in a flow of He/F2/NO ~z oo I 4 I 4,6 I 4,2
in copper connecting tube 2 on a section 35 cm
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5 M M '
~
3
1
, 2- 4 ' S
6
He E-- COp
+ } to pump
FZ NO Dp
Fig. 5,15. Purely chemical laser with longitudinal circulation: 1--working reac-
_ tor tube; 2--inlet of He/FZ/NO mixture; 3--end face of the reactor; 4--inlet of
- C02/D02 mixture; 5--mirrors; 6--branch f~r evacuation of gas
long, and the resultant gas mixture was fed to the end face of the reactor 3. Con-
necting tube 4 was used for inlet of gas mixture C02/D2. This mixture was injected
into the reaction space through a number of orifices around the perimeter close
to the end face 3 of Teflon tube 1. A semiconfocal cavity was formed by gold-
- coated mirror 5. The stimulated emission was coupled out on the side of the flat
mirror through an orifice 1 mm in diameter. The pressure at the inlet to the reac-
tion space under the conditions of the experiment was 2-2.66 kPa. To ensure ade-
quate velocity of the gas stream through reactiori tube l, it was connected to the
ballast tank through larger-diameter tube 6. This provided an average flow velocity
of ~200 m/s.
The flowrates of working components of the mixture that are optimum with respect
to radiation power were experimentally determined in Ref. 43 [mmole/s): NO--0.04;
F2~ 0.451 DZ--0.37; CO --1.65; He--5.07. Fig. 5.16 shows how the power of a cw
chemical laser with longitudinal circulation depends on gas flow`iates. Since the
~~p - Ne
fz
� NO
+ �
~ DL C01 +
o +
~ 45 ~ ~ ~'5 1
+
I
+
0 1 Z 3 G/Gapt 0 0,5 1,0 ~,5 G/Gopt
a b
Fig. 5.16. Power of cw chemical laser as a function
of gas flowrate for reagents:
a--of reaction (5.12), (5.13); b--of reaction (5.11), (5.17, (5.18)
111
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output power of purely chemical cw lasers is appreciably dependent on the rate
of mixing of initial reagents, the conditions of reagent mixing in Ref. 43 were
altered by reducing the diameter of the injection orifices. For example at an
orifice diameter of d= 1 mm the pressure differential between the inj~cted fluid
and the reaction space was ~p = 1.33-2 kPa, while at d= 0.35 mm and retention of
the same gas flowrate, ~p ~ 0.1 MPa. A reduction in the diameter of the orifices
increased the velocities of the injected jets, i. e. it improved the conditions
of mixing of the components. An imporvement in mixing conditions at d= 0.35 mm
led to an increase in tr.e power of cw emission by approximately a factor of four
to 2.1 W.
Electric-Discharge Subsonic Chemical Lasers. Amplification of radiation in the
continuous mode due to chemical reactions excited by an electric discharge was
first achieved in reactions of exchange type [Ref. 44]. The reaction took place
in a stream of a mixture of H2 and halide, vibrationally excited molecules of hydro-
gen halides being generated under conditions of low pressures of 1.33-0.13 Pa:
l~I-}-CIZ-~HC1*-}-Cl; (5.21)
H-~-I3rz--> HBr*-~Br; (5.22)
CI -}-HI--~tICI*-~- I . (5.23)
At higher pressures--from 0.66 to 2 kPa--a chemical laser operated [Ref. 45, 46]
in which atoms of F were produced in an electric discharge in a gas mixture of
He, OZ and SF6. Then the SF6 was mixed with hydrogen that fed into the flow region
upstream along the axis of the transverse optical cavity.
3 5.
0-300MA , '
~ 0 - 20 kV
L
H2 _ 4
~
SF6
6 t pump
Np '
H '
He ~
,
/
~ 0-300nA
0-20 kV . ~
- 3
Fig. 5.17. Diagram of subsonic cw electric-discharge HF rhemical laser with trans-
verse circulation and mixing of reagents: 1--Pyrex discharge tubes; 2--ballast
resistors for discharge stabilization; 3--discharge power supply; 4--injection
tube; 5--opaque mirror; 6--gas flow; 7--mirror with hole for coupling out the
radiation
Fluorine atoms have also been produced in a dc discharge in a mixture of N2, He
and SF6 [Ref. 47], after which these atoms were reacted in the same way with H2
or DZ.
112
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The facility described in Ref. 47 is diagrammed in Fig. 4.17. A characteristic
feature of this installation is that the location of the injection tube can be
changed. Gas mixing, chemical reactions and lasing take place in a flow with cross
� section of 30 x 1.25 cm. The optical cavity is formed by mirrors with radius oI
curvature of 2 m separated by a distance of 45 cm. Emission is coupled out of
the cavity through a hole with diameter of 5 mm in one of the mirrors.
The typical gas flowrate [mmole/s]: H2--3, N2--20, He--10, the flowrate of SF6
varied from 3 to 20. Increasing the amount of SF6 in the mixture led to an in-
crease in the impedance of the discharge, and consequently in the power consumption.
Adding NZ to the mixture also increased power consumption since there was a rise
in the voltage drop across the discharge. Helium was added to the mixture to stabi-
lize the discharge and reduce the gas temperature.
- 90K 90K
120 V ' 0-17,6 kV
O,o>4 60 H~ 600MA . 0,014
i 3
~ N 2 N2 i~
025Mrt
to pump
2 6 ~ ~ B
R�4n - Lv.J
~ ~ 38MM ~
~ CS2/02 5
CS~/02 135cM
~ - ~
Fig. 5.18. Diagram of electric-discharge chemical laser with longitudinal mixing
of reagents: 1--discharge tubes with inlet of N2; 2--injectors with inlet of
CSZ/OZ mixture; 3--electric supply for the discharge; 4--radiation detector; 5--
flat mirror; 6--gas oiitlet with evacuation rate of 5 m3/min; 7--spherical mirror;
~ 8--working reactor tube
- At an evacuation rate of 0.236 m3/s, the pressure in the flow in the intermixing
re~ien was about 0.7 kPa, and the velocity of the flow was about 4�103 cm/s (ac-
- cording to estimates, the speed of sound in the mixture is 7�10`' cm/s). Under
these conditions, adequate efficiency of operation of the chemical laser was
reached only when the tube through which H was injected was located in the vicinity
of 2� 0.5 cm upstream from the cavity axis. From tl~is we can estimate the lifetime
of the excited gas mixture at about 3.6 us the upper limit of the lifetime of
eYCited HF molecules associated with the specific conditions in the given facility.
The HF inakes up a smalt fraction of the total number of particles, and the tempera-
ture of the mixture is approximately 150�C. A relatively short time for the mixture
to stay in the optical. cavity is useEul., since HF moleciil.es that are in the ground
1 3
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4 3 4
Oz~He~Nz
3 2 ~ C'~ 6
~ f
' ~
- 0-25 V
A 0-200nA
~ a
4 5 8
O~He
o ^
CS~, e ' - o
- ~ o
0
0
0 0
e ~
6
d- 4 9
Fig. 5.19. Subsonic electric-discharge chemical laser with transverse flow: 1--
discharge section; 2--anode; 3--mixer; 4--adapters; 5--working channel; 6--injec-
tors with CS2 inputs; 7--cathode; 8--resonators; 9--branch pipe for gas outlet;
10--ballast resistor; 11--discharge supply source
state are carried off with the flow out of the cavity, and consequently there is
the possibility of achieving lasing on transition (1-0), in contrast to systems
in which the gas flow is directed parallel to the axis of the cavity.
The power of stimulated emission of this kind of HF chemical laser depended on
the electric power of the supply. The maximum power of 5.5 W with lasing on HF
corresponds to intensity of stimulated emission of 700 W/cm for beam diameter
of about 1 mm. DF lasing power is about half this level under analogous condi-
- tions. The ratio of the energy of stimulated emission to the electrical energy
expended on initiating the reaction (called the electrical eff iciency of electric-
discharge chemical lasers) was about 0.1%.
By using separate discharge tubes and longitudinal circulation of the reagents,
a chemical laser has been made that is based on CS2/02 and nitrogen [Ref. 9, 48]
(Fig. 5.18). When N2 is dissociated in the electric discharge in tubes 1, atoms
of N are formed which are then mixed with CS2/02 in the Teflon injectors 2 inside
the optical cavity longitudinal to the flow that is formed by flat mirror 5 and
spherical mirror 7. The radiation is coupled out to InSb detector 4 through an
aperture in the flat mirror.
Here there are two possible paths of initiation of the reaction. One is by disso-
ciation of N2, and the other is by dissociation of 02, in the case where discharge
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tube 1 is filled with a mixture of 02 and He. It was found in Ref. 48 that increas-
ing the flowrate of 02 or N2 raises the output power of the chemical laser. The
reactions that take place in such a laser are similar to those in the CO photochemi-
cal laser described in Ref. 7.
A subsonic electric-discharge chemical laser with transverse flow operates on an
analogous mixture [Ref. 49]. Fig. 5.19 shows a schematic (a) and the outside view
(b) of this laser. The discharge section is made of Pyrex tube 1, at the inlet
of which is copper disk anode 2 with central orifice for passing a mixture of gases
02, He, N2 coming from mixer 3. From discharge section 1(90 cm long, 2.5 cm in
diameter) the gas stream passes through adapter 4 into the section of rectangular
working channel S(50.8 x 30.5 x 1.3 cm) with adjustable positioning of injectox~s
6 for introduci.ng CS2. The reaction-initiating discharge takes place between anode
2 and cathode 7. Adap'ters 4 and channel 5, made of copper and stainless steel
respectively, are water-cooled. Transverse resonators 8 are installed on channel
5. The gas is evacuated through outlet 9. Ballast resistor 10 is used to stabi-
lize the discharge.
A power of 4.5 W was achieved in such a chemical laser with flowrates of 7.7, 33.4
and 2.4 g/m for He, 02 and CS2 respectively at a total pressure of 0.72 kPa, dis-
charge power of 800 W, and distance between the CS2 injector and the optical axis
of the resonator of 1.5 cm. The electrical efficiency was 0.56%, and the chemical
eff iciency was 2.7%. Fig. 5.20 shows curves for the output powar Wout as a func-
tion of the invested power Winv and partial pressures pi of 02 and He (the unstable
discharge region is shaded).
6 5 +
Oz
5 ~ ~ He
3 q i~ 3 3 +
~
+
0 +
3 T Ile " 3 2
2 /
~ ~
a b
0 2 4' S 6 7 6 0 0,2 0,4 QB
Winv~ 102 W pi, kPa
Fig. 5.20. Output power of chemical laser as a function of
invested energy (a) and partial pressures of 02 and He (b)
The described chemical laser [Ref. 49] operates with greater eff iciency than simi-
lar lasers described in Ref. 8 and 11. This can apparently be attributed to the
capability for optimizing the position of the CS2 injector in the resonator cavity.
Another factor is in the effect of reduced rotational temperature of C0.
Similar in design to the chemical laser depicted in Fig. 5.19 is the miniature
cw HF (DF) subsonic electric-discharge chemical laser shown in Fig. 5.21. The
115
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H~~SF6 ~~2
+ 10 kV Hp(D2)
~ 0. 5 A 4~ 7,5 to 20 x, cn
~ a I
I
6 n- n o u ~pst~max
W >0~9 ?2~1114-?13
5-r4 7#6 9--B fl~?1013?12~
levels without appreciable quenching ~2y~~
on high levels. ~ 2~~_~
It should be noted that the amplifica- Fig. 5.30. Output power of
tion characteristics of CO chemical chemical laser on different
lasers are not very sensitive to many transitions with introduction
gas additives, and this relaxes the re- of NO additive
quirements for diluents, and expands
the range of both diluents and reagents such as those used for fuel of chemical
lasers. It is also typical that the total power drops rapidly in a multilevel
124
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cascade chemical laser with a reduction in the length of the cascade [Ref. 59]
as can be seen from Fig. 5.30.
�5.3. Flame Lasers
The Flame Model. Flame chemical lasers include devices in which induced radiation
is obtained with free combustion of the initial reagents in a flare. This gives
a continuous laser on a self-maintained flame. Such a self-maintained system is
an example of a purely chemical laser that does not require electric or other power
for support of the process except as for a system for feeding the reagents and
evacuating the combustion products, or for igniting the flare.
Ref. 60 considers two gases A and B that enter into a chemical reaction with each
other after they have been brought into contact in a common space. The reacting
mixture is in motion and has a total pressure of some hundreds of Pa. It is as-
sumed that one of the newly produced types of molecules is partly or completely
in the excited state. It is further assumed that there are two energy levels cor-
responding to the reaction
A B k'~ Cl .
k (5.29)
A-{-B >C.~-?-.. ,
where k, and kZ are specific r.ate con~tants of the second-order reaction, sub-
scripts 1 and 2 denote the lower and upper quantum state of C respectively. The
concentration of molecules in states 1 and 2(nl and .i2 respectively) is determined
by the radiating transitions characterized by lifetime z12. The influence of re-
laxation and damping processes is disregarded.
Approsimate solution of the rate equations leads to the following expression for
the steady-state population difference, incorporating the characteristic rat~ con-
stants for the different processes:
( n2-,i, 1 --~(fz-f,)--i"'----~ f tM-r~,ln(1 T"'-/1, (5.30)
\ r:o ~~X Tnt-{-Tp Tia L \ Tn
where n~ denotes identical initial concentrations of gases A and B; f~,a = ki,z~(hi 'f- h2);
i~, ~~?to ~hi -I- k2); iK is the time over which the difference n2 - nl reaches the
mar.imum value. Obviously, population inversion occurs only when k2~ kl. The pump-
ing conditions can be obtained by compari.ng the population difference with the
threshold conditions
na n, ~ ~Nvib (5.31)
where
- ~ ~ ~ t1~o
A vib- 8nc ~ Tia (0~ - (o ~Ref . 61 ] (5 . 32)
c is the speed of light, is the wave number of the Lransition between C1 and C2,
(1- r) and Z are determi.ned by the properties of the resonator of the chemical
laser. Thus the requirement for the relative reaction rate is defined by the ex-
pression
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fz-fi> ONvib Tn~l-jM + TP-~-T~t rl- Tp ln(1 11. (5.33)
nn tM Ti~ I. TM l ip lJ
If we assume that the parameters of the system are w= 2�103 cm-1, ~w/c~= 10'6,
1- r= 10-2, Z= 10 cm, T12= 10-2 s, np= 1016 cm~ ~ TM= lO-3 s, then Tp may vary
over a range of 10-2-10-4 s without causing great changes in pumping conditions,
i. e. the f2 - f 1 vary from 6� 10 2 to 9� 10 2. The reaction rate constants associated
with these values of Tp have values of 10-14-10'12 cm3/s, or 10~-109 (mole�s)-1.
To bring about conditions under which stimulated emission from a flame becomes possi-
ble, it is important to have detailed data on the magnitude of absorption for dif-
ferent states of the flame. An oxyacetylene flame was considered as the flame
quantum system in Ref. 69. It is well known that the reaction zone of this flame
emits in the visible and ultraviolet regions of the spectrum, part of this emission
being chemical rather than thermal [Ref. 62]. The studies were done on low-pressure
oxyacetylene flames burning at pressures of 0.1-2 kPa. Particular attention was
given to determination of the population of energy levels of such components as
C2 and CH. At a total pressure of 0.66 kPa, absorption bands (0-0) and (1-1) of
C2 were observed together with five bands of the (1-0) sequence. The lower limits
for the absorption coefficients were calculated:
(0--0), IO-~ CM-1; (1-1), 2� 10-4 ctit-~; (1-0), 2� 10-4 cnt-1;~
(2~1), 3� 10-4 cM-1; (3-2), 3� 10-; cM'1; (4-3), 2� 10-� cM-'~
(5-4), 1 � 10-4 cn~'1.
Observation of higher vibrational components, in particular of the (1-0) sequence,
showed a greater degree of vibrational excitation of the Xt3IIu state of C2 under the
selected conditions of the experiment. The same is implied by the distribution
of intensity in sequence (1-0) with observation of radiation from the A31Ig state.
Absor~-tio:. for CH is ohrainP~l ~n the region of 43~ nm. The effect is very slight,
and depends in large measure on the state of the flame. In Ref. ~3 an ekperl�?~ntai
determination was made of optical gain of a freely burning oxyacetylene flame in
the pressure range of 0.4-2 kPa, the lower pressure limtt being determined by the
conditions of flame cutoff, and the upper limit--by the conditions of reduction
in flare volume, increase of energy release and so on.
It was established by the measurements that amplification of radiation takes place
directly in the flame front in some optimum range of flare parameters. It was
shown that in the oxyacetylene flame an appreciable part of the CO is produced
in the nonthermal vibrationally excited state. This agrees with the results of
studies of the kinetics of the oxygen-acetylene reaction in Ref. 64-66. However,
in Ref. 63 lasing was not achieved in an oxyacetylene flame since not a single
transition had a gain greater than the losses in the cavity, equal to about 5%.
Obviously a more promising mixture is CS2/02, which was used for the first flame
chemical lasers [Ref. 67].
Examples of Realization of Flame Chemical Lasers. Side by side with the conditions
that are conducive to development of flame chemical lasers such as the presence
of a self-maintained process and the absence of a need for energy sources, there
126
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are also difficulties. These include the high flame temperature that reduces gain,
- and the fact that only a few of the large number of high-temperature chemical reac-
_ tions participate in the mechanism of pumping of upper energy levels.
Besides, the rates of propagation of fuel-oxygen flames are unusually slow--from
a few centimeters to several meters per second, and because of this there is a
limit for increasing the volumetric efficiency of flame chemical lasers. Nonetheless,
flame lasers are attractive for simplicity of construction, zero or small expendi-
tures of energy from an outside source, since branched chain reactions are realized
in the chemical laser itself. Such reactions maintain the equilibrium concentration ~
of intermediate active centers, making up their losses from the flame due to dif-
fusion and reactions that take place in the flame itself. The rates of these
branched chain reactions to a considerable extent determine the success of using
a specific system as a flame chemical laser. In making a flame laser, it is
usually desirable for the chain reactions to be as rapid as possible and to have
minimum activation energies.
The possible reactions in a CS2/OZ flame at low pressure [Ref. 67] are analogous
to (5.4)-(5.6), (5.24).
To achieve lasing, as has already been pointed out, a high temperature is undesira-
ble as this reduces amplification and is conducive to relaxation within the flame
itself. Since the degree of impact relaxation depends strongly on the rate of
flame propagation, whi.ch determines the time of interaction of molecules, and con-
sequently the number of collisions within the resonator of the chemical laser,
the most advantageous systems are those with rapid kinetics of all processes, which
in turn presupposes a high rate of. propagation.
to pump
To reduce the temperature and impact relaxation rate `
in the flame, it is desirable to work at lower pressures. ~
The results of er.periments with chemiluminescence at / 4
an overall pressure of 66-80 Pa in a CS2/OZ flame were 3
reported in Ref. 68, where it was assumed that inversion
exists on certain V-R transitions of C0. At higher pres-
sures [Ref. 69] it was Lound that in a freely burning 2 5
CS?/0?flame the amplif.ication on V-R transitions of CO i
in bands 8-7, 9-8, 10-9 amounts to about ~
two percent. - ~
Although the designs of flame chemical lasers differ in ~ -
details, they are basically quite similar. A general 1
design of such a chemical laser is shown in Fig. 5.31. H
Burner 1 is installed so that it can be moved vertically ~
in vacuum chamber 3 equipped for cooling 2. Above the CSZ O7
burner is a Eine-mesh screen 4. Cavity mirrors S are
placed in the direction of the optical axis passing Fig. 5.31. Diagram
tfir.ough the reaction zene. The position of the reaction of flame chemical
zone relative to the ar.is of the cavity is shifted by laser: 1--burners;
mec~tanism 6, enabling measurement of the gain at any 2--cooling; 3--evacu-
flame height. In Ref. 67 tlle burner was made in the ated chamber; 4--screen;
form of a row of parallel t~ibes. Each tube was 60 mm 5--mirrors; 6--burner
long and 6 mm in otitside diameter, and had 50 orifices shifting mechanism
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1 mm in diameter. Alternate tubes injected CS2 and 02. The dielectric mirrors of
the resonator had reflectivity of 99.2%. Emission was coupled out through a 0.5 mm
hole in one of the mirrors. Estimates gave total lo,:ses of no more than 3% in
the resonator. The output radiation was modulated by a frequency of. 150 H~ ancl
detected by an Au-Ge detector at 77 K. Measurements were made by a tunable ampli-
fier. A C02 electric-discharge laser was set up inside the cavity outside of the
flame zone. With this laser switched on, the cavity wa tuned and the amplifica-
tion was measured. A vacuum chamber 120 cm in diameter and 270 cm long was con-
nected to a vacuum pump with capacity of 9 m3/min. The flame was ignited by a
- glow dischargP located a few cm above the burners. Combustion continued indepen-~
dently after ignition.
At pressures below 266 Pa, the blue luminescence of the flame was diffuse and homo-
geneous. As the 02 pressure was increased while holding the CS2 gressure constant,
beginning at a ratio of pCSz~POz= 0.5, the flame broke up into several hundred
tongues uniform]_y distributed in the upper part of the burners. To achieve appre-
ciable amplification, the boundaries of the flame had to be raised somewhat, which
was accomplished by further increasing the OZ pressure. Lasing occurred at pres-
sures of 02 of 1.2 kPa and CS2 of 80 Pa, the flame being inhomogeneous with signs
of some spatial instability. Lasing was interrupted with a slight change in CS2
pressure by about 13 Pa.
The emission spectrum was determined by a monochromator. Continuous lasing in
Ref. 67 was observed on three transitions of CO with wavelengths of 5.216, 5.297
and 5.421 um. The measured total output power of stimulated emission was 1 mW.
The initial components in flame chemical lasers of the type shown in Fig. 5.31
are mixed either directly in the reaction vessel or in a special mixer installed
at the inlet of gases to the burner or in a feed line.
In Ref. 70, nitrous oxide N20 was added to the reaction mixture of CS2/OZ in the
- flame laser to increase the gain. Different versions of premixing of the components
were used: either two of them N20/02, or all three components CS2/02/N20. In
the case of separate delivery of the N20/02 mixture and carbon disulfide, the power
of coherent radiation was approximately half the level for delivery of the three-
component mixture, which is due to inadequate mixing in the reaction region of
the resonator cavity.
_ ~ 1,00 +
~~N20/011/7
~ 0,75 ~~,~v5 Fig. 5.32. Power W of stimulated
+
ri ~ emission as a function of pressure
~ 0,50 ~l ~ l~~ in the evacuated chamber
3 75 ~
~ ~
0 2 ~
p, kPa
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Investigations of the optimum conditions of operation of chemical lasers based
on CS2/N20/02 mixture with respect to pressures and the relati.ve content of com-
ponents o� the reaction mixture have shown that these conditions are similar for
a mixture prepared beforehand and held in the mixer for 3-4 hours and for a mixture
freshly prepared by mixing the streams in the mixer at the inlet to the burner.
_ For the latter case, Fig. 5.32 shows typical dependences of the power of stimulated
emission on the pressure of the mixture in the evacuated chamber. Power maxima
lie in a range of 2-2.66 kPa. The reduction of emission power in regions of lower
and higher pressures relative to the maximum can be attributed respectively to
a reduction in the density of inverse population in the cavity, and an increase
in the rates of relaxation processes that equalize the nonequilibrium distribution
with respect to vibrational levels of the CO molecules. The dependence of lasing
power on the composition of the mixture is characterized by curves with maxima
in the region satisfying the ratio
=-1.10-0.13 (5.34)
~N, t~/u,
There is also an optimum ratio with respect to CSZ concentration.
CO chemical lasers typically operate with small ad-
ditives of N20 (Fig. 5.33). As N20 is added to the o
cnixture, the radiation power increases sharply as 1~~~ o0
~
compared with that in the state cN2p = 0 even at a
ratio cN20~~02/N20 = 1/240, and the power rises nearly ~ 0,75
linearly upon a further increase in this ratio. The �
abrupt change in lasing power at low relative concen- r' 050-
~ ~
trations of N20, in the opinion of the authors of
Ref. 70, cannot be explained by the peculiarities 3 0,25
of the mechanism of vibrational exchange of energy
[see, for example, Ref. 69]. At such low N20 concen-
trations as (3-S) � 101 5 cm-3 the main contribution ~0,001 q01 0,1 1,0
to vibrational relaxation of CO molecules with con-
centration of the order of 1016 cm-3 is from CO-CO ~NZO/~oZir+Zo
collisions in which the probability of exchange of Fig. 5.33. Power of stimu-
vibrational energy is two to four times as high lated emission as a function
as in CO-N~0 collisions. It is assumed in Ref. 70 of. the relative concentra-
that the abrupt increase in radiation power with tion of N20
small additives of N?0 ~s due to dissociation of
these molecules in the zone of a flame with temperature of the o~der of 1200 K.
Actually, calculation of the equilibrium constant for
Nz0 t' N2 I- 0 (5.35)
at nN p of 3(1015-1017) cm 3 gives nearly complete dissociation of N20 molecules
at 10~0-1200 K. An increase in no intensifies the process of formation of CO*
iu the course of the reaction
CS 0-} CO* S (5 . 36)
and consequently incr.eases the power of stimulated emission.
129
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Use of a burner with spacing between injection orifices
for fuel and oxygen equal to 1.3 mm with special screens
provided rapid mixing of gases on its surface [Ref. 71]. ~ 30
A burner of this kind was used in the investigation �
of working characteristics of a flame laser on CS2/02 ~ 20
and of the way that these characteristics are influenced ~
by additives of He, SF6, N20, C0, C02, N2, SOZ and N02. ~ o
The resultant dependence of power on CS2 flowrate is ~ a0 000
shown in Fig. 5.34. Maximum radiation power of 0.6 W ~
was attained in operation of a chemical laser on a ~ ~
mixture of CS2/02/N20 with corresponding molar flow-
1 2 ~ 4
rates of 3, 9, 110 and 7.6 mmole/s.
G~S2, mmole/s
Considerably higher output radiation powers of f lame
chemical lasers were obtai.ned in Ref. 72-74--of the Fig. 5.34. Dependence of
order c~f 10-25 W with specific energy of 13 J/g and power of a flame laser on
chemical efficiency of 2.5%. Powers measured in the CSZ flowrate. Distance
tens of watts have also been attained in systems with of optical cavity from
predissociation of the reagents, and estimates have burner l.l cm
been made of the param~ters and working conditions
of plasma chemical lasers in the kilowatt range [Ref. 75].
�5.4. Subsonic Lasers Based on Metal Vapor
When Ba, Ca and Mg are burned in mixtures of N20/He/C02, amplification of emission
- is observed on the transition 00�1-10�0 of C02. On this same transition in Ref.
76, continuous lasing was achieved upon ignition of Mg vapor in a mixture of N20/C02.
Pumping was by the fast exothermic reaction
- ]~4g -I- NZO Mg0 -I- NZ, (5.37)
during which Mg0 molecules are formed in state B1E.
B,~ 1998~~~M.~ Among the various possible schemes of energy transfer
from reaction products to C02 molecules, the most proba-
8'E ~~~--008 ble is the transfer of energy of excited electronic
~ states of the Mg0 molecule t~ vibrational levels of
I
I the ground electronic state of the C02 molecule (E-V
Q51~m~ transfer). Such a process can take two paths: di-
~ rectly from levels B1E and b3E to high vibrational
A'~ 6~o~M.,l \ I levels of C02 , or af ter decay of the excited B1 E state
aJn j~ 2349tn 0006um of Mg0 to state AlII (3563 cm-1) and subsequent popu-
~00 ' lation due to internal conversion of inetastable level
x'E 000 Q3I[ (2610 cm 1)--to level 00�1 of C02 (2349 cm-1).
ngo ~oT Both possible schemes are shown in Fig. 5.35.
E-state V�state
Fig. 5.35. States of Mg0 V-V transfer of energy from Mg0 and N2 to C02 is improba-
and CO? with possible E-V ble sinie the vibrational levels of Mg0 are about
transitions 760 cm- apart [Ref. 77] and do not coincide with C02
levels, and the N2 molecule formed in the reaction
130
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rtg+N20 is practically une~:cited. Formerly E-V quenching of excited electronic
states has been observed in mixtures of Na, Rb, Cs and Hg with H2, and Na with
N2 [Ref. 78, 79].
The results of ineasurement of the gain in flames show that a more probable process
of E-V transfer is a transition between high levels since the addition of nitrogen
increas~d the gain on transition 00�1-10�0 [Ref. 76]. If excitation had been trans-
ferred directly to the upper level, the addition of nitrogen would have meant that
a part of. the energy woul.d go to level v= 1 of NZ, and the population of level
00�1 should have been reduced. On the other hand, if 1eve1 00�1 is populated as
a result of V-V relaxation of upper vibrational levels, then all the energy that
goes to vibrational levels of nitrogen should in the final analysis reach level
00�1 of C02. Consequeni.ly an increase in nitrogen content in this case cannot
reduce the gain.
8 3
Ne N20/C02 ~ N20~CU2 He
{ l ~ ~ ~ _ _
~ ` ' ' 6
r------t r------i ~
5 ~______J L______J
~ ~ ~ ~
- M9 \ ~ ~ M9 -
~ " \ ;
~ 4 \ ^
2 ~ ~ ~ ~
He Ne
Fig. 5.36. Diagram of inetal-vapor flame chemical laser: 1--heaters; 2--crucibles;
3--working tubes; 4--injectors; 5--flat mirror; 6--concave mirror; 7--bellows; 8--
evacuation channel
The construction of a subsonic chemica.l laser based on metal vapor is shown in
Fig. 5.36, and in many ways is similar to those used in Ref. 35, 80.
Heating of inetallic magnesitun in aluminum crucibles 2(2.5 cm deep, 2.5 cm inside
diameter) by ttingsten heaters 1 produces Mg vapor that is carried by a stream of
He into tube 3. A mixture of C02/N20 is introduced into the Mg/He stream through
radial.ly pl.aced injectors 4 at the inlet to the active region. Additional low-
intensity streams of helium are introduced into tube 3 close to mirrors 5 and 6
to prevent the reaction products from reaching them. The reaction itself takes
place inside stainless steel bellows 7(inside diameter ]..9 cm, length 7.6 cm).
Two such units are connected into a single channel with common exhaust 8.
The cavity is formed by a flat op~.ique mirror 5 on a silicon substrate, and a con-
cave ~iirror 6 with r.eflectivity of 98% on a germanium substrate (dielectric mirrors
were used). The mi.rrors were 12.7 mm in diameter and separated by a distance of
65 cm. The pasition of the mirrors was stabil.ized by three Invar rods. Coarse
131
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and fine adjustment of the cavity was provided by gas-discharge excitation of lasing
on COZ and Nz0 respectively in this same tube 3.
'~he crucibles usually held 1.5 g of Mg each, which was vaporized within 3 minutes
at a heater power of 300 W. About 50% of the resultant Mg vapor reached the ac-
tive region (the rest condensed on the walls), and uniform blue-green chemilumi-
nescence filling the entire cross section of tube 3 arose close to injectors 4.
Chemiluminescence in the vicinity of ~0.5 um corresponding to transition of Mg0
from state B1E to the ground state exists over a length of ~l cm at a flowrate
of 1400 cm/s, and consequently the time of mixing of the gas mixture was ~l ms.
The bellows within which chemiluminescence takes place are practically unheated.
Maximum power of stimulated emission was S mW, and was reached under the same con-
ditions where gain was maximum in the absence of mirrors (~10-2 cm 1). The maximum
was observed at a total pressure in the tube of ~1.33 kPa and with proportions
of the partial flowrates of gases of He/N2/N20/C02/Mg = 50/15/15/15/5.
In Ref. 76 it is noted that many effects that determine the operation of the de-
scribed chemical laser are still unexplained. For example the rate of deactivation
of excited molecules of COZ and N2 by atoms of alkali metals is f airly low, and
therefore the only channel of losses in the tube is extraction of radiation through
the output mirror. The radiation power should be 0.5 W/cm3, which corresponds
to a yield of one photon on a wavelength of 10.6 um for every Mg atom that enters
the active region. However, considerably weaker lasing is observed in the experi-
ment, which may be a consequence of either resonant absorption of radiation by
the thermalized reaction products, or the presence of additional intracavity losses
due to scattering of radiation by Mg particles of 1 um size produced when it evap-
orates. E-V quenching of luminescence of atoms and molecules that are the products
of exothermic chemical reactions determines lasing parameters in other gas mixtures
as well. For example, in an N20/CO/Na flame the vibrational levels of CO that
are resonant with respect to electronic state 3p of the Na atom are nonequilibrium-
populated [Ref. 81]; in flash photolysis of mixtures of C02/N20, C02 lasing is
observed that is most likely excited by energy transfer from high electronic levels
of the NO molecule that is one of the products of photolysis [Ref. 82].
The investigation of chemical lasers excited by E-V transfer is of great interest
since it enables us to find molecules such as Mg0 that are formed in the course
of exothermic reactions and store energy on metastable electronic levels. Mole-
cules of this type are the basis for chemical lasers that emit in the visible re-
gion of the spectrum. Some problems that are associated with design and develop-
ment of chemical lasers that radiate in the visible range on electronic transitions,
in particular in the process of the gas-phase reaction Ba + N20-~BaO* + N2 and others
are examined in survey articles 83 and 84. Ref. 31, 85 deal with processes in
flame chemical lasers with periodically repeated pulses.
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1.32
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136
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_ 64. Clough, P. N., Schwartz, S. E., Thrush, B. A., "Infrared Chemiluminescence
From ~arbon Monoxide in the Reactions of Atomic Oxygen with Acetylene and
Carbon Sul~oxide", PROC. ROY. SOC., Vol 317A, 1970, pp 575-586.
65. Greek, D. :I., Melliar-Smith, C. M., Jonathan, H., "Infrared Emission From
the Reaction of Atomic Oxygen With Acetylene", J. CHEM. SOC., Vol 1970A, 1970,
pp 646-651.
66. Gutman, D., Matsuda, S., "Shock-Tube Study of the Acetylene-Oxygen Reaction.
I. CH (A2~-~XZII) Chemiluminescence and CO Production During the Induction
Period", J. CHEM. PHYS., Vol 52, 1970, pp 4122-4132.
67. Pilloff, H. S., Searles, S. K., Djeu, N., "CG1 CO Laser From the CS2-02 Flame",
APPL. PHYS. LETT., Vol 19, No l, 1971, pp 9-11.
68. Foster, K. D., Kimbell, G. H., "Vibrational Population Inversion of CO in
a Free-Burning CS2/02 Flame", J. CHEM. PHYS., Vol 53, No 6, 1970, pp 2539-2541.
69. Suart, R. G., Arnold, S. J., Kimbell, G. H., "Power Enhancement of a CO Chemi-
cal Laser by the Action of Vibrationally Cool Gases", CHEM. PHYS. LETT., Vol 7,
No 3, 1970, pp 337-340.
70. Dudkin, V. A., Librovich, V. B., Rukhin V. B., "Investigation of a Chemical
CO Laser Based on a Carbon Disulfide Flame" in: "Khimicheskaya fizika protsessov
goreniya i vzryva. Kinetika khimicheskikh reaktsiy" [Chemical Physics of
Processes of Combustion and Explosion. Kinetics of Chemical Reactions], Cherno-
golovka, Institute of Chemical Physics, USSR Academy of Sciences, 1977, pp 13-16.
71. Searles, S. K., Djeu, "Characteristics of a CW CO Laser Resulting from a
CS2-02 Additive Flame", CHEM. PHYS. LETT., Vol 12, No l, 1971, pp 53-56.
72. Linevsky, M. J., Carabetta, R. A., "Continuous-Wave (CW) Laser Power From
Carbon Disulfide Flames", APPL. PHYS. LETT., Vol 22, No 6, 1973, pp 288-291.
73. Foster, K. D., Kimbell, G. H., Snelling, D. R., "Near Single-Line Operation
of a Free-Burning CSZ/02/NZO Flame Laser With a Nondispersive Optical Cavity",
IEEE J. QUANT. ELECTRON., Vol QE-11, No 6, 1975, pp 253-258.
74. Solimeno, S., "Chemical Lasers", PHYS. BULL., Nov, 1974, pp 517-520.
75. Jeffers, W. Q., Ageno, H. Y., Wiswall, C. E., "CO Chain Reaction Chemical
Laser. I. Experimental", J. APPL. PHYS., Vol 47, No 6, 1976, pp 2509-2510.
76. Bernard, D. J., "CW Chemical Transfer C02 Laser", APPL. PHYS. LETT., Vol 26P
No 10, 1975, pp 542-~44.
77. Schamps, J., Lefebvre-Brion, H., "Vibrational Relaxation of N2 and C02(001)
by Alkali Metal Atoms", J. CHEM. PHYS., Vol 61, No 5, 1974, pp 1652-1657.
78. Lee, P. H. et al., "Direct Observation of Vibrationally Excited Hydrogen Pro-
duced by Collisional Energy Transfer I'rom Electronically Excited Sodium, Ru-
bidium, Cesium and Mercury", J. PHOTOCHEM., Vol 2, No 2, 1973, pp 165-172.
137
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79. Krause, H. E., Fricke, J., Fite, M. L., "Excitation of Na D-Line Radiation
in Collisions of Sodium Atoms With Internally Excited H2, DZ and N2", J. CHEM.
PHYS., Vol 56, No 9, 1972, pp 4593-4605.
80. Benard, D. J., Benson, R. C., Walker, R. E., "N20 Pure Chemical CW Flame Laser",
APPL. PHYS. LETT., Vol 23, No 2, 1973, pp 82-84.
81. Walker, R. E. et al., "Vibrational Disequilibrium in a Low-Pressure Sodium
Catalyzed Carbon Monoxide Nitrous Oxide Flame", CHEM. PHYS. LETT., Vol 20,
1973, pp 528-s33.
82. Lin, M. C., "Photoexcitation and Photodissociation Lasers. Part I. Nitric
Oxide Laser Emissions Resulting from C(2T[) A(2E+) and D(2E+) A(2E+) Tran-
sitions", IEEE J. QUANT. ELECTRON., Vol QE-10, No 6, 1974, pp 516-521.
83. Jones, C. R., Broida, H. P., "Chemical Lasers in the Visible", LASER FOCUS,
Vol 10, No 3, 1974, pp 37-47.
84. Benard, D. J., "Sensing Chemically Excited Metastable Populations by C02 Laser
Gain Measurements" in: "Electron Transit Lasers", Cambridge Massachusetts,
London, MIT Press, 1976, pp 60-67.
85. Limpaecher, R., Woodroffe, J. A., "Flameout in Repetitively Pulsed Chemical
Lasers", AIAA JOURN., Vol 15, No 11, 1977, pp 1612-1616.
CHAPTER 6: SUPERSONIC CHEMICAL LASERS
�6.1. Diffusion Chemical Lasers With Thermal Initiation of the Reaction
Working Principles and Design Diagrams of Supersonic Chemical Lasers. Feasibility
studies were done in Ref. 1-10 on achieving inverse population in gases by thermal
methods of excitation: rapid heating or rapid adiabatic cooling. In particular,
it was shown in Ref. 6-10 that a high-velocity flow of a two-component gas mixture
in a Laval nozzle can be used to get inverse population of molecules for operation
of a cw laser in the infrared range. If the components used in the mixture are
capable of chemical reaction, then gas dynamics, chemical reaction and optical
radiation, and convective transfer as well when the components are preseparated,
can convert the energy of the chemical reaction to energy of excitation of molecules.
In supersonic flows, it is possible to bring about conditions for the most efficient
conversion of the energy of the chemical bond to energy of coherent induced radia-
tion with fairly high rates of transfer of components into the reaction zone and
with weak reverse diffusion out of the reactive zone and low collisional deactiva-
tion in the active medium for the time preceding stimulated emission. The produc-
tion of such f_lows in turn requires high-temperature heating of the gas mixture,
which can be utilized at the same time for dissociation of the medium into chemi-
cally active centers, i. e. for thermal initiation of a reaction in supersonic
chemical lasers.
Here as well, just as in the case of subsonic chemical lasers, the chemical reaction
can also be initiated by the process of combustion, electric discharge, such as a
- 138
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microwave induction discharge, or shock-ti~ave initiation. The design peculiarities
oE the chemical laser determine which methods ot initiatingthe chemical reaction
will be used in processes that take place in supersonic chemical lasers.
The working principle of a supersonic diffusion chemical laser with thermal initi-
ation of the chemical reaction is based on sequential realization of the following
processes:
heating of the heat-transfer fluid to a temperature that ensures the required degree
of dissociation of the chemical reagent;
mixing of the chemical reagent with the heat-transfer fluid, and dissociation of
this reagent into chemically active centers in the mixing process;
acceleration of the mixture of heat-transfer fluid and chemically active centers
to supersonic velocity;
injection and diffusion of fuel molecules into the supersonic mixture flow that
enter into a pumping reaction with the chemically active centers that are in the
flow;
excitation in a downstream resonator of the process of stimulated emission by the
active molecules formed in the pumping process.
Fi . 6.1. Dia ram of 10 ~
~ K
supersonic chemical laser \ .i r
with thermal initiation
of the reaction: a-- g
laser construction; b-- Hp(Dp)
element of nozzle array $Fs(FZ) ~
and flow scheme; 1--elec- N7(HE) Np(H21
tric discharge chamber; ~ _
2--cathode; 3--anode; 4-- y 5\ g ~
inl.et for heat-transfer i I _
gas; S--auxiliary coolant I
injector; 6--secondary 2 +
chamber; 7--expansion \ - + ~
head; 8--injector of chemi- ~ ~ -
ca1 reagent (oxidant); 9-- I
supersonic nozzle module; 3 6 I
- 10--semitransparent or a
apertur.ed mirror for ex- ~ -
traction of radiation; 9
11--opaque mirror; 12-- HZ(D2) 7
fuel injector
/ ~ p+F ~-HF'`+ N f1= ~
N (Ne)~ F / S ~
~
H2(Dy)
b
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These processes are realized for example in the supersonic diffusion chemical laser
design shown schematically in Fig. 6.1 [Ref. 11-13]. In this cw laser with thermal
initiation of the reaction, N2 or He is heated by an electric arc and then mixed
with SF6 producing dissociation that results in F atoms in expansion head 7 accord-
ing to reaction (S. 1) .
Inversion is produced when H2 or D2 diffuse into the supersonic flow containing
F atoms. As it passes through the nozzle array, the gas is accelerated to supersonic
velocities, and H2 is injected into this stream. In analogy to process (5.1) as
a result of the pumping reaction
F-}- i-i2 HF (v) -I- H(-134 kJ/mole , a C 3) (6.1)
vibrationally excited HF is formed. The HF molecules approach the state of thermo-
dynamic equilibrium thanks to induced radiation and processes of collisional de-
activation. The latter can be written in the form
N i' (v) M--~ I-1 F(v 1) M; ( 6. 2)
~-li' (v) M (u') HF (a - 1) M (u' 1), (6.3)
where (6.2) and (6.3) are respectively V-T and V-V collisions. Gasdynamic and
energy parameters obtained in chemical lasers [Ref. 12, 13] are summarized in Table
6.1. (Hereafter the subscript "0" denotes gas parameters in an electric discharge
chamber, while subscript "j" denotes gas parameters at the outlet from the nozzle
module.)
TABLE 1.6
Example of the gasdynamic and energy parameters of a
supersonic diffusion chemical laser
- ,
Conditions i.n ~rechambe~ -
mgp~ W. I ~F nz~%
g T.. K (PF/P1� GF~ G~
g~ watts mole/s sFe
0,105 90 4150 0,014 0,00431 1,00 15,8
0,203 167 3970 0,0267 0,90833 1,00 15,2
0,297 236 3870 0,0387 0,0122 1,00 14,7
0,400 293 3660 0,0513 0,0164 I,00 13,5
0,505 357 3510 0,(~i39 0,0`l07 1,00 13,1
0,600 415 34(~ 0,075 0,0296 I,00 12,8
0,800 514 3200 0,0976 0,0328 1,00 11,9
1,00 586 2920 0,116 0,0396~ 0,96 11,2
1,25 648 2680 0,~35 0,0473 0,9'l 10,4
1,40 692 2580 0,145 0,0515 0,90 10,2
1,60 722. 2480 0,153 0,0548 0,83 10,0
1,80 738 2400 0,155 0,0555 0,75 10,1
2,Q0 732 23G0 O,15G 0,056U ~1,G8 9,9
2,20 710 2320 0,157 0,0564 U,62 9,7
Constant conditions were: rifi12= 8.5 g/s, mH2 = 1.0 g/s, po= 0.166 MPa, beam power
42.5 kW, Mach number rij = 4.4,
~ T~ ~,205 To; p~ = 3,92 � 10-:' p~; u~ = 2,03 �]0'x
x (To/2500)'/a m/s; (~f)~ = 1,55 � 10-' � (pr~p)o ~25~~17~0) mole/cm3 .
140
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;,~r. tu get eFficient cur,.v~rsion of the energy of the cher~ic~al hc;~~d ~.o "
';~_rcnt i.nduced emissi.on it i.s necessary that the rate at whic~l~ El? di�`~,::.
;;~t. :law, and the ra.tc: ~~f ~;urnping reaction (6.1) must Ue greater. t~l-:t11 t.l;~
~_;,l.l~.sic;~al deacr i.~,~:t: i~~zi ~6.2) ,(6.3) . These rates can Ue estim,~t
*
N2 drX~ ~ H F
- ~ . . . x
h ~
HZ ,.~..,T, r
~ - '2
~ . / H ~ � 3
f ~ ~
N2, ~ S ~ L ~ .;r-:.,,.. ~
. , � !
~/...i./ ~~z � - - . . .
. 5 6
, `,.j
~
/
~1 ~ ~
r i.~ . G.2. The process of sup~~rsonic diffusion of fuel: 1--supersonic nozz~.es:
_ ~nulated emission; 3---f~ydrogen--filled space; 4--region of mutual d3.ffu~ i~~--.
c.~~~onents; 5---shock waves foz-~ed by the chemical reaction; 6--shock wavr~:=
flected from the walls
~.~u: ~~SCiltlilg ttie flow in the Fi2. di.fft~sion region as shown in Fig. 6.2, wtiere 1;-.,'
t_a::~ u.:undary of tile d5.ffusi~~n region in the y-direction. For laminar. flo~a :
. - . rel.ation
i~ lt~(Uxlu~)'~2,
:i.s :a constant ni tl~e order. of unity. When H2 diffuses into Id2.
r~ i~.~ ~ tc,-~ ~;~2 r~' m/S c~~~,~
i:_, in K, p~ is in P~) . Let ~ be the hal.f-width of the flow (see Fi.g. 5`~, ~
i~ 'a ~'~e charact~risti.c di_ffusion j.pngtti x=LD will correspond to 8=hy~ Z a..s:~
~ ~`x~~i;i equa~:.i.ons (6.4,1 ,(6.5) , e~pressing u~ in terms of thP Mach numt~~:r. '
T~ n~~ ~t It/2 Itl 1' 7~p 10~ G~'
~'nl~~ ( :?9 ,r C ? / 7.5(1Q ( ) ~~u~ I /2 ~D Ml~
~ is molar ID~1SS.
~:e reagents are mi:ced at x= 0, the rate of initial development ~f ProcF.:;~. ,
be represented as
uf(dc~:/ri.ti?r-o __(~~J~Er,~F)r~o. (.-.7.
..;~ar _~cteristic ].engch of the reaction along the flow is determined by th~
1 . .1
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c~;
1'R - dCFI~x IX_o� (6.8)
J
Here LR is the longitudinal distance that must be covered by the flow for a11 F
atoms to be reacted if the overall reaction rate remains at the original level.
If we use a local partial pressure of atoms of F equal to pg = 8�106 cFT, then we
get from (6.7) and (6.8)
� 1,4 ~/2 ~tt, _5,0 Pp Tj~2
C 28 y) [ cF M 10a LR ~ k1 ' (6 . 9)
- The first member includes parameters that characterize the operating conditions
of the supersonic diffusion chemical laser, and the second member of (6.9) is the
function T~, where
/z~ = 12,0 � 10'~ exp [-1710/(1,987 T~)1. (6.10)
The relations LD = fl(M~) and LR = f2(Tj) are used to evaluate LD and LR in order
of magnitude, assuming that kf/kb~lfor typical operating conditions of the super-
sonic diffusion chemical laser. If in this event LD/LR~1, then it can be assumed
that H2 has been completely diffused into the flow at x= 0, and the reaction zone
should be treated as in a one-dimensional flow. On the other hand, if LD/LR~1,
the reaction zone is due to diffusion mixing. For typical working conditions of
a supersonic diffusion chemical laser with the parameters indicated in Table 6.1,
when T~ = 500 K, Mj = 4.4, it follows [Ref . 12] that LD ~ 4 cm and LR p 0.4 cm. This
means that the reaction zone is determined by supersonic diffusion of components.
The component mixing pattern depends on the nozzle
module design that is used. Fig. 6.3 shows some
of the most widely used nozzle configurations.
Ref. 14 points out the advantages of nozzle blocks ~
of axisymmetric matrices over slit injectors due
to ease of manufacture, better initial mixing a
characteristics and small size of the nozzle at b
the outlet (2-3 mm).
Of greatest interest is the investigation of such
parameters of the supersonic diffusion chemical
laser as power W and chemical efficiency rlX. A
study was done in Ref. 12 on the way that these
parameters are affected by changes in flowrates r
of the components of the working mixture and the
distance x~ of the optical axis of the cavity from
the outlet tip of the nozzle, as well as by various ~
gas additives.
Fig. 6.3. Nozzle designs:
Fig. 4 shows how the chemical efficiency and power a--with perforated tubes;
of stimulated emission of an HF supersonic diffusion b--with slit feed; c--with
chemical laser depend on mass flowrate mgg6 at annular feed of the component
constant flowrates of NZ and H2 and fixed flow
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~x,% W,kW parameters. Power was measured in a cavity with
W opaque mirrors at x~= 1.9 cm, radius of curva-
15 ~X 0,8 ture of the mirrors was 1.15 m, distance between
mirrors was 1 m. The chemical efficiency of
� 0,6 ~he supersonic diffusion chemical laser was de-
termined from the relation
~ W (kW)
~~4 nX 133GF (mole/s) ' 100. (6.11)
5 Equation (6.11) is the ratio of the actual lasing
Q,2 power to the power that is theoretically attaina-
ble on the basis of reaction (6.:). Chemical
~ ~ efficiency decreases from 16 to 8-10% at maximum
power. The shaded region in Fig. 6.4 corresponds
0 0,5 1,0 1,5 mSFs' g~s to the spread of data on chemical efficiency
obtained as a result of a large number of experi-
Fig. 6.4. Chemical efficiency ments. This scatter is due to errors in evalua-
and lasing power as dependent tion of Gg associated with determination of the
on mass flowrate of SF6 at con- concentration of SF6, and errors in determination
stant mass flowrates mN = 8,5 of the electrical energy transferred to the gas
2 by the arc. At low SF6 flowrates, such errors
g/s and mg2= 1.0 g/s are lower since under these conditions the SF6
is almost completely dissociated, and the flowrate Gr corresponds to the flowrate
of. SF6. A reduction in chemical effieicncy with increasing Gg may be due to an
increase in HF-HF collisional deactivation.
Lasing power increases with an increase in SF6 flowrate, and reaches a maximum
at mSF6= 1.8 g/s. The maximum is due to a lowering of chemical efficiency and
a reduction in the dissociation of SF6 (Gg/6GSF�) at large SF6 flowrates. At maxi-
mum power the flowrate of H2 is nine times as high as the stoichiometric value
required for reaction (6.1), i. e. GH2/Gg = 9. A reduction in the flowrate of H2
reduces the lasing power due to a corresponding reduction in the rate of diffusion
of HZ into the supersonic flow.
The parameters of the supersonic diffusion chemical laser can also be optimized
by changing the materials of the heat-transfer fluid and additives, and their flow-
rates. Since SF6 is incompletely dissociated even when lasing power is maximized,
the power can be increased by additional injection of oxygen into the high-pressure
chamber. For example at T~~ 2000 K, po~ 0.1 MPa, another source of fluorine atoms
in addition to (6.1) could be the reaction
sr-, 02 so2r, -f- 2r. (6.12)
- In Ref. 15, in addition to investigating the effect of 02 additives, the authors
studied the change in parameters of an HF supersonic diffusion chemical laser when
He was substituted for N2 as the heat-transfer agent. The data found at x~ = 1.9 cm
(see Fig. 6.4) are compared in Fig. 6.5 with other conditions of operation of the
HF supersonic diffusion chemical laser. The comparison shows that adding a small
amount of oxygen to the heat-transfer agent increases power emission by 20-30%.
Probably this is due to the effect of reaction (6.12). A supersonic diffusion
chemical laser with helium as the heat-transfer fluid has higher parameters than
143
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when nitrogen is used. Typically, the use of helium
makes the emission powers nearly identical in HF fiX~~�
and DF supersonic diffusion chemical laser, whereas ~ W
when nitrogen is used as the heat-transfer fluid, 20 x~ 1~6
the maximum power of the DF laser is only 70% com- ~
pared with that of the HF laser [Ref. 15]. f5 ~ ~ 1,2
~
As has already been pointed out, the characteristics f0 j 0,8
of flow chemical lasers are determined by competing ~~~~2
processes: formation of excited molecules, inter- 5/ 3 0~4
diffusion of two flows with reagents such as H2 ~
- and F, and deactivation of the excited molecules by ~
collisional processes. It can be assumed that 0 ~ 2 3 mSFs,g/s
the process of formation of HF* is fast compared
with the other two. If the diffusion time is less Fig. 6.5. Lasing power
than the deactivation time, chemical and quantum- and chemical efficiency
mechanical processes must be controlled by the as functions of the mass
deactivatio:~ process, and the processes in the flowrate of SF6
chemical laser are not dependent on mixing. In
the case *ahere the deactivation time is less than a`~i'
or comparable with the diffusion time, the quantum- Mixture m, g/s ~ Ref.
mechanical effect of stimulated emission decreases
owing to absorption during the time preciding total ~-Ie~H,~~' 2,06/ J [14)
expenditure of the reagents. 1,25/0,75
Na/N9/O~ 8,5/1,0/ 2 [12,15]
Parameters of a transverse-flow chemical laser b,4
with microwave initiation of the reaction increase As in Fi~. 6.4 8 [14]
considerably in an accelerated flow. Fig. 6.6 shows an improvement in a fromer
subsonic design made in Ref. 16. Zone A between the micruwave discharge region
and the H2 injectors contains a mixture of fluorine atoms, inert gas and products
of SF6 dissociation. Hydrogen accelerated at the nozzle inlet in zone B diffuses
quite rapidly into rhe fluorine jet. A homogeneous mixture of flu~rine and molecu-
lar hydrogen is formed. Formation of HF(v) occurs in zone C by reaction (6.1).
Stimulated emission is coupled out of the cavity with distance of 40 cm between
mirrors.
8
~ H2 C H2
A \ F / ~ -
. ~
18� . H? /A C
a b
Fig. 6.6. Diagram of working chamber (a) and gas inlet (b)
in HF diffusion chemical laser
In such a chemical laser, the power W ~f stimulated emission increases linearly
with an increase in the ionization potentials of the inert gas additives. The
higtier their ionization potential, the higher will be the average electron energy,
and hence the greater the dissociation of SF6 at inelastic electron collisions
in accordance with
144
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~I'� I ~ ? ~('i~ ~I (G ~ i) f' 2e (i 1, 6). (6.13)
In Ref. 17, this increase in W is attributed to a mechanism of electron-impact
dissociation of SF6 according to which as many as three fluorine atoms are produ~ed
from a single electron with kinetic energy close to the ionization potential of
He, while only one fluorine atoms is formed from a single electron with kinetic
energy close to the ionization potential of Ar. On the other hand, there is a
linear relation between W and the injected microwave power. The strong dep~ndence
of W on additives of inert gases and the weak dependence on 02 additive shows that
the dissociation of SF6 with formation of chemically active centers--F atoms--
- takes place due to electronic collisions. On the other hand, atoms with a meta-
stable state cannot contribute to dissociation when Kr and Ar are used, and their
contribution is small in He.
The efficiency of chemical lasers increases considerably in the case of repeated
use of chemically active centers such as oxygen atoms as a result of a chain reac-
tion comprising (5.4) and (5.6):
O CS-rC0* S, (6 .14)
S Oa-~SO U. }
Here CS is the fuel, 0 and S are the active centers.
The efficiency of repeated utilization of each atom in a fuel-oxidant mixture is
measured by the average length of the chain
Z * = Gend~Gbeg. (6.15)
CO 0
Here G~$d is the flowrate of CO at the outlet of the cavity, G~eg is the flowrate
of the oxygen atoms that initiate the reaction. In essence, Z* is the average
number of cycles of the pumping reaction with participation of an oxygen atom until
it is lost in some quenching reaction such as 0+ OCS->CO + S0.
6 B
9 N e 2 3~ 5 7~~
~ :
. g
CS/CS?/Ne i
-r
.
.
0/01/He r_~
rig. 6.7. Diagram of CO diffusion chemical laser: 1--electric heater; 2--super-
- sonic nozzle module; 3--supersonic diffuser; 4--annular in~ector; 5--transition
section; 6--resonator; 7--rows of orifices; 8--tubing; 9--mass spectrometer
Chain reaction (6.14) is real.ized in the experimental facility shown in Fig. 6.7.
A stream of C52 flows through electric heater 1 in which the CS2 molecules are
145
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thermally dissociatecl into CS and S. Heating temperature is about 2400�C. The
flowrate of CS reaches 1 mmole/s, and the ratio of molar concentrations of CS and
CSZ at the heater outlet is 2.2. The temperature of the gas flow is reduced and
the pressure is increased by injecting helium into the hot CS/CS2 gas through super-
sonic nozzle 2, and passing the resultant mixture through supersonic diffuser 3.
At the output of the diffuser is annular injector 4 that enables homogeneous intro-
duction of various dopants into the flow. Before entering cavity 6, the flow passes
through transition section 5 with change in cross section from circular to rec-
tangular (height 0.95 cm, length along the optical axis 9.84 cm). In the wedge-
shaped region (length along the direction of flow equal to 15 cm), the flow is
accelerated and expands from 0.95 to 3 cm.
The pumping reaction is initiated at the inlet to the cavity by injecting a mixture
of 0/02/He into the flow of CS/CS2/He at sonic velocity through two rows of aper-
tures 7 located opposite each other (diameter of the holes 1.5 mm, distance between
centers 2.0 mm, 48 holes in a row). At the outlet from the active region, the
gas flow enters a large section of branched tubing 8, the chemical composition
of the flow in this region being determined by quadrupole mass spectrometer 9(the
measurement technique is analogous to that used in Ref. 18).
Principles of achieving lasing with the use of low-toxicity reagents that are con-
venient to handle have been worked out, and the operation of continuous chemical
lasers with high flowrate of reagents has been modeled on compact shock-wave chemi-
cal lasers as well, for example of the type of a shock tube with supersonic nozzle
and mixing of the flow at the outlet of this nozzle with fuel injection [Ref. 19].
In a device of this kind (Fig. 6.8) the dissociation of oxygen takes place in three-
section tube 1 behind the shock wave reflected from the constriction at the inlet
to nozzle 2.
+CS2~He 4
1~He He-- 02~Ar 5 -
~8 cM 2 ~CS~Ne
~ 3
Fig. 6.8. Diagram of chemical laser with shock-wave initiation of the reaction:
1--three-section tube; 2--nozzle; 3--injector; 4--cavity; 5--receiver
The supersonic wedge-shaped nozzle with critical cross section of 0.3 x 70 mm was
equipped with injector 3 in its flared section. The flow was ejected into the
cavity of resonator 4 communicating with receiver 5.
A mixture of oxygen and argon was admitted to the low pressure chamber separated
From the nozzle by a diaphragm. The injected gas, a mixture of CS2/He was fed
through an electromagnetic valve that opened 5 ms after triggering of the shock
- 146
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tube and had an opening time of less than 0.5 ms. Discharge of the 0/0~/Ar mixture
from the stiock tube began within 3 ms after opening of the valve. To prevent con-
tamination, the mirrors of the cavity were blown with helium through another solenoid
valve synchronized with triggering of the device.
Another shock-wave design of a chemical laser with mixing of reagents was proposed
in Ref. 20, where the mixture was heated in the configuration of shock waves re-
flected from the constriction at the inlet of thE~ supersonic continuous flow to
the resonator cavity, with chemical reaction
N 2-}- CF 3I -I-- 2-~ C~ 3-F- I*-}- N 2. ( 6.16)
The excited atom of iodine in the vicinity of the resonator produces a photon down-
st ream I* I+ hv .
The cited examples of shock-wave chemical lasers should be supplemented by the
method proposed in Ref. 21 For shock-wave initiation of a reaction, and the at-
tainment within 1.8 ms of continuous operation of a supersonic diffusion chemical
laser in reflected shock-wave geometry [Ref. 22] in a mixture of F2/HC1. In this
wave fluorine wa~ partly dissociated F2+ M-~2F + M, and then the resultant flow
expanded in a nozzle with Mach number M= 4. HCl expanded in a nozzle with M= 2
to a static pressure identical to this flow. The gas streams were mixed in a two-
dimensional diffusion zone with reaction F+ HC1-}HF* + C1, and the output power
was generated in an optical cavity transverse to the flow. The supersonic diffusion
chemical laser also uses the pumping reaction C1+ HI } HCl~ + I. In this case,
rtX x 3.5% for mixture He/C102/NO/HI.
The thermal energy required for a supersonic diffusion chemical laser is also ob-
tained by combustion in a high-pressure chamber [Ref. 23] into which part of the
flow of F2 is injected to react with H2 and attain a temperature that ensures dis--
sociation of the remainder of the F2.
An attempt to combine electric heating in a high-pressure chamber with combustion
at the nozzle outlet is described in Ref. 24. The action of a discharge tempera-
ture of about 6000 K was used to convert N2 into a stream of active nitrogen in
the form of a mixture of vibrationally and electronically excited molecules. This
mixture expanded through a nozzle into the reaction chamber at a velocity of up
to 15 km/s. 7'he pressure in the chamber was about 1.33 kPa. A bright flame ap-
peared at the nozzle outlet when carbon disulfide was injected into the supersonic
flow of active nitrogen. Analysis of the chemil~iminescence of radiation of this
Fla~ue showed a photon yie]d of 18.5% Eor CN A21I-~ X2~:+ radiation when C2F4 was used
as the reagent. Estimates in ReE. 24 showed that under conditions of vibrationa].
cooling ef tt~e populations of electronicall.y excited states it is possible to at-
tain a pusitive gain in such a system.
_ In Ref. 25, a mixture of oxygen and argon was heated to temperatures in the range
of 1000-4000 K at a pressiire of 20-50 kPa in an electric-discharge chamber and
the resultant supersonic flow with oxygen atoms was injected witli a Cs2/Ar/He mix-
tuer at the nozzle outlet. This ensured efficient production of CO* and l.asing
in a cavity transverse to the flow with power of 34 W in the band of V-R transitions
fr.om 4.9 to 5.7 Um.
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The search for substances that are convenient to handle for producing chemically
active centers has led in particular to the use of liquid fuels such as toluene
(C6H5�CH3) or C6F6 that react with NF3 [Ref. 26]. In such a liquid-fuel supersonic
diffusion chemical laser, burning of the reagents produces excited fluorine, which
after dilution with helium expands through nozzles from 0.3-1 MPa in the combustion
chamber to 0.133-1.33 kPa in the resonator cavity. In the nozzles, the fluorine-
containing flow is mixed with the injected deuterium, and the resultant excited
molecules of DF* produce lasing of up to 8 kW for 120 s.
�6.2. Supersonic Chemical Lasers With Energy Transfer
A method of getting stimulated emission in the cw mode with an auxiliary component
was proposed in Ref. 7, 27. Such a purely chemical laser in which the rapid ex-
change of reagents enables the use of components that react at a high rate without
any initiation was first proposed in Ref. 28. The process is based on the reaction
of DZ (HZ) with F2 with subsequent transfer of the energy of excitation to C02,
i. e. the same reaction (5.9) as in the chemical lasers described in �4.1 and �5.2.
Examples of other reactions are given in Ref. 29.
The gasdynamic laser described in Ref. 2, 6 is an example of a device that is capa-
ble of operation at rather high static pressures in a resonator with the capability
of restoring the static pressure to the atmospheric level at the diffuser outlet.
In the case of a supersonic chemical laser the use of an analogous open-cycle gas-
dynamic laser would enable elimination of the complicated system for evacuation
of depleted gases that is required for maintaining low pressure in the resonator.
Dz 4 2
3 ~
C02/Ne F2/He
0
~ ~o
CO 1400K ~ ~o400K - ~0�o He
02/He ~1's ~ 4o0,0f -24%C02 ,
~ Q,~ MP 6~ DF
~
~ ~2~~ ~1,~1~~~4J i~s) ifs) il~)
Fig. 6.9. Diagram of supersonic chemical laser with energy transfer: 1--combus-
tion chamber; 2--diffuser; 3--nozzle module; 4--resonator mirrors; figures in paren-
theses (1)-(7) denote cross sections of the laser channel
- The hybrid supersonic chemical laser design described in Ref. 30 (Fig. 6.9) is
analogous to the C02 gasdynamic laser of Ref. 31 in flow conditions. This design
is in principle the same as shown in Fig. 6.1, but the electric-discharge chamber
is replaced by combustion chamber 1, and supersonic diffuser 2 is installed at
the flow outlet. The flow passes through nozzles 3 and a resonator formed by
mirrors 4. Approximately half the gas flowr'ate is provided by the combustion chamber
where CO is burned in helium-diluted oxygen that can reach a temperature of 1400 K
at pressure of 1.5 MPa. The hot gases at the outlet to the supersonic nozzle module
form a mixture of He, C02, F2 and F. Upon passage through the nozzle, this mixture
is accelerated to supersonic velocity, mixed with deuterium and enters the cavity.
A pressure of. about 8 kPa can be attained in the resonator by selection of the
parameters in the nozzle. The diffuser installed after the resonator brings the
l48
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static pressure to ttie atmospheric level. A total output power of stimulated emis-
sion of more than 500 W at nX= 3%, specific power of about 30 kW/(kg�s) and pressure
in the resonator cavity of p~= 3 kPa was achieved on a small model of a supersonic
hybrid chemical lasPr in Ref. 30.
A large-scale DF/CU2 chemical laser with energy transfer has been realized in sub-
sonic ~~IRIS-I) and supersonic (IRIS-II) versions (Ref. 32]. Nitric oxide mixed
- with carbon dioxide was used as the fuel, and helium-diluted fluorine was the
o:cidizer. These two versions differ from one azother only in the supersonic noz-
zles in the IRLS-II to accelerate the flow to Mach numbers M= 1.75. Such a Mach
number is attained as a result of expansion of 6:1, which is due in turn to the
pressure in the ~ombustion chamber and resonator cavity. The pressure in the com-
bustion chamber should be no greater than about 13 kPa to minimize the formation
_ of NOF, which appreciably reduces the output cha~acteristics of chemical ~.asers,
but shou].d be greater than 2kPa in the resonator cavity to support the chemical
reactions. The output powers attained in the subsonic and supersonic modes are
respectively equal to approximately 5-15 kW at pressure in the cavity p~= 8-4.7
kPa, and 6-7.7 k[d at p~ = 1.8 kPa.
Thus a considerable constraint on operation of both subsonic and supersonic hybrid
chemical lasers is that they are capable of stimulated emission only at resonator
pressures below 8 kPa. However, it has been found that a radical change in the
current concepts of designs of supersonic chemical lasers and of their operating
conditions enables development of chemical lasers with resonator pressures exceeding
27 kPa [Ref. 33]. What distinguishes the design of such a laser from conventional
supersonic l.asers is that they use a single nozzle rather than a block of many
- small nozzle;, and that the gas in the high-pressure compartment is at room tem-
perature as contrasted with chemical lasers with electric-arc heating or combustion
- to produce atomic fluorine.
Let us examine in more detail this chemical ~ _~2 3 g 5
laser that is so unusual compared with estab- i r-~
lished concepts (see Fig. 6.10). The primary FZ/He f~~
gas flow consists oF a mixture of F2/C02/He f
Lormed in mixing compartment 1. This primary
room-temperature flow passes through grid 2 C02/He NO~Az
that is designed for breaking up large-scale
eddies in the Flow. Downstream is injector Fig. 6.10. Design of hybrid
3 for gases NO and DZ with outlet placed along supersonic chemical laser with
the axial. line of two-dimensional nozzle 4 with elevated pressure in the reso-
ratio of areas of the outlet tip and the critical nator: 1--mixing compartment;
cross section equal to 1.14. This gives a Mach 2--grid; 3--injector; 4--two-
number oE the flow at the nozzle outlet of about dimensional nozzle; 5--resonator
1.5. Dirnensions oF the outlet tip are 1.488 x
4.445 cm with the longer. side in the direction of the axis of cavity 5. The
NO/D~ mixture is injected into the primary flow inside the nozzle through 20 tiny
tt.~bes with inside diameter of 0.122 cm and outside diameter of 0.183 cm, each
ter.minating in 17 orific_es with diameter of 0.024 cm. These orifices ensure dis-
ctlarge of the gas at a maximum angle of 20� to the direction of the primary flow.
The entire unit is made of aluminum and Teflon.
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The jet is discharged into the large chamber of the resonator, which is evacuated
by a machenical pump. The two gold-coated mirrors were water-cooled and had di-
mensions of 10 x 10 cm, forming a cavity with opaque mirrors for measuring the
power of optical radiation on a wavelength of 10.6 Um.
In the immediate vicinity of the jet are helium feed tubes for preventing strongly
absorbent COZ (100) in the hot ambient gas from getting into the path of the stable
resonator.
A curved mirror was incorporated into the design that could be moved to determine
the change in power as a function of the position of the optical axis.
When the NO/D2 gas is mixed with the primary flow, fluorine atoms are produced
in the reaction F2+ NO-~ F+ NOF. These fluorine atoms then excite the DF chain
considered in detail in �4.1:
P-~- DZ DF' (v) D; D-I- F, DF* (u) -I-- F,
and the excited DF(v) pumps the C02 to state (001) which then yields the quantum-
mechanical effect of st imulated emission. An increase in the efficiency of this
effect requires a large C02 concentration. Without C02, the excited DF is col-
lisionally deactivated too rapidly, and the lasing effect does not arise.
Power measurements us~n g a resonator with opaque mirrors showed some gain of
0.7 cm 1. A power of 1.45 kW was measured in a chemical laser with optical axis
located 3.89 cm downstream from the nozzle tip. This power corresponds to nX = 1.9%.
Under such conditions, the pressure in the prechamber was 84 kPa, and in the reso-
nator proper--31 kPa. The flow in the jet consisted of 5.29 g/s F2, 57.8 g/s COZ,
15.1 g/s He, 1.61 g/s D2 and 1.53 g/s N0. It should be noted that these mass
flowrates, resonator pressure, and position of the optical axis were not the optimum
" for maximizin~ power.
_ Hybrid s~.pers�:~ic chetnicai laser designs can also be developed on the basis of
- dissociatio� uf molecular deuterium in a mlxture with argon behind a reflected
shock wave [Ref. 34]. On the facility shown in Fig. 6.8, lasing was also achieved
on a mixture of D2/03/COZ in the quasi-cw mode. The mixture of D/D2/Ar obtained
behind the reflected shock wave flowed through a flat wedge-shaped supersonic
nozzle into the injector, where it was ~uixed with a subsonic flow of a mix ture
of ozone, carbon dioxide and helium fed through a solenoid valve. Mixing of the
flows led to the basic reactions:
D Oa OD* (v) Oz;
OD* (v) COZ (00~0) OD'~ (v - 1) COa (00�1).
From the mixing chamber of the injector, the flo~ entered the region of the resonator
- with transverse optical axis. The operating time of such a chemical laser was
determined by the discharge time of the gas heated behind the reflected shock
wave, and amounted to 4.5 ms. Lasing duration was nearly four times as long as
the time of existence of the quasi-steady state behind the reflected shock wave
front.
]50
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Lasing was obtained under the following conditions: initial pressure of the mix-
ture D2/Ar = 1/15 in the low-pressure channel of the shock tube was 9 kPa; velocity
of the incident shock wave--1.48 km/s; pressure of the mixture 03/C02/He = 1/3/17
in the valve at the instant of beginning of discharge was 50 kPa. The cavity
was made up of an opaque spherical mirror with radius of curvature of 3 m coated
with gold, and a flat dielectric output mirror with transmission of ~1%.
Under the given conditions, lasing was achieved with peak power of 1.5 W at an
aver3ge power equal to 0.4 W over 4.5 ms. Control experiments with elimination
of deuterium or ozone from the mixtures were done to prove the chemical mechanism
of formation of inverse population of C02 molecules. Lasing was absent in both
cases. Lasing was achieved when hydrogen was substituted for deuterium, although
the emission power in this case was considerably weaker.
�6.3. Chemical Gas-Dynamic Lasers
The actual conditions of processes in gasdynamic lasers often result in chemical
A reactions, depending on the method of producing the working gas and the laser
design, especially in cases where the gasdynamic lasers design is optimized by
_ using special mixtures, fuel ignition, gas mix ing, and stimulation of certain
- chemical reactions [Ref. 35]. Chemical gasdynamic lasers may include for example
devices in which nonequilibrium chemical combustion reactions form vibrationally
~ excited molecules used as the working medium of gasdynamic lasers [Ref. 36]. For
example when CO is burned in air, vibrationally excited C02 molecules are formed
with vibrational temperatures exceeding the gas temperature. When CO or hydro-
carbons are burned, more than 20% of the heat is emitted in the infrared region.
Part of this emission is the 4.4 um V-R band that is used to pump energy to
the upper energy level [Ref. 37]. Excited C02 molecules may also be formed as
a result of additional burning of the mixture in the nozzle. For example, Fig.
6.11 shows a diagram of a cw chemical laser
of tilis type with supersonic flow of material
that operates on a chemical reaction with non-
toxic products. The device uses the reaction
of oxidation of CO + 0.502 in a mixture of ~ 2 4~ 5
CO/0.502/HZ/He. ~
The working mixture was admitted to combustion
chamber 2, after which it was ignited by a spark. Fig. 6.11. Diagram of chemical
Pneumoelectric valve a enabled admission of the combustion laser: 1--pneumo-
ignited mixture to nozzle 3 at nearly any instant electric valve; 2--combustion
of the ignition process. chamber; 3--nozzle; 4--reso-
nator; 5--receiver
The purely gasdynamic mode was studied in addition to the chemical-gasdynamic mode
for purposes of comparison. It was found that the power in the former case drops
considerably when the combustion chamber is opened on the leading edge of the ig-
nition front, which is responsible for the most intense combustion of the mixture.
A drop in power can be attributed to the fact that there is an insufficient amount
of COZ and the temperature is low on the leading edge in the mixture.
In contrast to the gasdynamic mode, in the chemical-gasdynamic mode the maximu?t?
power was realized in just that region where the conditions for thermal pumping
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are far from optimum. Maximum power in this case is observed when the combustion
chamber is opened on the leading edge of the ignition front where the temperature
is 600-900 K. When the chamber is opened on the trailing edge, lasing is absent
even at the same temperatures. Thus the given experiment shows that the excited
C02 molecules are formed due to additional burning of the mixture in the nozzle.
When the resonator axis was moved away from the critical cross section of the nozzle
the power reduction was much smoother than in the gasdynamic mode, which can also
be explained only by formation of excited C02 molecules due to a chemical reaction
in the cavity region. The power W1 of the chemical laser was slightly higher than
the power W2 of the gasdynamic laser (W1/W2 ~1.25) with the same mi.xture caloricity.
The use of chemical reactions for additional pumping of gasdynamic lasers based
on products of the reaction of carbon monoxide wi.th nitrous oxide was also studied
in Ref. 39. It was shown that the gain in the temperature region of 1500-2000 K
is appreciably higher for the reacting mixture than for the premix that simulates
the products of the same chemical reaction.
�6.4. Analysis of the Efficiency of Diffusion Chemical Lasers
Particulars of Analysis of Chemical Lasers of Diffusion Type. The energy of the
chemical reaction in cw diffusion chemical lasers is only partly used. For example
the chemical efficiency of conversion of the energy of reagents to the energy of
radiation is no more than 10-20%, and the total efficiency with consideration of
expenditures such as those of thermal energy for preparation of the mixture is
still rather low: n~ 2-3%. This is due to the fact that there is an equilibrium
store of vibrational energy in the presence of radiation, and this does not permit
conversion of the total vibrational energy of the molecules to the energy of a
radiation f ield even in the absence of V-T relaxation. Another factor is rapid
relaxation of the working molecules on reaction products and incomplete mixing
of the reagents in the resonator cavity during the cycle of stimulated emission.
The necessity for simultaneous consideration of these factors considerably compli-
cates theore*ical-analysis of operation of cw diffusion chemi.cal lasers.
In the supersonic diffusion chemical laser inversion is formed either as a result
of direct chemical interaction upon diffusion of a single component like H2 into
a supersonic jet that contains another diluent component (He) [Ref. 15], or as
a result of energy transfer to an auxiliary reagent like CO 2[Ref. 27, 40]. In
the diffusion mode the time of convective travel of the reacting particle (T conv)
must be greater than the time of diffusional travel of the particle Td, i. e.
Tconv > Td. (6.17)
Introducing the Schmidt number Sc and the Reynolds number Re, and assuming [Ref.
41] Tconv= lp~u~ id = 1i/1), where IN and [y are characteristic longitudinal and trans-
verse dimensions of the channel, D is the coefficient of diffusion, u is the
characteristic flow velocity, we get
Sc Re < ep/el. (6.18)
In the case of a purely diffusional mode we have ScRe :~;1, i. e. for example
ScRc ~ l),1.
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~~o~ t~r~N'~c'i~~t. vsF, t~~vi.~~
_ Far cunti?iu~>us l;~sint; i~ is n~~c~~~ssziry ~l~at tfie lasing time T be greater. than the
transit time of the reafients T~, i. e. T> T,; /~~/u, whence u> l~~~i.
For the minimum value of Z~~ = 1 cm and T= IO-4-IO-5 s, typical of pulsed chemical
lasers at pressures of the reagents up to a few kPa we have
v~ 10`'-105 cm/s.
As a rule, the longitudinal dimension of the channel is greater than 1 cm, and
T decreases with increasing pressure and specific lasing power. Therefore, suc-
cessful operation of actual cw chemical lasers requires high-velocity flows of
reagents moving at the speed of sound or faster. These high velocities on the
one hand create additional rechnica]. difficulties associated with the need for
having powerful evacuating systems, and on the other hand enable the use of com-
ponents that react with one another rapidly upon mixing without any initiation.
Besides, efficient operation requi.res that the time Td of mixing of components
and the time TX of the chemical reaction be less than the time of collisional re-
laxation Tp, i. e.
id, ix < zu.
ror a purely chemical laser operating without preliminary external initiatior.,
~ suitable from ttiis standpoint are exchange reactions of atoms or radicals with
molecules as considered in Chapter 2, but it is more advantagec~us to use chain reac-
tions such as the H2+ FZ type, and to introduce additional reagents for the origi-
nal initiation of the reaction that react with the main component and yield seed
atoms or r.adicals.
Laminar Mixing Model. In theory, the highest efficiency of a supersonic diffusion
chemical laser can be realized at comparatively low pressures in the cavity and
at 1ow Reynolds numbers, i. e. with laminar flow conditions. However, in actual
cw chemical lasers, wl-~ere high pressures are used, the rate of laminar mixing be-
comes inadequate to compete with deactivation of excited particles. As a conse-
quence, more rapid--turbulent--mixing becomes desirable. A solution can be found
[Ref. 41] for linear differential equations of tnulticomponent diffusion with con-
sideration of nondiagonal diffusion components:
P �
_~~nt -F up~ri - ~ ~ir~ O2 rth -~-a,i ~li = 0� (6.19)
- k- I
lIere u is the mean velocity vector of. the flow, asi are the dissipative coefficients,
Dik are coefficients of dif.f~tsion that are related by Onsager laws.
On the basis of (6.18), the second term in (6.19) can be disregarded for the purely
diffusional mode. Besides, when the inequality
~ ~~st - arh T~ ~ ~6. 2~~
is met, whicl~ is often the case in practice, we can disregard differences in the
dissipative coefficients, and then instead of (6.19) we have
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a~'j = ~ Uih~Zn~,-a,ri~. (6.21)
dt
k=1
This sum of equations is reduced to a system of p indspendent equations by diaga-
nalization of matrix D. Multiplying the equations of system (6.21) by the elements
gia of auxiliary nonsingular square matrix g, summing with respect to i and sub-
stituting subscript k for i in terms with simple summation, we get
a~~ b'n~ na = div grad ~ nn ~ b'tl ~th-ae ~ Bhl ~th~ ~ c~, 2, p. ~6.22)
vt k`~ r=i k~i
Introducing the notation
G~ ~ b'n~ nh, H~ ~ gi~ Dir~, (6.23)
k=~ gh~ i=!
we get from (6.22)
~3G~lat = H j~aG~ - a,G~. ( 6. 24)
The elements of matrix H are found from the condition
det (Dih - HSi1).
It was assumed that the only pum~ing reaction was
1~ -f- DZ DF -I ~ D, (6.59)
with integral rate constant taken from Ref. 47. The distribution of products of
relaxation with respect to levels v and J is taken from Ref. 48, in accordance
with which the distribution maximum for v= 1, 2, 3, 4 falls respectively to J=
13, 11, 9, S. Numerical calculations were done for active medium F/He/HF/DZ =
3/6/3/ 14 at T= 300 K, u= 2.13 km/s, pLd = 1.66 kPa� cm, pL~ = 13. 3 kPa� cm, p= 133 Pa.
High amplification on transitions of strongly rotating molecules immediately after
the onset of mixing shows up experimentally in the development of lasing in this
region simultaneously on several lines. Calculations of lasing intensity also
show that after the beginning of mixing, lasing takes place at the same time on
many lines, those lines with small J ceasing to emit with the course of time, and
the maximum of the spectrum being shifted toward higher J. Amplification on purely
rotational transitions of DL (v = 2) may increase considerably. For example at
p= 0. 66 kPa, a> 1 cm-1 at distances x< 0. 3 cm.
Violation of rotational equilibrium leads to a reduction of power in a nonselective
cavity by 14%, and with selection of a single line--by 35%. According to calcula-
tions, in the case of selection of individual lines, the output power is appreciably
dependent on the choice of the rate constant of rotational relaxation.
Other Numerical Studies of the Supersonic Diffusion Chemical Laser. The idealized
flow pattern with laminar diffusion of a stream of H2 of finite width into a semi-
infinite stream containing fluorine and a diluent was considered in Ref. 49 in
a coherent radiation field. Mises transformation was used to simplify numerical
solution of equation system (3.38)-(3.41) of boundary-layer type with consideration
of multicomponent diffusion, radiation and chemical reactions. At constant values
of the initial velocity of the flow, temperature, width of the stream of H2 and
initial partial pressure of fluorine, direct relations were found for the pressure
dependence of the integral gain and ttie effective specific output power of chemical
lasers, and inverse relations for pressure dependence of the length of the active
region and the chemical efficiency.
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Similar constraints on the length of the active zone and efficiency with pressure
increase due to processes of mixing of reagents in the laminar mode of operation
of an HF supersonic diffusion chemical laser were found by numerical calculation
in Ref. 50. However, the total efficiency of chemical lasers with consideration
of thermal expenditures on mixture preparation increase in the case of operation
in the mode of a chain mechanism of excitation, which ~s analyzed in Ref. 51 in
chemical lasers with a small degree of dissociation of molecular fluorine. The
comparative efficiency of different fuel compositions of chemical lasers on an
H2/F2 mixture can be evaluated by using calculation based on an instantaneous mix-
ing model [Ref. 52J.
Numerical analysis of the efficiency of energy conversion in HF diffusion chemical
lasers [Ref. 53] shows that the use of turbulent injectors in chemical lasers leads
to an increase of pressure in the resonator cavity. This ensures a high rate of
mixing of the components of the mixture under conditions of a turbulent flow mode.
For HF chemical lasers, especially with a chain reaction mechanism, there is typi-
cally multilevel excitation with kinetic pressures in the active zone that take
place against a background of diffusion flow with gradients of the index of refrac-
tion in flow beyond the nozzle tip. Calculation of the structure of amplitude
and phase diagrams of the radiation field in the near and far zones [Ref. 54] for
typical conditions of operation of HF chemical lasers has shown that the use of
- telescopic cavities leads to an increase in the directionality of emission with
moderate reductions in efficiency.
Numerical analysis of the kinetics of physical processes has also been done for
a chemical-gasdynamic laser on a mixture of CS2/CS/02/0 [Ref. 53]. Simultaneous
solution of equations of chemical kinetics, vibrational relaxation and gas dynamics
for a logarithmic nozzle shows that efficient chemical pinnping and gasdynamic
cooling should give comparatively high values of total inversion (~1014 cm 3) and
gain (~0.1 cm-1).
�6.5. Open-Cycle Chemical Lasers With Pressure Recovery in the Diffuser
Since gas flow with Mach number M~ 1 takes place at the inlet to the cavity of
a supersonic chemical laser, it is possible, as pointed out in �6.2,to use a dif-
fuser for restoring the pressure from the range of 0.66-3.33 kPa required in the
resonator to 26.7-53.3 kPa at the diffuser outlet. From this level, a mechanical
pump or ejector can bring the exhaust pressure up to the level that is required
for example when chemical lasers work into the atmosphere [Ref. 56]. Energy ex-
penditures on evacuation must be minimized to increase the overall efficiency.
From this we can see that the requirements for pressure recovery in the diffuser
are important in calculating and designing supersonic chemical lasers.
In the open-cycle chemical laser (see Fig. 6.9) the primary fue]. mixture is formed
on section (1)-(2) and is accelerated in nozzle (2)-(3) to supersonic velocity
at low static pressure. In the cavity (3)-(4), heat release takes place in the
flow as the primary and secondary mixtures burn, and in the diffuser (4)-(7) the
flow is decelerated from supersonic velocities with a corresponding increase in
gas pressure. A one-dimensional analysis of such a flow in chemical lasers is
given for example in Ref. 57, where an examination is made of chemical and
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thermochemical processes in the cavity, the hydrodynamics of the flow with consider-
ation of the boundary layer and deceleration of the flow in a d~ffuser with constant
cross section of the intake and throat (4)-(6), and with a subsonic expanding dif-
fuser (6)-(7) at the outlet.
If we denote the parameters of the primary flow of oxidant by subscript p, and
those of the secondary flow of fuel by subscript s, the molar flowrates of oxidant
in the nozzle are Gpg and Gpg2. The relative dissociation of fluorine is then
defined as a=~GPF/GpFZ, where GpF2= ~GPg + GpF2=G is a normalizing parameter that
characterizes the flowrate of all fluorine in molecular form. The dilution of
components i(F, F2i D, D2, He, DF and so on) in the cavity is described by the
degree of dilution ~yPi = GPi/G, the total dilution of the primary oxidant flow being
expressed as ~iP = Ei~Pi. The molar flowrates of F and F2 will be GpF = 2agG and
GPF2 = (1 - aF) G.
The normalized molar flowrate of fuel with consideration of the ratio R~ of com-
ponents of the mixture in the cavity will be GSD2= R~G, and the flowrate of diluted
secondary flow ~SG. Overall molar flowrate of fuel: GS = G(R~ +~S).
The total molar flowrate at the cavity inlet (3) (see Fig. 6.9) with consideration
of dilution is equal to the sum of the flowrates of fuel and oxidant:
Gy = G~] OCF mP Q~a -I- R~)� (6 . 60)
Since F and F2 react completely to DF at the cavity outlet, and the diluent does
not take part in the chemical process, the equality G,,DF = 2G is satisfied in cross
section (4), and for atomic deuterium G4D = aDGpF = 2aFaDG, where aD is the relative
dissociation of D atoms. Then the flowrate of molecular deuterium at the cavity
outlet G4D2=G(R~ - 1- agaD), and the total molar flowrate at the cavity outlet is
G4- G(1-}-ar�an-{-~'n-1-~'r-f-Ro)� (6.61)
Thermochemical processes in cavity (3~-(4) are described b~ the expressi~ns
He3= G3he3 and He4= Gyhey, which are equal in the adiabatic state. However, the
cavity releases the power of stimulated emis~ion W= G3u3wsp, where u3 is molar mass,
wsp = W/m is the specif.ic power of stimulated emission, m3 is mass flowrate. Then
He3=He4+W or
(Ga he04 -G9 I1e03) C?s N~a ~ap - ~ ~Gst h~~ -G4i h~~), (6 . 62)
r
where h~i is the specific heat of formation of the i-th component. For diluents
Gsi - G4i and for FZ and D2 h j~2 = h~D2 = 0, therefore
Q = Gpg/l~g - G~DF ~~fDP GqpI1jD� ~6.63)
The specific energy release in the cavity with respect to oxidant F2 is
9=QIG~ 2aF(h~F-aDh~o)-2hf~F� ~6.64)
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~~oH o~'~'ic-t.~t. t~~~~: o;~~~.ti
From (6.60)-(6.62) we can get a relation for the spec:~fic enthalpies of deceleration
of the flow in the cavity:
~ Q~~IQpP ~~a~1ep_ r
heoal h~oa = 1-~- - - , , ti 51
~a ~'~'ap-{'~P '~PheoP
where ~p = GP/G3 is the mole fraction of oxidant, heOP is the specific enthalpy
of deceleration of the primary flow at the nozzle outlet; as is a parameter that
describes ttie influence ot the secondary flow,
~s _ 1 t_ X9l+eos . (6.66)
~ P lr~pp
In general, as can be seen from Fig. 6.2, the flow at the nozzle outlet is inhomo-
geneous and may have a complicated system of compression shocks. However, these
effects, which are associated with energy release and mixing, play a major role
only in the inlet part of the cavity, and in the remaining part they can be disre-
garded. The contour of the walls on section (4)-(5} is usually smooth with a large
radius of curvature, and therefore there are no large pressure gradients. Thus
since transverse velocities of the flow are small throughout the entire extent
of the channel compared with axial velocities, deviations from unidimensional flow
can be treated as quantities of the second order of smallness. In this connection,
the homogeneous flow parameters at the outlet of the nozzle array in Ref. 57 are
obtained by integrating the inhomogeneous distributions across the nozzle by the
- method given in Ref. 58. The diffuser (4)-(6) is equipped with a throat with cor~-
stant cross sectional area and length sufzicient for conversion of the flow in
the shock wave system from supersonic to subsonic flow, and also for equalizing
inhomogeneities of the flow at the diffuser outlet. Thus the one-dimensional ap-
proximation can be used in analyzing the flow in cross section (6) as well.
The equation of momentum for the inviscid control volume I of the cavity in region
- (3)-(4) is written as
4
f PS (1 YM2)1~~ _ [PS -f- YM')~s S pdS. (6.67)
3
Here the cross section of the inviscid control volume Sqj = S4- Sd, Sd characterizes
the boundary layer i.n the cavity determined by the thickness of displacement d
and the hydraulic diameter Dg as Sa= S44S/Dg.
The solutions of the equations of momentum, energ} and continuity give expressions
for the velocity of the flow u3, enthalpy he3 and pressure p3:
u;? = Y~,un Y,u, m3' [pl,S,, Ps~S9 - P3 ~Sn _r ~Ss)1; (6.68)
Il~y = XP Ilen -I- ~Y.. ~t~e -I- ~2�:~)- ~[Y,, u;, Y s u; -u31; (6. 69)
P~ = m~ R~ 7~a~~t~~ S~) ( 6. 70)
r~
(R is the gas constant, h,,~ C~,+dT is the enthalpy of the j-th state of the
~ n
medium, for example j'~ p, s, 3; ~~~~;/f~~f is the mass fraction of component i) from
163
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which, by iterations with the use of temperature dependences of the gas properties,
we determine p3, u3, T3, and then p03 and M3. For the general case p= f(S), the
rel.ation
pSc~�-'~-c~nst (0
i ~ ~
~ 1 2 ~ M
P ~ N~ N~ N~
2
a b
Fig. 7�6. Exa.mples of application of the Ferma.t principle to the detonation pro-
cess (detonation collima.tors): a--with two continuous explosive media 1 and 2
~ 7' 1/D2 ~ 1~; o--with separate explosive channels
in Fig. 7.6a, b. In the two-dimensional case, for simultaneous emergence of a11
points ~f the detonation front fl emanating from a single initiation point I at
straigh~ line P1P2 (see Fig. 7.6a) when a compound charge is used with two med.ia 1
and 2 having different detonation rates D1 and D2, the shape of the boundary be-
tween media 1 and 2 is calculated from the equations:
T= 1/'X'-}-y2~D1~-(z`-x)/Dz~ ~7.13)
T~n = zo/D1 (x" - y,l lD z. ~ 7.14 )
~dhen D1/DZ~ l, the boundary C between the media is a hyperbola. Such a generator
of a straight wave ~Yont ( collima.tor ) may be important for chemical detonation
lasers as a device for simultaneous input of gaseous detonation products into the
optical cavity. The detonation wave generator shown in Fig. 7.6b can serve the
sa.me purpose.
Here the line M1Mn is a channel filled with a detonating medium having detonation
rate D1, and the lines MiNi (i= 1, 2,..., n) are channels with a medium detonating
at rate D2. ~e condition of simultaneous arrival of the detonation fronts in a11
channels MiNi at the level of straight line M1Nn is
Mt Nt INn
T._ 1M~ + - OT T= ,p 1 Iry~ 1V~ ,v0 j~~ I/Mi,~O' ~ 7. 15 ~
D1 D~ . 1
:rr.e:~ ce
pl = D$ sin ~/sin a. ( 7.16)
If a= S, then D1 = D2 and Iidl = INn. An e::cample of realization of such a scheme is
linear detonation generators filled with gaseous expde vice based on an a,ria,logousof
detonation cha.nnels of the same length [Ref. 3]�
principle focuses the detonation wave by using holiow cylindrical shaping lenses
made in the form of a stack of cylindrical diaphragms that are roughened in the
central part an d smooth on the edges.
A number of wave generator designs based on the Fermat principl~ are shown in Fig.
;.7a-r [Ref. 40]. Shown are: a, r, i, o-- desi~s with focusing of detonation
176
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a b h y~efcba.~a ~ ~ D
~
~
\ D ZR
S~-~ ~in~ ~ 1 ~
I ?
~ R-1 ~ I
_ I i~~ ~rF~ r 2 ~ � I Ro
1 1 ~ F ~ 2
/ t ? I

..'f d Do ~ D= Do ~ ~R ~ l,\ ~ D2 DZ D~ cos a ~
~ ,p Ro =1 p I
- r Ro I a ~ I I
~ f ~ j, 1 ~ I I3 14 f
I h x=ach(y/a~-a y ti Cone
9 Pcvca.no~a Z ~e~cba~a
~
F-
- x
Q -
f I f ~F
z Exp2.
1 I ne.'c.t ~ p~ I ~ I ~ac eh.
ma.telr.i.a,~ ~X~ � neJc.t 4'
.~ay Z f� ,~~�h.s
~ o
z. ~ ? ~ /
~ Ine~r,t
m n F xf~ � f. ~ .~ayvc
~a~v.~c3 I viceh,t o/~ I
= I I ma,tetc.i.a,e ~ ~
I ----~p I -10 , ji \ ~j.~
~ " I ~ ~i
~Y~ I4
p ~rt~r~F ~
i~
'~Tf i
~t~ ~ .
I I j
Fig. 7.7. n~agrans of detonation wave generators
- ~onts at a point ; c, d, e, g, h, r-- linear detonat ~on front; f, 1-- focus-
ing of detonation on the axis of the system; j, k-- generation of a planar deto-
nation front; n-- generation of a curvilinear detonation front; p, q-- dif-
iraction of detonation fronts. Designs p, q and r are based on the diffraction
properties of detonation waves occasioned by the physical rather than the geometric
vp* i ~s of the s;rstem.
= rlit:~in tiie frsmework of physical optics of detonation, the Huygens-Fresnel prin-
r_iple enables construction of the detonation wave front for some instant if the
~ra.ve front is know-r~ a preceding time. Such a construction is based on the fact
tnat esch point of the medium reached by the wave front ~s treated a.s a new source
ot oscillations.
177
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The regions of collisions of kinks triple Mach configurations act as such new
sources of pulsations in a detonat~on wave. The sources of new pulsations in the
detonation front are responsible for the phase nature of pro~agation. After each
collision of kir~ks, a new pulsation arises with parameters that depend only on the
initisl conditions. This can explain the effect of detonation wave diffraction
that takes place for exa.mple when detonation waves flow around corners, or the
effect of refraction on interfaces [Ref. 41~. The pattern of phase propagation of
a detonation front is shown schematically in Fig.
7.8, where the numbers 1-8 denote positions of ~ D~
~ulsation fronts corresponding to times from tl
to tg. The heavy lines depict regions of maximum
energ,y release that renew pulsations in tr~e wave.
Phase propagation of suciz a structure at velocity q
D, as can be seen from ~'~g. 7.3b, c[not included v
~
with the translation] forms patterns similar to v,
those observed in hydrodyn~.mics during flow of U u+C U
shallow water (motion in a field of gravity of an -
inco~pressible liquid with a free surface a.nd with
depth of a layer oF this liquid that is sma11 com- ,
~ared with the characteristic dimensions of the
flow). It is known (see for example Ref. 42) that 5
wave processes on shallow water are described by
tne :Cortweg - de Vries equation 7
~~t ~x ~xxz ~x = 0 ~ 7 � i7 ~ 12 3 4 8
(D is wave velocity, b= DZ2, Z is the scale fac-
tor). S~ecial cases of this equation for propa- Fig. 7.8. ~iagram of phase
gation of small and finite perturbations in a propagation of a detonation
medium with a chemical reac:tion were considered wave. For tangential veloci-
in Ref. 43� ty of development of pulsa-
tion c~v l,~ ~ 7� 39 )
where t~~e latter condition means that the tangential velocity of point A is close
to the speed of sound in the initial shock-compressed gas in state l.
Suppose that shock waves collide, and Chapman-Jouguet waves are reflected. When
condition (7.38) is satisfied, the conservation equations yield
1,~,~2 = Yl-f-1 2Y~ (3-Yi)-~-Y~ (4-Y~)-3
2Yi {IYa (Yi-1)-4-2Yi (Y~-2)1'-4Yi (Yi-3) ~2Y3 (Yi-3) -1-
---i Y~-1 �
-f-yi ~Yi-~) 31}~~~-Ya ~Yi-�5)-4-Yi - 3 + 2Yi ~ 7. 40 )
In .~e�. 38, 47, the motion of ignition point A during detonation is treated in a
coordinate syst?m fixed to this point as supersonic flight of a poi.nted wedge in a
gas ~i.xture with an~xothermal reaction in the wedge. Let us represent the flow
in :he neas vicinity of the point A as shown in Mig. 7.11. Since t:ne collisions of
ignition points (lines) are s;rmmetric relative to x
the di.rected average velocity D, the absolutely
rigid Wall x-x can be taken as the axis of sym- M~ ~
metry oi the process. +Je will ta.ke AB as the s~~ ~ Ds
incicient wa~re front of oolique Mach reflection, 0 M~~D
Ai1 a~ the ~~Iach disk of this reflection, the dot- ~
~n d-dash line indicating the direction of "flight" B ~
of i~ni~ion point A with dispersal of the products a N
of ~sctner~i~ reaction to both sides of this line
~t yn~les ~ 1~~2 , and AEC indicatin~ the limit of ' ~ ' A M2~D2
dispersal in the fcrm of a compressicn shock that '
changes into a i~Iach wave. In order for an oblique ~ ~ ~
Mach reriection to ~orm again after collision with K
x-:c, tne condition /
x
,
arcct l~ Y'`~ 1?0 (1- P0 l ~ 7�~l ~ 1 lg. 7.11. Diagram of flow in
g I 2 P~ 1 P~ 1 ~
the vicinity of an ignition
^~ust ce sat;sfied. Foint in the ~~etailed struc-
j ture of a detonation wave
iaic~ ng the equal si t~ , and assumin~; that the ~r~.in-
siiior. 0-2 :5 stron~~ enough ~hat pp/p2 ~(Y2 - 1)/(y2 + 1) , we get from (7.~+1.)
~=arcct~Y(YZ-1)/(Y2+ 1). ~7.~2)
1~3
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For angles Q1 and ~2 we have
n~
W~~= Ws=a-~x= 2-~'~-x=~, (7.43)
where
x = arctg (D/DZ) = arctg (Mlco/MZcI); ~ 7,1~4 )
co/cl = {~Yi 1)' ~Yo - 1)/2yi ~Y~- 1) [2 -I- ~'Yo - 1)M~1}~/2. ' ~7�~+5)
From (7.44 and (7.45) with consideration of (7.43) we get
cp = arctg Y~+ 1-I- �sl / L1 _(Y~+ w~ J~ ~ ( 7. 46 )
m m
where
m = Mz~2Y~ ~Yi - 1) [1 2/Mi ~Yo - 1)1}~/2~
�a = ~ ~Ys = 1)~ ~Ya 1)~~~2�
ror the pressure in region 2 we have [Ref. 48]
2 po D; sinz ( 7� 47 )
Pa = n~,+ 1
which with consideration of the fact that DS= D/sin K(see Fig. 7.11) becomes
1-~ (Y:- 1) 9/2y= / 2Q
n~- 1-F(Ys-1)9/2 \9 P~IPs ~7.48)
Here, in accordance with Ref. 48,
p: _ 2Yo Mi sin' ~
Po na-1- 1 sin9 x~ ~ 7�~+9 )
~n the given calculations, pl/pp a.nd P1IP0 are related to M1 by the respective
�ormulas
P~ _ YoMi+1 YoMi -F 1 ls 2YoMi (Vo-Y~) _
Po Yi-f-1 +I.\ Yi-1-~ / + (Yi-~t)~Yo-1)
_ 2YoMi-(Yi-1) 1~/2, ~?�S~)
Y~ -I- ~ ~ ~
P~/po = 1-a- Vi-t' ~ 2Yo Mi l YT- ~l 4Yo
~ Yi- ~ L\ Yo-f- Vo-~ ~ J~ L Yo -1
~ 2YoMi 1-1 ~7�51~
Yo -f- ~ ~ ~
184
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rOR ~~rrICIAi: USE 0[~1I~Y
`~'tier~~ ;xre ~in~~.loF;ou; f'ormulss for n2/~1 ruicl u2/(~1.
From ~7.40), (7.44), (7�~+5) for a stoichiometric hydrogen-o~ygen mixture at
Yp = 7/7, Y1 = 8/6, YZ = 9/7 we get calcul.ated values of K= 55-56� close to the ex-
perimental results at Mach numbers M1= 5-6 typical of pulsating detonation.
n ~ ~
OQ=13,a4 M`'~ lOf
0,6 ~k~ f
_ ~ (
0~5 Q~= 3,77 ~=J r~rs/ /
O,y ~ J I 103
~ i'
_ 0,3 J
/ J
. I
0~2 2H1t ~2 - ; ~ ~ ~Q?
s ~/5 ~ _ (
~~B/6 = ~
_ ; ~ 10~
~2=9/7 Lj~
l~ k~~ _ i '
I, I, I~oQ
0
= 2 3 4 5 6 7 8 9 M~
r''16� 7�12. Graphic solution of equations (7.48}, ~7�~+9) for @1=3.77 and Q~=13�~+~+
i~IJ/kg, and comparison with the limits of the experimental spectrum of detonation
frequencies
The .~iach nuraber M1 of the detonation wa~re in this sa.me mixture can be conveniently
determined from the graphic soluticn of equations ('T.~B) and (7.49) on Fig. 7.12,
which ?lsc shows for comparison the experimental spectrum of detonation frequencies
ia coordinates ifl, S?= v/vp. For puisating detonation the region of this spectrum
cr. t ~e grapii is oounde~ by the shaded dot-and-dash line. Solutions L1 and I~~ of
ecuatior.s ~ 7. 48 j a.nd ( 7. 49 ) for ~1 = 3� 77 ana a~ = 13� MJ/kg respectively shcti*
little 3ifferencG from the indicated region of the e:cperimental spectrum of deto-
nation trequerici_es. Here ~1 is the energy release for near-limit pulsating deto-
nation ~aith fundamental mode SZ = 1, is the maximum theoretically possible ener~y
release accompan~ing chemical reaction in a detonation ~~rave. The point L30
cerresr,onds ~o detonation of a mixture of 2H2 + 02 under norma.l initial conditions
-aith natural frequc:ncy characterized by the mode SZ = 30 and v= 1.5 MHz.
In the fan of rarefaction waves tnat is fcrmed ir, region 2 as the reaction produccs
disperse frcm i~i+,ion point the incoming �lux may be deflected to the point
trhere compression takes place in r~aion ( see Fig. 7. _ll a.nd self-regul.ation is
effec~ed by ~nia kind of "feedback". It is by this that the detonation wave
1.85
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":cnows" in what tangential geometry it is propagating: in channels of circular or
perhaps rectangular cross section, and at the same time does not know the geom-
etry of the space in the direction norma.l to its flow, for example whether the ends
of the channel are closed or open.
�7.3. Overdriven Detonation
Of interest in application to chemical lasers of detonation type is an exa.mi.nation
of conditions of overdriven detonation, since it is in ,just such modes that the
effect of direct stimulation of coherEnt emission has so far been realize d[Ref.
4]. Corresponding to modes of overdriven detonation are states on the Hugoniot
adiabat lying above the Chapman-Jouguet point, e. g. on curve CG (see Fig. 7.2).
Such modes can be realized by preventing the formation of a rarefaction wave behind
the detonation wave �ront, e. g. by using a piston or some other method to compress
the resction products [Ref. 10~. Overdriven detonation is rea]..ized for example by
a change in the channel geometr;~ tangential to the wave in a narrow tube as deto-
nation passes to it from a wide tube, by setting up an electric discharge current
layer in the explosive mixture to act as an impermeable piston that pushes the
shock wave [Ref. 49]�
Overdriven detonation can also be r~alized by "driving" the detonation wave out of
a hi~-pressure section into a section with a low-pressure explosive medium that
is sepax ated from the high-pressure section by a breakable diaphragm.
Unless they are maintained, overdriven waves havt damped velocity, and in essence
s'tiould not be considered detonation waves , for whicil one of the ma,jor properties is
steac~y-state propagation tm der fixed initial conditions.
However, there is another �eature of detonation that must be taken into account
the ~eriodic structure identified by the wake method [Ref. 15~� '1'he presence of
such a structure in a reactive meditmm is evidence of energy release immediately in
the wave front, and in particular during overdriven detonation.
rrom ~he way that pulsation spacing ~x changes on wake prints for known initial
con ditions p0~ dtube~ one can judge whether overdriven detonation occurs, and crin
select st ructures with a smooth front that are of interest for chemi.:a.l lasers.
Fig. 7.13 shows diagrams of such wake prints for some methods of exciting over-
driven detonation, a.nd graphs of the cha~ge in pulsation spacing ax as the detona-
tion waves from overdriving are reaching the steac~y Chapman-Jouguet st ate on length
L~G from the cross section in the detonation channel that corresponds to over-
3riving at point C of ~he Hugoniot adiabat until the steady state of detonation is
reached, corresponding to point G(see Fig. 7�2)� The overdriven detonation mode
with velocity D~ was realized both by stimulated excitation (broken curves on Fig.
7.13) ~d by the natural onset of detonation from the unsteady combination of an
accelerated flame G preceded by a shock wave S(solid curves) propagating at
velocity Dy.
ide c~.n see from these diagrams that chemical detonation lasers can utilize pro-
cesses shown in diagrams I, III and V on sections corresponding to overdrive com-
pressions befond the limit va1 ues, i. e. downstream from cross section C to points
where high-irequency detonation pulsations arise. Use can also be made of the
overdriven processes with smooth fronts found in Ref. 52�
- 186
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~ Fig. 7.13� Diagrams of wake printa
x
C_C ~ and graphs of the change in pulsation
- I~ sca.le ~x on the length of transition
of overdriven detonations to the
JJ � steady state , LCG : I--spin detonation
wave transition of a pulsating deto-
flf o nation axtificially produced under
~ overdri ving conditions in a tube with
IV x c.+ dx, MM a wire helix [ R~~f. 2~+, 50 II--pul-
60 sating detonation transition of an
.7~~ 50 induced spin detonation produced in a
D D~ ~ 40 tube with a helix at fixed initial
=
yD~ parameters of the mixture (an analo-
V/ 0 30 gous result was obtained in Ref. 36
by changing the initial density of the
I/!1 � 20 ~~~e) ; III--strong initiation by an
electric discharge [Ref. 51]; IV--
/ onset of detonation from unsteac~y G-S
/ X complex; V--strong initiation by an
~ el.ectrodetonator or a suspension of
/ 10 lead azide; VI--collision of spin
~ detonation with unsteady G-S com-
.b -d ~ plexes ; VII--collision of pulsatin~
~ detonation with unsteac~y G-S com-
~ r o 5 plexes
4
} . 3
d /
~ 2
� o
+
q' 1
~ + D~, km/s
0.~~~`~~.p1 x ~...~~"~V~ p~ '72
~~~~~o -~~~1D~ 2,7
~ '
0 0,5 2 2
Xl~c~

~
tili~cture iE:~~eriment p, kPa I~ube I LCG
CHd/20, X 40 20 90
2H,/O~ ~ 13,3 16 40~
17 , 3 18 50
p 26,6 IS 800
D 90 20 30 -
~ 53,3 20 40
66 , 6 20 SO
? 9,3 l6 30
p 40 16 8
1.87
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The process b;~ which detonation arises under conditions of overdriving is identical
to the process of stimulated emission in lasers and masers, and is characterized by
shoc!: wave a.mplification and coherent energy release (for example, IV on Fig. 7.13)
called the "swaser" effect in Ref. 53�
�7.4. ~iechanisms of Population Inversion in Chemical Detonation Lasers
Pumping the active substance by the energy of the chemical bond. To increase the
coefficient of utilization of pumping energy, it is suggested in Ref. 4 that ex-
plosion energy be converted directly by dissociation, including by photolysis,
impact dissociation or some other chemical reaction through the process of pre-
mixing tne working substance of the laser with the initial explosive. Such a
method of producing a medium with negative absorption factor is based on the fact
that any e~ml.osive in the initial state ca.n be treated as a medium with population
inversion for which the state of the combustion products is a stable state. In-
version upon detonation of an explosive can be realized by a variety of reactions
in the deton ating e xplosive medium. Let us consider some of these reactions.
a. Z'r~o-component m2xture : explosive + working ( emitting) substa.nce.
:or this case, ener~,y ~onversion is realized as follows. The explosive XY disso-
ciates:
vY-' ~`~Y~+`~~~+hv'~' (7�52)
where the XY~ are products of dissociation of the initial substance; ~E~ is the
kinetic energy of the reaction products; hv~ is the ener~}r of a quantum emitted
upon dissociation of the intial substance XY into components XY~; m is the number
of terminal products.
Jpor. exolosion, the ener~ of the praducts of dissociation is e:tpended on decompo-
sition an d emission of the introduced working substance AB:
AB -I- ~E1-~ AB*; ( 7. 5 3)
AB -I-- hv~ AB*. ( 7� 5~ )
;=~3* in turn may emit a quantsm as a result of reactions
AB* A-f- B'' --r A-F- (B hv); ( 7� 55 )
AB A-i- B-~- hv DE. ( 7� 56 )
Reaction (7.55) corresponds to emission of a product of dissociation (B~') of the
axcited A3* molecule, and reaction (&.56) corresponds to conversion of the working
substance from the e:ccited to the dispersed state.
Instead of the diatomic working molecule AB, the workin~ substance may contain a
monatomic substance A that in the excited >t ate forms a metastable molecule with a
nispersed lower state. The reaction scheme for this case is as follows:
pT~E~ A*, (7�57)
hv~
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A i-- A* --r A2; ( 7� 5 8)
Az A A ~E hv. ( 7 . :9 )
From an energy standpoint it is more advantageous to use substances with 1ow ciis-
~ociation potentials such as metal salts in reactions ( i. 35 7� 56 On the other
hand, reactions (7.57), ~7�5a) can utilize noble gases or metals such as Zn, Cd and
Hg that are capable of forming dispersed molecules as the substance A.
b. Pure expZosive. The most interesting method of energy conversion is that in
which the initial substance XV, one of the fission fra~nents xi~ an d intermediate
3issociation fra~ent YY~ are excited or deactivated according to re actions (7.53)-
(7�56) or (7�57)-(7�59)�
Let us examine each reaction individually. The initial substance XY dissociates
into
XY S(YY~ DE~). ( 7. 60 )
~~i
Upon collision of the initial substance with fission fragment XY~, a molecule XY of
+his substance is excited:
XY ~E~ XY* ~ 7. 61)
and emits a quantum of li~t with transition of the molecule to the dispersed sta,te:
XY* -}-XY' XYa hv ~1E1 -i- ~E2. ( 7.62 )
As the dispersing fragments interact with each other, they are converted to the
ter*ninal products of the dissociation reaction of the initial substance ~Y, i. e.
m
XY'-f- XY'--� ~ (XY~-{-c1E~)� ~ 7.63)
~m?
'I'he dissociation reaction products XY~ in turn enter into reaction with the initial
substance ~`l, a.nd tr.e chain reaction continues until the initial reserves of sub-
stan.~~~ XY are completely e:thausted, the greater part of the energy stored in the ~
substance being con~rerted to emission energy in reaction ( 7. 61) . `I'he terminal
?roducts of such a reaction have a low temperature since the kinetic energr of the
- reaction products XY~ is con~re r+~d to luminous radiation in reaction (7.61).
Another mechanism of transformation oi the ener~ of the chemical bond to luminous
radistion is dissocistion of the initiai. explosive XY in accordance with scheme
(7.b0). One of' the fission fragments, for exa.mple XYi that has sufficiently low
�iissociation ener~ emits a photon by reaction scheme (7.53)-(7�56), i. e.
XY~ -'r- r~L�~ XY! Xt -f- Yi ; ( 7. 64 )
(7�65)
yi Y~ hv~; ~ 7. 66 )
X t-}- Y, X Y~.
`I~Yius ti~e ki:ietic ~~ner~f of fission f~agments is transformed to luminaus emission,
~~.nd t:~e fina]_ ~,hemica.l makeup of the mixture rern~.in_ un~.ltered.
189
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Also of some interest may be the following reaction mechanism that leads to con-
version of the ener~r of the chemical bond to luminous radiation, and that is: the
initial explosive is divided into several intermediate fission fra~nents (talsen as
two in our case for the sake of sim~licity):
XY XY~I~ XY~z~. ( 7. 67 )
`I'he fra~ments dissociate further into the terminal products of the decomposition
reaction
k
XY~~~--} S (XY~-{-~E~); (7.68)
~a ~
m
?CY~2~ J~ (XY; + DE~). ( 7. 69 )
~ak-}- t
, The unstable intermediate dissociation products (complexes) msy emit a light
quantum wi~h the following reaction schemes in the medium:
one of the complexes X`1~~~ is formed in the electron-excited state, and its deacti-
vation takes place upon radiative transition of the complex to the dispersed state:
k
Xycn ~ ~ (XY~ ~E~) hv ~ 7 � 7~ )
9- ~
or as a result of spontaneous emission with transition to the ground state
XYu~�-} XY~~~ -~hv (7�71)
with subsequent dissociation in accord with reaction scheme (7.68), (7.69)~
the intermediate complex is formed during collisions with the terminal reaction
product
XY~~~ ~Ei XYc~~� ~ 7� 72 )
and emits a quantum upon transition to the dispersed state
XY~n� ~ (XY~ -I-- ~E~) hv ( 7 � 73 )
9- ~
or with tr2.nsition to the ~round state
(7�7~+)
XYci~' XYc~~ /rv
with further dissociation
k
XY~~~ ~ (XY~ ~E,). ( 7 � 75 )
~m ~
'I'hese cases do not co-rer a11 possible reactions that convert tae energy of the
cnemical bond to radiation. The given reactions are typical in that they are non-
e~~uilibrium, and that pooulation inversion with stimulation of coherent radiation
m~~ ta:~e place in ~he me3iur.i in ~ahich t:7e;~ occur.
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. _
Feasibility of lasing on the CO molecule betiind an overdriven det~nation front
~~e 74 ~e detonation process , as we pointed out i:~ �7.1, is characteri~~d 'oy
^onstant avera~e parameters that are high inside the limi.ts oi detonation propa-
oatio:~. `i'his makes it difficult to vary temperature or density oi the reaction
_ ~rcducts for exa.mpl� when using mixtures in which tiie ratios of components are
outs~de +he concentration linits of detonation. So far no methods have been found
ior chemical laser utilizstior. of the high-frequency processes in detonation wave
~~ructure described in �7.1. Accounting for the~ is quite co~aplicated, and so far
it can only be assuned that the r_onlinearity of the detonation structure, the local
innomrager_eities of ~emper~,ture and density fields, and alternation of zones of
- ~,~^rAacted mixture and combust~on products must reduce the maximum possible gain
o~ eWission. These constraints c~.n be removed by using a mode of overdriven deto-
nation from plane snock wave S and trailing combustion zone G. In this case, the
izduction time of chemical reactions may be r~ore thsn five times as long as the
JEZ'lOG for reachin~ tkie thermoc~}rnamica.llf eauilibrium state of the gas behind the
~i:ock wave. It was shown by ca.lculation in Ref. 54 that under such conditions it
i, :ossibl~ to r.~e CO cne~ical de+onat~on lasers oased on a CSZ+ 02 mixture.
:irs~ the parameters ber.ind the snock wave front are calculated without consider-
-~t_or. ~f chemical ~ra.ns�or~!ations. 'I'ne Runge-Kutta method is used With a com-
~uter to calcul.ate the ccncentrations of all components from the equations of
:^~~^,.~cai :~ine~ics. ~acn vibra~ional level of the CO(v) molecule froM zero-ener~
~::Q seventeenth was taken as a.n indi~ridual comronent . The thermoc~ynamic quanti-
p, and crave vei~cit~� ~aere taken ~.s constant at er.er~ releaae Q less than
~e:ae predetermined -ralue ~q. After calculating the new ,ralues of the thermoc~yna.mic
:suar:t~~ies an d velocity corresponding to the calc ulated concentrations, the rate
constants of ~he chemicai reactions *aere found ai; ~~e new temperature values. The
~ :~eti-iod oi iterations ~Nas ssed to account for the temperature dependence of specific
neats .
"~:e ~rincipal reactions a.mcng more than 40 elementary reactions known from data in
;ile ~~terature for '.:he g~ ven mix~ure were selected from consideration of their role
::~e iirst 75 '~s �rom tne instan: whe~ the shock wave acts on the mixture. Rea.c-
:~or.s ~.rere not considered i~ their elimination during this period caused no more
'::an 0.17 de ~.aticns in thA concentrations of components. T!Ze given time interval
cor~pi~~~~y covers +,:e tine of existence ef inversion under the conditions assum.ed
`~r ;r.e ;~iven prob~em with respect to: a) composition of the mixture CS2/02/Ar =
i/~.~i`~0, 1/1/30, ~.j/1/i0; b) temperature range T=1b00-31+00 K; ci pre~sure
n~ u. ~`~I?a; d) c:.e:n:~ca1 kinetics in the given initial time interval of 75 �s de-
~e~�~ti ned by 1o selec+ed principal eQUations o� reactions with the following rate
_~::s;,ar:ta o" t:.ese reactions (k, cm3�r~ole~`�s-1; E, kJ�mole'1; R, kJ�mole-l.K-1)~
~ 1. CS3 CSZ : CS S-}- CSZ , k1= 0,166 � l Ola ;t ~
xer.P(-183iR7~; [55]
2. CS~ Ar ~ CS S-}- ~r, k2 = 0,364~ 10~8 x
xexp(-336/RT); (55J
3. CS~ 1- 0