JPRS ID: 8969 SUB-SAHARAN AFRICA REPORT

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~
QUANTUM ELECTRONICS

S DECEMBER i979 CFOUO Sl79) i'OF i
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FOit OFFICIAI. 1!SE ONI.Y
JPRS L/8800
5 December 1979
L
1
USSR Re ort
p -
PHYSICS AND MATHEMATICS
CFOUO 5/79) -
Quantum Electronics
.i
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_ JPRS L/8800
5 December 1979
USSR REPORT
PHYSICS AND MATHEMATICS ~
(FOUO 5/79)
QUANTUM ELECTRONICS
Moscow IC~ANTOVAYA ELEKTRONIKA in Russian Vol 6, No 9, sep 79
pp 1866-1870, 1903=1910, 1932-1941, 1953-1959, 1966-197~0,
2024-2027, 2033-2U34, 2036-2038 ,
CQNTENTS PAGE
~as~s anm r~asn~s
Decisive Role of Viscoelastic Properties o~ Polymers in
~ the Mechanism of Their Iaser Destruction -
(M. I. Aldoshin, et al.) 1
Gas Dynamical Laser With Thermally Nonequilibrium
Electric Arc Heating of the Working Medium
(B.V. Abakumov, et al.) 8
Quantum Statistics of the Photocurrent of Optimal ~
Detectors of Light Radiation Under Conditi ons of
Atmospheric tViewing~
(P. A. Bakut, et al.) 20
Investi gatior.. of Characteristi cs of a Fast-Flow
Continuously Operating C02 Laser r,lccited by a
Self-Maintained Dii~ect-CLZrrent Discharge
(A. G. Basiyev,,et al.) 34
~ Analytical Theory of Pulsed Lasing of a CO Laser With
Line Selection
(S. A. Zhdanok, et al.) ........-0 44
- a- IIYI USSR - 21Ii S&T FOUO]
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COMl't~,Ml'E~ ( Con t, i.nur:d ) p~,f.~.
Efficiency of ~imer Lasers Ut~~lizing Molecules of
Halides of Noble Gases Excited by an Electron Beam
(V. V, Ryzhov, A. G. Yastremski) 52 '
Periodic-Pulse Oper~,ting Mode of a Quartz-Iamp-Pumped .
Iodine Ultravilet Laser
(V. S. Zuyev, et al.) 60
Theory of Cavities With Wavefront Reversing Mirrors
(I. M. Beltdyugin, Ye. M. Zemskov) 63 -
~
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TA5ERS AND MASLRS
UDC 678:539.26
DECISIVE ROLE OF VTSCOELASTIC PROPERTTES 0~ POLXMERS IN THE MECHANISM OF
THEIR LASER DESTRUCTION
'J Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 6 No 9, Sep 79 pp 1866-1870
manuscript received 16 Apr 79
[Article by M.I. Aldoshin, B.G. Gerasimov, A.A. Manenkov and V.S. Nechitaylo,
Scientific Research Institute of Organic Tntermediate Products and Dyes,
Moscow, IISSR Academy of Sciences Physics Tnstitute imeni P.N. Lebedev, Moscow]
[Text] A study is made of the laser destruction of organic glasses with the
repeated and onetime effect of radiation pulses of nanos~cond duration. A
- correlation is established between the laser strength of transparent polymers
and their viscoelastic properties, in particular, their yield point.
- Investigations made earlier [1] have shown that an important role in the
mechanism of the laser destruction of polymers with the effect on them of
nanosecond radiation pulses is played by the viscoelastic properties of the
matrix. In recent times studies [2-4] have appeared in which the laser strength
of organic glasses is explained by their tendency toward carbonization during
thermolysis [2] or by their supermolecular structure [3]. In [4J a molecular
method is suggested for.regulating the laser strength of polymethyl methacrylate
(PMMA). However, the conclusions of the authors of [2-4] were made without
taking into account the viscoelastic properties of polymers and in the absence
of contrvl of their optical purity (from the viewpoint of the presence and
dimensions of absorbing~inclusions). -
This study has been made for the purpose of further studying the mechanism,of
the laser destruction of transparent polymers and the relationship between
the laser strength of these polymers and their viscoe~astic properties.
For the purpose of eliminating the influence of the o.ptical purity of polymers
on the results of investigation of their laser strength, in the experiments
were used the same materials, the optical purity of whiah remained unchanged,
and whose viscoelastic properties were varied by adding to the polymer a _
highly volatile plasticizer or by changing the temperature of the specimens
over a wide range (from -60 to +80�C).
1
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- A determination was made of the bulk failure threshold of polymers with a
~ single burst, Td , under the influence of a giant (length of approximately
20 ns) radiation pulse af a ruby laser focused by a lens with a focal length
of f= 4 cm , as well as of their laser strength with the repeated effect
of radiation pulses of a fixed prethreshold strength, If , determined by
the number of laser bursts, N, prior to the appearance in the matrix of
macroscopic (approximately greater than 100 u) fractures.
~
In one series of experiments with specimens of PMMA, the initial content of
highly volatile plasticizer in which equaled 20 percent, a determination was
made of Id and N from the degree of volatilization of the plasticizer.
_ It is obvious from Pig 1 that with a decrease in concentration of the plasti-
cizer and with an increase because of this in the yield point, ~ , of the
_ polymer, I and N are reduced. A similar reduction in the laser strength
of plastic~zed PMMA (with a fixed plasticizer content of 20 percent~ is ob-
served also with lowering of its temperature: With T=+20�C , N> 10`~ ,
~and with T=-60�C , N ti 103 .
In another series of experiments an~i:~vestigation waG mane of the laser strength
of unplasticized PMMA at different stages of polymerization (fig 2). As in
[1,3], with an increase in conversion of~~the monomer, the sample's Id is
diminished. A rise in its temperature results in an increase in Id , which is
apparently associated with a reduction in Q in heating. With an increase
in conversion of the monomer N is also reduced (for a monomer N> 104 and
f or PMMA N ti 20
Id,amN. td 1)
1,5 N>lOk
1,0
N=700
~ ~54 ' 6 B ~'e,,kr/Mn~)
Figure 1. Reduction in Laser Strength Under the Anetime.and Repeated
Effect of Radiation Pulses in Proportion to Volatilization
- of the Plasticizer and an Increase in the Polymer's Yield
Point
_ Key: 2
1. Id , relativa units 2. QVe , kg/mm
An increase in the optical purity o~ the monomer results in even more drastic
reduction in the failure threshold in the process of conversion of the monomer f
into a polymer (table). Let us note that the effect of a reduction of I
in the process of conversion from the state of liquid aggregation ta the d
solid state is apparently of a general nature, which has been confirmed by us
in freezing organic solvents (e.g., glyceryne).
2
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Id~omN. ed. l~
T ,
- - ~
- ~ T=BO�
~
~
20�
0 10 '10 BO 90 B,%
Figure 2. Dependence of Bulk Failure Threshold, Id , on Degree of
Conversion of the Monomer, B
Key:
1. Id , relative units
Table
3~ HcaonxwR ~ 4~ Ovxu~enNdp ~ I1M~tA c
6~:I~CTII~N-
K:1 TO p0 M
~ M1~IA I[MDt,~ ,~iM.~ I nMMA (20�.0)
QzP ~ Kl'/~IMZ l~ 8~)
aB3, Kr/Mn~= 2~ 12 ' 12 3,9
/ 2,4 1,0 ;0 �3,5 1,4
~ 20 90 > 10;
Cnpaeovxde Aaxnae
Key:
1' kgl~~~brittle ~ailureJ ' S. ~'~~~ied -
_ /
2' kv ~}rield point] ' 6� pMM~ ~-th ~;:asticizer (20 percent)
g~ 7. Handbook data
3. Initial
Experimental investigations have shown that with the repeated effect of
laser radiation with a strength of If < Id~ thoroughly purified P1~Il~IA with-
stands about 90 radiatio~ pulses prior to fhe formation of macrofailure,
wher.eas unpuri~ied with the same strength, T~ , witAstands about 20
x~a,diatton pulses (c~. tat~],e), Such an insign~.~icant (~xom 20 to 9Q radiation
pulses) incr~ase tn the laser strength of PN~fA on account o# improvement of
its optical purity is practically the limiting increase ~or matrices whose
yield point is higher than their brittle failure point. On the other hand,
3
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_ plasticized PI~II~fA withstands mor~ than 104 radiation pulses of strength If
even with a lower failure threshold.
These results demon3trate that for polymers with different viscoelastic pro-
perties there is no correlation between I and N. Consequently, a high
value of Id per se, obtained only on account of improvement of the optical
purity of a polymer, cannot ensure a high value of N. For polymera with
identical visco~lastic properties the correlation between N and Id is
observed fairly distinctly. It is obvious from fig 3 that with a 10-fold
reduction in If relative to Id unplasticized PNIl~tA withstands not more 4
than 100 radiat3on pulses, whereas pl-~:~ticized PMMA withstands more than 10
laser bursts with a considerably lo~er (threefold) reduction in I relative
to Id (samples were selected with an identical failure threshold~.
lgN
4 2
~ 3
1 ~
~ ~ b
0
1 3 5 7 Id /I
f
Figure 3. Laser Strength of TJnplasticized (1) and Plasticized (2) ~
~1A with Onetime Effect of Radiation Pulses of Prethreshold
Strength
For the purpose of revealing the nature of viscoelastic properties of polymers
playing an important role in the mechanism of their laser destruction, by
~ means of a plane.polaroscope a study was made of the morphology of fractures
in PMMA with the onetime effect of laser radiation of strength I ti I
It was shown that in a series of successive laser bursts in the case 6~ un-
,plasticized P1~fA a macrofracture measuring approximately greater than 100 u
arises in a threshold manner in the last burst of the series and is accompanied
by a bright spark. Furthermore, around the fracture a stressed-state region ~
is practically not observed. In plasticized PMMA after a certain number of
bursts (the more, the greater tha~ difference of Id - I ) a macrofracture
originates, measuring approximately less than 10 u, in ~he form of an opaque
melted area gradually increasing in size with successive exposures. Purther-
more, a visible glow is not observed, and the stressed-state area around the
_ strain fracture is increased (fig 4a). Tn the last burst is observed a bright
spark, a macrocrack is formed and almost total removal of stresses around the
fracture takes place (~ig 4b).
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.
Figure 4. Photographs o� Laser Micro- (a) and Macrofractures (b) in
Plasticized PMMA with a Plane Polaroscope
Thus, in the Iaser fracturing of polymers a visually observed glow (spark)
arises only in the process of formation of macrocracks and this is apparently
caused by tribo-effects ~5] accompanying failure of the material near ab- ~
sorbing f.laws resulting from thermoelastic stresses.
Heating of unplasticized and plasticized PMMA to the vitrification temperature
resulted in the total removal of stresses and strains around fractures, which
testifies to their forced elastic nature. "In this connection the correlation
which we discovered between the laser strength of polymers and their yield
point becom.~s understandable.
For the purpose of explaining the experimental results presented let us make _
use of the mechanism suggested in [1] for the laser fracturing oz polymers,
associated with their viscoelastic properties. As follows from an analysis
- of the system of heat conduction and elasticity equations, in a medium with
an absorbing flaw important for the process of laser fracturing is parameter -
S, characterizing the thermoelastic properties of the matrix aizd equal to the
ratio of the energy of strains in the medium caused by heating of the flaw
to the energy of the laser r3diation absorbed by it:
T 1' v 2 2 2
o -r
~ ~
Cy 1 - v
(1)
where c is the velocity of sound, CV is the specific heat, v and a
are the ~oisson bracket and coefficient of linear thermal expansion, re-
spectively, and T~ is the initial temperature of the spec:imen. Substituting
in (1) the parameters of PMMA gives s= 0.06 , which exceeds by a few orders -
of magnitude ~ calculatec by (1) for inorganic glasses (e.g., for fusad
quartz S ti 10 5). Consequently, the effectiveness o~ the conversion of .
the energy of laser radiation absorbed by a~1aw into the energy of elastic
strains of the matrix differs substan ially for such "soft" materials as
polymeric glasses, for which S~ 10 and for such_3hard" materials as
fused quartz, sapphire and the 1 ke for which R< 10 . This difference
ti
results in the fact that in real (i.e., those containing absorbing flaws)
5
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~ transparent dielectrics with S ti 10 3 laser fracturing originates as the
_ result ~f the thermal rupturing of absorbing flaws [5-7], whereas ~n polymers
~R ~ 10 2) elastic stresses comparable with breaking points originate with
slight heating of the flaw.
Calculati n of rupture stresses, ~eg , near an absorbing flaw measuring
a>(XT)i92 (X is the thermal conductivi~y of the medium and T is the
length of the laser pulse) gives ~
Qee ~t) _ ~ C~~ TTo)
~ (2~
where
T t-- I f Q(t') dt'
( ) - ~v~ (3)
0
is the temperature~ of the absorbing flaw at moment of time t with a power
density of the absorbed energy of Q; and p is the density of the medium.
. Estimates made in accordance with (2) and (3) demonstrate that in P1~tA _
og e stresses exceeding its breaking point are reached when the absorbing
flaw is heated a total of 100�C. Therefore for the formation and development
of a fracture in polymeric materials heating of flaws to considerable tempera-
tures (wt;~.en nonlinear effects of the absorption of the energy of laser radia-
tion beco~ne substantial) is not necessar}?. In connection with this fractures
are obserced in polymers with considerably lower (by more than an order of
magnitude) radiation strength as compared with the threshold strength for
"hard" materials.
The experimentally observed dependence of the laser strength of polymers on
their viscoelastic properties, as well as the correlation established between
Id and N and the yield point, can be explained in the following manner.
If ~a a well-known fact that in the plasticization of polymer.s, as well as
in heating them~, the yield point, v e, is reduced [8]. This results in the
fact that in the process of pulsed ~ieating of the absorbing flaw and a gradual
increase in ae according to (2) the yield point is reached earlier than
the breaking po~nt. As a result, the material around the flaw experiences -
forced elastic strains characterized by considerable percentage elongation
and is strafn hardened severalfold as compared with the brittleness point,
~khr~8~� In unplasticized PM~iA the yield point is higher than the breaking
po3nt and the material is fractured in an embrittlement manner with the forma-
~ tion of cracks. The relationships given far c~ and okhr explain well the
increase in the laser strength of plasticized ~ with tI~e onetime and re-
peated effect of rad3ation pulses as campared with unplasticized PMMA.
From this viewpoint the effect of a reduction in laser strer.gth in the proceas
, of conversion from a monomer to a poly~er also becomes understandable. The
6
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fact is that in the conversion of a monomer we have P'k~A plasticized by its
own monomer. The reduction of the content of unpolymerized monomer results
in an increase in the y1e1d point and as a result in a corresponding reduction
in laser strength.
The ideas developed here regarding the mech%.~iism for the laser fracturing of
polymers can be enlisted also for the purr,use of explaining the increased
strength of their surface as compared wf,ch their volume [9]. This fact is
Evidently associated with the difference in thermoelastic stresses originating
in the vicinity of absorbing flaws located near the surface and in the material's
bulk.
In conclusion the author~ express their thanks to A.S. Bebchuk for his helpful
'discussion of the results of this paper and to V.A. Golovina for assistance in
conducting the experiments.
Bibliography .
1. Aldoshin, M.I., Gerasimov, B.G., Mizin, V.M. and Nechitaylo, V.S.
"Tezisy VIII Vsesoyuz, konf. po kogerentnoy i nelineynoy optike" ~
_ [Theses of the~ Eighth All-FJnion Conference on Coherent and Nonlinear
Optics], Tbilisi, Mersniyereba, 1976, Vol 1, pp 136-137. _
2. Butenin, A.V. and Kogan, B.Ya. KVANTOVAYA ELEKTRONIKA, 3, 1136 (1976).
3. Agranat, M.B., Novikov, N.P., Perminov, V~P. and Yampol'skiy, P.A.
KVANTOVAYA ELERTRONIKA, 3, 2280 (1976).
4. Yemel'yanov, G.M., Ivanova, T.F., Votinov, M.P., Ovchinikov, V.M.,
Piterkin, B.D. and Smirnova, Z.A. PIS'MA V ZHTF, 3, 687 (1977).
5. DanileylGo, Yu.K., Manenkov, A.A. and Nechitaylo, V.S. KVANTOVAYA ELEK-
TRONIKA, 5, 194 (1978).
- 6. Danileyko, Yu.K., Manenkov, A.A., Nech itaylo, V.S. and Ritus, A.I.
iCVANTOVAXA ELEKTRONIKA, 1, 1812 (1974).
7. Danileykn, Yu.K., Manenkov, A.A. and Nechitaylo, V.S. ZHETF, 63, 1030
(1972). -
8. Kargin, V.A. and Slam~mskiy, ~.L.~ "Kratkiye ocherki po fiziko-khimii _
polimerov" [Brief Synopses on the Pt~~ysical Chem3stry of Polymers],
Moscow, Khimiya, 1967.
- 9. Bebchuk, A.S., Gromov, D.A. a~nd Nechitaylo, V.S. KVANTOVAYA ELEKTRONIKA,
- 3, 1814 (1976).
COPYRTGHT: Izdatel'stvo Sovetskoy.e Radio, KVANTOVAYA ELEKTRONIKA, 1979
[27-8831] -
CSO: 1862
8831 7
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LASERS AND MASERS
UDC 621.375.826:537.523.5
GAS DYNAMICAL LASER W~TH THERMALLY NONEQUILIBRIUM ELECTRIC ARC HEATING OF
THE WORKING MEDIUM
Moscow KVANTOVAYA ELERTRONIKA in Russian Vol 6 No 9, Sep 79 pp 1903-1910
manuscript received 24 Nov 78 ~ ~ ~
[Article by B.V. Abakumov, Yu.V. Rurochkin, A.V. Pustogarov, N.N. Smagin,
B.A. Tikhonov and V.V. UkolovJ
[Text] The feasibilitq is discussed of creating a gas dynamical laser (GDL)
with thermally nonequilibrium electric arc heating o� the energy carrying
component of the working medium and with selective excitation of the optically
~active component by mixing it with the hot gas in the area of the critical ~
cross section of the throat channel. The results are given of experimental
investigations on detection of the vibrational nonequilibrium of nitrogen
when it is heated in a high-current elevated-pressure arc discharge stabilized
_ by rapid injection of the gas through the porous wall of the discharge channel.
In the range of parameters realized in the experiment (I = 100 to 300 A,
p=(1 to 2)�105 Pa) the vibrational.temperature of the ground state of nitrogen
molecules exceeded the translational temperature of the gas by 1000 to 3000�K.
An indication is given of the possible advantages of a GDL with thermally non-
er~uilibrium electric arc heating as compared with a traditional GDL with
equilibrium heating of the working medium.
1. Introduction
Interest in GDL's as sources of dirc:cted electromagnetic radiation for
different technical applications has been growing steadily; however, charac-
t~eristic of this type of laser are a number of disadvantages. which considerably
restrict their introduction in industry. First among these are the low
efficiency of the conversion of thermal energy into laser radiation (0.5 to ~
2 percent) an3 the existence of expansion of the gas at high Mach numbers
(M = 4 to 5). The first disadvantage results in the need to heat and pump ~
a great mass of gas ~ox the purpose o~ achieying high output power, and the
second ~n complication o~ systems ~ox delivering the woxking medium and ex- ~
hausting the spent gas into the atmosphere. -
Of course, the ef~iciency of the conversion o~' the thermal energy of the
gas flow into induced emission ~or a~DL is determined by the competition
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" of two factors: by the le~- vibrat~,onal enexgy stored in the gas, charac-
':terized by the vibrational temperature, T, ~nd by the rate of DT relaxation,
determined by the temperature of translational iegrees of freedom, T. With
'*hermodynamic equilibrium heating the maximum v31ue of T is deter~iined by
the temperature of tt?e gas in the inlet of the throat uni~. For ordinary
GDL's (hea~ing of a preprepared mixture or production of it in the process of
burning fuel) the optimal v~~.lue of the braking temperature, T= 1600 to
_ 1800�K , is limited b,y collision relaxation losses in expansion of the gab
in the throat unit [1]. ~
- The employment of GDL's with mixing of the optically active component (C02)
with a preheated energy carrying component (N2) has made it possible to
raise the braking temperature of nitrogen to Z500 *0 5000�K and to obtain
experimentally record values of unit power output of 25 to 30 kJ/kg [2,3].
The most effective devices for heating gas to such high temperatures are
electric arc high-pressure plasmatrans, which have been used successfully by
a number of investigators for the purpose of heating gaseous working media in
GDL's [3-5].
It must be mentioned, however, that in spite t~f the encouraEing res~ilts ob-
tairled in model e:cperiments the creation of steady-state GDL's with high-
temperature heating and selective excitation of the ~caorking medium involves
considerable difficulties. In this paper is considered the feasibility of
improving the efficiency of a GDL with electric arc heating of the working
- medium by utilizing the effects of thermoche:nical nonequilibrium in the dis-
charge, stabilized by the rapid transverse in~ection of gas through the
porous wall of the channel. As experimental investigations have demonstrated,
in an arc discharge of this type it is possible to heat the energy carrying
- component of the workin~ medium, e.g., nitrogen, with the gas's vibrational
!-emperature higher than iia translational. Subsequent expansion of the nitrogen
in the supersonic throat unit with mixing of the optically active component
in the near-critical region of tne throat, as the result of the high value
of T> 2000�K , makes it possible to increase the inversion density, and
the possibility of thereby lowering the translationzl temperature, T<
< 1500�K , permits expansion of the rlow to lower Mach numbers of MP< 3,
which simplifies solving the problem of mixing components and exhausting the
spent gas irito the atn?osphere.
2. Experimental Setup and Investigation Procedure
In an investigation of electric arc plasmatrons ~rith delivery of the working
medium through the porous wall of the disch:.rge channel [6,7] it was dfs-
covered that as the result of rapid therraal and hydrodynamic interaction of
the radial gas stream with the current ccnducting nucleus o~ the discharge
are formed two zones which differ drastically in their para~neters: a high- -
temperature zone of ~low of ionized gas with low density, and a periph.eral .
- region o� ~1ow with a temperatuxe close to the temperature of the in~ected
gas. These two zones are separated by a region o~ quite h~gh temperature
gradients, velocities and concent~ations o~ components o~ the arc plasma.
The sudden change in parameters resulting from the rapid removal of heat
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into the gas surrounding the arc, di�~usion and also the dif�erence at medium
energies in the light and heavy components of the plasma are responaible for
the possibility of its deviation from thermodynamic equilibrium.
For the purpose of solving this problem it is necessary to establish the
ex~stence or absence of equilibrium between ~he vibrational and translational
degrees qf freedom of molecules of the plasma forming gas, e.g., nitrogen,
since it is precisely vibrational excitation of nitrogen which determines the
inverse population density of the uppex laser level of the radiating molecule,
e.g., CO . For this it is necessary to measure the vibrational temperature
of molecules of nitrogen in the electronic ground state and the translational
temperature of the gas. 7'he absence of equality between these temperatures
will indicate deviatiun from equilibrium with regard to vibrational-translational
degrees uf freedom.
The experimental unit (fig 1) was a direct-current electric arc plasmatron.
The arc discharge, 1, was struck between a cathode, 2, and anode, 5, separated
by an insert, 3, between electrodes, with a cylindrical discharge channel
- made of a porous ceramic material, 4, through whose walls was injected the
plasma forming gas--nitrogen. In the experiment were measured the current and
voltage of the arc, the rate of flow of the gas and the pressure in the channel.
The arc's radiation spectrum was photographed with a KS-55 spectrograph, 8,
- through quartz windows 6 and 7 in the middle cross section of the channel.
Investigations were made with the following discharge parameters: arc current
and voltage, I= 50 to 500 A, II= 200 ta 13~J0 V; intensity of injection of ~
~as through porous wall, m= 2 to 16 kg/(m2�s) ; pressure in channel, (1 to 20)�
�105 Pa . The inside diameter and length of the ch.3nne1 F:qualed 0.02 and
0.05 m, respectively.
e
3 4 6 7 S
1
~ : '
\ ~ \ ' ~ `I
2~
- / I I
. 1--1 ~ ~-1
2
Figure 1. Sketch Qf Expexi~qental Unit
The translational tetnpexature o~ the gas was identi~ted with the temperature
o~ the population o~ xotational ].eyels, which was determined from allowed
rotational lines K~ 12-55 0~ band 0-0 (391.4 nm) o~ the ~irst negative
system of nitrogen. The concentration of ~lectrons, ne , was determined from
- 10 ~
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the intensity of cont~.nuous radiation = 495.5 nm), taking into account
the contribution o~ the negat~ve continuum [8].
Of course, direct measurement oflt~e vibrational temperature o~ the ground
state of a molecule of N2, T(X requires the employment of special -
methods of IR diagnostics, t~ie uti~ization of which under conditions of a
- high-current e3evated-pressure discharge involves great difficulties and does
not make it possible to analyze fully mechanisms for the origin of nonequi-
librium. In this study, based on the results of [9], a method has been
develo~ed of determining T (X1E+) .~.from ,~1ne measured temperature of a
molecular ion of nitrogen, V~ g N2 (B2~u) .
_ In [9] ~~as established the absEnce o~ equilibrium between the electronic and -
- atomic-ionic components o~ the plasma of a high-current arc discharge sta- ~
bilized by the intense in3ection o� nitrogen through the porous wall of the
discharge channel. It was demonstrated that in a great portion of the channel's
cross section the temperature for population and distribution of atoms by
excited levels and the tempera~ure of electrons substantially raise the trans-
lational temperature of the gas.
~ In another study by the same authors of [9] a determination was made of the
composition of the nonequilibrium plasma of nitrogen and an analysis was made
of the mechanisms for the population and deactivation of electron-excited
- levels of atoms, molecules and molecular ions, from which it follows that
:.n the plasma of an elevated-pressure arc ~ischarge a major role is played by
collisions with heavy particles. State B II is excited in collision wi~t#
vibratio~ally excited molecules and molecule~ in the metastable state A E .
State C II is populate~d on account of step-by-step excitation by electron
collision ~rom state B II . Consequently, under the conditions considered
it is not possible to det~rmine the vibrational temperature of the ground
state of a molecule from vibrational temperatures of electronically+excited +
states of molecules obtained by measuring the intensity of ban3s 1 and 2
of tne positive system of nitrogen, as was done for low-pressure discharges
[10].
It2i,~ another matter wi.th the state of the molecular ion of nitrogen N+
(B E), which is populated primarily by electron collision and is deac~ivated -
in t~ie process of extinguishing with electrons. In one case and the other
considerable disruption does not take place in the nature of distribution by
vibrational energy levels,2s~nce the moment of momentum and the vibrational
_ energy in population of B~ by electron collisio~ va~ry+but slightly, in
addition to which the potent'~al energy curve for N(B is shifted but
slightly in relation to ~he $o~ential energy curve o~ theuelectronic ground
state of nitrogen ion N2 (X as a result o~ which the distributions by _
vibrational energy2l~~el in tli~se states are sim~lax. Consequently, the
temperature, T(B , measuared in ~the experitqent ~hould ag~e~ with the
vibrational tem~erature o~' the ground state o~ the ion, T(x Since
the exchange o~ vitirational quanta between ~olecule N2 ~nd io~ NZ' takes
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place as the result of the rapid charge transfer reaction N2 + N2 } N+2 + N2
and the characteristic exchange time is two to three orders of magn~tude ~
- short~r+than than the VT2r~laxation time [}1~, it is possible to state that
T~ (B E) equals T~ ~X E) equals T~ (X E). The transfer of vibrational
energy ~rom N2 to N2 a~ the result of th~ charge transfer reaction,
caused by the difference in_~he m~gnitude of the v~brational energy quantum
of molecules (w = 2359 cm and 2207 cm does not ~esult in a
difference in v~~rational temperature~2of molecules H and N2 , since this.
effect under the conditions considered will be substan~ial only at fairly ~
low translational temperatures (TP < 1000�K), e.g., under conditions of a -
low-pressure glow discharge.
In our experiment the vibrational temperatures of the different electronic
states of molecules and molecular ions of nitrogen were determined from the
radiation intensities of the appxopriate system of molecular bands. The
absolute intensity was determined from a trace obtained in processing a
photograph of the spectrum with an MF-4 microphotometer. The sensitivity
and its dependence on the wavelength were determined from the spectrum of an
SI-10-300 standard tungsten lamp. The error in measuring the absolute in-
tensity of radiation equaled 40 percent. The error in measuring relative
intensity, compared with reference to the ratio of the heights of peaks of a
band to its area, did not exceed 20 percent. _
_ The vibrational temperatures of a specific electronic state were determined
from the tangent of the angle of the slope of the direct dependence of
ln ~Jv'v"~Qv'v"~4~ on the energy of the vibrational level, E, (where
and v are the intensity and frequency of the radiation at the v'-v"
transit3on and q__, � is the Franck-Condon transition factor). An approxima-
tion was made of ~h~s d~,p~ndence by ~the method of least square~.+ The vibrational
temperature of state B E , which was identified with T(X E), was
measured in relation to ~}-0, 0-1, 1-1, 1-2 and 2-4 transi~ions ~f the first
negativ~ system of nitrogen with an error of not greater than330 percent with _
T= 10 �K . The vibrational temperature of states of N(C II) were
measured in relation to 0-5, 1-5, 2-5, 3-8 and 4-10 transitions of the second
positive system of nitrogen with an error of not greater than 16 percent.
_ 3. Experimental Results
In fig 2 are given graphs of the distribution over the radius of the discharge
channel (r = 1 cm) ~f+the vibratiqn~l temperature of the ground state of the
molecule N2 (T (B Eu) = T~ (X E)) (curve 1) and of the translational
temperature of ~he gas (curve 2). gAs can be concluded from these graphs,
in a great portion of the channel the vibrational temperature is greater than
the translational, which testifies to deviation from equilibrium with regard
to vibrational-translational degrees of freedom, especially in the peripheral
zone of the discharge.
Mention should be made of the fact that in peripheral region3 of the discharge
(r > 7 mm) according to [9) in population of state B2E+ a considerable role
begins to be played by interactions with solid particles and identification of
vibrati~nal temperatures of the electron excited ground state of the molecular
ion of nitrogen and of the ground state of the molecule requires additional
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refinement. Nevertheless, as follows from fig 2, obtained with discharge
parameters lying ~~rtthin the range of certainty for experimental determination
of the vibrational temperature of the ground state of molecule N, the
vibrational temperature is greater than the translational tempera~ure of the
gas by 2200�K (T = 4200�K and T=-2000�K Let us note that, according
to the results o~ [9], the degree gf deviation from equilibrium and, consequently, _
the separation of T from T, their absolute values and the dimensions o�
the zone of existence of noneq~iilibrium make possible regulation of variation
: in the intensity of injection and in the discharge current. So, with an in-
crease in injec*ien and a steady discharge current the separat~on of T from
T grows on account of a reduction in temnerature of the gas. With an~increase
- i~i current and steady intensity of injection the central equilibrium region
of discharge is expanded and the senaration of temperatures in the peripheral
- regi~n is maintained with higher absolute values of TP and Tv .
T�f0-J K Lgn~,n J
10 T6
8 24
2 ~
6 ~ 12
e
n
4 \ ~o ?0
~ ~ \e
2 ~ 3 1B
\
~ ~ l6
D 2 4 6 r,MM
Figure 2. Experimental Distribution of Vibrational and Translational
Teu4peratures and of Concentration of Electrons in Relation
ta Radius of the Channel
In fig 2(curve 3) is given also the distribution, measured experimentally,
of the concentration of electrans, n, as campared with that computed for
an equilibrium composition in terms o~ temperature, T= T (curve 4). From
the results obtained it follows that deviation from equil~brium is expressed
not only in a separation of temperatures, but also in concentrati.ons of com-
ponents of the plasma, e.g., electrons, considerably exceeding eg~ilil~rium
values. For example, at r= 6 mm with T= 3000�K , n= 10 m ,
whereas corresp~nding to the equilibrium ca~e at the same ~emperature is
ne = 5.4�105 m [12].
Thus, the plasma of the arc discharge under the conditions discussed is not
only nonequilibrium thermally, but also chemically, and the electric arc
1.3
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. pZasmatron with stabilization o~ the diacharge by means of intense "pore"
injection in this case can be regarded as a generator of a stream of a non- '
equilibrium plasma of an elevated-~density molecular gas.
4. Discussion of Results
The results obtained indicate the feasibility of utilizing vibrational non- ~
~equilibrium electric arc heating of the gas for the purpose of improving the !
efficiency of a GDL with excitation of the optically active component by '
mixing it with the heated gas. By combining the discharge chamber of the ;
plasmatron with the receiver of the GDL's throat unit it is possible to arrange
for removal of the gas into the throat from the nonequilibrium peripheral zone
of a discharge with a moderate translational (T < 2000�K) and a high vibrational .
_ (Tv > 2000�K) temperature. Here it is importan~ that the distance f~om this
zone to the throat's critical cross section, where the vibrational energy is
quenched, be less than the length of vibrational relaxation of nitrogen with
the parameters of the gas in the receiver. Since the vibrational relaxation
_ time for pure nitrogen at not too high a translational temperature (T <
< 2000�K) is comparatively long, these conditions can be fulfilled. ~or
example, with T= 1500�K and Tv = 4000�K (cf. fig 2)g TN = 0.94 ms [11].
Assuming that th~ pressure in the receiver eAv~s p~ = 10 Pa 2 and the mean
rate of flow in the subcritical section of the throat equals approximately
300 m/s. we get a relaxation length of R= 28 mm , which testifies.to the
_ r
feasibility of withdrawing nitrogen into the throat while maintaining non-
equilibrium vibrational excitation. A basic system for implementing one of !
the possible variants of such a unit is shown in fig 3. ~
,
~ 1 2 3~2 5 6 ,
~
~
~ ~
~
. ~ ' ~
\
; ~ ,
� � k
; Figure 3. Diagram o~ GDL with Nonequilibrium Electric Arc Heating of
. the Working Medium; 1--cathode; 2--arc; 3--porous channel; i
4--C02-He in3ection receiver; 5--anode; 6--glow discharge;
, 7--optical cavity
>
,t The advantages of nonequilibrium heating of the energy carrying component
of the working medium is illustrated quantitatively in fig 4 for a C02-N2
GDL. Illustrated in this figure is the supersonic throat of a GDL through ,
~ which the nitrogen heated in the electric arc discharge is expanded with
~ subsequent mixing fn the near-critical section of the throat of a C02-He
~ mixture, and illustrated conventionally is the change in translational and ~
! vibrational temperatures of the gas.
~
f
r l~
s '
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i
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T
~
~
~ COt + Hz o (He1
Nz
3000 j"--
1000 Tv_ T~
- er2
10~70 -r~-- ~ dI -
- .
~ x
Figure 4. Quaiitative Picture o~ Expansion of the Gas in the Supersonic
Throat of the GAL
With equilibrium heating (solid-line curves) the inversion density is deter-
mined by the difference DT1 (it is assumed that ~2 (v = 1) equals TC02 -
(001) and T~p2 (100) equals T. With nonequilibrium heating two variants
are possible for increasing the~efficiency of the GDL. In the first variant
(dot-dash lines) even before the critical cross section of the throat T>
> T and the inversion density is determined by the value ~T2 > T1 , v
whi~h generally corresponds to high energy output. The simplest quantitative
estimate shows that with a value of T- T = 2000�K before the throat's
cxitical cross section the reserve of vibra~ional energy in the nitrogen which
can be converted into induced radiation is three- to fivefold greater than in
equilibrium heating of the nitrogen to TP = 2000�K .
The advantages of the second vari~nt of nonequilibrium heating (cf. fig 4,
dotted linea) are evidenced in the fact that with a lowered_translational
temperature, T, for the purpose of achieving the same static parameters ~
in the cavity ~re required lower Mach numbers, which simplifies the problem
of mixing components, reduces losses on account of gas dynamical inhomogeneities -
in the stream and lowers the pressure in the throat unit's receiver required
for exhausting the spent gas into the atmosphere through the superaonic exit
cone.
Let us indicate two more advantages of n~nequil'_brium electric arc heating of
the working medium of a GDL. The first cons;~ts in the ability to increase
the pressure in the cavity, since the relaxation time, T[C02(001)] , is reduced
linearly with an increase in pressure and is increased exponentially with a
reduction in the gas's temperature. The second advantage consists in the
fact that because of the reduction in the rate of collision deactivation of
C02 molecules with lowering of Tp C02 in a mixture wifh H20 or He can "
evidently be mixed in the subsonic zone of the throat unit, which considerably
improves mixing efficiency and the homogeneity of the flow.
~ ~5
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. rux ur~r~l~t[~ U5~ uNLY
From the results o~ a determination of the camposition of the nonequilibrium
_ plasma of an arc discharge in [9] it follows that in the peripheral zone from
which the gas is removed through the supersonic throat the conc~~tratior~8of_3
electrons is considerably greater than the equilibrium (n = 10 to 10 m;
. cf. fig 2, curves 3 and 4). Taking into account the poss~bility of quenching
the nonequilibrium concentration of electrons in the superson~!c throat [13],
- in principle it is possible to introduce additional vibrational energy beyond
the critical cross section of the throat, e.g., in the glow discharge [14].
In this case the main arc discharge in the plasmatron, in addition to heating
the gas, will perform the role of a preionizer for the semi-self-maintained
discharge in the region of the cavit~ (cf. f ig 3).
5. Numerical Investigation -
For the purpose of a quantitative verification of the influence of preliminary
electric arc heating of nitrogen on characteristics of the inverse medium,
a calculation was made of the supersonic flow of a vibrationally relaxing
mixture of N-CO -He with a determination of inversion density and gain.
Gas dynamics2equations ~for the two-dimensional flow of a nonviscous and non-
heat-conducting gas were solved by the method suggested in [15] together with
equations for vibrational relaxation for a mixture of gases with four vibra- -
tional modes [16J.
For the case of equilibrium heating, in the critical cross section of the t
throat was set a value of T= Tv , and for the purpose of modeling non-
equilibrium heating, ~T = T P- T. Tn modeling separate heating of the
nitrogen and excitation of ~he o~tically active CO2-He mixture was employed
a model of instantaneous mixing. To the point of 3n3ection of the COa-He,
the flow cf the N2-C02-He mixture was considered by taking into account only
VT relaxation of 1V2 for N2. At the point of in3ection were included the
mechanisms for the vibrat3onal exchange of N2 and CO , W exchange in C02
and VT relaxation of CO for N2, C02 and He. Thus, ~he flows of N2 and
C02-He were separated (~rom the viewpoint of relaxation kinetics, but not
of gas dynamics). �
Calculations were made for a profiled throat with an expansion ratio of
A/A* = 30 , a critical cross section height of 1 mm and a supersonic section
height of 25 mm. The point of injection of the C0~-He mixture, i.e., the ~
point for includir.g vibrational exchange of N2 molecules with the optically
active component, was set at coordinate x. Calculation with x= 0 can
be regarded as modeling of simultaneous heating and expansion of t~'e mixture.
In fig 5 are given characteristic distributions over the axis of the throat
of vibrational temperatures of nitrogen, T, of the antisymmetric mode of
CO (v3) , T3 , of the combined mode of CO ~vlv2), T2 = T1 , of the trans-
la~ional temperature of the gas, T, of ~he absolute value of the inverse
population, ~N , and of the gain, It follows from this figure that
for equilibrium and coml~ined heating of the mixture (x~ = 0 and ~T = 0)
the gain is a= 0.3 m (dotted line), which in order of magnitude agress
with the eicperimental results obtained under approximately the same conditions
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[16]. Mixing the C02-He in the supercritical region at a distance of 4 mm
downstream fram the critical cross section with equilibrium heating (x =
= 4 mm and ~T = 0) results in a fourfold increase in a(dot-dash ~ine),
which agrees qualitatively with the experiment in [1]. The results of
mode.ting nonequilibrium heating (~T = 600�K , x = 4 mm , solid-line cur~~es
in fig 5, and ~T = 2500�K , x = 0, fig 6) demonstrate the possibility of
increasing the gain six- and 1~-fold, respectively, as compared with equi-
librium heating. Furthermorei~the_~nversion density in the latter variant
(cf. fig 6) equals DN = 3�10 cm , which ~s an order of magnitude higher -
than the inversion value with_qrdinary high-temperature heating. The high _
value of the gain of a= 6 m with ~T = 2500�K and x= 0 (cf. fig 6)
is caused by the great difference in temperatures T3 and� T2 , i.e., by
the differenc.e in populations of the upper and lower laser levels of C02
molecules. It is characteristic that in this case T3 approaches T4 more
quickly than in the calculation variant in fig 5. Th3s testifies to the =
effectiveness of the exchange N2 (v = 1) + C02 (000) N2 (v = 0) + C02 (001) .
T�f0-';N;oc,M-~~dN�JO ~6CM~J
4
dN '
J T4
2
~n ~
~
~ TJ T,T, a
~ _
0 5 10 15 70 X~HfY
Figure 5. Calculated Distributic,n of Parameters Over Axis of Throat
for Mixture 0.2 ~02 + 0.35 N2 + 0.45 He with TP = 2600�K
and p~ = 1.8�10 Pa
- T 10"'~H: d.M-~;dN�;0"';c,N"s -
5 a
4
3 r4
2 Tj
dN
/
Ip T~
0 S 10 x,nn
Figure 6. Calculated Distribution of ~arameters Over Axis of Throat
~or Mixture o~ 0.1 CO + 0.35 N+ 0.55 He wlth T= 1000�K ,
~T = 2500�K and p~ ? 1.8�106 ~a and xV = 0 P
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Let us note in conclusion that the advantages of thermochemically nonequilibriu~
electric arc heating of the working medium of a GDL di~cus~ed in this arfiicle�~
with a C02-N GDL as an example can be more considerable when using as
energy carry~ng component gases such as CO or H2, since the effectiveness o~
vibrational electron exchange in these gases is considerably greater than in
nitrogen.
Bibliography
- 1. Kroshko, V.N., Soloukhin, R.I. and Fomin, N.A. FIZIKA. GORENIYA I VZRYVA,
10, 473 (1974). ~
2. Krauklis, A.V., Kroshko, V.N., Soloukhin, R.I. and Fomin, N.A. FIZIKA
GORENIYA I VZRYVA, 12, 792 (1976). -
Tazan, I.P.E., Charpenel, M. and Borgki, R. "AIAA Paper, N73-622" (1973).
4. Shall, Migamoto, Horioka,. Murasaki. JAP. J. APPL. PHYS., 15, N2 (1977).
5. Kasuma, Migamoto, Murasaki. JAP. J. APPL. PHYS., 15, N7 (1977).
6. Kurochkin, Yu.V. and Pustogarov, A.V. In "Eksperimental'nyye issledo-
vaniya plazmatronov" [Experimental Investigation of Plasmatrons], Novo-
sibirsk, Nauka, 1977 p 82.
7. Kurochkin, Yu.V., Pustogarov, A.V. and Ukolov, V.V. IZV. SO AN SSSR,
SER. TEKH. NAUK, No 13, 23 (1978). :
8. Biberman, L.M. and Norman, G.E. UFN, 91, 193 (1967). .
9. Rurochkin, Yu.V., Polak, L.S., Pustogarov, A.V., Slovetskiy, D.I. and
Ukolov, V.V. "Materialy VII Vsesoyuz. konf. po generatoram nizkotempera-
turnoy plazmy" [Data of the Seventh Al1-Union Conference on Low-Temperature
Plasma Generators], Alma-Ata, Kitap, 1977.
10. Novgorodtsev, M.Z., Ochkin,.V.N. and Sobolev, N,N. Preprint FIAN,~Moscow, _
1969, No 172.
11. Yeletskiy, A.V., Palltina, L.A. and Smirnov, B.M. "Yavleniya perenosa
v slaboionizovannoy plazma" [Transfer Phenomena in a Slightly Ionized
Plasma], Moscow, Atomizdat, 1975.
12. Burchorn, F. and Wiencke, R. Z. PHYS. CHEri., 215, 265 (1960).
13. Bazhenova, T.V. and Lobastov, Yu.S. In "Svoystva gazov pri vysokikh
temperaturakh" [Properties of Gases at High Temperatures], Moscow,
Nauka, 1967.
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- 14. Biryukov, A.S., M~trchenkv, V.M. and Shelepin, I,.A. TRUAX ~~AN, 83,
' 87 (1975).
15. Tvanov, M.Ya. and Krayko, A.N. ZHURN. VXCH. MAT. I MAT. FIZ., 12,
No 3 (1972).
1G. Losev, S.A., Makarov, V.N., ravlov, V.A. and Shatalov, O.P. FIZIKA ~
GORENIYA I VZRYVA, 9, 463 (1973). -
COPYRIGHT: Izdatel'stvo Sovetskoye Radio, KVANTOVAYA ELEKTRiDNIKA, 1979 _
[27-8831]
CSO: 1862
8831 _
~
,
~9
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LASERS AND MASERS
UDC 621.378:535.3.087
QUANTUM STATISTICS OF THE PHOTOCURRENT OF OPTIMAL DETECTORS OF LIGHT RADIATION
UNDER CONDITIONS OF ATMOSPHERIC 'VIEWING'
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 6 No 9, Sep 79 pp 1932-19~+1
manuscript received 15 Jan 79
[Article by P.A. Bakut, K.N. Sviridov and N.D. UstinovJ
[Text] Taking into account quantum effects and registration noise, statistics
were obtained and investigated, of the photocurrent of optimal detectors of
incoherent broadband light radiation for different conditions of atmospheric
- "viewing." It has been demonstrated that the presence of atmospheric phase
- distortions results in alteratinn of the statistics 6or the photocurrent of
optimal detection and worsens the energy characteristics of the distributions
gotten. ,
Introduction
In recent years a number of studies have appeared, devoted to the optimal ~
processing of coherent~ [1] and incoherent [2] light fields under conditions
of atmospheric "viewing." Investigations conducted have demonstrated that
optimal are those detectors which form quadratic functionals of the detected
light field. However, in these studies the quantum effects of registration ~
[2) are either totally not discussed or the influence of tur~ulence of the
atmosphere on their statistics is n~t taken into account [1]. In connection ~
with this, in thi~ study is considered the.influence of turbulence of the ,
atmosphere on statistics of the photocurrent of optimal detectors of incoherent
broadband light radiation. ~
1. Realization of Optimal Detection
Based on the investigations made in [2], the quadratic functional, Z, of
detected incoherent broadband light radiation, E(p,t) , synthesized in the ~
absence of atmospheric phase distortions, has the form
Z= 2 ~Zn~s ~ dw ~ v(r, w) dr ~ T E(P, t) e-`~~ H~ (P - r) dt dp ? '
s. sA ~
~ (1)
20
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where
- V (r~ w) = No ~ nNo)I ~ - ~ ~r~ r ~2~
J(r) is the spatial distribution of the ob~ect's intensity; Nn is the
spectral power density of the background radiation; J(w) is tTie frequency
distribution af the obj ect's intensity in the transmission band of the pro-
cessing s}TStem; SD is the area of the object's pro3ectic~n onto the picturE:
plane (the plane located near the object and perpendicular to its viewing ].ine);
H(p-r) is a function characterizing in a Fresnel approxirnation the propalSation
_ o~ light waves from the pictuxe plane of the object, r, to the plane of the
telescope's receiving aperture, p; and SA is the area of the telescope's
receiving aperture. ~
Taking (2) into account, expression (1) can be rewritten in the form
Z- 2 ~2n)= f V~r) dr f J(w) dc~ j~ E~P, t) z r~,r HW ~P - r) dt dp 2, -
. sA o
(3)
~Jtilizing the spectral representation
E(p, t) ~ E(p, co) e r~,r dw~
_m -
i ~ ~4~
we convert (3) to a form convenient ~or physical interpretation o~ operations
required for practical realization of Z:
Z = 2 ~ V (rl dr ~ dt ~ .l E ~P, H~ ~P - ~ (w) e`~r dw dp 2 .
s, o -m sA (5)
where k= 2 exp (-ixT/2) sin (xT/2) (dx/x) is a real constant; and H(w)
is the ~re'quency characteristic o~ the matched filter, whereby
~H (w)~c2= i H~ (w)121 HA (~)J2=J (~u), ~
(6)
where H(W) is the ~requency characteristic o~ the equivalent filter of
the dete~tor, taking into accoimt the dependence of the photodetector's
_ sensitivity on frequency, defined as -
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IHu ~m)1z=Y ~~~'~~~i~), (7)
(y(w) is the quantum efficiency of the photodetector); and Hf(w) is the
frequency characteristic of a physicallq realizable matching f3lter.
Let us note that the transition from (3) to (5) is made on the assumption that
2~r/T is much less than the bandwidths of the matching filter, Hf(w) , and of .
the equivalent filter of the detector, H(w) , and that the detector itself
(an energy-sensitive recorder) includes ~ree main elements: a filter, a
squarer and an integrator.
The optimal processing arrangement realizing (5) can be represented in the
form shown in fig 1. Telescope reflector 1 performs a Fourier transform
operation of the type
E~~~ W) E~P, H~ ~P - r) dP;
SA
matching filter H(w) , 2, matches the �requency characteristic, Hd(c~) , of
filter 4 and of de~ector 3 with the frequency characteristic, J(w) of the
rece~ived radiation; photodetector 3 together with matching filter 2, filter
4, squarer 5 and integrator 6 performs the operation
r m 2 ~
~ dt f E(r, w) H~ (w) Hn (w) et`~~dW = Jp (r)
and forms in the output the image to be registered of the ob~ect, J(r) .
Then this image is scanned photometrically, is digitized and entered~ into
- the c~mputer, 7, where in keeping with (5} from it is formed the value of
quadratic functional Z .
This system realizes the magnitude of Z only as an average, and at each
moment of time t the value of. Z is random. This randomness is caused
firstly by the randomness of the received light radiation, E(p,t) , and
secondly, by the randomness of events of interaction between the light and
the material of the light-sensitive screen of the photodetector and is
cha.racterized by probability distributions P (n) and P~~(n) ,
where n is the number o~ events of interact~on b~etween the l~g-ht and the
material of the detector's photosensitive screen, and Ps+ Sh~(n) and Psh(n)
are the probability distributions of the magnitude of Z in t-he presence
and in the absence, respectively, o# a useful signal from the ob3ect. Let
us find these distributions.
2. Statistics of Photoreadings of Optimal Detection
Let us consider two possible casea: when processing is tqatched with the
atmospheric channel, i.e., optimal processing is synfihesized in the absence
22
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of atmospheric diatortion (and it actually is absent or is negligibly slight),
and when processing is not matched with the atmospheric channel, i.e., optimal
processing is synthesized in the absence o~ atmospheric distortion and it
actually exists. -
~ 19956
_ ,
' / ~ :
~
Figure 1.
Processing Matched with Atmospheric Channel
In this case the detected field, E(p,t) , represents a steady-state normal
random process [2]. With a fixed field, E(p,t) , the distribution of the
number of photoelectrons, n, in an optical detector with direct photodetection
obeys Poisson's law
P [ri/E (p, t)l =(Z^ln!) e-z
(8)
with characteristic function
(ir~) =exp {Z [exp (ir~)-1]}.
~9) -
For the purpose of finding the characteristic function o~ magnitude Z and
its probability distribution taking into account the Gaussian statistics of
field E(p,t) , it is necessary to average (9) for all possible realizations
of E(p,t) , and then from the averaged characteristic function of magnitude
Z obtained to proceec~ to ~.ts probability distribution.
In the observation of an extended source of broadband radiation quadratic
functional (5) can be represented in the form
T T
Z= 2 ~ f`~ E' ~Pi~ ti) E~Pz~ tz) V~Pi. Pz~ t i, fz) dtl dts dpi dPx,
SA SA S 0 ~1~~
where
m
v~Pi, Pz, t~~ tz) _~2n)z v~r, w) exp [-iw (ti tz)1 X
s.
X N;~ ~P~ - H~o ~Pz - r) dr dw, ,
(11)
~ 23
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?
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and the correlation ~unction o!' the detected ~ie1d, ~(p,t) , is detertqined
by the relationship
R~P~~ Pa~ tl, t)= I ~
- s (2n), f.f J(r, w) exp [-iw (t, -12) NW (Ai - r) X
- s.
X Nw (Pa - r) dr dw Nos ~P~ - Ps) a~t~ - tz)� ,
(12)
Employing the procedure for finding the characteristic furiction of the
quadratic functional for a Gaussian field in [3], we find that the character-
. istic function of magnitude Z has the form
~%~u) _ 4 cm and CO concentrations of 7.5 to 12 percent with
effective ti~hes within the range o~ 0.2 to 0.3 ms. For the purpose of comparison
let us use the data on vibrational relaxation coefficients from survey [6].
For these we have (in units o~ (mm Hg~s) 1):
-I ~
~PT)co,-co, = 350; ~PT)co,-N, = 106; i~Pi)co;-H,o = 3' 104~ ~Pti)rv~=x,o = -
= 35.
Comparis~on Q~ these. cQet~icients s~eaks~ in ~a~yor o~ the ~act that the ~qa~or
channel ~or the relaxation o~ vibrat~qnal enexgy~ is CQ2~^H20 co7.lisions.
The characteristic re~,axa,tion time ia the, c~,se o~ s hot~ogeneous medfum with
our composftion would equal TX = 0.2 to 0.6 ms , which is close to that
m~asured experimentally.
~ 41
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~ The investigations saade make it possibl,e to dxaw� a nu~qber of conclusions re-
garding dif~iculties in the creation o~ and op~rz~fiiag features o~ a~ast-flow
steady-state laser utflizing aix and mi~cing o~ CO2 beyond the discharge zone.
The experiment has~den~onstrated that it is possibie to cxeate an e~fectively
operating discha,xge chantber w3:th an e~~3,ciency~ qt 0.7 and air pressure of
up to p= 7.00 mxq H~ and ~1ow� rates o~ approxi~atel,y 200 ~q/s.
For the spe~i~ic el.ectrode sy~stem de$ign the unit di.scharge power equaled
E ti 70 W/c~p , which ~r�ith a dischz~xge zone length o~ 2 to 25 cm iqakes it
possible to contribute up to 300 to 400 ,~/g. ~s coirtpared wlth known designs
of electrode s}rstems with tubular (c~., e.g., [9,10]) or plate-type [7]
cathode elements, the emplo}rment of pins protruding into the gas stream
makes it possible to increase severalfold the e~fective pressure of the
m~lecular gas (cf. [9,10]) and the specific bulk power of the discharge and -
to reduce considerably losses of vibrational energy on account of relaxation
in the discharge chamber (cf. [7]). The gin design of the cathode is simple
to make and, as demonstrated experimentally, does not require special cooling
in operation.
As far as the problem of supplying C02 beyond the discharge zone and sub- -
sequent mixing of it with the active medium is concerned, it has been shown
experimentally that although it is apparently not possible to achieve homo-
geneous mixing of CO at the molecular level, the value of the gain is totally
sufficient for effec~ive operation of the cavity. With a mean relative C02 i
concentration of about 10 percent, the value of the gain equals Kp ti 1%/cm .
The absolute value of the gain would correspond in a homogeneous m3xture to
_ a lower C02 concentration, and the rate of the drop in gain on account of the ;
relaxation of vibrat~,onal energy has been proven to be close to that expected
in the case of a mixture of homogeneous composition.
Thus, based on the experiments conducted it is possible to conclude that the ;
COZ laser system discussed is promising. ~
We wish to express our thanks to Ye.P. Velikhov for initiation of this study
and A.A. Vedenov for the interest he has shown.
Bibliography ;
1. Hill, A.E. APPL. PHYS. LETTS., 18, 194 (1971). '
2. Bullis, R.H., Nigan, W.L., Fowler, M.C. and Wiegand, W.J. AIAA J., 10, '
407 (1972). -
_ 3. Kovsh, I. B. Z.~RUB~ZHNA`XA RADZOEI,EKT~QNZK~1, No 3, 86 (1973) .
4. Ti~~any, W.B., Targ, R. and ~oster, J.D. ,E~~L. ~'IiXS. L~TTS., 15, 91 (1969).
5. Vedenov, A.A. et a~. TVT, 14, 441 C1976),
1+2
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6. Taylox, and B~t~~e~n, ~Qp. ~"~5,~, 4~, 26 (1969).
7. Artaut~nvv, A.~`, et a1. KVANTOVA`~A ELEKTRONxKA, 40 581 (1977).
8. Devix, A,D, and Opp~nhei,t~, U.~, A;P~'T� O~TxCS, 8, 27.2X (1969) .
\ 9. Ben-Josef, N. et a,~,. ~HX`~.. ~ 4, 708 (1977.) .
COPYi~~GHT; ~zdate7,tstvu Sovets~koye Radfo, K'~1ANTOVA'XA ~LEKTRONZKA, 1979
[ 27-~8831]
C90: 1862
8831
~+3
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r~ux ur�r~t~t~u, USL~ UNLY
LASERS AND MASII~S
UDC 621.378.33
ANALYTICAL THEORY OP PULSED LASTNG OF A CO LASER WITH LTNE SELECTTON
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 6 No 9, Sep 79 pp 1966-1970
manuscript received 22 Jan 79
[Article by S.A. Zhdanok, A.P. Napartovich and A.N. Starostin, Institute of
Atomic Energy imeni I.V. Kurchatov, Moscow]
[Text] An analytical theory is constructed for the non-steady-state lasing ;
of a CO laser with line selection and a comparison is made with a precise ;
numerical calculation. Equations are given for key characteristics of the
lasing pulse, such as maximum power, lasing efficiency, delay time and pulse ;
duration. Also discussed is the establishment of generation when the pump
is turned on.
As we know, the lasing spectrum of a CO laser contains a great number of !
vibrational-rotational transitions of the CO molecule. However, in an
entire series of applications, such as isotope splitting, laser spectroscopy,
- and laser chemistry, it is necessary to have radiation at only a certain
single transition. In this connection the investigation of lasing of a CO
laser with the selection of different lines is important. In [1] an analytical
theory was constructed for a steady-state CO laser with a selective cavity,
in which simple expressions wexe obtained for the generation characteristics '
of these syste~s. In this paper an analytical theory is constructed for non-
steady-state generation of a CO laser with line selection, and a comparison
is made with precise numerical calculations made in [2]. ~
The system of kinetic equations describing the generation of radiation in a '
selective cavity at the (m 1; (m; 3+ 1) transition of the CO molecule,
where m and j are the vibrational and rotational quantum numbers, has the
form ~
dfo/dt=IIo+, - na+r~, ~=0,1, ~1~ '
;
' ' dl/dt=c(k-A)l, ~2~ _
,
where f is the percentage of Ca molecules in tfie ~,th excited state;
Ii~,1 fsvthe flow o~ vibrational populations in the space of vibrational ~
~+4 ~
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nwnbe~s in the cross seGtiat~ between the v~th and (y + 7,)-th leyels; i is
the ~requency o~ excitation o~ the v-th 1eve1 by extern~l sources~ T,�k and
0 are the �rt~di$tipn intensity~, fihe gain and losses in the transition con-
sidered; and c is fihe speed v~` light. fin the appxpxi~tion for single-
quantum 'W exchan~e, the expreasion ~or i~~~ has the ~'orm in [1,3~5];
~0}1 v, 1, a a 1 0' ~ �F ~ f+
Q~-I-~ +lf -E f-" Qo. v-}-i~�fofo'~f-1~ ~po-1-1 Av 1 a 1-~-
a'
/a
, ~fo-FI - s f
o~ Sa. ntr
(3)
where ~'~'~t+l A and ~ are the frequencies of W exchange, spon-
~
taneous s~.ntegration and relaxation.from the v-th lev~l .(thermal excitation
from the v-th 1eve1 is unlikely); ct ti(m + 1) exp [~-B~ /(T)] is the effective
cross section af induced radiation at the (m + 1) m transition at frequency
w; d= exp (-2Bj/T) ; B is the rotational eonstant; d is the Kronecker
symbol; and T is the temperature of the gas. Be1ow we w~I~ be interested in ~
the case when an external source excites only lower vibrational levels and the
~eneration of radiation takes place only at frequencies where VT losses and
spontaneous radiation can be disregarded. Then, proceeding to continuous
variable v and using the approximation of resonance W exchange in [1,3-5),
system (1) can be approximately substituted by the equation
at� =v a
~ ~(v+l)~fn) + a ~h~ ~
af~ +vfo~a(v-m)~, .
_ 2AE a'. a' -I- I (v - o')s i
7~ ~ Qv-}-t�a (v-~,1)(v,,~f-1) dv ~ N~p (T), -
(4)
where d(x) is the Dirac delta function; y= 1- S; ~E is the energy of
anharmonici~y; and N is the density of CO molecules. As is obvious from
equation (4), f changea at characteristic times on.the order of v 1
The establishmen~ of intensity takes place after a cavity period on the order
of (c~) 1. As a rule, v� c~ , which makes it possible Lo employ an approxi-
ma.tion of quasi-steady-state generation;
Q~m+~ S f r~ =~/N~p.
(5)
Now substituting (5) in (4) and integrating (4) in the yicinity of point m
it is easy to get
~~=v~ u~(m-L 1)2~fm fm+t ~N~o�
- (6)
~+5
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- Since the value of is ~ottnd ~~co~q (4~ (with ~ ~ 0?, and o~ ~~~.1~rom
- (5), then the prob],em posed has in principle been solv~d, Let us note that
the value of distxibution tunction ~ in region v R m does not depend on
the existence o~ generation and is de~eriqined only~b~ excitation conditions.
The time fox the start and texminatiqn o~ genexation can be found from (6)
by having equ~ted the radiatton intensity~ to zexo~ i,e., by having solved
in terms o~ t~the equation
f,,,~t) = fm+~~t) � ~7 ~
It follows from (5) and (7) that the time ~or the start and termination of
generation corresponds to moments at which at level m is reached a threshold
population of f~ _ ~(vYN~~) 1. The threshold characteristics (energy con-
trib~ution and pumping power) are now defined as the values of the corresponding '
p:arameters with which for the first time a solution is found for equation (7).
Let us dwe11 in greater detail on the problem of co~P uting f(t) . Equation
(4), for v< m, by substitution of variable T= r v dt ismreduced to the
form p
~ = a
s [(v+ I)2 f~], ~8~
which makes it possible to take into account the change in v over time,
caused, e.g., by heating of the gas. Of greatest interest are the cases of
generation with pulsed excitation and when steady pumping is switched on.
As demonstrated in [6,7], it is precisely in these cases that it is possible
to find fairly simple solutions to equation (8). In particular, for pulsed
excitation with an energy contribution density ~f e, when for a single
molecule are necessary n= e(N pi~w) 1 vibrational quanta, in [7] the following
solution is gotten to equation ~(8):
fo ~t~ _ r 3 n1'l. t ~ 1,
l 4 l ~-~-tT~.- ~
~9)
Equation (9) describes the propagation in space o~ vibrational numbers of
the excitacion "wave," which was origina7.].y ].ocalized in the area o~ low
v. By its ~eans are easily ~ound the ~o].lowing ~axametexs characterizing
the process of detern~inatipn a~ tlie distribution function ~ox vibrational
numbers : ti~e T ~ox the arriy~,1 0~ the. excitation ~'W,aye" at point m,
and time TM ,~oxiIlachie~ying maximun~ population density at le~yel m, and '
its value, ~M ;
~m=(m-~-1)=/(12 n); T~=(4~3)�rrn; fM=(6~~-1.
(10)
_ ~+6
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~'rom cond~tip~ (7~ it f~ pQ.s.~th7,e to o~~ain the ~o~.7.Q~rfin~ expxes~ion ~ofi the
tin~e ~or the beginning, T~ ,&nd end, T~ , o~ generationa
4
Ta,~ _---1/: l~!/ t YA/~2~ ~
J) -~'/~J~ ;
z . ~ ~ '/i
y - al + a~' a'~z = 28a � ~ ( 2Ba )f - ( 3!t ~3 J ; -
1 A = ~3~4n)~~` B = B (vyNco)-`�
tll~
ti
If the threshold value of f is much lower than the maximum population
density of level m detertained by~ equation (10), i.e., the condition is
fti~filled of
~/(6YNco) ri (m-~-1) 2,
(12)
then the time for the start of generation practically coincides with the time
for the arrival of the excitation "wave" at point m. The equation for the
time for the termination of generation is also simplified in this case:
. T~ ~ ~~Nco Y~0)/'~, [3/an(m.{-1)-z]~. (13) -
Obviously, corresponding to the threshold case are those values of parameters
when the maximum population densitq of level m agrees with the threshold:
f~=0/(QY1Vco). - - .
(14)
Utilizing (10), from (14) we find the threshold reserve of quanta and the
threshold time for the start of generation, T:
4 n- 27 o N m I~? 1 aYNr~ ~
Y co ~ ~ ~ 6 ~
(15)
Since cr ti(m + 1) , then from (15) it follows that
n,~, ("i-~- l) A exP IBI'l(T)1 , nT ~(m-{- 1)a.
N~p I - exp (-2B j/T)
cxb>
In fig 1~s ma,de a, co axi,~pn o~ ~(t) cur~es, one o~ which has been cal-
culated by equat~qn (6~ with v= cons~t , and the second was obtained by
a numerica~ solution to sy~stem (1), (2), taking fnto account heating o~' the
gas [2]. The agreement is obviously fairly convincing. Let us note that
47
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rvx Ur~~1c:tAL US~ UNLY
disregaxding heating o~ the, gas. is ~y~7,id in describing on7.Y~ the ini~ia~.
stage o# gen~xation. ~~king into account he,at~ng o~ zhe gas, as already
entioned, reduces~ to replacing in a11 equations~ ~pa,g~ctitude vt by
~ v dt , which with a kno~n T(t) dependence complicates the pxoblem inr
~igni~icantly.
_ As is obvious ~rom (6) the intenaity o~ xadiation xeaches a tqaximum value of
~ at moment o~ time T~ , wherebq~
1'~~=NCO''~w~m+t)2[f~Y~2-Y)- aN~o ~1-1'~fM- Q
N2
co
~ (17)
~rom (lZ) it is easy to find that near the generation threshold IM ti
ti(n - n)(m + 1) , and when the threshold is exceeded considerably, ~ ti
ti e2(m + 1) 2~ 1N~~[1 - exp (-4Bj/T)] . For the efficiency of selective
generation, in disregarding heating of the gas, it is possible to obtain
the following equation:
~I = ~1� nE~ (m -I- 1)$ [F (tl) - F ~tz)~ ~
(18)
where E1 is the energy of the lower vibrational quantum; n is the per-
centage of energy goi.ng toward the excitation of vibrations; �t~ 1= TO lv 1;
, ~
F~t~ � QN~~,, ~ 1-. Y) ]n t- Y 12v=~ Y) - 2 e^t 4-" 3
Q ~ Y)�
- NcoY (19)
Unde~ over-the-threshold conditions from (18) and (19) it is easy to fSet
~l ~loNco~ WE-'Y(2-Y)^~ [1-exp(-4Bj!T) J.
(20)
As is obvious from (20), with high energy contributions (with condition (12)),
the efficiency of selective generation tends toward a constant value slightly
dependent on the number o~ the vibrational level, m(only in terms of ~
and ~r ) and on losses, Near the generation threshold (18) takes the
form
~ ~ 16 (
3 110 ~eve (10 - 7~y) C n - 1 ,
~ n
(21)
~+8
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I, MBn~/cnt 1) '
� ~ ' .
1
O,B .
Q4
. z
Q 4' B 1Z t, n,rc
_ Pigure I. I(t) Curves with Pulsed Excitation, Obtained in [2]3(1) and
from Calculation by Equation (6) (2): e= 0.05 J/cm ;
mixture of CO:Ar = 1:10; p= 100 IIan Sg; T= 80�R; A= 10-3cm l;
m=9;~=13
Rey :
1. I~~ ~/~~2 2. t, u~
. Let us now consider selective generation in the case when in the system a
steadq pumping source with power W(in terms of a single molecule) is
turned on aiid off. Then, as demonstrated in [6,7], distribution function
f~ in reg3on v< m is determined by the equation
fo=c/~v+t)-~I~2~~
(22>
for the case of turning the source on, and
~+1 f 1-exp(- cl IJ' ~
l \ ~C
fa =
tV (n-~- 1) ~ v2C1
(23)
for the c$se o~ turnin~ fihe .s.ource o~'~, whe~e C~- ~(~~v . Substituting
(22) and (23~ with ~ A~q in (6), it is, poss~ible to o t~in the dependence
T(t) Solwing (7~ with. ~ ~xot~ (Z2~~ we obtai;n the following.expxession
for the tiine, T~ ,~q9C tlie ~e1gy, o~ genexation ~hen the source i~ turned on:
~+9
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to = 2 r m+ i QYNco 1- .
~ ~
~ , (24)
ti
The threshold pumping po~er, W, can he obtained ~rom (24), with T~ tending
toward in~`inity~;
e 2 Z E, ~s eXp (Bjz/T) ~
l~-v �YNCO ) ~m-~1) ~Iv ~ I1-exp(-2BjIT)~~ N~~ ~
~ ~25)
In the case when the threshold is exceaded considerably, when the condition
C>> ~~m-F' 1)~~QYNco) ~
(26)
is fulfilled, the time for the delay of generation agrees with the time,
Tm , for the arrival of the excitation "wave" at point m: ,
� T'"-~m~-1)~~2~~ . (27) ,
I, HBm/c~i
1)
. a4 , ~
0,3 ,
0,2 '
0,1 Z
2~ `
� 0 ~i0 QO 110 160 t, n,rc
~igure 2. I (t) CuxVe ~lotted ~xom Equat~.on3 (6) ~o7c ~u7Cning the Source ,
On ~nd 0~~ C2~ s~1 ~ 77.4 W~~c~q 3 xe~in~ng paxameters the
~~?as~~i8~.
Key : , , ;
1. ~ , ~iJ/c~q2 2~ t , ~t~ ;
50 '
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Tn fig 2 as an exa;tqp~e i~� giyen the zesult o~ ca7.cu?~~ting the xadiation in-
tensity, I(t), ~rnm ec~ua~ion Cb~ ~or the cas~e o~ turning the source an and
off and disxegardiag heat~:ng of the $as.
In conclusion let us aote that the equations which we nave obtained can deacribe
selective generation a7,s4 wfi.th other diatomic ~qolecules o~ the HC1, H~', etc. ,
type, and are als0 eas~ly$eneraltze3 for tlie case o~ selective generation
with overtones o~ diatomic ~ol.ecules~.
Bibliography
1. Napartovich, A.P., Novobrantsev, ~.V. and Starostin, A.N. KVANTOVAYA
ELEKTRON~KA, 4, 2125 (1977).
2. Konev, Yu.B., Kochetov, I.y. and Pevgov, V.G. "Tezisy dokladov II Vse-
soyuznogo seminara po fizicheskim protsessam v gazovykh ORG" [Theses of
Papers ~t the Second All-Union Seminar on Physical Processes in Gas Lasersj,
Uzhgorod, 1978, p 58.
3. Brau, C.A. PHYSICA, 86, 533 (1972). -
4. Gordiyets, B.F., Mamedov, Sh.S. and Shelepin, L.A. Preprint FIAN, 1974,
No 28.
_ 5. Gordiyets, B.F. and Mamedov, Sh.S. ZHURN. PRZKL. TEKH. I TEKFIN. FIZ., -
No 3, 13 (1974).
6. Zhda.nok, S.A., Napartovich, A.P. and Starostin, A.N. "Tezisy dokladov
II ~Vsesoyuznogo seminara po fizicheskim protsessam v gazovqkh OKG," -
Uzhgorod, 1978, p 46.
7. Zhdanok, S.A., Napartovich, A.P, and Starostin, A.N. ZI~ETF, 76, No 1(1979).
COPYRIGHT: Izdatel'stvo Sovetskoye Radio, KVANTOVAYA ELEKTRONIKA 1979
~ [27-8831] ' .
,r
CSO: 1862
8831
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i
Ll1:;1,'RS AND MA."~P' S �
UDC 621.373.826
EFFICIII3CY OF EXIMER LASERS UTILIZTNG MOLECULES 0~' HAL~DES OF NOBLE GASES i
_ EXCITED BX AN ELECTRON BEAM
Moscow KVANTOVAYA ELERTRONIKA in Russian Vol 6 No 9, Sep 79 pp 2024 202~7 ~
manuscript received 12 Jul 78
[Article by V.V. Ryzhov and A.G. Yastremski, USSR Academy of Sciences Siberian '
_ Division Institute of High-Current Electronics, Tomsk] .
;
[Text] By mears of solving equations fo~c the kinetics of processes in the
pl~.sma of eximer lasers utilizing molecules of halides of noble gases,
equations are obtained which make it possible to estimate the efficiency of ;
such lasers exc3ted by an electron beam. The numerical modeling of processes
_ in eximer lasers has demonstrated that the equations obtained can be used for' ,
calculating efficiency with a gas pressure from 1 to 10 atm. The results are ~
give of calculations of the limiting efficiency of lasers utilizing molecules
of KrF*, XeCl* and ReBr*.
The mechad of exciting gases with an electron beam is one of the promising
methods of pumping high-power gas lasers generating radiation in .the sho~t
wavelength region. One of the main problems of the theory of these lasers is
the determination of the efficiency, n, of the conversion of the beam energy ~
absorbed in the gas into stimulated radiation. Usually for the purpose of
es~timating the maximum efficiency of a laser is utilized the quantum efficiency,
equal to the ratio of the energy o~ a laser photon, hv , to the potential for
the formation of active particles of plasma, I, whose energy,as the result
of a series of e~-~mentary pracesses can be transferred to the~upper laser ;
level: n~ax ~ kv ' nkv - hv/x . ;
i
It is well known that such esti~qates are quite appro~cimate and for some '
systems can exceed the real ef~iciency o� a].asex by tqore than an order of
magnitude. ~n this papex equatiqns axe qbtained which ~ke #,t pqssible to -
refine, as co~Qa,red ~rtth n~ , the esti~~e o~ the ~c~um e~~icienc}r o~ ;
_ las~rs uttl~zin$ ha7.ides Q~ ~ob.7.e gases excited by~ an e7.ectron beapq, because
of taking into account the e~~ecti,venes.,s� o~ ~he ~n~ut o~ be~ e~ex~y~ into -
fihe gas and the kinetics� o~ pxoces~ses� tn tRe pl,assqa~
,
- Let, in the worlcing space o~ a laser, pex unit o~ ~itqe, a be~m ~orm N
active particles�, expending on this a portion of the absorbed energy,
i
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and 1et eacti active, paxtic~.e as� the res�u7.t o~; a chain oF re~ctions be able
to result in pu~fng o~ the upper ~.a,sex 7.e~ye.7.. If then the laser emits n
photons, t11en the e~'~'iciency o~ tliis 7.as~r tn the steady~�~state mode is
determined by~ tlie equa~t~on
r~= `S~n~N)(hvl/)= ~Y~Ixe�
(1)
Here factor ~y = n/N characterizes the effectiveness of the transfer of
. excitation through the reaction chain to the working 1eve1; it is equal to
the mean nu~ber of laser photons required for one active particle fortned by
the electron beam in the working ~pace o~' the laser.
Equation (1) determines the effectiveness of a laser in the case when pumping
of the upper level takes place through a single channel. grom this viewpoint
the kinetics of processes in the plasma of eximer lasers utilizing halides of _
noble gases are fairly complex. An analysis has shown [1-3] that in the case
when the buffer gas is argon, the working molecule RX* (R is an atom of xenon
or krypton and X is a halogen atom) is formed through several channels.
- Thus, the energq expended by the beam for the ionization of atoms of argon
is transmitted, ~ia conversion pro~esses and resonance charge transfer, to
elemental ions R. In addition, R ions can be formed directly by the beam.
Eximeric molecules of RX* are formed in these two reaction chains as the
result of tlie process of ion-ion recombination. This channel for the formation -
of RA* we wr~l ca11 the ionic channel.
The energy spent by the beam for the excitation of atoms of argon is trans-
mitted via processes of resonance excitation transfer and conversion to
metastable levels of R* atoms. Thes~ levels in addition can be excited by
the beain directly. Molecules of RX* are formed in this channel, which we
will call tHe excitation channel, as the result of the reaction of R* with
a halogen c~rrier.
The kinetic link between channels is accomplished via processes of electron
recombination, as the result of which metastable states of Ar* and R* are -
formed. Tn certain cases these processes can be disregarded by comparison
with the mor'e rapid reactions o~ ion-ion recombination. zn such a model
the link betwaen channels is broken, and the formation o� RX* can be con-
sidered independent �or both channels, whi~ch consider~bly simplifies the
calculation of e~ficiency.
As follows ~rom the sys~te~ emp],Q~red, the beatq energy~ is transmitted into
_ each channel+ in two w~yg; yia iQnization ~x e~ccitation of atonqs o~ the
buf�er gas and ato~s o~' kr~rpton or xenon. Thexe~pre it ~qus~t be expected
that the total e~~fciency vf a 1.asex uti7.izing h$lides o~ noble gases will
be equal to the suzq o~ the e,~~iciencies o~ ~each enexgy~ txans~'ex channel.
Actually~, solving ki~aeti.c.s.~ equafiions, for the stead~state c~se tn an approxi--
mation ~or tndependen~t ciianne7,s, it is� ppssible to olitain ari expxess~ion �or
e~~i.ciency in tYie ~o~ _
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n=r~r-}-~�,
~!-~ArVAr~lp~ I'~RYR~IR~ ~g=hv//d, '
~~-~ArVAr~Ar+~RYR~R. t~g=hv//B.
(2~
n*~i~ is the e~~iciency of the excitation channel (or ionic channel);
y*~Bg is the mean nua~ber of laser photons ~orm~d as the result of transfer of
the beam energy towaxd ~he excitation o~ metastable states of B* atoms (or
for the ~ora~ativn o~' B fon~~ ca7.culated for a single active particle; ~
and r~B(i) is the quantum e#~iciency o~' the respectf.ve energy transfer channels.
If one disregards the process of collision disintegration of eximeric ~~~ecules
of RX* by equating with the pracess of induced radiation, then for YB
the follawing fairly simple equations can be obtained:
_ '
YR= G-1, ,
1'Ar YR~aiaalArizlR)/(1-~-a1C[Ar]2)(1--FaYC[RI), '
yR= (1-}-~s IAr I~R )~acz I Xn ~)-1,
' 1'Ar YR~~1-F-ae~IXn)~~:~Ar]z, ~3~ ; .
where p,l 2 are the constants for the convers~on of elemental ions of argon ,
into moleL~ular and for charge transfer from Ar2 to R; gl 2 are the conversion
constants for Ar* into Ar2 and R* into R*2 , respectively; and q, are _
the constants for the reaction of Ar* and R* with halogen carrier1Xn2.
Let us note that the values of coefficients YB~i~ depend on the model used '
for processes in the active medium of the laser. Thus, if we use as a basis
the model of processes suggested in [1], but assume that in the recombination
of Ar* and R2 ions molecules of ArX* and RX* are formed (model 1), then G= 1.
And i~ it is assumed that as th~e result of this reaction are formed the com-
plexes Ar2X* and R2X* (model 2), then
~=(1-FaaCIAr1 [R 1)~
where a3 is the conversion constant for R+ into R2..
Coefficient C included in t~1e exp~ression ~ox Y~ and ~ i~ equ~l to the _
ratio of the tota7. concentraXion q~ po.s.�itii.ye i0A$ ~il Xh~ p7,astr~, to the
rate of ~orcqatton o~ e~ectrons� the heata, V~ t
e
� C=[P+J/t~e.
(4)
~
5~+
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In the steady,s.t~te cas.e
~~e[~ i~(~ i~au;~,lx~~ 1=;',,.,.�,~)''-1i1�?,,~Ix,~ I, (5)
where a is the constant ~`c~x the adhesion of electrons to thP halogen
carrier ~nd a is the ion recombin~tion cvns~tant. 'Values.o~ can be
computed by ~he equation e
� 1pr== jDleEl. �
(6)
Here j is the current densityo~ the beam; e is the charge of the electrons;
e~ is the energy for the ~ormation of an electron-ion pair, whose values for
mixtures o~ noble gases are g~ven in [4]; and D is the amount of energy
absorbed p~r unit volume of gas, calculated for a single beam electron, taking
into account processes o~ the scattering of electrons and the absorption of
energy in the foil [5].
For calcul~'tions by equation (2) it is necessary to know the perr~entage of
energy spent by the biam for the ionization of atoms of argon, ~A , and
xenon (or krypton), ~R , as well as the energy which went to the ~ormation of
metastable and resonance levels of these atoms, ~p*~ and ~R*~~ We calculated
the values of these magnitudes for mixtures of Ar=7Zr and Ar xe by modeling
the exchan~e of electron energy by the Monte Carlo method [6]. This method
makes it possible to make a deta3led analysis of expenditures of beam energy
for the formation of atoms and ions in different excited states. An analysis
of the results of calculation of the distribution of the energy of an electron
beam in mixtures of Ar-Kr and Ar-Xe, given in table 1, show that for a mixture
in which the relative concentration of the second component is less than 0.1,
the main share of the beam energq (approximately SO~,percent) goes toward the
ionization of argon, whereas for the formation of R ions five- to 10-fold
less energ~ is spent. Approximately 25 percent of the energy in these mix-
tures goes toward the excitation of atoms of argon, whereby almost a third
_ of it goes to ttie formation of atoms of argon in metastable and resonance
~tates, Ar*(m + r) , and just as much for the formation of atoms of argon,
Ar*(p) , iri~ p states. It is interesting to note that for the excitation of _
R atoms is used ~ ust as much energq as ~or the ionization of these atoms,
whereby the beam mainly ~orms atoms of Kr* or Xe* in metastable or resonance
states, R* (m + r) . As demonstrated in [6], this ~act is explained by the fact
that the cfoss seetions for the excitation o,f these levels by an electron
beam are not screened by the cross sections o~ axg4n. _
Let us note that the potentia],s ~ox tti~ exci,taXion o~ ~he ].owex e7.ectxonic
states o~ atoms o~ nab7,e $ases~~ Z* , axe ht~h; thex~~pfie a cansiderable portion r
of the enexgy (q ti 20 pexcenfi)'i,n t~fxtures o~ noble ga;ses i~ txans~exred to
subthreshold electxons~ whose energy~ is lowex than Z* .~n 1,as~ex mixtures
the energy o~ these e7,ectrons~f~ txans~exred to ~qolecules o~ the halogen
_ carrier and is 1os~t in e~astic collis~ions with ato~s o~ the noble ga,s.
_ Calculations made ~or three~eo~sponent mixtures have ~Y?own that in connection
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with the ].qw cpncenCxatiQn o~ ~olecu],es~ o~ the h~1,o~en caxxier in lasex
mixtures the addi~ion o~ it to a tqi~ctu~e o~ nobl.e gas.es p~actica7.~.y does not
change expenditures o~ the Bea,m~s energy~for the ionization and excitation of
atoms o~ Ar tind it~ There~oxe ~or approxi~mate estimates o~ the e~~iciency of
- lasers employ~ing ha~~c~es o~' noble ga~es ~,t is possible to use the results of ~
calculations o~ obtained ~or s~ixfiures+o~ noble gases.
For the purpose o~ re~realing ~he area o~ applicability o~ the equations ob-
tained, a program was written for the numerical solutton of the kinetics
equations suggested in [1], together with equation~ ~or the flow o~ laser -
photons. In the program were taken into account processes of the collision
and spontaneous disintegration of eximer molecules and the absorption of
_ laser photons in the active medium, as we11 as processes of electron-ion re-
combination, which were not taken into account in deriving equations (2) to _
(5). Calculations were made for an XeCl laser utilizing a mixture of Ar-Xe-
-CC1 excited by an electron beam. The results of calculations of the power '
of laser radiation agreed with those experimentally observed in [4], and
the real efficiency of a laser excited by a beam of 50 ns duration equaled -
three to four percent.
In~~fig 1 are given the results of calculation of the efficiency of the steady- '
state operating mode of an XeCl laser. Efficiency was defined as the ratio
of the power of laser radiation in the steady-state region of the laser's
operation to the power of the electron beam entering the gas. Comparison
o� these~results with the results of calculations by equations (2) to (5)
shows that the expressions obtained are of an approximate nature and can be
used only for estimating the maximum efficiency of lasers utilizing halides
of noble gases. gurthermore, as would be expected, the equations obtained in
= model 1 give an upper estimate of the efficiency of these lasers, while
model 2 with sufficiently high pressures can prove to be unacceptable for '
such estimates. Analysis of the results of calculations by these equations '
showed that the main contribution to the laser's radiation is made by the
ionic channel (as much as 80 percent in model 1). The low contribution of
' the excitation channel is caused by two facts: First, the percentage of ~the '
energy w'~ich goes toward the formation of atoms of noble gases in metastable
and resonance states is not greater than 10 to 15 percent (cf. table 1), and
secbndly the efficiency of the transfer of energy to the excitation channel
is 1ow (e.g., yA* = 0.1 to 0.5 Let us note that the conclusion regarding ~
the decisive role of the ionic channel in the formation of eximer molecules
in excitation with an electron beam has been confirmed experimentally [2,4]. .
Taking into account the ~act that the ionic channel makes the main contribution ;
to the formation o~ eximex molecules, approxf~qate estimates of efficiency can
be ma~e without taking into accaunt the contxibution o~ the excitation channel,
n ti n �
Let us note that in model 1 y$i and the ~alues o~ ~i , as fndicated
b}r calcu7.ations; axe a7.so ~aix7;y liigh and depending Qn tl~~concentxation o~
_ R atoms and tfie pxes�aure o~ fihe ga~s ~ax~ ~rom 0.6 to 0.9. ~hexe~oxe, ~or
- r~ugh e~tfmates o~ the uppe.x ~~3~it o~` e~~fciency~ it fs possible to assume that
YAr ~R � 1 and to use tfie equation
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r-
. ~Imaz