JPRS ID: 10072 USSR REPORT PHYSICS AND MATHEMATICS

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• Content Type: REPORTS

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JPRS L/ 10072
26 October 1981
- U SSR Re ort
p
PHYSlCS AND MATHEMATICS
CFOUO 9/81)
Fg f$ FflREIGN BROADCAST i~lFORMATION SER~/ICE
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JPRS L/10072
' 26 October 1981
USSR REPORT
PHYSICS AND MATHEMATICS
(FOUO 9/81)
CONTENYS
ACOUSTICS ~
Two-Dimensional Nonlinear Wave Pr~,.~sses in Pul~ed Local
Heat Release in a~as Flow 1
- CRYSTALS AND SEMICOND~UCTORS
Registration of Parameters of Pulsed Radiation Using the
- Semiconductor-Metal Phase Transition in Vanadium Dioxide........ 13
Laser Screens Made of Single-Crystal ZnSe and ZnTe Films Grown
O11 Sapphire~~..�~.�..��..�~��~~~~~�~~~~�~�~~~~~~��~~~~~�~~~~~~�� 1.8
FLUID DYNAMICS
Boundzry Layer of a Body of Revolution '_n a Drag Reducing
Polymer Solution 21
LASERS AND MASE~S
Pro~agation of Laser Beam in Turbulent Atmosphere.................. 32
High-Power Pulse Laser 37
Investigation of Gasdynamic Laser Using Acetylene Combustion
Products.....~ 43
- Chemical DF Laser With D"iffraction Radiation Divergence........... 50
Stimulated Emission on 18.4 um in C02 Gasdynamic Laser With
- Electric-Arc Heating 58
- a- [III - USSR - 21.H S&T FOUOj
r�~~~ ~nrnn~ ~ r i~nC AAii V
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Feasibility of Using Liquid Metal Heat-Transfer Agents fnr
Cooling the Elements of High
Power Optical Systems Based
on Porous Structures.~~�~.��~~�������~~��~~��~���~��~��~��~~~~�� 62
C02 Laser With Radiation Energy of 3 kJ Excited Under Ma.tched
Conditions...........a...~ 67
Conversion of CUZ Laser Emission to 0.5 um Region in Nonlinear _
Crystals 71
Influence That Heating of Active Medium During Excitation Has on
Characteristics of Pulsed El~ctroionization CO Laser Using
Pure Carbnn Monoxide "/4
OPTICS AND SPECTROSCOPY
' Wave Front Sensor Based on Talbot E�fect 78
Feasibility of Making an Absorbing Cell for 1315 nm........... '86
fi
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i ACOUSTICS
UDC 534.2:532
TWO-DIMENISONAL NONLIIv~ ~~c WAVE PROCESSES IN PULSED LOCAL NEAT RELEASE IN A GAS FLOW
Moscow AKUSTICHESKIY ZHURNAL in Russian Vol 27, No 4, Jul-Aug 81 (manuscript re-
ceived 13 May 80) pp 595-604
[Article by A. T. Fedorchenko, Moscow Physicotechnical Insti~ute]
[Text] Development of nonline3r wave processes in a homogeneous
gas flow near a stationary zone of pulsed heat release is numeri-
cally studied within the ~ramework of a planar model. The study
is done over a wide range of transonic and supersonic velocities
of the unperturbed flow. Optimum conditions of generation to
maximize pressure amplitudes are discussed.
A separate field of r2search [Ref. 1-7] involves the investigation of wave processes
generated by a thermo-opti_cal source moving in a gas (or equivalent processes in
flow around a stationary beam along ttze normal to its axis). The phenomenon of
- amplification of sound waves as they are generated by continuous radiation in
a transonic gas flow has been examined as a resul*_ of approximate analytical solu-
tions (linear [Ref. 1-5] or with consideration of weak nonlinearity [Ref. 7]). An
anaiagou~ effect has been expnrimentally detected [Ref. 8] at near sanic velocities
of scanni;~g of a laser beam over the surface of an absorbing ?iquid.
Ho~aever, the approximate salutions have not enabled investigation of appreciably
unsteady processes of pulsed excitation of acoustic waves of finite amplitude,
- much less under conditions of strong n~nlinearity (i. e. at acoustic Mach numbers
_ Ma of :he order of unity or more). Obviously in solving nonlinear spatial problems
of the given type under general conditions it is necessary ro use a complete (two-
- dimensional as a minimum) system of gasdynamic equations. But solution of such
problems as of now can be handled only on the basis of numerical methods with
, up-to-date computers. In doing this, both the construction of mathemati.^.al models
and development of the appropriate numerical algorithms for solution constitute
a separate class of problems, usually attended by considerable difficulties.
In tt?is paper, numerical integration o~ complete two-dimensional equations of
gas dynamics is used to solve some model problems where an investigation is made
of appreciably nonlinear pulse processes of optical generation of intense waves
in plane-parallel gas flows. In the given range of velocities of the undisturbed
1
~
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flow (transonic and sugersonic) and heat-release levels, pronounced two-dimensional
effects of nonlinear in~eraction of the generated waves wit~ the flow are o'oserved.
A detailed exam~na~ion is made of the formational processes and subsequent evol~ucion
_ of shock waves; an analysis is made of some optimum conditions of waye generation
to maximize pressure amplitudes. Notice is tak~n of the possibilit~ of realization
of resonant oscillatory phenomena in a supersonic fZow by using a serie.s of succes-
sive pulses.
~ Two-dimensional unsteady flews of perfect gas were studied in the rectangular
region G{.rElx,: U~(0: y-). x,0} , The coordinate system that is used is
fixed to the stationary axis of the beam (axis Oz) normal to the plane of the
flow. The initial dimensionless system of gasdynamic equations had the form
a~ 8pu 8pv
ac+az~ay=o, . _
a~u a 8puv .
ac ' dz~Pu'+P)+ a =o,
y
apc ~3puv 8
~ 1~ at ~ ~3x + ~y ~PUZ~"P)
.
~~pF-~- a Iu(pE+F)1~-a I~tPE~"P)~=Qu1~ �
~t az � � 8y
: :
p = PT , E=e u -f-u , e= c9T = T , =Cp ,
~f 2 1f i ~ ~a
= aorolo
Q 1~
POCO
The dimenisonless values of coordinates x, y, velocity components u, v, time t,
density p, pressure p, t~mperature T, internal energy e, volumetric absorption
factor c~, and radiation intensity I are respectively expressed in units ro, co,
- ro/co~ Po~ Po~o~ To~ ~o~ ~o~ Io~ where ro is characteristic radius of the beam,
po, To are parameters of the unperturbed gas flow, co= ~To is the adiabatic
speed of sound, ao is the average value of the coefficient of absorption on the
investigated section of the length of t'ne beam, Io is the characteristic (maximum)
radiation intensity.
The principal dimensionless number Q can be xegresented as a product of two dimen-
sionless parameters:
Q=sB, where ~=aoro, B=Io%Po~o�
Obviously formulation of the planar problem is correct only when ~a'1.
It is assumed that the power or the sources of heat release is independent of
a change in the local thermodynamic parameters of the gas in the zone of absorption,
(i.e. a= const = 1), and is completely determined by the unchanged spatial dis-
- tribution (in the given case gaussiati) of radiation intensity and ~he predetermined
function f(t) ~ 0(with norming condition fmax - 0(1)) that characterizes the time
modulation of the pulse:
al=f~t)8~z, y)~ g~x~ y)~e~p ~-z=-yz),
t>Q,-z, yEG.
2
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Pulses are considered with characteristic times of action Tf ~ 1.
` At the ini.tial instant t= 0 throughout region G
(2) u=Me, v=0, T~p=1, p~paml/Y.
On the lower boundary G(xE(z,; s:), y=0, t>0) symmetry conditions are u~ed: v= 0,
3u/ aj~ = ap/ ay = aT/ ay = 0. The parameters of the unperturbed f low (2) are assigned
on the left boundary (a=z,, y~{0; y=) 'I'he upper and lateral boundaries of G
were sufficiently far away (y,~1, ~x,~~1, s,~1) so that during the entire investi-
gated time interval (0; tk) the influence of these boundaries did not reach as
far as the investigated local zone close to the beam. In all calculations y= 1.4.
For numerical integrati~n of system (1), a difference scheme was used [Ref. 9] of
the "predictar-corrector" class with seconci order of central spatial approximation.
The presence of model viscosity (evaluated and adjusted in the computational pro-
cess) enabled straight-through calculation of shock waves without appreciable
manifestation of dissipating factors out~ide of the zone of discontinuity. Non-
uniform grids were used with step hX = hy = 0.1 in the central zone of G(the tota~
_ number of intersections of the grid ovsr the region N?~200). The step witk re-
spect to time ht= 0.015-0.02.
- The main seri~s of calculations was done w.i_th the use of the function ~1(t):
~i) =1 exp (t/T~) ~ T~=3, t~0.
The maximum value of (fl)max = 1.29 is reached at t= 2.12. The quantity J(f~),
which in the first approximation is proport~onal to ttte total pulse energy
we introduce in accordance with the formul.a
f;~t)dt~ t=>t~~0~
where [tl; t2] is the characteristic time range of action of pulse f~,. For fl(t)
we ~et
' 1(1 = f 1 ~ (t) di=~,~12 =4,5.
Settin~ tl = 0, t2=2T1 = 6, we find thE similar value J(fl) = 4.4. '
A number of variants correspondtng to fixed numbers M~ = 0.8, 1.0, 1.2, 1.6, 2.0
and 2.4 were calculated at a constant number Q= 10. Let us consider the main
peculiarities of the investigated nonlinear ~,�ave processes based on the re~ultant
series of numerical solutions at 0< t~ 6-7.
An increase in heat release near the axis of the beam causes formation of a zone
of compressed heated gas with initial (at t~ 1) spatial distributions of p and T
close to gaussian. Then intense wave radiation is observed to develap from the
compression zone along with continuing heat release. At Ma,~l, this radiation
could have been treated within the framework of the one-dimensional model of di-
vergent cylindrical waves, but in the investigated range of M~ and Q, complicated
nonlinear interaction shows up between waves and flow, lead3ng to ~n appreciably
3
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a
, ~`1
~
J
~
~
b
~
c
~
~
Fig. 1. Pressure distribution along the zone of absorption at different ~values of
t= 2 (a) , 4(b) , 6(c) (Q = 10, M~= 1)
4 ~
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- two-dinensional pattern of the process. For example, in the direction opposite
to the flow, characteristic nonlinear distortion of the compression wave profile
was observed (fairly rapid at Q= 10), terminating in formation of a discontinuous
shock wave front at 0.8 ~ Ma,~ 1.6. At the same time, the wave radiation propagating
in the direction of the flow (i. e, in the direction mak.ing angles 8+E(0; n/2) to
vectnr u~) leads to constant outflow of energy from the compression zone. In
the er~tire series of calculations, formation of local zones of rarefaction (minimum
pressures reaching p(1.7; 0; 6.5)/pa= 0.7 in the variant with N~,= 1.2) was observed
behind the compression wave downstream along axis y= 0 at t~ 3-4. This physical
effect is typical of divergent waves that are cYose to cylircdrical [Ref. 10].
~
Shown in Fig. la-c are pressure surfaces in the part of the camputational region
{.r~[-3; 8), y~[0; 5]} at t= 2, 4, 6 for the variant with Q= 10, M~= 1. This series
oi graphs gives a clear representation of formation of the shock wave and the
following rarefaction zone. The arrow indicates the direction of the velocity
of the unperturbed gas flow.
It should be noted that in the variants with Ma,~ 1.6 d+sring formation of the shock
wave and its departure upstream, the heat release process still continues (at
least until t= 6-7), and as a result, effects of shock wave interaction appear
on ~he part of perturbations propagating from the paraxial zune of the beam through
the region of locally subsonic flow behind the 5hock wave front.
Further contrary motion of the curved shock wave (with initiaZ radius of curvature
rW = 3-4 at t= 4, y~ 2, M~S 1.6) is accompanied by a reduction in p�(t) (p,~(f)=
n~`~a x 0, t) =p (ze, 0, t) both due to wave radiation with respect to angles 6+,
sclz~,s~) P ~ ~
and as a consequence of spatial divergence of the shock wave (with increasing rW).
At M~ ~ 1 there is continuous mution of the forming shock wave against the flow
with monotonic reduction in p,~(t) (p,~(t)~Po, ~'r(t)-'--a�, a~~?ar-?Ata-1 as t-> .
At M~71 (more precisely at 1 0 for the duration of the whole pulse. Let us note that in
variants with M~> 2 at t' S momentary maxir,.::*~ pressure amplitudes (throughout
the region G) were observed on sloping sections of the compression wave (i. e. at
y> 0) . For example at M~= 2.4 P(4, 3, 6) /pa = 1.74, pW(6) = p(1.7, 0, 6) = 1.39.
It can be seen from Fig. 2, 3 that the condition ~xW(t) 0.5 at 0o
curves 1-4 respectively on Fig. 4. The extremum values p~, Tm, M~ in each variant
were determined from the set y~G, tE(0; 6).
Thus from Fig. 4 we can graphically determine the "optimum" Mach number M~ = 1.9
at whicti the absolute maximum (pII/pa)max- P~S~Pa = 2�56 is reach~ d.
An ana?ogous series of experiments was also done for Q= 1(f=f1(t)). In this
case we found M~ = 1.3 (pW/pa = 1.15) . For the variant with M,~= 1.1 (i. e. in the
- near optimur.i mode of generation), graphs of the instantaneous distributions of
parameters along y= 0 are shown in Fig. 5(notation analogous to Fig. 2). In
the given case, a shock wave was not observed to form (analogously to M~ = 2 at
Q= 10) and for the entire heat release process ~y.(t).~50,15 .(tE(0; 6)).
PIPQ
1, 1B y .
Z
TM
� i Z 6
- ~~Z
./i YZ - y \
1, 06 , ~
~ ~
, ~
i~~' \ ~
~ 1
~ -7 0 I Z 3 Sl
~
0, 9y - ,
Fig. 5. Instantaneous distributions of garameters: p(x, 0, t)/pa
--solid curves; T(x,0, t)--dashed curves; M(x, 0, t)--dot-and-
dash curves at Q= 1, M= 1.2 . Numbers near the curves denote the
values of dim~nsionless time t
It is characteristic that in the two series of calculations with Q= 1 and Q= ~0 the .
quantity n* =(M~- 1) const = 0.3 (the parameter r1 =(M~-1) / Q is proportional
to the dimensionless number d introduced in Ref. 7 for the model of one-dimensional
wave processes raith weak nonlinearity). General similarity of solutions with
respect to the parameter n was not observed, which is natural in light of the
considerable differences of the given problem (strong nonlinearity, two-dimen-
sionality, the pulse nature of heat release, etc.) from the conditions of the
one-dimensional model of Ref. 7.
In a series of corresponding one-dimensional calculations (v- G, g= exp(-x2)),
the maximum pressure amplitudes were considerably higher, which was to be expected
_ 8
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a since no consideration was taken of wave propagation in the transverse direction.
For example in the one-dimensional problem with f= f 1(t) , Q= 10, M~= 2 the result
was pW(4) /Pa = 4.4; Tm = 2.9.
It is natural to assume that at ag/at = 0 for any fixed number M~~ 1 and given
- time interval Tf= 0(t2- tl) '1 tha~ determines the characteristic duration of
the heat release pulse there is some set of pulses {Qf} (similar with respect
to norm IlQfll = QJ(f)/(t2 - tl)) for which the compression wave is generated with
attaininent of maximum pressure amplitudes pw on line y= 0 at t~(t,; t:). This opti-
mum mode of generation, apparently, i.s realized simultaneously with satisfaction
of the condition
~4~ IZn~t~ I~E~ ~E~tli t2~~
where e< 1 is a rather small quantity that may depend in turn on Qf, Tf, g,...
In the general case, pw can be determined either as the absolute maximum of
p(x, y, t) (.x, yEG, tE (t,, t2) or as the maximum average pW (for the required time
interval (ta; tb) evaluated with resp~ct t~ a set of points x, y belonging to
some subregion L~G.
- In the i_nverse problem being considered here (finding the "optimum" number M*~
for a gi.ven pulse shape Qf(t)), the optimality of the selected set {M~, Qf} is
determined to a considerable extent by the smallness of the quantity e found in
the process of solution. Taking as the initial field the solution of variant
_ {Q = 10, M~= 1.6} at t= 7(i. e. after practical cessation of the action of pulse
fl and at x~,,~(7) =-0.4), a solution was found for the problem of the effect of
the second pulse f 2(t) (Q = 10, M~= 1.6, t~ 7, tm= 8, T2 = 1) , where
~ cos` (n (t-tm j/2TZ) when [t,~ T:; tm~-~':],
- (5) fl 't~ - ~ p when t>tm-~-Tz,
(fZ)~mu=f~(8) �1; ~(f=) =0,75.
r
P/PQ
3 g S
B, 5
M ~y Fig. 6. Distributions of
~ B5 / p(x, 0, t)/pa, T(x, 0, t),
\ M(x, 0, t) in the variant with
~ ~ Q= 10, M- 1.6, f= f2(t),
~ Z ~ 3 (t~ 7). Numbers near the curves
~ 9 ~ correspond to different t.
, /
_ 2
~ \
/ Il i ~
~ r- ~
0 ~ -I 0 1 2 4
~
9
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Graphs of insr.antaneous distributions of parameters along the Ox axis at 7< t~ 11
are shown in Fig. 6(notation analogous to Fig. 2). In the investigated process
at total pulse energy ~(f=)s:c~3~(ft)/6 not only higher amplitudes pW are reached than
in Fig. 2a (pW(8)/pa = 3.1), but also greater average values p~: pW(7; 11) = 2.4 1
pW(0; 7) = 2.1, where
~e
P� (t,~ tb) - pa ~t6-ta~ f p� (t) dt, tb>to~0.
.
It is characteristic that at t= 11, the field of parameters close to the beam takes
on qualitative and quantitative similarities to the initial field (at t= 7), so
th~.t repeated application of a pulse of type f2 (with t~ = 12, T2 = 1) will give
a presumably analogous effect in the range tE(11; 15).
For the sake of comparison, calculation was done where a pulse of type f2(t) was
given as the original pulse (Q = 10, M,~= 1.6, t~ 0, t~= 1, TZ = 1) . In this case,
a maximum pressure was attained of pm~pa - pw~ 1~ ~pa � 2� S ~xm =-0. 6) .
Obviously the examined phenomenon of "summing" of the actions of. sequential pulses
can show up most effectively only in the case of relatively small time intervals
= between pulses, and also upon satisfaction of condition (4) (at least with e= 0(1))
throughout the time of action of pulses fl, f2,...
Thus in the case of a stationary beam position, the conditions that are optimum
(in the sense of attainment of maximum pressure amplitudes) for a sufficiently
- long process of generation of intense waves in a flow with M~~ 1 can be realized
by different methods: either by ensuring continuous energy release by means of
an isolated pulse Qf at MW = M~ (and accordingly under condition (4)), or by using
a series of successive short p�ilses (Qf)i (i = 1, 2, 3,...) synchronized with tfines
ti corresponding to return of the shock wave to x= 0(each pulse in the series
being obliged to advance the compression wave against the flow by a certain amount).
In the second case by special selection of the sequer.ce of pulses (Qf} it is pos-
sible to generate a resonant oscillatory process.
At xW' 1, uW ~ 0, or at M~~ l, effective additional energetic pumping of the priMary
wave is possible only ~~y shifting the beam along the Ox axis behind point xW(t),
i. e. it is necessary that ag/at # 0. This motion of the beam under certain con-
- ditions may be equivalent to transition to a new value of relative velocity of
the flow I~# M~.
The problem of determining the optimum conditions of generation brings forward
- the general problem of controlling the gasdynamic system to be modeled by by means
of distributed sources of volumetric heat release. The obvious advantages of
modeling are associated with the capability of a rather arbitrary change in the
"controlling functions" a, I(or f, g) directly in the process of calculation
with continuous analysis of some set of parameters from the solution of the problem
on the preceding time interval. The given approach is actually realized in variant
(5), where selection of the algorithm of the controlling action (i. e. selection
of f2(t) for the second plilse) is determined by solution uf the problem on the
preceding time interval (0; 7).
10
~
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Naturally the process of operational "external" control of heat release sources
(especially within the limits of quite short time intervals) is not always feasible
under the conditions of an actual experiment. However, in some cases internal
physical mechanisms of regulating local levels of lneat release are possible. There
are real situations where the coefficient of volumetric absorption a increases
strongly in some region with in::reasing p or p(for example the mass coefficient
_ of absorptior~ am= a/p = const) . Then under certain conditions the forming shock
wave may make perioaic advances a~ainst the flow with Ma,~ 1, receiving energetic
additional pumping in the.zone~of the undisturbed beam with practically constant
level of radiation intensity I.
In the case where a depends mainly on temperature (f~r example aa/aT ~ Q), the
problem of optimum energy pumping of the compression wave is complicated it1 view
= of displacement of the hot spot along the flow (at any M~ > 0).
In studying processes of generation of intense compression waves, an important
question is the form of the function g(x, y) that def ines the spatial distribution
of radiation intensity. For example when g(xa y) = F[(x/rl)2 +(y/r2)2], where
r2~ rl, the zone of energy release extends in the transverse direction over the
wave front, improving the optimality of wave amplification. Obviously a technique
of this kind can be used in some cases to increase maaimum pressure amplitudes
without changing the overa]_1 pulse energy.
The question of possible effects of thermal self-stress of the beam (change in
function g along axis Oz) at conside.rable levels ~f heat release remains open
since an answer would require solution of an appreciably three-dimensional non-
linear pr~blem (in contrast to the linearized problems of Ref.. 3, 11).
The a:~thor thanks K. I. Artamonov, S. A. Akhmanov and 0. V. Rudenko for discussing
the results and for constructive remarks.
:tEFERENCES
l. Hayes, J. N., "Thermal Bl.ooming of Rapidly Slued Laser Beams", APPL. OPTICS,
Vol 13, No 9, 1974, pp 2072-2074.
2. Ellinwood, J. W., Mirels, H., "Der..sity Perturbations in Tran.sonic Sluing Laser
Beams", APPL. OPTTCS, Vol 14, No 9, 1975, pp 2238-2242.
_ 3. Wallace, J., Pasciak, J., "Thermal Blooming of a Rapidly Nioving Laser Beam",
APPL. OPTICS, Vol 15, No 1, 1976, pp 218-222.
4. Belokon', V. A., ~udenko, 0. V., d~hokhlov, R. V., Aeradynamic Phenomena in.
Supersonic Flow Around a Laser Beam", AKUSTIC~i.ESKIY ZHURNAL, Vo1 23, No 4,
1977, pp 632-634.
5. Kogan, P4. N., Kucherov, A. N., Mikhaylov, A. S., Fonarev, A. S., "Planar Gas
Flows in the Case of Weak Energy Supply", IZVESTIYA AKADEMII NAUK SSSR:
MEKHANIKA ZHII~KOSTI I GAZA, No S, 1978, pp 95-102.
6. Akhmanov, S. A., Rudenko, 0. V., Fedorchenko, A. T., "Optical Generation of
Intense Gdaves in Transonic GaG Flows", PIS'MA V ZHURNAL TEKHNICHESK.OY FIZIKI,
Vol 5, No 15, 1979, pp 934-936.
11
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7. Karabutov, A. A., Rudenko, 0. V., "Nonlinear Plane Waves Excited by Volumetric
Sources in a Medium Moving at Transonic Velocity", AKUSTICHESKIY ZHURNAL,
Vol 25, No 4, 1979, pp 536-541.
8. Bunkin, F. V., Malyarovskiy, A. P., Mikhalevich, V. G., Shinulo, P,,, "Ex-
perimental Study of the Sound Field of a Moviug Optical-Acoustic Antenna",
KVANTOVA'YA ELEKTROIvIKA, Vol 5, No 2, 1978, pp 457-459.
9. Fedorchenko, A. T., "On a Method of Calculating Two-Dimensional Unsteady Flows
of Viscous Gas in Nozzles", vOKLADY AKI~DEMII NAUK SSSR, Vol 251, No 3, 1980,
pp 578~582.
10. Landau, L. D., Lifshits, Ye. M., "Mekhanika sploshnykh sred" [Mechanics of
Continuous Media], Moscow, Gostekhizdat, 1953.
11. Kogan, M. N., Kucherov, A. N., "Self -Focusing of a Gaussian Beam in a Super-
sonic Gas Flow", DOKLADY AKADEMII NAUK SSSR, V~1 241, No 1, 19:~3, pp 48-51.
COPYRIGHT: Izdatel'stvo "Nauka", "Akusticheskiy zhurnal", 19$1
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CRYSTALS AND SEMICONDUCTORS
UDC 621.378.9:535
- REGISTRATION OF PARAMETERS OF PULSED RADIATION USING THE SEMICONDUCTOR-METAL PHASE
TRANSITION IN VANA.DIUM DIOXIDE
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 6(108), Jun 81 pp 1363-1366
[Article by L. P. Ageykina, V. N. Gavrilov, V. V. Kapayev, V. G. Mokerov, '
I. V. Ryabinin and A. A. Chastov]
[Text] An investigation is made of the feasibility of ineasuring
the cross sectional area of beams S and the energy E of pulsed
radiation by utilizing the photoinduced stepwise change in the
electrical resistance ~p and coefficient of light transmission
~t associated with the semiconductor-metal phase transition in
V02. Based on measurement of the amplitude and duration of the
photoresponse pulses ~p and Ot as functions of E and S, an analy-
sis is made of the shape of these two pulse responses. It is
shown that measurements ot amplitudes and decay times of pulses
~p and ~t can be used for simultaneous determination of S and E
of pulsed radiation.
The strong change in coefficients of reflection R and light transmission t, and
in the electrical resistance p accompanying the semiconductor-metal phase transition
in vanadium dioxide [Ref. 1], and the feasibility of optically inducing this phase
transition [Ref. 2] enable the use of V02 for determining the parameters of optical
radiation [Ref. 3, 4]. However, although higher sensitivity was attained in Ref. 3
than for conventional pyroelectric sensors, the pr'inciple of controlling a"string"
of inetal phase that was used in that research is inconvenient because of the small-
- ness of the effective sensing area. The method used in Ref. 2 to record laser
intensity from measurement of the change in R during 'the phase transition is limited
- to the case of short pulses (10-6 s or less) during which the rel~ation of heat
in the substrate can be disregarded. The pulse energies E mea~ured in Ref. 2 were
of the order of the latent heat of the phase transition in thin V02 layers.
In this paper we will investigate for the first time the feasibility of simultaneous
determination of two parameters of laser radiation--energy E and cross sectional
area of the beam S--by recording either the amplitudes of responses with respect
to electrical resistance ~p and light transmission ~t, or their decay times Tp and
Tt accompanying an optically induced phase transition. In doing this, the require-
ments for focusing of radiation are less severe than in Ref. 3, and the range of
measurable energies is shifted toward higher values than in Ref. 2. The relaxation '
of heat into the substrate in our case enables registration of laser pulses with
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s r
4, D
dtm�; rel . ull3.tS dJ~m~~ ~ 1. u11~tS Z ,
170 14 ~ p 3
1
~ ' 4 .
- dp / ~ 16 1,~ �
3 e
� 5
~
4Q ' j/� B 1, 0 ~
J0
P
= 0
0 f0 10 30 S, nn t ~ 200 400 600 f, mJ
Fig. 1. Maximum values of response Fig. 2. Transmission signal decay titrie
with respect to electrical resistance Tr, (1-4) and electrical resistance decay
~pmax (1) and with respect to light time Tp (5) as dependent on pulse energy
transmission ~tmax ~2 ~ 3) as dependent E for area S= 2.43 (1) , 10. 6(2) , 18.5
- on the area of irradiation S on a (3), 45.0 (4) and 10-SO mm2 (5)
wavelength a= 1.06 um for pulse energy
E= 660 (1, 2) and 470 mJ (3)
- duration of 10-3-10-2 s, which gives the capability of working with cw radiation
sources as well when the appropriate modulators are used.
The V02 specimens were thin epitaxial layers (0.2-0.5 um) produced by precipitation
fr~m a vapor-gas mixture of VOC13-C02-H2-Ar on single-crystal sapphire substrates.
Specimen diameter was 30 mm, substrate thickness 0.3-0.4 mm. The jump in p(T)
at the phase transition was by a factor of 104, the zone of "smearing" of the phase
transition ~Tt = 3 K, and the width of temperature hysteresis ~TH = 0.5 K. For mea-
surements of p and ~p, point metallic electrodes were sputtered on diametrically
opposed edges of the specimens. The wavelengths J~ of the pulsed radiatic~n were
0.69 and 1.06 um� We point out that the given method is suitable for any 1.2 um
(in the vicinity of strong absorption in V02). The duration of laser pulses TP was
10-3 s, E= 40-700 mJ, S= 2-50 mm2. In the measurements, the V02 spec ~nens were
thermostatically held at 3 K(t0.1 K) lower than the temperature of "onset" of
the phase transition. Heat exchange conditions were such that the initial state
of the specimen after completi~n of a laser pulse was restored by heat exchange
with the ambient medium in a time of ~100 s. An Ai,-107A light-emitting diode with
radiation max~i.mum close to a= 0.85 ~m was use~3 to record the response with respect
to ~t. There was at least a five-fold ~ump in ~ during the phase transition on
this wave.length. The diameter of the readout beam in the plane of the specimen
was ~0.8 mm. Radiat~on with any a in '~he range of 0.7 um ~ a~ 6 um can be used
for "readout", where the junp in t during the phase transition exceeds a factor
of 2, and the substrate is transparent. The angles of incidence of the recording
and "readout" beam on the specimen were ~10� and 0� respectively. The measured
nulse and thn pu.lse responses ~p(T) and ~t(T) were recorded on an oscilloscope
with a relative error of amplitude measurements of �5Y.
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It was found as a result of the measurements that there is a considerable difference
in the shape of pulse responses with respect to resistance ~p(T) and with respect
to transmission ~t(T): c1p = ~p~X was reached in time T~ 10-3-10-2 s(dependin~
on E and S)y and the fall time Tp was 0.1-1 s; 4t = ptmax Was reached in T~ 10- -10-1
- second, and fall time Tt was 1-5 s. We point out that since there was a noticeable
change in p with T not only during the phase transition, but also within the limits
of the semiconductor phase, T~ was defined as the time of fall-off of ~p to a sFeci-
f ied level of 25 kS2 (for ~pma = 250-300 kSZ) with relative error of �10-12%. On
- the other hand, since the change in t(T) took place only in the zone of "smearing"
of the phase transition, Tt was taken as the time for Ot to a certain fraction
of ptmax (1/20), the relative error for Tt being t5-7%. Curves for ppmax~ ptmax
and Tp, Tt as functions of E and S are shown in Fig. 1 and 2.
Now let us turn to discu~~sion of the principal results. Since the substrate is
transparent far the wavelengths that we have chosen, the radiation energy is ini-
- tially absorbed in the V02 film, and then transmitted to the substrate after a
characteristic time TD =Y12~K ~ 10'2 s(K is the coefficient of thermal diffusivity
of the substrate, and h is its thickness). Since this time is commensurate with
Tp and the size of the irradiated region was always greater than h, the temperature
of the film and substrate becomes equal during the action of the pulse, and when
T~ TP the response pulse shape should be determined by the diffusion of heat along
the subst~ate (since the thickness of the VOZ film is much less than h, the role
of the pulse shape at T> TP reduces to indication of the substrate temperature).
The actual dependences p(T) and t(T) [Ref. 1] of the invPStigated VOZ f.ilms in
the vicinity of the phase transition can be approximated by piecewise-linear func-
ti.ons, i. e. at T1 < T< T2 p, t~ yT (Y is a coefficient that is different for p and
t; T1 and TZ are the temperatures of "onset" and "completion" of the phase transi-
tion) and p, t= const at T~ T2 and T< T1. In view of the narrowness of OTH, the
temperature hysteresis can be disregarded here. Let us denote the changes in p and
t during the phase transition by Sp and St. Let us arbitrarily break down the
a.rradiated f ilm area into three regaions S1, S2 and S 3 in which ~~'r2 , T1 < T< T2
and T< T1 respectively. Then the change in transmission during irradiation can
be written as
er=a~s,+d'ts2~kz� ~1~
where 8r dt ~TS2"- Ti~%~T2-T~). Here T~~X is the maximum temperature of the film at
the given instant in region SZ, the coefficient k2~ 1 is introduced to account
for the way that temperature in region S2 depends on the x coordinate in the plane
- of the film (the quantity k~ = 2 for a linear function T(x)).
Since the temperature To of thermostatic control of the specimen is close to T1,
we can assume (disregarding heat transfer to the ambient space) that all the energy
E is concentrated in regions 1 and 2. In this case
max max
L\ Tsi - T2 1 Tsz - T~ ~2)
E=-_ c Tz - Ti -f- k I Si -F- k Sa ~
i / z
where c is the heat capacity of the substrate; kl plays the same role as k2 in (1);
TSiX is the maximum temperature in region S1. Expressing S2 from (2) and
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substituting in (1), we readily see that the quantity ~t increases with decreasing
S1. At S1 = 0, pt = ptmax _ E8t/ [c(T2 - T1) ] is determined oniy by the energy in the
pulse, and is independent of the irradiated area and Tmax. This explains the wide
interval of S over which the quantity ptmax does not depend on S(see Fig. 1).
The reduction in Ot (from ptmax~ at large S is due to drainage of heat from S2 to S~.
For the response with respect to resistance we can write
er~~bpli+dp 12~kz~ ~3~
where Z1, ZZ are the linear dimensions of regions S1 and S2 (Z1~ Z2~ S~-
Substituting S2 from (2) in (3) we can see that ~p in contrast to ~t de-
creases with a reduction in S1 (at least at small S1)., This shows that the maxi.ctium
value of ~p is reached at S~# 0(rmax ~ T2~~ i. e. prior to ptmax. Fo~ this reason,
Tp~ Tt. The maximum ~p depends on the value of Tmax~ and hence on the initial
area of irradiation. Thus the given simple arguments enable us to understand not
only the difference in the shape of responses ~t(T) and ~p(T), but also to explain
the behavior of the curves shown in Fig. 1 and 2.
Taking considzration of the fact that there is a segment of ~t~X(S) on Fig. 1 that
is independent of S, measurements of the dependences of ~t~aX and ~pmax on E and S
can be used for simultaneous determination of the E and S of light beams. Vapori-
zation of the V02 film is observed at high radiation density. This sti~ws up as
a steep drop in ptmax and ~pT'~X as S decreases for S< 10 mm2 on Fig. 1. As a result
of ineasurements of the dependences of Tp an E and S it was established that like
~ the case of ~tm~(S) in the interval S= 10-45 mm2, Tp was independent of S, and
was determined only by E, which shows up as coincidence of curves Tp(E) for dif-
ferent S(see Fig. 2). On the other hand, Tt depends on both E and S. This dif-
ference in the behavior of Tp and Tt may be due both to the different definition
of T~ and Tt in our experiment, and to the above-mentioned differences in the nature
of the description of responses with respect to p and t. These data are certainly
of practical interest since measurements of Tp and Tt can be used as well as mea-
surements of ~t~aX and ~pm~ for si.multaneous determination of E and S. The former
method is preferable in view of the great simplicity and accuracy of determining
time intervals. Here the value of E is first determined from Tp (for the response
witti respect to 4p), and then S is determined from this E from family of curves
- (1-4) on Fig. 2. It has been established that thrsshold sensitivity with respect
to E is 0.14 J/cm` for registration with :::~p~ct to ~p, and 0.21 J/cm2 for regis-
= tration with respect to ~t, and the maximum permissible energy of the registered
energy is 34 J/cm2 (at E> 34 J/cm2the material vaporizes). The error of determining
E within these limits is no greater than �10%. Our. measurements of S ranged from
10 to 50 mm2.
REFERENCES
1. Mokerov, V. G., Rakov, A. V., FIZIKA TVERDOGO TELA, Vol 10, 1968, p 1556;
Verleur, H. W.! Barker, A. S., Berglund, C. N., PHYS. REV., Vol 172, 1968,
p 788.
2. Roach, W. R., Balberg, J., SOLID STATE COMMS, Vol 9, 1971, p S`~1.
16
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3. Jelks, E. S., Walser, R. M., Neal, W. H., APPL. PHYS. LETTS, Vol 26, 1975,
- p 355.
4. Semskov, K. I., Kazaryan, M. A., Mokerov, V. G., Petrash, G. G., Petrova, A. G.,
KVANTOVAYA ELEKTRONIKA, Vol 5, 1977, p 42~.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
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UDC 621.373.826.038.825.4
LASER SCREENS MADE OF SINGLE-CRYSTAL ZnSe AND ZnTe FILMS GROWN ON SAPPHIRE
- Moscow KVANTOVA~A ELEKTRONIKA in Russian Vol 8, No 6(108), Jun 81 pp 1380-1382
[Article by A. V. Dudenkova, A. S. Nasibov, E. A. Senokosov, S. D. Skorbun, Yu. M.
Popov, A. N. Usatyy and V. M. Tsaran, Physics Institute imeni P. N. Lebedev, USSR
Academy of Sciences]
[Text] Lasing is realized on single-crystal ZnSe and ZnTe films
grown on sapphire with longitudinal eZectro~:-beam excitation.
At the present time, the process of making semiconductor laser screen~ for cathod~
ray tubes consists of a number of technological operations: growing single crystals,
making disks from these crystals up to 50 ~n in diameter with subsequent chemical
and mechanical polishing, application of reflecting coatings and cementing to a
transparent backing (Ref. 1]. Of considerable interest is the possibility of simpli-
fying the technology of making laser screens by growing a single-crystal semicon-
ductor film directly on a transparent substrate such as sapphire. In this case,
the reflective coatings that form the optical cavity are ~ppli~d to the surface
of the semiconductor film on the side where the electron beam is incident on the
backing.
A promisi.ng semiconductor material for laser screens that radiate in the blue region
of the spectrum (a= 450 nm at T= 80 K) is ZnTe. At present there are a number
of reports on production of single-crystal layers of ZnSe on sapphire backings
~ (e, g. Ref. 2-4). These reports note a high degree of perfection of the epitaxial
layers, effective radiative recombination in the region of 445-450 nm, and also
laser emission with transverse electrun-beam excitation [Ref. 4]. Material of
much higher quality is required to get lasing with longitudinal electron-beam exci-
tation. .
This article is the first to report attainment of lasing with longitudinal electrnn-
beam excitation of a laser screen in which the active element was epitaxial layers
- of ZnSe and ZnTe grown on thin sapphire backings (300 and 500 um thick).
- The single-crystal layers of ZnSe and Zr~re were grown by a quasi-clased volume
technique [Ref. 5]. The substrates were sapphire crystal plates of various orienta-
tion. The grown layers of ZnSe 20-50 Um thick and 20-50 mm in diameter had quasi-
parallel orientation relative to the substrate with retention of the following
epitaxial relations: (111) ZnSe parallel to (0001) A1Z03 and (111) ZnSe parallel
to (2110) A1203.
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I, re1. un~ts A
~
A-LO A-2L0
~
- 440 4a5 450 a, nm
Fig. 1. Cathodoluminescence spectra
of single-crystal ZnSe f ilms grown
on sapphire
The surface morphology of the ZnSe layers
depended to a great extent on the orientation
of the substrates. Layers grown on sub-
strates (0001) had a smooth surface showing
growth figures in the shape of triangles
or hexgons formed as a result of superpo-
sition of several triangles. For ZnSe layers
- on substrates (2110) A1203 a typical feature
is growth in steps with dimensions that 450,5 44B,5 a~ nm
- reach 0.1-0.5 mm.
Fig. 2. Spectrum of stimulated
- X-ray and electron-radiographic studies emission of a laser screen based
and investigation of the spectra of photo on a film of ZnSe on sap~phire;
and cathodoluminescence showed that the Eo= 75 keV, 100 A/cm , T= 80 K.
grown layers have a high degree of crys- Thicknesses of the film and sap-
tallinity, with a quantum radiation yield phire plate 4U and 300 um respec-
approaching that of massive single crystals tively
[Ref. 6]. The catho~'o~uminzscence spectra
of such layers (Fig. 1) at low excitation levels (energy of excitation electrons
E o= 20 keV, pumping current density j< 1 A/cm2 , T= 80 K) show lines of emission
of a free exciton (A) and its phonon repetitions (A - L0, A- 2L0).
_ In making the laser screen the surface of the film was mechanically polished to
get a mirror surface, and then the resultant destroyed layer was etched away by
a polishing etchant. The finished thickness of the investigated ZnSe films was
18 and 40 um. A silver reflective coating (R1 = 92%) was applied to the semicon-
- ductor film, and a multilayered dielectric mirror (R2= 80%) was applied to the
sapphire. Excitation was realized in the television mode by an electron beam with
Eo= 75 keV and diameter on the target of 10 um. The laser screen was attached
to the sapphire window of a nitrogen cryastat.
Lasing was observed at a current density of about 90 A/cm2. Removal of the reflec-
- tive coating applied to the sapphire increased the threshold to 200 A/cm2. Fig. 2
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shows tt~e spectrum of stimulated er~i~sion of the laser screen. The distance be-
tween modes corresponds to a compound cavity, and maximum intensity is shown by
the modes that are simultaneously Lhe fundamental of the epitaxial layer and the
cavity formed by the mirrors. The compound mode mskeup and the considerable in-
crease in the threshold upon removal of the reflective coating from the sapphire
show that lasing took place in the cavity ~~ith external mirror.
Similar results were found on laser screens made from single-crystal ZnSe ~'ilms
grown on sapphire (jth= 90 A/cm2), 531 nm; width of the spectrum at half-

~ amplitude 0.96 nm. Emission power on the lasing threshold ~50 mW).
A reduction in the thickness of the sapphire to 50-100 Um or an increase in the
diameter of the electron beam to 100 um should reduce the lasing threshold several
. times. Practical use of such a technique for making laser screens necessitates
an increase in active element diameter to 50 mm, improvement of semiconductor layer
homogeneity, and a higher quantum yield.
REFERENCES
1. Basov, N. G., Bogdankevich, 0. V., Kamenev, V. M., Papusha, V. P., Pocher-
nyayev, I. M., Nasibov, A. S., Pechenov, A. N., DOKLADY AKADEMII NAUK SSSR,
Vol 205, 1972, p 72. '
2. Ratcheva, T. M., Dragieva, PHYS. STAT. SOL., Vol A 29, 1975, p 579.
3. Stutius, W., APPL. PHYS. LETTS, Vo1 33, 1978, p 656.
4. Dudenkova, A. V., Popov, Yu. M., Senokosov, E. A., Skorbun, S. D., Usatyy,
A. N., Tsaran, V. M., KRATKIYE SOOBSHCIiENIYA PO FIZIKE, FIAN, Vol 4, 1978,
p 3.
5. Senokosov, E. A., Usatyy, A. N., Tsaran, V. M., Tsirulik, L. D., in: "Fiziche-
skiye protsessy v geterostrukturakh i nekotorykh soyedineniyakh A2B6i [Physical
Processes in Heterostructures and Some A2B6 Compounds], Kishinev, Shtiintsa,
1974, p 85.
6. Dudenkova, A. V., Popov, Yu. M., Senokosov, E. A., Skorbun, S. D., Tsaran,
V. M., "Tezisy dokladov XXVII soveshchaniya po lyuminestsentsii (kristallo-
fosfory)" [Abstracts of Reports to the Twenty-Seventh Conference on Lumines-
cence (Crystal Phosphors)], Ezerniyeki, Latvian SSR, 13-16 May, 1980, p 203.
COPYRIGHT: Izdatel'stvo "Radio i svyaz"', "Kvanzovaya elektronika", 1981
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FLU~D DYNAMICS
UDC 532.135;532.526
BOUNDARY LAYER OF A BODY OF REVOLUTION IN A DRAG-REDUCING POLYMER SOLUTION
Moscow I'LVESTIYA AKADEMIY NAUK SSSR: MEKHANIKA ~HIDKOSTI I GAZA in Russian No 3,
_ May-Jun 81 (manuscript received 8 Aug 39) pp 40~-48
[Paper by V.B. Amfilokhiyev, V.V. Droblenkov, G.I. Kanevskiy and N.P. Mazayeva,
Leningrad]
[Text] The reduction of the viscous resistance of solids moving in a
drop liquid by means of dissolving certain long molecular chain polymers
in it must be recognized as one of the most promising methods of de-
creasing resistance at the present time [1]. Since the major effect
of the introduction of polymers is a sharp reduction in turbulent fric-
tion, it is natural to make use of a semi-empirical turbulence theory
f or the calculation of flows of weak polymer solutions. One of these
theories [2] was successfully applied to the calculation of the bound-
ary layer at a flat plate [3] and a cu~rent with a pressure gradient
near the flat contour [4].
A possible method of calculating an axially symn?etric boundary layer
is presented in this paper for the case of the motion of a solid in
weak polymer solutions with a constant concentration. The method is
based on the utilization of the velocity profile and a system of in-
tegral equations which most completely take into account the effects
of the transverse curvature of the streamlined surface. The compu-
tational scheme makes it possible to account for a change in flow
conditions i.n the boundary layer.
1. One of the major features of the calculation of an axially symmetric boundary
layer is the necessity of taking into account the transverse curvature of the stream-
- lined surface, and related to this, the finite thickness ~f the layer as compared to
the local cross-sectional radius of the solid of revolution. It is insufficient to
~ calculate the axially symmetric boundary layer as a thin layer, i.e., with the as-
sumption that S� RW, where d is the boundary layer thickness and RW is the cross-
sectional radius of the solid, especially in the case where a polymer solution flows
around the solid, ar~u where the calculation errors whicti follow fram the assumption
that S� RW can substantially distort the gain predicted through the use of poly-
mers. For ti~is reason, it is expedient to handle the calculation of the boundary
layer of a solid of revolution as a"thick" one, for which one can use either partial
21
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- differential equations for the boundary layer, or integral relationships. From a
practical viewpoint, the integral equations are more attractive, first of all be-
cause of their economy, and secondly, because of the fact that in tlieir application,
no data is needed on the fine turbulent mechanisms, and e~ly a successful approxi-
mation is needed for the prof~.les of the longitudinal components of the averaged
velocity. At the same ti, e, it has been demonstrated for a plane boundary layer
[5, 6], that if the ~amily of these profiles is specified as a multiparameter family,
the results are L~ot inferior in terms of precision to those obtained by means of
differenti2~ techniques, while accounting for the introduction of polymer additives
into the flow causes no fandamental difficulties j3~ 4].
The integral method of [7] is adopted in the following for the calculation of the
- boundary layer on a body of revolution around which the polymer solution flows,
where this method is based ~n a three parameter family of profiles for the lnngi-
, tudinal cnmp4nent of the averaged velocity, which has the form:
(1.1) U/v'~-_;;'' In (t~*Y/~~) -f-/3~-r''! ( (X) ti~( Y/b) -f-/(1'll~~)
Here, U is the longitudinal averaged velocity, v* = zW
p is the dynamic velocity,
- TW = TW(X) is tangential stress at the streamlined surface, X is the longitudinal
coordinate which coincides with the meridian line circling the solid, p is the fluid
density, K= 0.4 is the first constant of turbulence, Y is the transverse coordinate
normal to the meridian line circling the solid, B is the second constant of turbu-
lence or the parameter which takes into account the influence of the polymers,W is the
Coles function, f is a function which takes into account the influence of the trans-
verse curvature of the streamlined surface and v is the kinematic fluid visccsity
coefficient.
It can be seen from formula (1.1) that th~ first two terms take the form of the usu-
al logarithmic law, justified in the region near the wall for practically any turbu-
lent boundary layer, while the third term reflects the special features of turbulent
intermix ing in the outer region, where the Coles parameter II(X) makes it possible
to take into account the influeace of the longitudinal curvature of the solid and
the external pressure gradient. To facilitate the calculations, the form of the
function W(Y/S) was simplified as campared to the usually employed cos~ne curve j8]:
(1.2) 4t'O'/~S)=G(Y/~i)z-!,(y/~)' .
The approximation (1.2) used here satisfies the boundary conditions W(0) = W'(0) _
= W'(1) = 0, W(1) = 2 and is in suff~ciently good agreement with experimental data.
The form of the fourth term of the right side of (1.1) was determined from various
considerations in [8, 9]; the proposed functions were different in form, but yielded
close results numerically. Since the form of both functions is rather complex [8],
a simple parabolic approximation is used instead of them:
(1. 3) f~)'lI~�) =Ax'' ( Yi R~) v,
which when A=-0.46 practically coincides with the curves of [8, 9). The match
of this approximation to the experimental data for gradient-free, axially symmetric
flow was confirmed in [7] by means of comparing the results of experiments on long-
itudinally streamlined cylinders.[10].
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By substituting expression (1.2) and (1.3) in formula (l.l}, and converting to
dimensionless quantities, we obtain:
(1.4) uc~~-'=x-'ln (c~ual3e~)-}-13+IIx-'[6(y/S,)Z-4(y/8)')-I'
-I-ft x-, ~y~r~~
S,=S/L, ~=Y/L, x=X/L, r,~=R�/L
c~~=v*/U6, u=U/Ue, ~r~=U,/v,,, Re=v�I,/v
Here, L is the l.ength of the solid, v,~ is the unperturbed flow velocity, Ua =
Ug(X) is the velocity at the outer boundary of the boundary layer.
Expression (1.4) defines the dimensionless family of profiles of the longitudinal
averaged velocity in a boundary layer containing three dimensionless parameters:
S1(x) , II (x) and w(x) .
The following are integrated to determine these parameters: the moment~m equa+tion~
the mass capture equation and the law governing the resistance, which follows from
expression (1.4). The integral momentum relationship is used in a form which con-
tains integral areas and is suitable for a thick, axially symmetric boundary layer:
(1.5) d0 + 1 ~a~e~*+2~,**~=r~,w'
dx ua dx
o e
0*= f (1-u)RdY, 0**=~u(1-ic)RdY
0 0
~,*=0*/L=, 6,**=0**/? Z, R=R�-f-Yros ~
Here, A* is the displacement area (per radian ~f the angular cylindrical coordinate),
A*~ is the area of loss of momentum, R is th~ radial cylindrical coordinate, S is zhe
angJ.e between the axis of the solid ~f revolution and tfie tangent to the line circling
it at the meridian.
The integration of the differential contin~ity equatior~ over the thi~kness of the
boundary layer, or the utilization of the equality of the fluid mass entering and
leaving a section of the boundary layer of length dX, gives a mass capture equation
which has the following form for an axially symmetric flow:
1 rl -~U~(U-0*) ]=db Vo
(1.6) L'elrn tlX [lX Ue
e
0= f lttl~'=1~W~1-f-0,55Z cos /te=R�-I-S cos ~
o �
Here, 8 is th e boundary layer area, Rg is its outer boundary radius and VS is the
transverse av eraged component of the velocity at the boundary of the layer.
The processing of the experimental data of [11] made it possible to establish the
fact that the right side of equation (1.6) can be replaced by a mass capture ~unc-
tion in form found in [8J, proposed for a plane boundary layer, if the argumen~ of
this function is computed not in terms of the thicicnesses, but rather in terms of
the areas of the boundary layer:
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rl~i/rl ~-V~/U~==1s (I/~) =Q,O:iOG (11~-3)-o,es~
(1.7) //,=(0,-0,*)/0,*~~ 0,=0iLZ
_ Taking (1.7) into account, equation (1.6) can be written in the form:
(1.8) d[un~~)~-Oi*))ldx=ls'ue?'e
The law governing the resistance is derived frocn thQ velocity profile (1.4) and
can be written in differen~ial form as follows:
9 ~1 dc5, dII 1 ,c dc~~
- ~-+2-+(---I--~-
- (1.91 b, ~'S,'',r�'" dz dx ~ c,~ d.c
t rlir ~ ~18,'~' dr~ dB
--'I-------Y. -
u~ ~lx. 3ru.'~' d.~ dx
In the absence of polymers, the last term disappearsl. since in this case, B= const.=
_ = 4.9.
The Runge-Kutta m~thod was used to integrate the system of three ordinary different-
ial equations (1.5), (1.8) and (1.9}. The calculations were performed on a BESM-6
digital computer programmed in ALGOL-60 and a YeS-1022 camputer programmed in FORT-
_ RAN. The initial conditions for ~he system af differential equations were derived
using one of three procedures:
1. If the boundary layer was ass~lmed to be turbulent, starting with the critical
- bow point, then at a distance along the axis of Z= 0 to 0.2, its characteristics
were deter.mined just as .for a fZat plate with the corresponding Reynolds mmmber.
2. If the boundary layer was calculated assuming t'~at the change of flow modes oc-
curs at a conditional lamina`r--turbulent transition point, then the momentum contin-
uity condition 6L~` = AT* d:as used at this point, where the subscripts L and T cor-
respond to the laminar and turbulent portions. ~he laminar section was camputed
by the conventional single parameter technique, while the transition cross-section
was defined ei~her as ~he cr~ss ~e~tion where an agitator is located~
~r on the basis of the empirical ~ormula of [7]:
1ieL,~**=esp (~i~i,~l-14,711), Rc**=Ua~**/v, 11=~i*lb**
(1.10) e o
~S*= f(1-~a)dY, S**= f c~(1-u)dY
~ o
Here, the double subscript LT indicates the transition cross-section, d~ is the
. displacemPnt thickness and d** is the momentum loss thickness. Formula (1.10) is
justified for a degree of free turbulence of e= 0.3 - 0.7%. The system of the
following transcendental equations was solved to determine the initial values of
aLT~ nLT and w LT: ei* = e*~*(dl), H= 8*/d'~* and (1.4) for the case where y= dl and
_ u = ub:
3. I� the boundary layer was calculated taking inr,o account the laminar, tY�ansition
and turbulent flow regions, then the characteristics of the laminar layer w~re de-
termined using the method of L.G. Loytsyanskiy, while the parameters of the transi-
tion region were determined on t~e basis of the distribution of the intermixing
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coefficient using the procedure proposed in [12]; following after the center of the
transition region, where the intermixing coef�icient was taken as 0.5, a cross-
section was chosen in which the momentum lo~s area of the laminar boundary lay~r
calculated fr~m the critical bow point matched that of the turbulent boundary layer
which was calculated from the transition onset point.
bp,B,, + 5
g2
~ ~ g x 6 !0. �
07
0 8 +
4 y ~
x
q 1f-
x y
Z 3 l~
4 $
1 ~
_ ~ f2 ,
~ O,Z 0,4 0,6 Q,9 Z
Figure 1.
It must be noted that f or all three variants of tne determination of the initial
conditions, the characteristics of the turbulent portion of the boundary layer
differ slightly from one anoth~r if the laminar--turbulent transition occurs far
' away from ttiie bow extremity of the solid, something which almost always occurs at
Reynolds numbers of practical interest.
The results of ~alculating the boundary layer of the solid of revolution deseribed in
[11], in the case where an ordinary viscous liquid flows around it, were compared
with the experime:ltal data of [11] for Re = 1.262 � 106 in Figure l. Curves 1, 2
and 3 correspond to the dim~nsionless characteristics of the boundary layer, S2 =
_ 10251, e2 = 1o3ei/rW and 02 = 1039i*/rW. Curves 11 and 12 take the form of exten-
sions of curves 2 and 3, drawn to a scale of 1:10. Curve 4 corresponds to the dis-
' tribution of the local coeff icient of friction C~ = 2Tk/pUa = Zw2, where C=_103Cf.
- Experimental points 5, 6, 7 and 8, which are given in the data of paper [11], cor-
- respond to these same churacteristics. As can be seen fram the comparison made
above, the results of the calculations are in good agreement w'i~h the me~surement
data, practically right out to the very tail end extremity of the body.
If the boundary layer is calculated as a thin one, i.e.. the assumption that d�
� RW is used, then d*RW must be substituLed for 6*, 8~`*Rw for 6** and SR~,~ for 9
in equations (1.5) and (1.8), while one must set f(Y/RW) = 0 in expressions (1.1),
(1.4) and (1.9) (thi.s can be donP by formzlly setting~A ~ 0). The results
of the calculation of the local coeffici2nt of frictir~n and the boundary layer
thickness, performed with these ass~nptions for the same body of revolution~ are
shown in Figure 1(,curves 9 and 10). The use of such simplifications leads to the
fact that the agreement with th~ experimental data in the region of the tail extre-
mity of the body becomes worse. The eited results confirm the expediency of taking
into account the finite thickness of the axially symmetric boundary layer.
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2. When calculating the boundary layer of a solid of revolution in a polymer solu-
tion, equations (1.5) and (1.8), which essentially take the form of the laws of
momentum and mass conservation, do not change. In equation (1.9), the last term
KdB/dx ~ 0, since the parameter B, included in the velocity profile (1.4), is not
a constant in a polymer solution.
Several semi-empirical theories exist at the present tfine, in which relationships
are proposed for B as a function of the p~operties of the polymer and the charac-
teristics of the polymer-solvent system. In the simplest of them, and apparently,
the first one to appear, i~ is proposed that B be treated as a sum [13]:
_-/~,~-I~.V;. ~~~~~-r.on.~~
(2.1) ~-`"'=i'~~a`: ;V;=l), r~+�1~~~~*: ~1/3=a ln ~i'*~1~~~*)
Here, Bo = 4.9 (for a tube, 5.5), ~B is the "polymer increment"~ the coefficient
a depends on the kind and concentration of the polymer, while vo is the threshold
dynamic velocity, starting at which the presence of polymers in the solution be-
comes effective. We obtain from formula (2.1):
(2.2) ~1RlcLt� --a(cnice)-~~~~c~~un)/~.r.
Expression (2.2) should be substituted in (1.9), and relationships (2.1) substi-
tuted in (1.4). The values of a and vo should be determined experimentally. For
example, for a solution of WSR-301 polyethylene oxide with a mass concentration
of c= 10-5 they are equal to vo.~ 0.023 m/sec and a= a(c, M) = 4.2 - 4.5 (it was
assumed in the calculations that a= 4.343; M is the molecular weight of the poly-
` mer) .
A more sophisticated theory to account for the ~olymer increments was developed in
[1 - 4]. In this case, one of the possible and simplest approximations of the
parameter B has the form [14]:
(2.3) /3- ;~,Sl, -_1-b arc~q [1,7~U*~~o*-1)
b==U,37 ~ircl~,l 1 1,? c�!ll�~"'')
As can be seen from the formulas cited here, it is not necessary with this theory
to determine the two parameters from experiments, since the first of them, b=
b(c, M), similar to a in Meyer's correlation of (~.1), is computed from the uni-
versal function (2.3), while:
v* = DM 0.89
(2.4) o
where D depends only on the type of polymer. The application of (2.4) to WSR-301
~ polyethylene oxide (D = 1.37 � 104 m/sec) yields vo = 0.0246 m/sec, which is almost
no different than the experimental value given above. 'I'he use of (2.3) yields a
value of b = 0.49.
It should be noted that the structure of expressions (2.3) is more reasonable than
that of relationships (2.1). Using formulas (2.1), it turns out that at high rates
of motion (v* , the ~olymer e��fect increases without bound (B . The use
of formulas (2.3) when v-> ~ leads to a value of F= F~, = 0.235, i.e., there is
no increase in the velocity that can lead to a reduction in the resistance of more
than that corresponding to B= 17.3.
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Differentiating expression (2.3) with rzspect to x, taking into account the fact
~ that v* = a~uav~, yields:
dB S,97GbF-'~�(v�luo*) d
(2.5) clx 1+[1,7(c~uo(u�1va*)-1)]zd;r ~wu,)
Attention is drawn to the fact that using Meyer's correlation, the increment added
to differential equation (1.9), besides the variables w and ug, contained only the
, constant parameter a, while in accordanre with the theory of (1 - 4], the added
increment contained the additional ratio vm/vo related to the rate of travel. The
influence of this added component is rather complex, but when v~ it turns out
that dB/dx } 0, i.e., the impact of polymers present in the flow in the case of th.e
transition to a resistance law in differential form for very high velocities, is
primarily taken into account solely throug~ the initial conditions, in which th~
undifferentiated resistance function plays a part. It is not precluded that such
a result is obtained only by virtue of the form of the proposed approximation (2.3).
In order to avoid the "disappearance" of dB/dx at large values of v,,, in the denom-
inator of expression (2.5), there should be a linear function. of v~/vo, rather than
a square law. One can arl'~ve at th~ desired result if the arctangent 3n the second
of the formulas of (2.3) is replaced by the logarithm:
(2.6) ;lrctg [1,7(v*~vo*-1))~aln (v*lvo*)
For a range of variation of the argument v'~/v~ = 1 to 10, good agreement is obtained
between the left and right sides of expression (2.6) when a= 0.945. In this case,
strict equality occurs when v*/vo = 4.4. Using this value, one can choose the co-
efficients of the linear expression with which it is desireable to replace the
- square law in the denominator of formula (2.5). As a result, one can derive:
a~ s,s~cvr-~~e~~mi~o~>
~ Z . - ---~G)Ue~
rf.r 1.-I-9,521i[waaa(v~/vo*) -9 ] rl.r.
It can be seen that when v~ , expression (2. 7) autamatically changes
over to a form analogous to (2.2). This is responsible for the possibility in the
case of using Meyer's correlation of not seeking out a each time experimentally,
- but rather determining its value analytically by means of the parameters of the
theory of [1 - 4]:
- ~2,g~ a= 0.913 b F~1'6 = 9.2 b
For the example considered here, formula (2.8) yields a z 4.48. The th~eshold
value of the dynamic velocity for both theories can likewise be caJ.culated from
formula (2.4) .
The calculations of the boundary layer of the solid of revolution described in [11]
were carried out fur the case of streamline flow around it by a solutiun of
WSR-301 polyethylene oxide with a molecular weight of M= 3� 106 at a concentra-
� tion of c= 10-5 in two variants: using Meyer's correlation and based on the theory
of [1 - 4J. All of the calculations were performed for two variants of the speci-
fication of the initial data:
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' Y
I
~
~ e2
I ~
:
4 -i - ~ i
~ii
- 2 ~~i
~ i i
~ J ' ~ ~i
~ ~ ' I
I ~ ~ ~4 ~i
, ~u6~ ~~i
- ~
~ 0, 2 ~O,u 0,6 U, B I Z
Figure 2.
= ei� i
_ I
I~
I
4 ~
I~
ll
2 ~ / 1 I
2 ~ ~ i~ il
~ ~4'~;~
I - / ~
_ ~,~u6..
D p,2=---0,4 0,6 O,B Z
Figure 3.
~ ~ -
f 2 d
- y -
~
2 ~=~z z~
Z
~ G,Z 0,4 0,6 0,8 Z
Fj.gure 4.
1. L= 1.578 m, v~ = 0.913 m/sec, Re = 1.262 � 106
2. L= 3.2 m, v,~ = 15.0 m/sec, Re = 3.057 � I~~
The results of calculations ot the dimensionless integral areas of the boundary
- layer and the coefficient of local iriction are ~iven in Figures 2- 4, where the
designations arP analogous to thase of Figure 1. In these flgures, curves 1 cor-
respond to streamline flow arr.,und rhe solid by an ordi.riary viscous liquid,
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curves 2 are for calculations using MPyer's correlation and curves 3 are calcula-
tions based on the theory of [1 - 4]. The solid curves apply to a Reynolds~number
of 1.262 � 106, while the dashed curves are for Re = 3.057 � 10~; curves 4, 5 and
6 take the form of extensions of curves 1, 2 and 3 on a scale ~f 1:10.
~ T
1
I
I I J ~
I _ z
-
zc - I -
~
~ ~
4 I
' ~ ' +S
~S }u S 6 ~
Figure 5.
The cited results shaw that when using any of the theories considered here, the
advantage gained in the frictional resistance increases with an increase in the
velocity of the body. Thus, the overall coefficient of frictional resistance falls
off by approximately 20% when the solid is sub~ected to streamline flow by a poly-
mer solution, as compared to streamline flow of the solvent when Re = 1.262 � 106,
and when Re = 3,057 � 10~, the decrease is 50%. The nature of the distribution
curves for the ~oefficient of local friction as a function of the Reynolds number,
the length of the solid and the rate of motion are in qualitative agreement with
the results obtained for a flat plate [3]. In the case of a smaller Reynolds num-
ber, somewhat of a divergence is observed between the results of calculations using
various ~orrelation formulas, which take into account the influence of polymer addi-
tives on the flow characteristics. When Re = 3.057 � 10~, the calculations based
on both theories yield very close results. Because of the definite divergence of
the calculation results based on different functions foY� relatively small Reynolds
numbers, i.e. in the region of the onset of the manifestation of the polymer ef-
f ect, an answer can be given to the question of the preferability of any one of
the theories only on the basis of a comparison of the numerical results with the
data of a carefully performed experiment.
- The profiles of the longitudinal component of the averaged velocity determined from
the calculation results are shown in Figure 5. The profiles were plotted for a
cross-section with a dimensionless abscissa of z= 0.662 in coordinates of
= U/v* and n= ln(v*Y/v) for a Reynolds number of 1.262 � 106. In the case of
streamline flow around th e solid without polymer additives (curve 1), completely
satisfactory agreement is observed between the camputed profile and the measure-
ment data of [11] (points 5). Lines 2 and 3 in Figure 5 correspond to the ~reloc-
ity profi~e determined from the results of boundary layer calculations using
Meyer's correlation and the functions proposed in [1 - 4]; curve 4 is the usual
logarithmic law. All of the data demonstrates the extremely strong influence of
polymer additives on the velocity prof ile.
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BIBLIOGRAPHY
1. Sedov L.I., Vasetskaya N.G., Ioselevich V.A., "0 raschetakh turbulentnykh
pogranichnykh sloyev s malymi dobavkami polimerov" ["On Calculations of Turbu-
lent Boundary Layers with Small Amounts of Polymers Added"], in the book,
"Turbulentnyye techeniya" ["Turbulent Flows"], Moscow, Nauka Publishers, 1974,
p 205.
2. Vasetskaya N.G., Ioselevich V.A., "0 postroyenii poluempiricheskoy teorii
turbulentnosti slabykh rastvorov polimerov" ["On the Construction of a Semi-
empirical Theory for the Turbulence of Weak Polymer Solutions IZV. AN SSSR,
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1970, No 2, p ].36.
3. Vasetskaya N.G., Ioselevich V.A., "Polimernyye dobavki v pogranichnom sloye
ploskoy plastiny" ["Polymer Additives in the Boundary Layer of a Flat Plate"],
NAUCH. TRUDY INSTITUTA MEKH. MGU [SCIENTIFIC PROCEEDINGS OF THE INSTITUTE OF
- MECHANICS OF MOSCOW STATE UNIVERSITY], 1974, No 32, p 178.
4. Ioselevich V.A., Pilipenko V.N., "0 turbulentnom techenii zhidkosti s polimernymi
dobavkami v pogranizhnom sloye s prodol'nym gradiyentam davleniya" ["On the Tur-
bulent Flow of a Fluid with Polymer Additives in a Boundary Layer with a~a Arhi-
trary Pressure Gradient"], DOKL. AN SSSR [REFORTS ~DF THE USSR ACADEMY OF SCIENCES]
1973, Vol 213, No 4, p 808.
5. "Computation of Turbulent Boundary Layer", 1968, Proc. AFOSR-IFR Stanford Confer-
ence, Ed. Kline S.J., Morkovin M.V., Sovran G., Cockrell D.J., 1969, Vol 1.
6. Levkovich, Khodli, Khorlok, Perkins, "Semeystvo 3.ntegral'nykh metodov dlya
rascheta turbulentnogo pogranichnogo sloya" ["A Family of Integral Methods for
the Calculation of a Turbulent Boundary Layer"], RAKETNAYA TEKHNIKA I KOSMONAVTIKA
[ROCKET ENGINEERING AND ASTRONAUTICS], 1970, Vol 8, No 1, p 51.
7. Amf ilokhiyev V.B., Droblenkov V.V., Mazayeva N.P., Shk?.yarevich A.I., "Raschet
eksperimental'noye issledovaniye tolstogo osesimmetrichnogo turbulentnogo
" pogranichnogo sloya" ["The Calculation and Experimental Investigation of a Thick
Axially Symmetric Turbulent Boundary Layer"], in the book, "Abstracts of Reports
to the All-Union Scientific and Engineering Symposium on Questions of Improving
the Propulsion Qualities and Operational Characteristics of Domestically Produced
Ships of the Future", Leningrad, Sudostroyeniye Publishers, 19'18, p 5.
8. Fedyaevskiy K.K., Ginevskiy A.S., Kolesnikov A.V., "Raschet turbulentnogo
pogranichnogo sloya neszhimayemoy zhidkosti" ["The Calculation of the Turbulent
Boundary Layer of an Incompressible Fluid"], Leningrad, Sudostroyenie Publ3:shers,
1973, 256 pp.
_ 9. Rao G.N.V., "The Law of the GJall in a Thick Axisymmetric Turbulent Boundary
Layer", TRANS. ASME, SERIES E., JOURNAL APPL. MECH., I967, No 1. p 237.
10. Willmarth W.W., Winkel R.E., Sharma L.K., Bogar T.J., "Axially symmetric Turbu-
- lent Boundary Layers on Cylinders: Mean Velocity Profiles and Wall Pressure
Fluctuations", J. FLUID. MECH., 1976, Vol 76, Pt. l, p 35.
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11. Patel V.C., Nakayama A., llamian R., "Measurements in the Thick Axisymtnetric
Turbulent Boundary Layer Near the Tail of a Body of Revolution", J. FLUID MECH.,
1974, Vol 63, Pt. 2, p 345,
12. Droblenkov V.V., Kanevskiy G.I., "0 postroyenii metoda rascheta ploskogo
pograni~hnogo sloya v slabykh rastvarakh polimex~ov s laminarnoy, perekhodnoy i
- turbulentnoy zonami techeniya" ["On the Formulation of a Computational Tech-
nique �or a Plane Boundary Layer in Weak Polymer Solutions with Lam~.nar,
Transition and Turbulent Flow Regions"], IZV. AN SSSR. MZhG, 1977, No 3, p 42.
13. Meyer L~I.A., "A Correlation of Frictional Characteristics for Turbulent Flow of
Dilute Viscoelastic Non-Newtonian Fluids in Pipes", AIChE JOURNAL, 1966, Vol 12,
No 3, p 522.
14. Vasetskaya N.G., Ioselevich V.A., Pilipenko V.N., "Mekhanicheskaya destruktsiya
polimernykh molekul v turbulentnom potoke" ["The Mechanical Destruction of
Polymer Molecules in a Turbulent Flow"], in the book, "Nekotoryye voprosy
mPkhaniki sploshnykh sred" ("Some Questions of the Mechanics of Continuous Media"]
Moscow, Moscow State University Publishers, 1978, p 55.
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR. Mekhanika zhidkosti i gaza",
1981
8225
CSO: 8144/1532
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LASERS AND MASERS
UDC 621.371:538.566:551.511.6
PROPAGATION OF ~SER BEAM IN TURBULENT ATMOSPHERE
Novosibirsk RASPROSTRANENIYE LAZERNOGO PUCHKA V TURBULENTNOY ATMOSFERE in Russian
1981 (signed to press 18 Feb 81) pp 2-8
[Annotation, preface and table of contents from book "Propagation of a Laser Beam
in a Turbulent Atmosphere", by V. L. Mironov, Institute of Physics of the Atmosphere,
Siberian Departm~nt, USSR Academy of Sciences, Izdatel'stvo "Nauka"]
[TextJ This boak examines the physical principles of the influence that spatial
localization of a field of wave beams has on processes of fluctuations of laser
emission during propagation in a turbulent atmosphere. Methods are given for ap-
proxim~ting the solution of the wave equation for the statistical moments of the
beam field based on spectral expansions.
A theoretical and experimental investigation is made of the influence that spatial
localization of the wave field has on the patterns of turbulent broadening of the
angular dimension, distortions of spatial coherence of the field, fluctuations
of intensity and phase, and random refraction of laser beams. An examination is
made of inethods of determining parameters of atmospheric turbulence by transillu-
mination of the atmosphere with a narrow laser beam. Results are systematized
for the first time on fluctuatiot~s of laser emission accompanying lidar location
- in a turbulent atmosphere.
The book is addressed to specialists in the field of wave propagation, and also
to developmental engineers specializing in atmospheric optical laser systems.
Preface
- The atmosphere has a considerable influence on propagation of optical waves. At-
mospheric gases and aerosols are chiefly responsibZe for energy attenuation of
optical radiation, whereas fluctuations of the index of rrfraction of atmospYieric
air that arise with turbulent intermixing of layers with different temperatures
lead to considerable random distortions of the field of coherent optical waves.
The timeliness of research on rrocesses of fluctuations of laser emission in the
turbulent atmosphere is dictated by the start that has been made on using laser
optical systems intended for operation under terrestrial atmospheric conditions.
In fact, the information c:apacity of optical communication lines, spatial and
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temporal resolutian of lidars, the accuracy of geodetic laser instruments and other
technical characteristics of laser optical systems can be evaluated only with con-
sideration of fluctuations of a field of optical beams. On the on e h and, the
results of investigations of the field of a laser beam are used for calculating
the limiting possible technical characteristics of laser instruments with operation
in the atmosphere. On the other hand, they are necessary in the process of utili-
zation of laser equipment under a variety of weather conditions. The latter circum-
stance is due to the considerable variations in technical characteristics of laser
optical systems as a result of changes in meteorological conditions, so that in
some cases the.very feasibility of using them is determined on the basis of oper-
ative forecasting of the fluctuations in the field of the laser beam.
Questions of fluctuations of laser emission in a turbulent atmosphere have been
studied especially intensely over the last decade. This problem is a component
part of the broader scientific field of radio physics--propagation of electromag-
netic waves in randomly inhomogeneous media--whose fundamentals h~ve been formu-
lated in papers by eminent Soviet scientists A. M. Obukhov, S. M. Rytov, V. I.
Tatarskiy and L. A. Chernov. Results of investigations of fluctuations of optical
waves in a turbulent atmosphere have been generalized on certain stages in several
surveys and monographs. Early surveys and a monograph by V. I. Tatarskiy give
mainly the results of theoretical and experimental studies of weak fluctuations
in the field of optical wavP~ in a turbulent atmosphere, where the relative disper-
sion of intensity f luctuatic~s is small compared with unity. All major conclusions
on the principles governing field fluctuations are formulat~d here for the simplest
types of waves--planar and spherical. The method of geometric optics and S. M.
Rytov's method of smooth perturbations were the principal working methods in theo-
retical studies of weak fluctuations of the field of optical waves.
The development of lasers has brought up fundamentally new problems in the area
of propagation of optical waves in a turbulent atmosphere. The small angular di-
vergence of laser emission has enabled transmitting the energy of optical waves
over great distances in the terrestrial atmosphere with ease. ~1t the same time,
- the high spatial coherence of laser radiation has made it possible to produce col-
~ limated and focused spatially baunded wave beams at a considerable distance from
the source without difficulty. In studying the process of propagation of laser
emission, a problem has arisen on the one hand of so-called strong fluctuations
- of the intensity of the optical wave (relative dispersion of fluctuations exceeds
unity) that are caused by multiple scattering on inhomogeneities of the medium.
On the other hand, it has become necessary to study the influence that the diffrac-
tion parameters of wave beams responsible for their original angular divergence
have on processes of fluctuations of laser emission in a turbulent atmosphere.
The solution of these problems is re�lected in more recent surveys and monographs.
The tasks that have been formulated have required first and foremost the develop-
ment of fundamentally new methods of the theory of wave propagation in randomly
inhomogeneous media with simultaneous consideration of multiple scattering of waves
by itihomogeneities in the medium, and diffraction of the wave beam by the radiating
aperture. The next stage in solving the problem of fluctuations of laser emission
in the turbulent atmosphere was solution of specific physical problems and theo-
retical investigation o� the patterns of field fluctuations under different con-
ditions of propagation in the atmosphere and beam diffraction parameters.
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As a consequence of using different kinds of hypotheses and assumptions made in
constructing the theory of multiple scattering and in describing thP statistical
properties of the field of the index of refraction in the turbulent atmosphere,
the solution of physical problems of this kind are always only an approximate de-
scription of real processes of fluctuations of the field of the laser beam in the
- atmosphere. Therefore, experimental verification of the major conclusions of ap-
proximate theories is an absolutely essential research stage. Of course, the part
played by experimental studies is not li.mited to checking the main relations of
a theory. In particular, it was experimer?ts that first revealed the fundamentally
new phenomena of saturation of relative dispersion ~f strnng fluctuations of inten-
sity, and saturation of focusing of laser radiation, that were later theoretically
substantiated.
The results of theory and experiment cannot be compared without access to means
- of on-the-spot measuremen~: of atmospheric turbulence. On long transmission ~~aths
(from a few hundred meter~; to tens of kilometers) the determination of par~met~exs
by meteorological sensor; that measure characteristics at isolated points become
- either less informative when a limited number of sensors is used, or else too expen-
sive and inconvenient for practical use if the sensors are t~ be placed along the
laser beam. In this connection it becomes necessary to develop methods of de-
termining the turbulence parameters by using the laser beam itself through measure-
ments of the distortion of the light f ield. One of the advantages of these methods
is that they give the integral characteristics of turbulence along the transmission
path. At the same time, they permit reconstruction of the spatia~. distribution
of these characteristics by methods of solution of inverse problems of optics of
atmospheric turbulence. We can conclude from this that development of laser methods
of determining turbulence parameters is an essential component part of studying
fluctuations of the field of a laser beam in a turbulent atmosphere.
Methods of the theory of laser beam propagation, results of theoretical and experi-
mental studies of the patterns of optical wave field fluctuations, laser methods
of determining optical parameters of atmospheric turbulence, systematized infor-
mation on the statistical characteristics of fluctuations in the index of refraction
in the'aggregate make up the physical foundations of engineerir,.g prediction of
fluctuations of the field of a laser beam in a turbulent atmosphere, which for
practical purposes is the most important result of physical studies.
This monograph presents the results of theoretical and experimental investigations
that encompass the above-mentioned components, and that are devoted to the study of
the influence that the diffraction parameters of wave beams have on processes of
fluctuations of laser radiation in a tur~ulent atmosphere. This problem has been
only partly studied in one previous monograph.
The first chapter contains background required for the presentation cn turbulent
fluctuations of the index of ref~action in the atmosphere, and methods of the theory
of propagation of electromagnetic waves in the optical band in a turbulent medium.
The second chapter is devoted to exposition of inethods of approximate solution
of the stochastic wave equation in a turbulent medium. Chapters three through
seven contain the results of investigations of angular broadening (chapter 3),
coherence dist~rtions and phase fluctuations (chapter 4), weak fluctuations of
the logarithm of amplitude (chapter 5), intens-Lty fluctuations (chapter 6) and
random refraction (chapter 7) of laser beams in a turbulent atmosphere. The eighth
chapter examines laser methods of determining parameters of the process of turbu-
lent micropulsations of the index of refraction.
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Section numbers in. the book are made up of the ordinal number of the chapter and
of the given section. For example �1.2 is the second section of the first chapter.
The formulas have their own ordinal numbering in each section, which is retained
within the conrines of that section. In cross references, the number of the formula
is made up of the number of the section and of the formula. For example the no-
tation (2.1.3) indicates the third formula of section one of chapter 2. To facili-
tate reading of the text, the section number is placed at the top of each page.
The monograph has been written from results of the author's research done at the
Institute of Optics of the Atmosphere, Tomsk Affiliate, Siberian Department of
the USSR Academy of Sciences, including work done jointl.y with colleagues of the
Institute of Physics of the Atmosphere, USSR Academy of Sciences, and the Buryat
Institute of Natural Sciences, Buryat Affiliate, Siberian Department of the USSR
Academy of Sciences. The book also contains a detail.ed analysis of the results
of research prior to the author's investigations and predetermining their formu-
lation. In addition, wherever possible a comparison has been made between the
results given and published research on the pertinent pro~lem.
I am deeply grateful to all my coauthors, without whose cooperation it would have
been impossible to study the complex problem of fliictuations of the field of a
laser beam in the turbulent atmosphere. The author also thanks K. S. Gochelashvili,
V. Ye. Zuyev, A. S. Gurvich, M. V. Kabano�~, S. M. Rytov, V. I. Tatarskiy, V. I.
Shishov and I. G. Yakushkin whose advice and constructive criticism to a great
extent determined the direction and results of the author's research.
Contents page
- Preface 5
Chapter 1: Propagation of 'Laser Radiation in Turbulent Atmosphere (Survey) 9
1.1. Statistical characteristics of optical inhomogeneities of atmospheric air -
1.2. Approximate model of altitude dependence of the structural character-
_ istics of fluctuations of the index of refraction 1~
1.3. Methods of the theory of propagation of optical waves in a turbulent
medium 22
Chapter 2: Phase Approximation in Spectral Expansions of Solution of the
Stochastic W~ve Equation 35
2.1. Phase approximation of the Huygens-Kirchhoff inethod in problems of
~ laser beam propagation in a turbulent atmosphere
2.2. Approximate solution of stochastic wave equation with expansion of the
field with respect to plane waves 51
2.3. Phase approximation with series expansion of the f ield of a beam with
respect to spherical and plane waves 54
2.4. Approximate solution of a stochastic wave equation in problems of
lidar ranging in a turbulent medium 60
Chapter 3: Turbulent Broadening of a Laser Beam 67
3.1. Focusing of a laser beam by a ring aperture 68
3.2. Average intensity of an asymmetric laser beam ~1
3.3. Laser beam broadening on oblique transmission paths ~j
3.4. Average intensity of a reflected laser beam 78
Chapter 4: Cohe.rence and Phase Fluctuations of the Field of a Laser Beam $5
4.1. Turbulent distortions of spatial coherence of a laser beam field 86
4.2. Spatial coherence of the f ield of a reflected laser beam 95
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4.3. Average diffraction rays in a turbulent medium 99
4.4. Phase fluctuations in spatially bounded laser beams 103
- Chapter 5: Weak Fluctuations of the Logarithm of the Amplitude of a Laser
Beam 105
- 5.1. Dispersion and spatial correlation of fluctuations of the logarithm of
amplitude 107
5.2. Time spectra of fluctuations of the logarithm of amplitude 121
5.3. Averaging effect of annular reception aperture 126
- 5.4. Fluctuations of the logarithm of amplitude when a spherical wav~e is re-
flected from a point reflector 128
Chapter 6: Fluctuations of Intensity of a Spatially Bounded Laser Beatn 132
6.1. Dispersion and spatial correlation of fluctuations of laser beam
- intensity 135
6.2. Measurement of the coefficient of spatial correlation by a variable-
diameter aperture 146
6.3. Time spectra of intensity fluctuations 152
_ 6.4. Influence of internal turbulence scale on dispersion of strong fluc-
tuations of intensity of a collimated beam 159
6.5. Dispersion and spatial correlation of fluctuations of intensity of a
reflected laser beam 165
Chapter 7: Random Refraction of Laser Beams 171
7.1. Dispersion of random displacements of a laser beam 173
7.2. Correlation of displacements of spatially separated laser beams 183
7.3. Time spectra of random displacements of a laser beam 192
7.4. Random displacements of the image of a lidar target in the focus of
a reception telescope 198
Chapter 8: Determining Turbulence Parameters by Transillumination of the At-
mosphere With a Laser Beam 201
8.1. Determination of parampter Cn and internal scale from the distribution
of intensity of the image of a laser source 204
8.2. Laser method of determining parameter Cn based on scattering of light
by atmospheric aerosol 210
8.3. Determination of altitude dependences of parameter Cn from fluctuations
of the logarithm of amplitude of the f ield of a laser beam 213
8.4. Phase optical measurements of internal turbulence scale 219
8.5. Determination of turbulence spectrum in the ground layer of the atmos-
phere from measurements of fluctuations of the phase of a field of
optical beams 221
Conclusion 225
References 228
Index of Abbreviations and Symbols 243
COPYRIGHT: Izdatel'stvo "Nauka", 1981.
6610
CSO: 1862/231
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UDC 621.375.8
HIGH-POWER PULSE LASER
Moscow IZVESTIYA AKADEMII 2dAUIC SSSR: SERIYA FIZICHESKAYA in Russian Vol 45, No 6,
Jun 81 pp 989-994
[Paper delive~ed to the Tenth All-Union Conference on Coherent and Nonlinear Optics,
Kiev, 14-17 October, 1980, by V. V. Apollonov, F. V. Bunkin, Yu. I. Bychkov, I. N.
Konovalov, V. F. Losev, G. A. Mesyats, A. M. Prokhorov, V. F. Tarasenko, K. N.
Firsov and S. M. Chesnokov, Physics Institute imeni P. N. Lebedev, USSR Academy
of Sciences, Institute of High-Current Electronics, Siberian Department, USSR Acad-
~ emy of Sciences]
[Text] T~ie development of powerful lasers with active volume Uf tens and hundreds
of liters is a timely problem as such lasers are widely used for studying the inter-
action of radiation with matter. There are reports in the literature on excimer
?asers and COZ lasers with energy of 102-104 J[Ref. 1-6]. lisually laser radiation
in the W and IR bands of the spectrum is pr~ducE3 or. different facilities since
considerably different conditions of excitation are required.
This paper describes a powerful universal laser facil ity that can proc~uce emission
in both the IR and W regions of the spectrum, and results are given on studiec
of stimulated emission on mo?ecules of C02 10.6 um), XeF* (a ~ 0.35 um), XeBr*
(a ~ 0.28 um) and XeCl* (a ~ 0.308 um) .
The laser facility consists of a pulse voltage generator supplying an accelerator,
a laser chamber, pulse voltage generators supplying the laser gap, main and remote
control panels, a synchronization system, a system f or evacuation and mixture prep-
aration. The mixture could be excited by an electron beam wi~h density up to
8 A/cm2 or by an electron-beam stabilized discharge. The laser chamber ~ras designed
for a pressure of ~!p to 2.5 atm, and the active volume could be varied over a wide
range. We did experiments with an active volume of 50 (20 x 20 x 125 cm) , 28 (20 x
10 x 140 cm) , 12 (12 x 8 x 125 cm) and 7(10 x 5 x 140 cm) liters . The accelerator
- was supplied by an 8-stage pulse voltage generator with LC correction, and the
~ gas chamber was supplie~ by three 5-stage pulse volta ge generators with LC corr~c-
tion connected in parallel. All pulse voltage generators used IK-100/C~.4 capaci-
- tors, and the LC correction circuit used IMK-100/0.1 capacitors. The impact ca-
pacitance of the pulse voltage generator of the accelerator was 0.08 uF, and of
the pulse voltage generators of ~he laser gap--0.24 uF; wave impedance and pulse
duration could be varied by changing the total inductance of the pulse voltage
, generators, and the inductance of the LC correction.
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u, kV ~r kV
- n . a
~ ~
J 00 a . ~ao b
_ I, HA ~ 0,5 1 1,5 i. S
0 ~ ~ 1, X~ ~
2
~ S 2
- okV 70
~oc Z y t us I, KA '
s a
1, xA ~B 4 d
0 ~ ~ .
J6
18 4 C
~s ? rel. units
_ 7,5
p rel. units
1 1 S
OS S C,5
0 2 4 6 t Ug 0 Z 4 6 t, }1S
,
Fig. 1. Oscillograms of voltage (1) and current (2) of the ac-
celerator, the voltage pulses across the gap (3) and the current
through the laser chamber (4) and voltage pulses (5). Mixture
C02:N2:He = 1:2:2, pressure p= 2 atm, ct~.arging voltage of the
- accelerator pulse voltage generator U~ = 50 kV, other parameters
as follows: a) correction inductancz L1 = 32 uH, inductance
of the pulse voltage generator L2~ 101 uH; b) L2= 5.1 uH, L1=
1.b4 uH; c) L2 = 101 uH, L1 = 32 uH, charg3.ng voltage of pulse
voltage generators feeding the gap, UZ = 58 kV, Va = 50 liters;
d) L2 = 101 uH, L1 = 32 uH, U2 = 52 kV, Va = 12 liters
Fig. 1 shows oscill~grams of the electron beam current behind the grid, and the
voltage across the vacuu:n diode for two modes of operation of the accelerator.
The use of LC correction gave close to square-wave beam current pulses. Screens
were used for focusing the electron beam. The vacuum in the accelerator was no
worse than 10-`` mm Hg. The electron beam was coupled out through aluminum foil
- or Mylar film. All pulse voltage generators used dischargers with dry air blasting,
enabling attainment of high firing stability, �20 ns, as well as synchronization
of the discharge current pulse in the gas chamber relative to the beam current.
The voltage pulse was fed to the laser chamber with dela~~ relative to the beam
current of 0.3 us, and as a result the discharge took ~~lace at constant beam cur-
- rent density and electron Energy; the latter is important for increasing discharge
stability since it gets rid of the low-energy part of the electrons formed on the
rising and falling sections of the accelerating voltage.
In the most powerful C02 lasers known in the literature [Ref. 3-5] that are excited
by a non-self-maintained discharge with duration of 10-6 s, controlled by an electron
. 38
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beam, pumping has been done under unmatched conditions, the energy reserve in the
accumulator being much greater than the energy introduced into the discharge. As
a result, when the excitation pulse has been completed a residual voltage remains
across the electrodes of the las~r chamber, and because of the possibility of dis-
charge contraction this limits the attainment of high field strength in the gas
gap and precludes high energy inputs. The use of matched conditions in pumping
a C02 amplifier with characteristic excitation time of ~10-6 [s] was first reported
in Ref. 6. However, no data were given on the output energy characteristics of
the radiation, and the specific energy inputs did not exceed 0.2 J"�c~ 3.
The use of pulse voltage generators with LC correction in the proposed laser pro-
vides effective transfer of energy from the accumulator to the discharge ir. the
matched mode. Realization of matching of the excitation system and discharge gap
does n~~t require exact satisfaction of the equality RZ = p(RZ is the load resistance,
- p is the wave impedance of the supply system) since the reduction in the power
of the energy input does not exceed 10% for 0.75p ~ RZ< 2p. The important thing
is that as Rz changes from 0.75p to 2p, the voltage across the plasma changes from
0.47Uo to 0.74Uo, i. e. by changing the plasma resistance, for example by varying
the beam current d~nsity, we can get an electric f ield strength in the plasma that
corresponds to maximum laser efficiency. WhEn a laser with active volume of 50
liters is used, the plasma resistance is RZ= 3.8 SZ for mixture C02:N2He = 1:2:2
- at a pressure of 2 atm.
0, kJ q, J� cm- a
J 0,1J E
, a l b ~
Z 0,10~ ~ y
~ . 0,05
0
4 6 � B f 0 , ~0, 3 U,5 0,7
w, kJ K% J� cm 3
Fig. 2. Dependence of total radiation energy on input energy
for active volume Va = 50 liters (a) and dependence of specific
radiation energy on specific input energy for Va = 12 liters (b).
Mixture C02:NZ:He = 1:2:2, pressure p= 2 atm (1, 2, 3) and 1.2
atm (4). Output window KRS (1, 3, 4) and NaCl (2).
Osciliograms of the vo.l.tage pulses across the plasma, the discharge current and
the radiation pulse at a charging vo].tage of U2 = 58 kV are shown in Fig. lc, and
the dependence of the total radiation energy on the energy stored in the pulse
voltage generators that feed the discharge gap is shown in Fig. 2a. Maximum radia-
tion energy was 3 kJ, efficiency -27%. In the central part of the output window
the energy density reached 15 J�cm 3.
To study the feasibility of high energy inputs under matched conditions, the volume
of the laser was reduced to 12 liters (8 x 12 x 125 cm). Plasma resistance in this
39

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case was 2.5 SZ. Oscillograms of the discharge current and radiation pulse are
shown on Fig. ld. Since the inptit energy in the second half-period does not exceed
lU%, pumping conditions can be taken as matched. The amplitude value of the voltage
across the plasma was 136 kV, accordingly E/p = 8.5 kV�(cm�atm)-1, and the energy
inputs were up to 0.6 J�(cm�atm)-1. Dependences of radiation energy on energy
input for mixture pressure of 1.2 and 2 atm are shown in Fig. 2b.
Optical cavities with output windows of NaCl and KRS were used. Maximum radiation
energy from a volume of 12 liters was obtained on a mixture of C02:N2:He = 1:1:2
and amounted to 1.8 kJ. The radiation energy on mixtures C02:N2:He = 1:3:2 and
1:1:1 was lower by a factor of 1'~. In operation on a mixture without helium
C02N2= 1:2 the r.adiation energy decreased in comparison with the radiation energy
on a mixture of C02:NZ:He = 1:2:2 at the same working pressures. Diluting the C02:N2
mi.xture with helium without changing other conditions also increased the radiation
energy. Let us note that as the energy inputs increased, the duration of the f irst
peak of th~e radiation pulse decreased, and its power increased (Fig. 1). At output
energy density >15 J/cm2 the output window of the cavity was damaged.
This facility was also used to study lasing on molecules of XeF*, XeBe* and XeCl*.
- In these experiments the working pressure of the mixture was 2 atm, active volume Va
was 28 liters for the XeF and XeBr lasers and 7 liters for the XeCl laser. The
active volume for lasing on XeCl* molecules was reduced to attain hi~her pumping
powers. The interelectrode gap was reduced to improve the homogeneity of ionization
of the gas mixture in the discharge gap since mixtures for lasing on excimer mole-
cules use gases with higher specific weight at higher pressures than in the C02
laser. The working mixture consisted ot argon, xenon and one of the halide carriers:
NF3, C2F4Br2 or CC14. The optical cavity was formed by a flat aluminu:r: mLrror
- with protective coating, and a plane-parallel quartz plate. A low-indibctance ca-
pacitor C, usually equal to 3 uF, was connected to the anode. The ind~ict~ince of
the discharge circuit was 155 nH.
Fig. 3 and 4 show curves for specific radiation energy Q and specific energy W
transferred to the gas by the beam and discharge as dependent on the initial elec-
tric fi.eld for mixtures of Ar:Xe:NF3, Ar:Xe:C2F~+Br2 and Ar:Xe:CC14 at different
beam current densities. The maximum specific radiation er.ergy on molecules of
XeF* was 0.9 J/liter (total energy 25 J), on XeBr*--0.32 J/liter (total ~nergy
9 J), and on XeCl*--0.4 J/liter (total energy 3 J). A distinguishing feature of
the given mode of excitation of excimer molecules is intense processes of gas
Q, J/Z W, J/Z
~ Fig. 3. Radiation energy (1,
0,8 ep 3, 4) and energy input to the
Z gas (2) as dependent on electric
, p''- -0 field strength for XeF* molecules:
y~ 3 1--in mixture Ar:Xe:NF3= 1000:10:1;
0,4 40 2-4--in mixture Ar:Xe:NF3= 2000:
p-"� 10:1. Parameters: 1--beam current
density j= 3 A/cm2, beam duration
0 T= 1.2 us, C= 6 uF; 2, 4--j = 1.2
~ Z 4 A/cm2 , T= 1 us; 3--j = 3 A/cm2 ,
Eo, kV/cm T= 1.2 us
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Q, J/Z W, ?/Z Q, J/Z W, J/Z
o s , ~s o,s , . z~n
' a =
- ,
_�r- s _,o
p~4 SO 0,4 _.r-'D"~ f60
4
1
J
p~Z ZS 0,2 80
a b
0 1 Z 0 2 ~
Eo, kV/cm
Fig. 4. Radiation energy (1, 3, 4) an~ energy input to the gas
(2, 5) as dependent on electric field strength for molecules
of XeBr* (a) and XeCl* (b): curves 1, 2--mixture Ar:Xe:C2F4BrZ=
6000:40:1, j= 3 A/cm2, T= 1.2 us; curves 3-5--Ar:Xe:CC14= 2000:
- 50:1, j= 6 (3, 5) and 8(4) A/cm2, T= 1 us
- amplification, enabling attainment of a rario of five for the discharga-to-beam
energy input to the gas for mixture Ar:Xe:NF3= 2000:10:1.
Let us note the peculiarities of excitation with gas amplification. In the case
of a non-self-maintained discharge, the discharge current pulse copies tne electron
beam current, and the energy input to the gas from the discharge under these con-
ditions is commensurate with the energy input to the gas from the electron beam.
The radiation pulse in this case is a bell cir.rve, and its delay from the onset
of the current pulse may exceed 150 ns. Witts an increase in the charge voltage;
and accordingly in the voltage across the discharge plasma, the discharge current
is determined not only by the intensity of the electron beam, but also by the ex-
tent of gas amplification processes. Under these conditiflns, the discharge is
volumetric for a time, and then contraction sets in. The duration of the volumetric
stage may exceed the duration of the electr~n beam pulse.
Efficient energy transfer from the storage element to the volumetric disc~arge
requires satisfaction of two conditions: first, pulse supply to the gas vessel
must be such that voltage is removed before,the instant of discharge contraction,
and second, the impedance of the storage element must be matched to the resistance
of the plasma. The resistance of the plasma in the case of excitation by a discharge
with ionization multiplication decreases during pumping, and therefore compl~te
matching can be realized only by using a stripline with variable wa~~e impedance.
Let us note that contraction in mixtures of inert gases with halides is much dif-
ferent from that in mixtures typical of G02 lasers. The channels that are foi-med
in excimer mixtures have comparatively high resistance, and may exist simultar.eously
with the volumetric discharge for a considerable time (~10-~s or longer).
We made an attempt to get thL maximum duration of the radiation pulse on the XeF*
molecule on the described facility. At a beam current duration of 5.4 us and current
density j= 0.~ A�cm 2 in a mixture of Ar:Xe:NF3= 1100:5:1 we attained a radiation
41
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pulse duration of 5.5 us. However, a reduction in pumping power led to a consider-
able reduction in radiation energy because the gain was unsaturated. Maximum radia-
tion energy at a pulse duration of 5.5 us in these experiments was ~1 J.
_ Thus a universal laser system has been developed that enables variation of excita-
tion conditions over a wide range, and that can use different gas mixtures to get
powerful emission pulses in the IR and W regions of the spectrum.
The authors thank B. M. Koval'chuk and V. I. Manylov for assistance in making the
pulse voltage generators, and V. A. Yamshchikov for helping with the experiments.
� REFERENCES
1. Hoffman, J. M., Hays, A. H., Tisons, G. C., APPL. PHYS. LETTS., Vol 2~, 1976,
p 538.
_ 2. Rokni, M., Mangano, J. A., Jacob, J. H., Hsia, J. C., IEEE J. QUANT. ELECTRON.,
Vol QE-14, 1978, p 464.
3. Orishich, A. M., Ponotnarenko, A. G., Posukh, V. G., Soloukhin, R. I., Shala-
mov, S. P., PIS'MA V ZHLJRNAL TEK~iNICHESKOY FIZIKI, Vol 3, 1977, p 39.

~
4. Bychkov, Yu. I., Karlova, Ye. K., Karlov, N. V., Koval'chuk, B. M., Kuz'min,
, G. P., Kurbatov, Yu. A., Manylov, V. I., Mesyats, G. A., Orlovskiy, V. M.,
Prokhorov, A. M., Rybalov, A. M., PIS'MA V ZHiIRNAL TEKHNICHESKOY FIZIKI, Vol 2,
1~76, p 212.
S. Adamovich, V. A., Baranov, V. Yu., Bevov, R. K., Samkovskiy, Yu. B., Strel'-
tsov, A. P., PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 4, 1978, p 988.
6. "Status Report on Laser Program at LASL (u)" LA-5251-PR, 1972.
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya~AN SSSR. Seriya fizicheskaya", 1981
- 6610
CSO: 1862/244
.
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UDC 621.375.826
INVESTIGATION OF GASDYNAMIC LASER USING ACETYLENE COMBUSTION PRODUCTS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 6(1G8), Jun 81 pp 1202-1207
[Article by Yu. N. Bulkin, B. A. Vyskubenko, G. A. Kirillov, S. B. Kormer,
- V. M. Linnik, Yu. V. Savin and V. D. Urlin]
[Text) The paper describes a gasdynamic laser based on combus-
tion of a mixture of C2H2-02-N2. Experiments and calculations
give the temperature and pressure dependences of the gain as
well as the total and specif ic powers of radiation in a com-
bustion chamber at pressures up to 70 atmospheres. Mathematical
modeling of the experimental facility gives the losses associated
with vibrational relaxation, heating of the cavity mirrors and
entrainu~ent of stored energy b}~ the gas �low.
1. Introduction
Active research is now in progress to develop different kinds of gasdynamic lasers.
Of particular interest among such lasers are those based on combustion of hydro-
carbon fuel [Ref. 1-5]. The use of acetylene or benzene gives optimum compositions
of working mixtures at fairly high combustion temperatures. Ref. 4 gives the result
of ineasurements o.f the gain in cw gasdynamic lasers based on products of combustion
of a benzene-air mixture at combustion temperatures up to 1700 K and pressure
pa~ 30 atmospheres. Experiments with acetylene-air mixtures at po ~ 20 atmospheres
are described in Ref. 3. The authors of this work ~stablished that at the ampli-
fication-optimum stagnation parameters (po = 5-10 atm, To = 1.4-1.7 kK) the gain
was 8�10-3 cm 1. Maximum specific lasing energy output was 7.8 J/g at po= 6.3
atmospheres. The power and specific energy output of lasing obtained in this work
are limited to the region of low stagnation pressures. Considering the necessity
of optimizing gasdynamic lasers not only with respect to specific energy output,
but also with respect to radiation power, as well as the fact that the used gas
may be exhausted into the atmosphere, it is of interest to study the operation
of a gasdynamic laser based on combustion of acetylene at higher stagnation pres-
sures.
Our paper is a report on optimization of a laser using products of combustinn of
a mixture of C2H2-02-NZ in the region of stagnation pressures up to 70 atmospheres.
The gain, power and specific lasing energy output were measured as functions af
the composition and stagnation parameters of the working me~iium in a quasi-cw
43
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gasdynamic laser. Two-dimensional profiled nozzles were used in the experiment
with different heights of the critical cross section and Mach numbers. The investi-
gated gasdynamic laser was optimized with respect to finding the region of stag-
nation parameters with near maximum specific energy output and lasing power.
The gain and the power of stimulated emission of the gasdy~amic laser were calcu-
lated in a one dimensional model in the geometric optics approximation for a plane-
parallel optical cavity. The mathematical model was analogous to that used in
Ref. 6-9.
2. Description of the Experimental Facility
The experimental facility is described in general outline in Ref. 9. The pulsed
combustion chamber was a steel cylindrical vessel with volnme V= 45,500 cc and
length of 1.6 m. The fuel mixture admitted to the chamber was ignited by an elec-
tric discharge. The resultant pressure pulse was recorded by an inductive pressure
sensor. The gas temperature T(t) in the combustion chamber and the flowrate G(t)
of gas through the nozzle were calculated by a method described in Ref. 9. Both
the composition and pressure of the initial fuel mixture were varied in the ex-
periments. The concentration of acetylene and oxygen in all experiments was chosen
on the basis of the stoichiometric ratio 1:2.5. 'I'he acetylene concentration in
the mi.xture was varied from 3.Ei to 6.0%. The nozzles used with critical cross
section height h* = 0.04 and 0.08 cm had geometric degree of expansion A/A* = 35.8;
a nozzle with h* = 0.025 had A/A* = 75.6. The width of all nozzles was 17 cm. The
profile of the supersonic part of.the nozzle was found from the method of charac-
teristics for a gas with constant adiabatic exponent without consideration of vis-
cosity.
The gain was measured b.y a conventional arrangement using a single-mode electric-
discharge C02 laser (transizion P(20) of band 00�1-10�0) with stabilized power
supply. The reference an:i amplified signals of the emission were registered by
photoresistors.
Lasing experiments were done using hemispherical resonant cavities arranged in
series along the gas flow, the axes of these cavities being 4.5, 8.5 and 12.5 cm
away from the critical cross section of the nozzle. The opaque mirrors (copper-
coated glass) had a rectangular cross section of 40 x 40 mm and radius of curvature
of 10 m. The flat output mirror measuring 40 x 120 mm made of BaFz with dielectric
coating was common to all three cavities, and had reflectivity r~ 93% at 10.6 um.
The leading edge of the first hemispherical cavity for all nozzles was 2.5 cm away
from the critical cross section. The mirrors were located close against the gas
flow. The pulse energy and instantaneous radiation power wer~e measured by calo-
~ rimeters and photoresistors. The optical measurement system was designed for mea-
suring the energy and shape of the radiation pulse separately in regions a~ 9.5
- and 10.6 um corresponding to P-transitions of band~ 00�1-02�0 and 00�1-10�0 of
C02 molecules.
3. Results of the Experiment and Calculation, and Discussion
The results of ineasurements of the power and specific energy output of radiatipn
as a function of pressure and temperature in the combustion chamber are shown in
44
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No, W/cm2 Curves for normalized radiation power
1~hI* No (broken lines) and specific energy
3 output N* (solid lines) as a function
80 of stagnation pressure po for a mixture
2 of 4.Sy C2H2 and nozzles with h* = 0.08
- ~ ~ (a), 0.04 (b) and 0.025 cm (c) (compositon
3 of combustion products C02:H2O:N2= 9.2:
4a 4.6:86.2y at To = 1.5 (1) , 1.7 (2) , 1.9
2 �
20 ~ ~ (3) and 2.1 kK (4)
1 ~
0 f0 20 30 pt� atm
a'
Np, W/cm2
lON* ~ J/8 I i 4, p
3~
f00 , 3 -
~ p 0
0
0
BO - - -
~ d 2 1
/i~. ~ ~ 4
60 I / ~ ' t~~ 3
3 ~i
- 40 ~ ~
~y/,~~ i 1 I ~ � --2 �
20 ~
~ ~ ~ �
- D >0 20 p a., atm 20 40 60p p, atm
b ~
TABLE 1
I N.
Mixture I h�. I A/a� I ve, aTM I r� KK J tw. J/g IW/cm2
I
0,08 35,8 24,0 t,5 5,9 40,0
30,0 l,5 4,5 40.0
37,5 l,5 3,0 32,6
3,6 %
CZH' 0,04 35,8 25,0 1,5 5,5 37,5
33,5 1,5 7.9 %5,5
42,0 1,5 4,7 5;,9
0,08 I 35~8 I 30~U I 2~3 I 3~6 I 21,9
6,0 %
CzHa p,p4 I 35,8 I 22,0 I 2.3 I 6.2 I 26,0
30,0 2,3 3,8 25,4
5,0 % I 25 I 14,5 I 1,62 I 5,9 I 34,0
CzHa (3] I
. CO--p2-NZ [liJ 0,08 I 14 I 17.0 I 1,4 I 4.3 I 66,7
I
45
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the figure and Table 1. The ~:h;sracteristic of radiation power of the gasdynamic
laser was the normalized emission power No= N/Sout~ defined as the ratio of the
generated radiation power to the aiea of the output cross section of the nozzle
(or nozzle cascade). The introduction of such a specific characteristic enables
comparison of different gasdynamic laser facilities with respect to their attainable
emission power level. For a gasdynamic laser of a specific type with known emission
power, this characteristic enables evaluation of the necessary overall dimensions
of the nozzle unit. Of course such an estimate requires correction of the emission
power with respect to possible variation of the cavity efficiency (in connection
with a change in length of the active part and the type of cavity) and losses ~f
stored vibrational energy in the wakes of the gas flow (with a change from a mono-
nozzle to a nozzle cascade).
As can be seen from the figure, despite the short length of the active part of
the cavities (17 cm), a mixture containing 4.5% acetylene gave maxi.mum specific
energy outputs exceeding those obtained in Ref. 3. Curves for N*(po) for nozzles
with h* = 0.04 and 0.08 cm have characteristic optima due to two factors. At low
gas pressures in the combustion chamber there is a small concentration of active
particles in the cavity region, which reduces the efficiency of the cavity that
is used. With an increase in pressure there is~a rise in the relaxational losses
of vibrational energy stored in the mixture as the gas expands in the nozzle,
i~ e. there is a reduction in both nozzle and cavity efficiencies. As thQ gas
temperature increases in the combustion chamber at constant pressure, al.l the in-
vestigated nozzles show an increase in both th~ specif ic energy output and the
radiation power. This is due to the fact that in the investigated temperature
region with increasing To the increase in vibrational energy stored in the gas
at the nozzle intake predominates over the increase in the vibrational relaxation
rate as the gas expands in the nozzle. Comparing the specific energy outputs for
nozzles with a similar profile of the supersonic part (see the f igure, a, b), we
can see that in the region of pa=~30 atm, as was anticipated [Ref. 10], it is pref-
erable to use nozzles with a lower height of the critical cross section. The use
of a nozzle with large aperture A/A* = 75.6 and h* = 0.025 cm, as can be seen from
Fig. c, gave a fairly high energy output (~8 J/g) at po~ 70 atm and To= 2.1 kK.
In this connection, no noticeable increase was observed in N* in the region of
low stagnation press:~res, which is apparently due to low cavity efficiency. It
can also be seen from the figure that the optima of specific energy output and
normalized power lie in different regions of po. Nevertheless, in the region
of stagnation parameters po= 40 atm, To = 1.9 kK for the nozzle ~with h* = 0.04 cm,
and p o~ 70 atm, T o= 2.1 kK f or the nozzle with h* = 0.025 cm one can get f airly
large normalized radiation power at specific energy outputs of ~70% of the optimum
values.
When mixtures were used that contain 3.6 and 6.0% acetylene in the initial state,
the maximum specific energy output and normalized radiation power were lower than
for the mixture with 4.5% acetylene (see Table 1). For the first mixture this
is due to the low combustion point of the f uel mixture; for the second, it is due
- to the the less than optimum copmposition of the working mixture after combustion.
For comparison, Table 1 gives the energy charac~eristics of gasdynamic lasers de-
scribed in other research. It can be seen that the maximum specific energy outputs
obtained in our work are greater than the known values observed with ignition of
acetylene [Ref. 3) and carbon monoxide [Ref. 11]. The maximum normalized radiation
46
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TABLE 2
pNC:, .,c~`^9,sum). .~a...~o.eum e c~.s um>. e(~...~o,e :um). Nozzle
8TM I �ia l % I J I J parameters
5,2 91,5 I 94,5 I 0 I 391
92,0 93,0 1,0 I 402 A~A ;-~35Cg
6,0 I 470 .
39,0 I 507
6,0 45,0 I ~4 h� ~0,025 cM
A/A - 75,6
6,8 I 88,5 0,7 I 680
_ Note. Composition of initial mixture 4.5% C2H2; pxcx is the
pressure of th2 initial mixture in the combustion chamber.
TABLE 3
Po. I To� I n~~ I E~ I N~~ I NPen. I Na~ I Nn, ~ kT� _ I k9~
aTM KK o~, J/g J/g J/ ~ J to' 1 ~o' ~M-~
1,7 I 58,0 I 35.0 I 7,5 I 2,6 I 2,9 I 22,0 ,
10 ~~4
- 1,9 I 58,8 I 45,7 I 7,6 I 3,4 I 3,0 I 31,7
~ l.7 I 47.0 I 28,6 I 8,3 I 3,6 I 3,2 I 13,5
20 7,8 8,5
1,9 I 48,4 I 37,6 I 9,2 I 4,8 I 3,6 I 20,0
1,7 I39,OI 23,6I 6,4 3,7 I 2,5 I 11,0
6,5 7,2
30 ~ 9 I 40,0 I 31,01 6,8 I 5,8 I 2,6 I 15,8
l,7 , 33,0 I 20,0 I 4,5 I 3,8 ~ I,7 I 10,0
40 5,4 5,5
I,9 I 33,6 I 26,0 I 4,6 I 4,6 I 1,8 I 15,0
Note. E is the stored vibrational energy at the inlet to the
cavity; Npen are the losses of stored energy due to relaxation
in the cavity; N3 are losses of energy in the cavity mirrors;
Nn is the vibrational. energy remaining in the gas flow; kT
is the calculated g~in at a distance of 4.5 cm from the critical
corss section of the nozzle; k3 ~re the experimental values of
the ga in .
powers found in our research are about double the values obtained in Ref. 3, and
coincide with the data of Ref. 11.
Investigation of the spectral composition of the radiation gave some interesting
results. Considerable instability of the emissi~n pulse shape was seen in the
first lasing experi.ments with identical initial conditions. Since the sensitivity
47
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of the Ge-Au photosensors that were used was not the same in the 9-11 um band,
this suggested a complex nature of the spectral composition of the radiation.
Table 2 shows the results of some typical experiments. It can be seen that the
pereentage of lasing energy on a~ 9.5 um increases if the reflectivities of the
output mirror on a~ 9.5 and 10.6 um are close, and if a nozzle with large aperture
is used. In the former case, this is a consequence of the fact that the storage
_ factor ~f the cavity Q~ 1/a. In the latter case, the observed behavior can be
attributed to a reduction in the competition ~f band transitions 00�1-10�0, 00�1-
02�0, since the density of radiation with a~ 10.6 um inside the cavity is low,
- and besides, level 02�0 is effectively deactivated as a consequence of the h~gh
concentration of water in the mixture.
Results of mathematical modeling of the investigated gasdynamic laser are reflected
in Table 3. The calculation was done for a nozzle with h* = 0.04 cm and co~p~sition
of working mixture C02:H2O:N2= 9.2:4.6:86.2% which correspands to an initia~ fuel
mixture with 4.5% acetylene, assuming complete combustion. O~r paper compares
the results of calculation and experiment with respect to gain and the specific
energy output of emission. As we can see from Table 3 and figure c, the results
of calculation and experiment are in satisfactory agreement. For some stagnation
parameters, Table 3 enables evaluation of the princioal losses of stored vibra-
tional energy in the gas as it moves through the cavity. For example for stag-
nation parameters po = 30 atm, To = 1.9 kK the efficiency of the nozzle n~= 40%,
cavity efficiency r1p = 21.9%, losses in the mirrors 8.6%, losses to relaxation of
vibrational energy inside the cavity rlpeJ, = 18.5%, ~nd 51% of the vibrational energy
was carried off by the gas flow. The resultant data imply that a further increase
in the spedific energy of the radiation xequires primarily an increase in cavity
efficiency, e. g. by increasing the active part of the cavity.

, REFERENCES
1. Tulip, J., Seguin, H., APPL. PHYS. LETTS, Vol 19, 1971, p 263.
2. Kozlov, G. I., Ivanov, V. N., Korablev, A. S., ZHtIRNAL EKSPERIMENTAL'NOY I
TEORETICHESKOY FIZIKI, Vol 6S, 1973, p 82.
3. KOZLOV, G. I., IVANOV, V. N., KORABLEV, A. S., SELEZNEVA, I. K., ZHURNAL EKSPERI-
- MENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 68, 1975, p I647
4. Ktalkherman, M. G., Mal'kov, V. M., Petukhov, A. V., Kharitonova, Ya. I.,
FIZIKA GORENIYA I VZRYVA, Vol 12, 1976, p 578.
5. Shmelev, V. M., Vasilik, N. Ya., Margolin, A. D., KVANTOVAYA ELEKTRONIKA, Vol 1,
1974, p 1711. ~
6. Losev, S. A., MAKAROV, V. I., KVANTOVAYA ELEKTRONIKA, Vol 1, 197!+, p 1633.
7. Losev, S. A., Makarov, V. I., ZHURNAL PRIKLADNOY M~KHANIKI I TEKHNtCHESKOY
FIZIKI, No 8, 1975, p 3.
8. Losev, S. A., Makarov, V. I., KVANTOVAYA ELEKTRONIKA, Vol 3, 1976, p 960.
48
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9. Vyskubenko, B. A., Demenyuk, Ye. T., Yeremin, A. D., Kirillov, G. A., Kolo-
byanin, Yu. V., Kormer, S. B., Ladagin, V. K., Linnik, V. M., Nitochkin, N. A.,
Urlin, V. D., KVANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 10.
- 10. Losev, S. A., "Gazodinamicheskiye lazery" [Gasdynamic Lasers~, Moscow, Nauka,
1977.
_ 11. Gerry, E. T., LASER FOCUS, No 6, 1970, p 27.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
= 6610
. CSO: 1862/242
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UDC 621.378.33
CHEMICAL DF LASER WITH DIFFRACTION RADIATION DIVERGENCE
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 6(108), Jun 81 pp 1208-1213
_ [Article by V. P. Borisov, S. D. Velikanov, V. D. Kvachev, S. B. Kormer, M. V.
Sinitsyn, G. V. Tachayev and Yu. N. Frolov]
[Text] An investigation was made of the feasibility of achiev-
ing diffraction diverence of the radiation of a pulsed chemical
DF laser with flashlamp pumpin~ when the planar cavity was re-
placed by an unstable cavity of telescopic type. Under optimum
working conditions of the laser witli unstable cavity, radiation
divergence of e0.5E -~0 urad, practically at the diffxactian
limit, was obtained at fairly high energy eff iciency (~60%) as
compared with the similar laser using a planar cavity. It is
~ experimentally shown that by appropriate "misalignment" of the
unstable cavity, the radiation energy distribution in the far
zone can be measured without using auxiliary focusing elements.
- 1. Introduction
One of the interesting peculiarities of chemical lasers is the capability for bring-
ing about conditions under which inhomogeneities of the working medium will be
comparatively small, which creates certafn prerequisites for getting the diffrac-
tion divergence of emission [Ref. 1].
One of the most promising and widely used methods of getting small divergence of
laser radiation is to use an unstable cavity of telescopic type [Ref. 2, 3].
In this paper we study the problem of effectiveness of using an unstable cavity in
a pulsed DF chemical laser with optical initiar�ton to get the diffr~.ctlon diver-
gence of radiation.
2. Formulation of the Experiment
The experiments were done on a pulsed DF laser with working mixture of F2:D2:SF6:02
= 22:7:22:7 mm Hg. The radiation of such a chemical laser occupies the spectral
range of 3.6-4.2 um.
The chemical laser cell was a auartz tube with inside diameter of 7.2 cm and length
of 70 cm with windows of CaF2. Diaphragms on the ends of the cell with inside
50
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diameter of 7 cm reduced the influence that bright reflections from the walls of
the cell have on lase~~ radiation.
Optical initiation of the chemical reactien was by a xenon flash lamp with design
analogous to that described in Ref. 4. Power supply to the lamp was from a capaci-
tor bank with capacitance C= 3 uF at voltage V= 20 kV.
An experimental study was done on the influence that the magnif ication M of the
unstable cavity (M = f 1/f Z, where f 1, f 2 are the f ocal lengths of the concave and
convex mirrors of the unstable cavity) has on the parameters of stimulated emission,
and a comparison wa.s also made with the parameters of a laser with planar cavity.
The planar cavity consisted of a flat copper mirror and a flat CaF2 plate separated
by a distance of 180 cm. The unstable cavity of telescopic type consisted
of spherical concave and convex copper mirrors.
3
The optical arrangement of the experiments is shown s
in Fig. 1. Emission energy was recorded by TPI calo-
rimeter 1. The time parameters of the lasing pulse ~--~C~__ i_~ ~
_ were registered by gold-doped germanium FSG-22-3A ' '
photoresistor 2, the signal being ~~ent to an 58-2 r
oscilloscop~.
1
The radiation divergence of the c~emical laser ChL
was measured by Ragul'skiy's wedge 3, using a method
described in Ref. 5. To do this, the radiation of Fig. 1. Optical arrangement
the chemical laser was focused by spherical mirror caf experiments
4 with fccus f= 11 m on screen 5 made of black photo-
grapllic paper. Placed in the path of the convergent beam was mirror-reflecting
Ragu1'~kiy's wedge 3 with semitransp arent mirror having transmission T= 50%. In
the experiments with the unstable cavity, the dynamic range of recordable intensi-
ties in the far zone was about 200Q.
When the planar cavity was used, the focusing mirror with f= 11 m was replaced
by a mirror with f= 1.5 m, and the range of recordable intensities was ~1000.
3. Results of the Experiments, and Discussion
The main purpose of our exp~riments was to study the feasibility of getting dif-
fraction divergence of chemical laser radiation.
Let us estimate the value of M of the unstable cavity necessary for attaining this
goal. The radiation of a laser with ideal unstable cavity and homogeneous working
medium should have diffraction divergence [Ref. 2, 3]. In the presence of inhomo-
geneities of the active medium, the divergence of radiation of a laser with unstable
cavity wi11 be greater than the diffraction level 8dif ~ 2�4�a/dl. (where a is the
- wavelength of laser emission, dl is the diameter of the working part of the con-
cave mirror) by the amount [Ref. 3]
0u ~ 2Za0n/(1 - 1/M) , ~1~
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_ where Za, on are the length of the active medium and the gradient of its index
of refraction.
Based on the defined value of inhamogeneities, we can estimate the maximum value
of M at which the radiation divergence will differ but little from the diffraction
- value:
edif ~ 108u. ~2)
From (lj and (2) we get
M> (1 - a.3Za0nd1 /a)'1. ~3)
- On the other hand, it is known that the diffraction divergence of radiation is
formed mainly by the rays that make the maximum number of passes mm~ inside the
unstable cavity before leaving it [Ref. 6]:
lrimax = 1.1- ln ~di j~21~f ~4~
ln M �
There is no distortion of diffraction divergence when saturation of the gain of
the active medium is attained after a number of passes m>~ax�
It follows from Ref. 1 that in tr~is case it is necessary that
lrimax ~ ln ~4nf~/di~ ~5~
2ale ~
where a is the gain of the active medium.
From formulas (4) and (5) we can determine the possible values of M for getting
the diffraction divergence:
M > ex 2ala tn ~d~/(2~,t1~~ ~6~
~ P ln ~4nf i/d~~ - 2ale .
Thus to get the diffraction divergence we should use an unstable cav~ty with mag-
nification M that satisfies the stronger of conditions (3) or (6).
In the experiments, the concave mirror of the unstable cavity had a focus f1= 200 cm.
To estimate On we can use the results of Ref. 1 since that research also used a sys-
tem of initiation of the chemical reaction, composition of the working mixture
and other conditions of experiments similar to ours. Therefore we will assume
that during lasing On < 5�10-8 cm 1.
According to our measurements, the gain of the active medium a~0.015 cm'1. At
- �~alues of dl = 7 cm, a= 3.9 um, fl = 200 cm and Za= 70 cm, we get M~ 2 from formula
(3), and .'~I~ 5.5 from formula (6).
Thus under the conditions of the experiments the condition M> 5.5 must be met to
attain the diffraction divergence of emission of the investigated laser.
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TABLE 1
Con3itions and averaged results of investigation of chemical lasers
cavity Eunst o e Tdur~ Itdel~
type nr Neq las~ J EPl mrad ~S I us
planar I - I I 6,7 I - , I 1.2 I 9~4 I 6,6
unst�able! 2,5 ~ 21 I 5~7 I 85 I 0,16 I 8,5 I 6,0
I ~
unstable~ 4,0 I 16 I 4,7 I 70 I 0,09 I 8,1 I 6,6
~
unstable~ 8,0 ( lo I 4,0 I 60 I 0,07 I 7,5 ( 7,0
I ~
Note. Tdur' Tdel are the duration and delay of the lasing pulse.
TABLE 2
Theoretical (th) and experimental (ex) dimensions of diffractior. rings in the
far zone of the laser, and distribution of radiation intensities and
energies with respect to these rings
Im~x~ I Imax~
th ex o
Ring N~ eth' e~' rel. unit rel. Eth~ % Eex~ ~
I mrad mrad ~ units I
1 ~ 0,117 I 0,12 I 1 I 1 I 65 I 40 .
2 I 0.266 I 0,27 I 0,07 ( 0,22 I 30 I 49'
- 2,5
3 I 0,369 I 0,39 I 0,032 I 0,023 I 2 I 6
4 I 0,452 I 0,50 I O,OOI I O,U05 I 0,2 I 1
1 I 0,126 I 0,13 I 1 ~ l ( 75 ! 60
2 I 0,266 I 0,28 I 0.038 I 0,1 I l5 I 32
4
3 I 0,340 I 0,39 I 0,011 I 0,01 2 I 3
4 I 0,480 I 0,52 I 0,0036 I O,OUS I 6 I 3
_ 1 I O,134 I 0,14 I 1 I 1 I 83 I 80
~ 2 ( 0,256 I 0,27 I 0,022 I 0,04 I 10 I 15
_ 8
_ 3 I 0,352 I 0,38 I 0,0027 I 0,005 I 2 I 2
4 ( 0,990 I 0,50 I 0,0027 I 0,005 I 4 I 3
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For experimental verification of the conclusions drawn above, unstable cavities
were used with magnifications M= 2.5, 4 and 8 and equivalent Fresnel numbers
Neq = 10-20 .
Table 1 gives the averaged results of experiments with planar and unstable cavities.
In the entire investigated range of magnifications of the unstable cavity M= 2.5-8,
the intensity distribution in the far zone had the form of concentric rings typical
of Fraunhofer diffraction.
Fig. 2 shows the distribution of lasing energy Fg~%
- with respect to angle for lasers with unstable MaB
cavities (M = 2.5-8) and with a planar cavity. BD
The radiation divergence of the laser with an 4 ~
unstzble cavity is less than that of a similar 60
laser with planar cavity by about an order of 4D Z~S
magnitude. With increasing M, the divergence .
decreases from 00.5E - 0.16 mrad at M= 2.5 to yp la~ar cavl~
0.07 mrad at M= 8. Th~ results of ineasurement
of the divergence of a laser with planar cavity ~ p,p 0,4 e, mrad
enable us to estimate ~n in the investigated
mixture in the lasing process [Ref. 8]: Fig. 2. Lasing energy dis-
~ tribution with respect to
pn ~ 0P1Zp/8Za~5�10-~, (7) angle for lasers with un-
stable and planar cavities
Which agrees with the results of Ref. 1.
The studies showed that the use of an unstable cavity in a chemical laser as com-
pared with a planar cavity results in a reduction of total lasing energy. Although
energy losses increase with increasing M from 15% for M= 2.5 to 40% for M= 8, the
axial luminance of the emission B increases, reaching 45, 125 and 180 times the Bpl
for M= 2.5, 4 and 8 respectively.
~ The method of calculation of Fraunhofer diffraction on an ~nnular aperture [Ref. 9]
was used to interpret the resultant distributions of radiation intensity of the
laser with unstable cavity in the far zone.
Table 2 gives experimental and theoretical results of determination of minima of
~che intensity in the diffraction pattern in the far zone, and also the distribution
of intensities and energies with respect to the rings.
Comparison shows coincidence of the calculated and experimentally determined po-
- sitions of minima of the diffraction pattern for all investigated values of M.
As we can see from Table 2, with increasing M there is an improvement in the
correspondence of energy distribution with respect to diffraction rings as deter-
~ mined from the experiments and calculated for an empty ideal unstable cavity.
At M= 8, this agreement is quite good, which confirms the conclusions.
To verify whether there are appreciable wings in the radiation distribution with
respect to angle, a number of experiments were done in which the radiation energy
. was measured simultaneously in angles of 61= 1 and 62 = 10 mrad by using
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TABLE 3
Parameters of chemical laser with "nisali~ned" unstable cavity
(M = 8, f 1= ~UG cm, f 2= 25 cm)
e, cM I R, ~ I Elas~ J I ~dur~ ~s ( Tdel~ us
- 0 I oo I 4,0 i 7,5 I 7,0
5 I 80,8 I 4,0 I ?,4 ~ 7,0
10 ~ 41,4 ( 3,8 1 7,3 6,9
30 I 15,12 I 3,9 I 7,4 I 6,9
~
" 6G I 8.56 I 3,8 I 7,4 I 7,0
~
calerimeters. It was established in these experiments that the radiation Qnergy
in the given angles is the same, proving ~~he absence of wings with appreciable
energy in the radiation pattern of the investigated chemical laser with unstable
cavity beyond the lim~ts of an angle of 1 mrad. This is further eviaence that
the energy distributions with respect to angle that are shown in Fig. 2 completely
- characterize radiation divergen~e.
' Analysis of ineasurements of the time parameters of the lasing pulse showed that �
~ pulse duration Tdur decreases by about 1 us with a change from planar to unstable
cavity. With increasing M, pulse duration decreases somewr.at (see Table 1).
Lasing pulse delay TdPl relative to the beginning of initiation of the reaction
- showed almost no change in any of the experiments.
In a series of experiments with a high-speed streak camera an investigati.on was
made of the time behavior of divergence of a chemical laser with uns~able cavity.
Black photegraphic paper was used as the radiation recorder. It wa~ found b}� this
_ t~chniqc:e that the radiation pulse of a laser with unstable cavity (at M= 4 and 8)
consists of regular inttnsity spikes with period coinciding with the round-trip
time of a light quantum through the cavity Trt = 2Zp /c (the photoreaistor-oscillo-
graph technique does not resolve these spikes). This was also confirmed by experi-
ments in which the distance between m~rrors of the unstable cavity was changed.
This same spike behavior of lasing was observed in Ref. 10, where an investigation
was made of an HF laser with unstable cavit}~.
An interesting feature of the unstable cavity is the capabilit.y of ineasuring small
radiation divergences with good precision without additional focusing elements
by "misalignment"of the unstable cavit~. When this is done, t'ne radius of curva-
ture of the convergent wave is defined by the ex~ression [Ref. 5]
R=f1+(i;--f2)~o-+-s, (8>
.
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where ~ is the amount of mismatch of the cavity, d is a corrective term that is
very small (daR) at M< 10.
By using this cavity detuning technique in several experiments, a lasing far zone
was found that is no different in energy distribution from that found conventionally
by focusing mirrors (see Fig. 2).
As we can see from Table 3, with a change in radius of curvature of the surface
of the radiating front from 8 to 80 m, the energy and time parameters of the radia-
tion did not change within the limits of ineasurement error. Thus when the unstable
cavity is intentionally detuned the major parameters of the laser remain gractically
' unchanged, and the far zone ~f the radiation can be obtained on a screen located
at a given distance R(see (8)) from the output mirror of the cavity.
4. Conclusion
j An investigation is made of the feasibility of getting diffraction divergence of
the radiation of a DF chemical laser with flashlamp pumping by using an unstable
cavity of telescopic type.
The theoretical estimates showed that an unstable cavity with magnification M> 5.5
must be used in this laser to get emission with divergence close to the diffraction
limit.
Unstable cavities with M= 2.5-8 were studied. It was experimentally shown that
- as M increases, the radiation divergence decreases, reaching a value of 60.5E -
70 urad, which is almost the diffraction limit. Althou~h in this case the energy
losses are 40% as compared with a chemical laser with planar cavi.ty, the axial
luminance of the radiation increases by a f actor of 180.
It was discovered as a result of the experiments that the lasing puls~ with an
unstable cavity at M= 4 and 8 consists of individual spikes with recurrence rate
T 2Zp/c.
It was shown that laser radiation can be focused at a given distance by appropriate
detuning of the unstable cavity. This causes no noticeable distortion of the
diffraction distribution of energy in the far zone; when this is done there are
no appreciabie changes in the radiation energy or time parameters of the pulse.
REFERENCES
- 1. Zykov, L. I., Kirillov, G. A., Kormer, S. B., Nikolayev, V. D., Sukharev, S. A.,
_ KVANTOVAYA ELEKTRONIKA, Vol 4, 1977, p 1336.
2. Siegman, A. E., PROC. IEEE, Vol 53, 1965. p 277
3. Anan'yev, Yu. A., KVANTOVAYA ELLKTRONIKA, No 6, 1971, p 3; USPEKHI FIZICHESKIKH
NAUK, Vol 103, 1971, p 705.
4. Batovskiy, 0. M., PRIBORY I TEKHNIKA EKSPERIMENTA, No 2, 1973, p 171.
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5. Ragul'skiy, V. V., Fayzwllov, F. S., OPTIKA I SPEKTROSKOPIYA, Vol 27, 1969,
p 707.
6. Zemskov, K. I., Isayev, A. A., Kazaryan, M. A., Petrash, G. G., Rautian, S. G.,
KVANTOVAYA ELEKTRONIKA, Vol 1, 1974, p 863.
7. Isayev, A. A., Kazaryan, M. A., Petrash, G. G., Rautian, S. G., Shalagin, A. M.,
KVANTOVAYA ELEKTRONIKA, Vol 4, 1977, p 1325.
8. Kirillov, G. A., Kormer, S. B., Kochemasov, G. G., Kulikov, S. M., Nikolayev,
V. D., Sukharev, S. A., Urlin, V. D., KVANTOVAYA ELEKTRONIKA, Vol 2, 1975,
p 666.
9. Born, M., Wolf, E., "Osnovy optiki" (Principle~ of Optics], Moscow, Nauka,
1970, pp 449-453.
10. Simonis, G. J., APPL. PHYS. LETTS, Vol 29, 1976, p 42.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
6610
CSO: 1862/242
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UDC 621.375.826
STIMULATED EMISSION ON 18.4 um IN COZ GASDYNAMIC LASER WITH EI,ECTRIC-ARC HEATING
Moscow KVANTOVAYA ELEK'!'RONIKA in Russian Vol 8, No 6(108), Jun 81 pp 1312-1315
_ [Article by D. G. Bakanov, A. A. Vedeneyev, S. Yu. Volkov, A. I. Dem~n, A. A. In-
fimovskaya, Ye. M. Kudryavtsev, A. I. Odintsov and A. I. Fedoseyev]
[Text] A report on activation and investigation of a C02-Ar
_ gasdynamic laser (a= 18.4 um) with pulsed electric-arc heating
_ of the working mixture. It is-prov~d by measurement of the wave-
length (18.38 � 0.04 um) that iasing occurs on the Q-branct! of
. transition 03~0-10�Q. The maximum energy in a pulse with dura-
tion of about 20 ns was ~0.04 J at stagnation parameters in the
prechamber of To = 1000 K, po = 10 atm for mixture C02 :Ar = 1:2.
In accordance with the tiieoretical data, the energy in a pulse
decreased smoothly with change in C02 concentration. Accordin~
to esCimates, the power density i*.?side the cavity was ~3 kW/cm ,
and the specif ic energy outpu~ from the flow was ~10 J/g.
The suggestion of development of a thermal gasdynamic laser on transitions between
levels of paired modes of C0~ was formulated in Ref. 1, 2. Rei. 1 was the first
report on attainment of stimulated emissior. on the transition (0310-10�0) with
_ wavelength of 18.4 um in a C02-Ar gasdynamic laser implemented by shock tube. This
same paper proposed a mathematical model of such a laser in whicti the process of
vibrational relaxation is described in terms of the total energy of paired raodes
vl, v2. In subsequent ttieoretical and experimental research an ~.nvestigation was
made of the way that initial pressures and temperatures and the composition of
the working mixture influence the extent of inversion and the gain [Ref. 3, 4],
and the anticipated lasing power was calculated [~.~f. 4, 5;. It was shown that
the C02-Ar gasdynamic laser on a= 18.4 um has advantages over the COZ-N2 gasdynamic
laser on a= 10.6 um in higher eff iciency (2%) and the possibilizy G~ a reduction
in the temperature of gas heating. However, until recently the ex~erimental study
of the 18-micron C~2 gasdynamic laser has been based on a facility using a shock
_ tube and having a comparatively short active region (9 cm). Therefore we have
had no clear idea of the outlook for realization of such a gasdynamic laser with
more convenient methods of thermal exci~:ation than heating in a shock tube. This
paper is a report on attainment of quasi-cw lasing on a transition with J~= 18.4 um
in a gasdynamic laser with electric-arc heating of the gas mixture. Preliminary
results are given on the investigation of characteristics of such a gasdynamic
].aser.
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The experiments were done on a facility [Ref . li]
used previously for studying a COZ gasdynamic 4
laser with emission wavelength of 10.6 um. The 2 3 ~
facility was altered only in the parameters of
the nozzl.e and optical cavity. A diagram of the Ar C02
setup is shown in Fig. 1. The gas was heated .6 5 ~
by a powerful pulsed electric discharge from ca- g
pacitor bank 1; the discharge with duration of
~0.1 ms was initiated b electric ex losion of
a fine wire. Immediately before energizing the I~U 8 Y, ~3
discharge, prechamber 2 of the gasdynamic laser ~ f2
was filled with the working mixture of gases by
high-speed solenoid valve 3. The pressure in
the prechamber was registered by piezoelectric Fig. 1. Diagram of the ex-
sensor 4. A specially shaped single nozzle was perimental �acility
used with critical cross section 0.1 mm in height
and degree of expansion of 150. The nozzle terminated in a channel of fixed cross
section connected to a vacuum chamber. Cavity 5 was placed immediately beyond
the nozzle outlet at a distance of 3.5 cm from the critical cross section; the
length of the active medium was about 40 cm. The cavity was formed by two mirrors
with f= 100 cm (6, 7) with gold reflective coating. In the center of the mirrors
were 0.5 mm holes for coupling out the emi~sion.
~ The lasing wavelength was measured by a monochromator in the Ebert arrangement con-
sisting of a diffraction grating of 50 lines/mm (8) and spheri~al mirrors with
f= 50 cm (9, 10;. The first collimated the radiation leaving the optical cavity,
and the second focused the beam reflected from the grating on output slit 11 with
a width of 0.5 mm. The radiation was registered by a variety of receivers. In
the investigation of the lasing spectrum, inertial semiconductor bolometer 12 was
used, which had an identical fairly high sensitivity over a wide spectral region.
The bolometer signal was sent to an oscilloscope. A copper cone polished on the
inside was placed in front of the bolometer for purposes of collimation. The sys-
tem was calibrated with respect to high-order diffraction maxima of the radiation
from helium-neon laser 13 = 0.6328 um). Linear dispersion in the plane of the
output slit of the monochromator was 0.04 um/mm. The emission wavelength of the
gasdynamic laser as measured by this system was 18.38 � 0.04 um, enabling us to
assign it with confidence to lines of the Q-branch of the vibrational transition
(0310-10�0) of the C02 molecule.
The radiation energy in the lasing pulse was determined by an IMO-2 laboratory
r~eter. A rapid-response photosensor based on Ge-Zn cooled by liquid nitrogen was
used to study the pulse shape. Fig. 2 shows oscillograms of the gas pressure in
the prechamber, and of the lasing pulse; the latter was obtained by a Ge-Zn sensor.
The total lasing pulse duration was about 20 ns. The maximum lasing power is dis-
placed relative to the maximum of the pressure pulse. This shows that optimum
conditions for stimulated emission correspond to pressures and temperatures of
the gas in the prechamber that are lower than those at the beginning of the working
cycle. The maximum output energy of the lasing pulse of 0.04 J was obtained for
a mixture of C02:Ar = 1:2 at initial values of the pressure and temperature of the
gas in the prechamber of po= 10 atm, To= 1000 K. In this case, the power at the
maximum of the lasing pulse was about 3 W.
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On Fig. 3, the experimental dependences kM_~ Pout~ re] . u.
of lasing pulse energy on relative C02 '
content in the mixture are compared with 2 ~1
theoretical curves for the gain. The 2 ~ o
calculations were done by simultaneous � ~ ~~~8
~ ~
solution of one-di.mensional equatic,ns 1,5 , 0,6
of gas dynamics and the relaxation equa- 8 0
tion for the total energy of modes vl, ~ o o pq
. o ,
v2, in accordance with a method given o o,
in Ref. 1, 3 with consideration of the o~ $ 0,2
nozzle profile used in the given facility. _
The experimental and theoretical results p 2p u0 60 80 C~oZ,%
_ agree fairly well, which confirms the
correctness of the mathematical model. fi ig. 3. Gain (calculated curves) and
The reduction~in gain and lasing power
at high C02 concentrations in the mixture lasing power (experime:~tal points) as
can be attributed on the one hand to re- a functior. of the relative canten~ of
duced cooling of the gas in the nozzle C02 in the mixture for the followin$
due to a lowered adiabatic exponent, and initial conditions: 1--po= _0 atm,
- on the other hand to a relative increase To= 2000 K; 2--po= 15 atm, T~= 1500 K
in the role of processes of VT-relaxation of paired modes of C02 [Ref. 3].
Let us note that the attained output power /~3 W) does not ~n the least character-
ize the energy capabilities of the given laser since the parameters of the optical
cavity were not optimized. Overly small dimensions of the beam holes in the mirrors
precluded efficient coupling of the radiation out of the cavity. Actually, in
experiments done with a mixture of C02-N2-He at flow parameters near optimum the
measurements o� lasing output power in the 10.6 um region were even somewhat less
than 3 W. 'rhis is indirect evidence that the two types of gasdynamic lasers are
comparable in power. An estimate of the power density inside the cavity with con-
sideration of the output beam hale of the mirror gives I~ 3 kW/cm2. If we take
a reasonable value for the beam cross section inside the cavity (S ~ 1 cm2) and
assume that the cavity losses per pass lie in a range of 0.02-0.05, we can get
a rough lower estimate ~f the lasing power taken from the flow of Plas- 60-150 W.
An estimate made with consideration of the gas flowrate (~10 g/s) shows that the
specific energy outpuC from the flow under the given conditions is ~10 J/G.
In conclusion, we note that this research marks the first realization of a.n 18-
micron gasdynamic l.aser witc? pulsed electric-arc heating of the working mixture.
- This facility is closer to a model of a cw gasdynamic laser than that based on
a shock tube [Ref. 1]. Froducts of dissociation of C02 and other contaminants
formed in the e~ectric discharge initiated by an exploding wire have no decisive
detrimental effect on the operation of *he laser. The results show that a cw gas-
dynamic laser with steady-state electric-arc heating is suitable for producing
radiation with wavelength of 18 um.
The next step in research should be optimization of the profile and dimensions
- of the nozzle, the composition and parameters of the working mixture, and also
improvement of the optical cavity. To do this, we are planning diagnosis of super-
soni.c flow pararieters and gain measurement. The comparatively long optical path of
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this facility gives us hope that lasing might be attained on some other transitions
of the C02 molecule as well [Ref. 1, 3], and also ~on transitions of other molecules
[Ref. 7].
- Just as important is the fact that the comparatively small overall dimensions,
the relative simplicity of the construction and utilization of the facility enable
its use for studying the capabilities for utilizing coherent emission with wave-
length of 18 um in science and engineering.
The authors thank A. M. Prokhorov for support in the work.
REFERENCES
1. Vedeneyev, A. A., Volkov, A. Yu., Demin, A. I., Logunov, Ye. M., Kudryavtsev,
Ye. M., Sobolev, N. N., PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 41, 1978,
p 681; Preprint of Lebedev Physics Institute, USSR Academy of Sciences, Moscow,
1978, No 68.
2. Konyukhov, V. K., Fayzulayev, V. N., KVANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 25$6.
3. Vedeneyev, A. A., Volkov} A. Yu., Gomenyuk, Yu. V., Demin, A. I., Kudryavtsev,
Ye. M., Poluyan, V. P., Preprint of Lebedev Physics Institute, USSR Academy
- of Sciences, Moscow, 1979, No 20.
= 4. Brunne, M., Zielinski, A., Milewski, J., Volkov, A. Yu., Demin, A. I., Kudryav-
- tsev, Y e. M., in: "Proc. Int. Conf. on Lasers", Ed. by V. J. Corcoran, McLean,
VA, LSA, STS Press, 1980, pp 554-561
5. Volkov, A. Yu., Demin, A. I., Kudryavtsev, Ye. M., Brunne, M., in "Gas-Flow
- and Chemical Lasers", Ed. by J. Wendt, Rhode-Saint-Genese, Hemisphere Publ.
Corp., 1979, pp 249-252.
6. 03intsov, A. I., Fedoseyev, A. I., Bakanov, D. G., PIS'MA V ZHURIVAL TEKHNICHESKOY
_ FIZIKI, Vol 2, 1976, p 145.
^ 7. Volkov, A. Yu., Demin, A. I., Gomenyuk, Yu. V., Kudryavtsev, Ye. M., Poluyan,
V. P., Preprin~ of Lebedev Physics Institute, USSR Academy of Sciences, Moscow,
1980, No 40.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
- 6610
CSO: 1862/242
,
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UDC 535.853.31
FEASIBILITY OF USING LIQUID METAL HEAT-TRANSFER AGENTS FOR COOLING THE ELII~'IENTS
OF HIGH-POWER OPTICAL SYSTEMS BASED ON POROUS STRUCTURES
Moscow KVANTOVAYA ELEKTRONIKA in Russiun Vol 8, No 6(108), Jun 81 pp 1328-1331
[Article by V. V. Apollonov, P. I. Bystrov, Yu. A. Broval'sk iy, V. F. ~oncharov
and A. M. Prokhorov]
[Text] A theoretical investigation is made of the heat and thermo-
- deformational characteristics of laser mirrors based on metal
fiber structures cooled by liquid alkali metals (Na-K coolant
of eutectic composition). The given estimates conf irm the out-
= look for using liquid metal heat transfer agents to cool the
heat-stressed elements of high-power optical systems with minimal
heat distortions of the mirror surface.
It was pointed out for the first time in Ref. 1 that the threshold of optical de-
struction of mirrar surfaces based on porous structures can be further increased
by using liquid alkali metals and their alloys as coolants. The outlook for using
= liquid metal heat-transfer agents to cool the elements of high-power optical sys-
- tems is dependent on the feasibil3.ty of attaining a high coefficient of heat exchange
in the pcsrous layer by a favorable combination of thermophysical properties of
liquid metals. This relaxes the requirements for heat conduction of the material
of the porous structure, wh ich opens up the possibility for using new structural
materials in the reflectors with a low coefficient of thermal expansion and poor
heat conduction.
Of particular interest for purposes of copling laser mirrors is the use of eutectic
alloys of liquid metals that have a low melting point (for example Na-K alloy with
melting point of -11�C). The use of liquid metal coolants will enable convective
cooling of reflectors at temperatures close to the that of f inal ad~ustment of
the mirror surface.
Ref. 2 generalizes processes of heat and mass trar.sfer in porous structures with
a decisive effect on the temperature fields and hydraulic characteristics of the
ref.lector cooling system. On this basis a method was developed for prediciing
the heat and thermodeformational characteristics of laser reflectors enabling de-
termination of the optimum type and parameters of the structure to ensure removal
of the required heat flows for permissible distortions of the mirror r,urface.
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Taking our lead from Ref. 2, let us consider some results of theoretical estimates
- of the heat and thermodeformational characteristics of laser reflectors cooled by
eutectic alloy Na-K.
Within the framework of the assumptions made in Ref. 2, the equation of heat ex-
change that describes temperature distribution with respect to thickness of a
porous layer can be written as
d2t hs (1)
~2 = ~ sv (t - tT) .
where hs is the coefficient of heat exchange between the material of the structure
and the coolant. In view of the lack of data in ttze literature on heat exchange
of liquid metals in a porous layer, we will use known data on heat exchange of
liquid metal coolants in bundles of triangular arrays of fuel elements in nuclear
reactors as the lower estimate of the coefficient of heat exchange in a porous
structure. According to Ref. 3, the f~llowing relations will be used to calculate
- Y~eat exchange of liquid metals in regular arrays of fuel elements:
in the cells of close-packed bundles (s/d = 1)
:Iu=NuZ+0.0408(1- 1/ 1.24e+ 1.15)Pe�'65; (2)
in cells of separated bundles with 1.0 < s/d < 1.2
3.67 1 ml (3)
, Nu = NuZ + 90 (s /d) 2 1 - { [ (s /d) 3 � - 1 ] /6 + 1. 24E + 1.15}Pe ;
in cells of separated bundles with 1.2 < s/d < 2
Nu= Nul+ 3.67Pe 2/90(s/d)2~ ~4)
where ml = 0.56+ 0.19 s/d- U.1/(s/d)80, m2 = 0.56+ 0.19s/d, Nu, Pe are the Nusselt
and Peclet numbers,
( 6.3 l~ _ 3.6
NuZ= L.551s/d- ~~(s
~ (~/d) )(s -o.ei) } L (s/d) (1+2.Se ' +3.2
is the Nusselt number for laminar flow, s/d is the relati~ve spacing of the fuel
elements in the array, e= ast/~c is the ratio of heat conduction of the fuel ele-
ment cladding material to the heat conduction of the coolant. Relations (2)-(4)
are valid for e~ 0.01, 1~ Pe < 4000. Assuming correspondence between the hydraulic
diameter of the array of fuel element bundles and the hydraulic diameter of the
porous structure of the reflectors (da = dP) and between the diameter of the bundle
of rods and the diameter of the wire (for a metal fiber structure), we can get
the f ollowing relation f or felt structures : da = dSI~/ (1 - Ii~) .
Formulas (2)-(4) apply to the region of stabilized flow of liquid metal coolant
in cel].s of rod bundles where there are practically no overflows of the stream
between cells. Therefore, using these relations to calculate the heat exchange
of liquid metals in a porous structure where there is actually additionzl turbuliz-
ing of the flow by the matrix of the porous material will give an understated value
of the coefficient of heat exch3nge.
63
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W ~ um - -
~ n,=soq 4o ; Fig. 1. Nomograms of thermodefor-
~0 30, mational characteristics of families
i ' of reflectors based on metal fiber
oos Bo ?0 porous structures of molybdenun
; cooled by Na-K heat-transfer agent
~o ea ~sa ~ in the zone of injection (a) and
0 4o runoff (b) of the coolant at
a045 B~ Z - ~o ds= 20 (1), 50 (2), 100 (3) and
200 um (4)
90 BO / 60 !0
SO
90 BO 7p
0, 04 60 _ !0
0 S 10 1S qs, ,~W/~;
a
W, m
O ID ~p SO 4U
n~ = eo9; so
D, 4 2� '
20 yp 60 Z .
D, 3 -
t0 ~ 1
Q 2 ~ 4 30 7p 1 4a3
40
' 0~ _ ~ 50 60 ~ SO 60
70 60 ^ 7p i
90 80 70 BO
0 ~ 1,0 Z,0 3,0 b 4,0 5,0 qs, 1~,~~/Cm2
_ W, um~ ~o y
7 Rr ' 4Q/e
QO -
1
JO SD
w ~ ~ - - 10 2
- ~n ~0,06 - .
4 f I
40
_ ~
B,9 - ~
so _~~~c4 J0 ; I Fig . 2. Nomograms of thermodef or-
5� i b so mational characteristics of families
,o 'o,o2 I_____ __'a 70 40 of reflectors based on metal fiber
B.6 eo eo I porous structures of Invar cooled
SO ~060 `0 S~ ~ by Na-K heat-transfer agent in
80
- the zone of in~ection (a) and runoff
4 n~-s~% o ~o z,o kW/cm2 (b) of the coolant at ds = 20 (1) ,
s~ 50 (2) , (100 (3) and 200 um (4)
e, 3 ro J ~
90 80 Zp I
Z
90 ,0 5n so 40 !
, ac a
90 !0 JO tp i
- SO f0 c0
= B,DD S ~p ---,5 qS~ kWICm2
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,
Based on the method of Ref. 2, equations (2)-(4) were used to calculate the heat
and deformational characteristics of laser mirrors made on the basis of inetal fiber
porous structures of various materials with cooling by Na-K alloy. It was assumed
that the coolant inlet and outlet system was made in the form of uniformly alternat-
ing holes. The distribution of the heat load over the mirror surface was taken
as uniform. The hydrodynamic characteristics of the flow in the porous layer were
calculated f rom generalized relations given in Ref. 2.
As an example, Fig. 1, 2 show the resu.lts of numerical calculations of the thermo-
deformational characteristics of a fami?y of reflectors cooled by eutectic heat-
- transfer agent Na-K. It was assumed that the porous structures of the reflectors
were made of molybdenum and Invar felt structures. The mean diameter of a fiber
~ and the volumetric porosity of the structure were varied over ranges of 20 ds<
- 200 um and 0.1 ~ IIv S 0.9. The curves of Fig. 1, 2 are envelopes of the working
thermodef ormational characteristics of a family of reflectors and are plotted under
condition of constant coolant pressure differential in the reflector at a maximum
- tem.perature of the cooled surface equal to 100�C as in Ref. 2. Let ~s note that
in the case of li.quid-metal cooling, th is limitation is not decisive (as for example
in the case of water cooling). The ~ange af working temperatures for liquid metals
can be considerably expanded, resulting 3n a corresponding increase in the heat
loads that can be removed.
Fig. 1 shows that deformation of the optica~. surface in the zone of coolant runoff
as calculated with consideration of heatiiig of the coolant in the porous layer
considerably exceeds the deformation in the injection zone, W2~ W1. The limiting
heat flux densities for tihe investigated family of reflectors were: in the zone
_ of coolant inj ection ql > 20 kW/cm2, in the outlet zon~ q1= 6.6 kW/cm2, with W2 =
0.3 um. The minimum level of deformation in the zone of coolant outflow for a flux
drain of 4.2 kW/cm2 is W2=0.12 um, which is considerably below the threshold of
optical breakdown of the reflectors of C02 lasers.
The thermodef ormational characteristics shown in Fig. la for a family of reflectors
show the potential capabilitY~~s of liquid-metal cooling. The considerable differ-
ence in the curves is due to the influence of warming of the heat-transfer agent
in the porous layer as a consequence of the relatively low heat capacity of the
_ alloy Na-K, and therefore the degree of perfe~tion of the flow part of the cooling
system is decisive in developing reflectors of this class.
Analysis of the theoretical results of Fig. 2 shows that the use of a porous struc-
ture made of materials with a low coeff icient of thermal expansion (Invar fibers)
considerably reduces the thermal deformation of the mirror surface in both the
inlet and outlet zones (by a factor of 3-4) when liquid-metal cooling is used.
The maximum heat loads that can be removed from the mirror surface to keep the
temperature at a level of 100�C in this case are: ql~ 20 kW/cm2, Q2 = 3.5 kW/cm2
[see R~f. 2]. The thermodeformational characteristics of a reflector based on
Invar fibers in the region of minisnum deformation of the optical surface (Fig. 2b)
and the point Wmin are characterized by deformation W2a 0.02 um with heat flux
drain of 2.4 kW/cmZ.
The behavior of the curves of. Fig. 1, 2 reflects the particulars of heat and mass
exchange with convective liquid-m~.tal cooling of reflectors. The fami~y of envelopes
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of thermodeformational characteristics enables determination of the optimum param-
eters oF a metal fiber porous structure that ensure drainage of the necessary heat
f.luxes from the reflector at admissible values of distortion of the mirror surface
wi~ich can be used to develop requirements for designing the cool~ng system.
In conclusion, let us note that because of the lack of reliable data on convective
heat exchange of liquid metals in a porous layer, the heat and deformational char-
acteristics of mirror surfaces given as an example in Fig. 1, 2 should be treated
- as estimates only. However, these results do show the good outlook for using liquid
metals to cool optical elements based on metal f iber structures. The use of liquid-

~ metal cooling in combination with porous structures made of materials with rela-
tively low coefficient of thermal expansion opens up fundamentally new capabilities
in the development of high-precision reflectors with a high threshold of optica'1
- destruction.
- REFERENC~S
1. Apollonov, V. V., Barchukov, A. I., Borodin, V. I., Bystrov, P. I., Goncharov
V. F. et al., PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 4, 1978, p 1193.
`L. Apollonov, V. Bystrov, P. I., Goncharov, A. M., Prokhorov, A. M., Khomich,
V. Yu., KVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 2533.
3. Subbotin, V. T,, Tbragimov, M. Kh., Ushakov, P. A. et al., "Gidrodinamika i
teploobmen v atomnykh energeticheskikh ustanovkakh (osnovy rascheta)" [Hydro-
- dynamic~ and Heat EYChange in Nuclear Power Facilities (Fundamentals of Calcu-
l.ation)], Moscow, Atomizdat, 1975.
COPYRIGHT: Izdatel.'stvo "Radio i svyaz"', "Kvantovaya elektronika", 1981
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F'UK Ul~'Fli:iAl. U~~ l)NLti'
UDC 621.375.82
COZ LASFR WITH RADIATION ENERGY OF 3 kJ EXCITED UNDER MATCIiED CONDITIONS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 6(108), Jun 81 pp 1331-1334
[Article by V. V. Apollonov, F. V. Bunkin, Yu. I. Bychkov, I. N. Konovalov, V. F.
Losev, G. A. Mesyats, A. M. Prokhorov, V. F. Tarasenko and K. N. Firsov, Physics
Institute imeni P. N. Lebedev, USSR Academy of Sciences, Moscow]
[Text] The article gives the results of investigation of a C02
laser with pulsed feed to the gas vessel under matched conditions. .
A total radiation energy of 3 kJ is obtained at a mixture pressure
_ of 2 atm and active volume of 50 liters. With excitation of
an active volume of 12 liters, the energy input to a mixture
of C02:N2:He = 1:2:2 was 0.6 kJ/(Z�atm), and the radiation energy
was ~80 J/(Z�atm).
In the most powerful laser systems known in the literature that are excited by
an electron-beam-stabilized discharge, the discharge is,supplied from a capacitive
accumulator connected to the laser gap [Ref. 1, 2] or from a pulse voltage gener-
ator [Ref. 3, 4]. In the former case, the energy stored in the accumulator is
much greater than that fed to the discharge, and as a result a high voltage re-
mains across the electrodes after completion of the excitation pulse for an ex-
tended time (as compared with the duration of the excitation pulse). The advantage
of this unmatched mode of operation is that the voltage across the electrodes of
- the gas gap does not change appreciably during r~umn`ng. However, the residual
_ voltage across the electrodes of the laser cell restricts the attainment of high
field strength in the gas gap due to discharge contraction, and precludes high
energy inputs, particularly in mixtures with low helium content. When a pulse
voltage generator is used for gap supply in known facilities [Ref. 3, 4], only
a part of the stored energy is input Co the gas during the action of the electron
beam, which limits the overall efficiency, and results in residual voltage across
the electrodes.
The use of unmatched conditions for pumping a COZ amplifier with characteristic
. excitation time of ~1 us was first reported in Ref. 5; however, the specific energy
inputs in that research did not exceed 200 J/liter, and no data were given on the
output energy characteristics.
The piirpose of our research is to study the feasibility of high specific energy
inputs and large energy outputs in pulses of ~1 Us duration in the matched mode
of excitation of a COZ laser.
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M`UR l1FF'lt'1.~1, l~tiK t1N1.\
0
~ a
U kV '
0~
~ b P, kJ
0 /,KA 3 .
1Gb c
ou v 2 ~
~ d
~ ~ a
KA
~ P, rel . units ~
0,5 e 4 6 8 10 W, kJ
= o,k,T/Z
~ 0,15
18
J6 f 0,10
k
/,,vA
P b
a.ns
g
0
0 2 4 t, }ts 0,3 Q4 q5 W, kJ Z
Fig. 1. Oscillograms of accel- Fig. 2. Dependence of overall
erator voltage (a) and current radiation energy on input energy
(b) pulses, voltage pulse across with active volume of 50 liters
the gap (c), current pulse (a) and dependence of specific
in the cell (d, e) and radiation radiation energy on specific
pulses (f, g). Charging voltage input energy in an active volume
- ef pulse voltage generators of 12 liters (b). Mixture
supplying the cell 58 kV, mixture C02 :N2:He = 1:2: 2, pressure
COZ :NZ : He = 1: 2: 2, pressure p= 2 (1-3) and 1.2 atm (4) ; win-
p= 2 atm, active voleune 50 dows of KRS (1, 3, 4) and NaCl (2)
(c-e) and 12 liters (f, g)
The laser system was made up of a gas cell, power supply and electron accelerator.
The active medium was excited by a non-self-maintained discharge. The maximum ac-
tive volume of the chamber was 50 liters (20 x 20 x 125 cm). The laser chamber pe~-
mitted operation at a pressure of up to 2.5 atm. Experiments were done in an active
volume of 50 liters, and also with a reduction in active volume to 12 liters (8 x 12
x 125 cm). The electron ~ccelerator provided a current density of the electron
- beam in the gas chamber of about 0.5 A/cm2, and accelerating voltage in the vacuum
diode of about 300 kV. Oscillograms of the accelerating voltage across the vacuum
diode and the current of the electron beam in the gas chamber are shown on Fig.
la, b. A distinguishing feature of the selected mode of laser operation was that
the electron beam pulse duration was double the duration of the current discharge.
The discharge in the chamber was delayed relative to the beam current by ~0.3 Us.
Thus the discharge took place at constant beam current density and electron energy,
which is important for improving discharge stability as it gets rid of the low-
energy electrons formed on the rising and falling segments of the accelerating
voltage.
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WP used I.C correc~io:l in the pulse voltage generator feeding the vacu~i diode,
giving near rectangular pulse shape (see Fig. lb).
- The supply to the gas chamber was from a pulse voltage generator in the Marx system
consisting of three p~ra:.lel branch~s of five stages each. The pulse voltage gener-
ator used IK-100/0.4 capacitor~s, and the LC correctiun circuit used IMN-100/0.1
capacitors. The equivalent capacitance of the pulse voltage generator was 0.24 uF,
characteristic impedance p= 3.3 S2; at a charging voltage of U= 58 kV, the energy
stored in the pulse voltage generator reached ?0 kJ. Dry air-blasting of thE dis-
charge gaps in the pulse voltagP generator ensured stable operation (�20 ns), and
~ enabled pulse synchronization of the discharge cui~rent in the gas ch.smber and the
beam current.
The following equation can be written for the discharge current of the given elec-
tric circuit:
I(t) _(Uo/wL) exp Rt/2L) sin wt, (1)
where (L/C - R2/4L2)z is the frequency of oscillations of the tank circuit;
R is the resistance connected in the tank. In the given case, R is the resistance
of the discharge plasma which can be considered linear and ccnstant in time to
a good approximation since the electron beam does not vary during discharge. Tne
- matched-load condition is R=(LC)~ - p, and (1) impli.es that the discharge current
pulse has the following parameters:
tp= 2~r(LC/3)~; tm= 2~r(LC/27)~; Im= [Uo/(LC}'~] exp (~r/3~), (2)
where Uo is the open-circuit voltage of the pulse vol~.age generator, tP is current
- pulse duration at the base, tm is the time to attainment of mahimum current, Im is
maxi~r~um discharge current .
_ There is practically no need for exac* satisfaction of the equali~y R=p since
when 0.75p ~ R 5 2p the reduction in peak power is only 10%. Let us call attention
to the fact that as R varies from 0.75p to 2p, the voltage across the plasma varies
from 0.47Uo to 0.74Uo. This circumstance must be taken into consideration to maxi-
mize laser efficiency. In thz described laser with maximum active volume of 50
liters for mixture CO~:N2:He = 1:2:2 ;.?t pressure of 2 atm the plasma resistance
was R= 3.8 2. For charging voltage iJ= 58 kV, oscillograms ~f the voltage across
� the plasma, the disc}~arge current and the radiation pulse are as shown in Fig.
lc-e. The dependence of the overall radiation energy on the energy stored in the
pulse vol.tage generator is shown ir. Fig. 2a. The distribution of radiation energy
in the cross section of the output beam was uniform, the energy density reached
15 J/cm2. Damage to the output window was observed. The overall radiation energy
reached 3 kJ, and ef.ficiency reached ~27%. The radiation energy was measured by
= scanning an IKT-1M calorimeter with the sapphire window taken out of the sensor
head over the cross section of the laser beam.
To determine tiie feasibility of attaining high energy inputs in matched operation,
the active volume was reduced to 12 liters (8 x 12 x 125 cm). With the 50-liter
volume, this could not be done because of the limited energy reserve of the pulse
voltage generator supplying the gap. In this operation, the plasma resistance fell
69
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to 2.5 S!. Oscillograms of the discharge current and radiation pulse for this case
- are shown in Fig. lf, g. The energy input in the second half-period does not exceed
10%, and therefore the operation can be considered practically matched. The ampli-
tude value of the voltage across the plasma was 136 kV (E/p = 8.5 kV/(cm�atm)),
_ and the maximum energy inputs exceeded 0.6 kJ/(Z�atm). Fig. 2b shows the dependence
of radiation energy on energy input at mixture pressures of 2 and 1.2 atm, and
also for different resonators using NaCl and KRS output windows. The maximum radia-
tion energy obtained in a volume of 12 liters was 1.8 kJ. We point out that lasing
efficiency decreases with an increase in energy inputs, which is in agreement with
the results of Ref. 3.
Thus our research has experimentally proved the feasibility of attaining high spe-
cific energy inputs in a large volume in matched operation.
REFERENCES
1. Yu. I. Bychkov, Ye. K. Karlova, N. V. Karlov, B. M. Koval'chuk, G. P. Kuz'min,
Yu. A. Kurbatov, V. I. Manylov, G. A. Mesyats, V. M. Orlovskiy, A. M. Prokhorov,
A. M. Rybalov, PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 2, 1976, p 212.
2. V. A. Adamovich, V. Yu. Baranov, R. K. Bevov, Yu. V. Smakovskiy, A. P. Strel'-
tsov, PIS'MA V ZHURNAL TEKHNICHESKOY FIZIi~I, Vol 4, 1978, p 988.
3. C. Cason, G. J. Dezenberg, R. J. Huff, APPL. PHYS. LETTS, Vol 23, 1Q73, p 110.
4. A. M. Orishich, A. G. Ponomarenko, V. G. Posukh, R. I. Soloukhin, S. P. Shala-
mov, PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 3, 1977, p 39.
S. 5tatus Report on Laser Program at LASL (u) LA-5251-PR, July-December, 1972.
COPYRIGHT: Izda*_el'stvo "Radio i svyaz"', "Kvantovaya elektronika", 1981
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UDC 621.378.4
CONVERSION OF C02 LASER EMISSION TO 0.5 um REGION IN NONLINEAR CRYSTALS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 6(108), Jut~ 81 pp 1361-1363
[Article by S. A. Andreyev, N. P. Andreyeva, I. N. Matveyev and S. M. Pshenich-
nikov)
[Text] An investigation is made of conversion of C02 laser radi-
ation to the 0.5 um region in a two-stage arrangement: f irst
the emission of the C02 laser was converted to the near infrared
region in crystals of the intermediate infrared range, and then
to the visible range in a lithium iodate crystal; the same YAG
laser radiation was used in both stages. With different crystals,
conversion coefficients of 8-14% were obtained, enabling reliable
registration of radiation in the intermediate infrared range
with sensitivity equivalent to that of a photomultiplier with
quantum yield of 1-2%.
One way to make C02 laser emission visible is conversion to the optical band in
nonlinear crystals pumped by a pulsed ruby laser [Ref. 1]. In this technique,
the converted emission falls in the 0.65 um region, where the most sensitive photo-
sensors (photomultipliers) have a quantum yield of 1-3%. However, this method
of registration has a number of disadvantages: in the first place the resistance
of current nonlinear crystals such as proustite and silver. thiogallate to ruby
laser radiation [Ref. 2] limits the coefficient of conversion of the converter
to the 8-10% level; at a higher coefficient of conversion, and hence greater pumping
power, the operation of the converter becomes unstable and unreliable. In the
second place, the converted emission f alls on the slope of the spectral curve of
the most efficient multislit photocathode, which limits the equivalent quantum
yield of the converter-photosensor system on the 0.2-0.3% level. In the third
place, the proximity of the frequencies of the converted and pum~ing radiation
does not permit effective spectral separation. In the fourth place, the frequency
of arrival of information received by such a sensor is limited by the pulse recur-
rence rate of the ruby laser, and in practice does not exceed 10 Hz.
More promising is a double conversion circuit where the radiation of the C02 laser
is first converted to the Q.97 um region in crystals of the intermediate infrared
range, and then to the 0.5 um region in crystals of the near-infrared band, the
radiation of the same YAG laser being used to pump these crystals. The two-stage
conversion arrangement with focusing of pumpino proposed in Ref. 3 gives a high
_ conversion coeffi~cient, and is quite effective for reception of one-dimensional
signals.
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0,96 fp,6 ao �
6~" I 10, 6; I, 064 ~ 1, 064 ~5
I ~ 6D ~
~B ~
~ f1
30
7 � ~ p
~ oq\
. 6
Z 11 ( ~ 30 SO 70 B�
-~~--~t~~
09~ , os.~ 30
. ~ 3
I" ~
13 13~ t,~ 60
9 10 0
Fig. 2. Curves of vector synchro-
Fig. 1. Diagram of the nism (dependence of angle a on 6)
- experimental facility for crystals of Ag3AGS3 (1), AgGaS2
at as= 10.6 um, ap= 1.064 um (2),
_ and LiI03 at as = 0.967 ~!m, aP =
1.064 um (3)
In this paper we examine a~ two-stage conversion scheme without focusing of pumping,
- which enables its use for image conversian. A dlagram of the experimental facility
is shown in Fig. 1. A distinguishing feature of the arrangement is that the radia-
= tion of pumping laser 1 arrives first at crystal 2 of the near infrared band, which
is more resistant to the pumping radiation, and then goes to crystal 3 of the inter-
mediate infrared band. The crystals used in the inCermediate infrared band were
A$3AsS3, AgGaS2, ZnGeP2 and HgGa2S4 in which close to collinear interaction of
type oee or eoo was realized, while tangential interaction of type ooe was realized
in the crystal of ~he near infrared band (LiI03). To accomplish this, the planes
of synchronism of crystal~ 2 and 3 were made mutually perpendicular, and the pola-
rization vector of the pumping radiation after crystal 2 was rotated through 90�
by polarization direction rotator 11. When the ZnGeP? crystal was used, near-90�
interaction of type eoo was realized, and the plane of synchronism of the: crystal
coincided with the plane of synchronism of LiI03. The optical delay around.the
ring irom the near-infrared crystal to the intermediate-infrared crystal and back
~ to the near-infrared crystal was less than 1 ns, i. e. considerably shorter than
Che durat:ion of the pumping pulse (by a factor of 30).
The signal radiation source was a stabilized single-mode single-frequency LG-76
C02 laser 4. The signal radiation together with the pumping radiation went to
- crystal 3 via the mixing mirror (plane-parallel plate 5 of barius fluoride with
a reflective interference coating applied to one of the faces for a wavelength
of 1.06 um). The pumping lase~ was Q-switched with pulse recurrence rate of 12.5 Hz.
The converted radiation (a = 0.967 um) went via reflective mirrors 6, 7 and BS-12
filter 8 for eli.minating 10.6 um radiation to crystal 2, which was lithium niobate
(the most effective crystal). The recording system enable%~ registration of both
the signal after the first conversion (a = 0.967 um) by image-converter tube 9,
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and the signal after the second conversion, either visually or by photomultiplier
10. Polarization direction rotator 11 was a quartz platn 1.3 cm thick with a wedge-
shaped plate for exact control of the angle of rotation of the direction of polari-
zation. The optical axis of the quartz plate coincided with the axis of the pwnp-
ing radiation.
The geometry of the nonlinear crystals was determined by a computer as follows:
for AgGaS2--6 = 40�, 0�, a= 0�; for Ag3AsS3--a= 0�, 6= 20�, 0�; for L~I03--
6=29�10', ~=0�, a= 18� (in air); for ZnGeP2--8=82�56', ~=45�, a=0�; for
HgGazSy--6= 41�34', 0�, a= 0�. Here 6 is the angle between the optical axis
of the crystal and the direction of pumping radiation, a is the angle between pump-
_ ing and signal wave vectors as read out toward the optical axis; ~ is the azimuthal
- angle in the XY-plane. Computer calculations for the interaction of 10.6 and
1.06 Um in ZnGeP2 and HgGa2S4 are given in Ref. 4, 5. Fig. 2 shows vector synchro-
nism curves for crystals of AgGaS2, Ag3AsS3 and LiI03 calculated by an analogous
method.
The power coeff icient of conversion of the two-stage arrangement n+-Pcon~Ps Was
determined by a direct method through measurement of the emission power PS of the
C02 laser by an IMO-2 power meter, and converted radiation power P~on (a= 0�5 um)
by a calibrated photomultiplier. The measurements gave the following results:
for HgGaZS4 ri+= 20%; for Ag3AsS3 r1.~= 8%; for AgGaS2 r1+= 14%; for ZnGeP2 n+= b%�
The pumping power density lay in a range of 0.5-1.2 MW/cm (depending on type of
crystal), was far from the admissible limit, and ensured stable operation of the
converter throughout the experiment (a few cycles in 0.5-1 hour). No deterioration
of the optical characteristics of the crystals was observed. The completed experi-
ments showed that the double conversion arrangement gives a sensitivity in the
intermediate infrared range equivalent to that of a photomultiplier with quantum
yield of 1-2%.
REFERENCES
1. Voronin, E. S., Divlikeyev, M. I., I1'inskiy, Yu. A., Solamatin, V. S., Badi-
kov, V. V., Godovikov, A. A., KVANTOVAYA ELEKTRONIKA, No 1, 1971, p 151.
2. Andreyev, S. A., Barashkov, M. S., Matveyev, I. N., Pshenichnikov, S. M.,
- Umnov, A. F., "Tezisy dokladov devyatoy Vsesoyuznoy konferentsii po kogerentnoy
i nelineynoy optike" [Abstracts of Reports to Che Ninth All-Union Conference
- on Coherent and Nonlinear Optics], Moscow, 1978, Part 1, p 194.
~ 3. Voronin, E. S., Solomatin, V. S., Shuvalov, V. V., "Tezisy dokl.a~lov vos'moy
Vsesoyuznoy konferentsii po kogerentnoy i nelineynoy optike" [Abstracts of
Reports to the Eighth All-Union Conference on Nonlinear dptics], Tbilisi,
Metsniyereba, 1976, Vol 1, p 184.
4. Andreyev, S. A., Andreyeva, N. P., Matveyev, I. N., Pshenichnikov, S. M.,
Ustinov, N. D., KVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 357.
5. Andreyev, S. A., Andreyeva, N. P., Badikov, V. V., Matveyev, I. N., Pshenichni-
kov, S. M., KVANTOVAYA ELEKTRONIKA, Vol 7, 1980, p 2003.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", Z981
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UDC 621.373.826.038.823
INFLUENCE THAT HEATING OF ACTIVE MEDIUM DURING EXCITATION HAS ON CHARACTERISTICS
OF PULSED ELECTROIONIZATION CO LASER USING PURE CARBON MONOXIDE
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 6(108), Jun 81 pp 1366-1368
[Article by N. A. Bulavin, A. A. Ionin, I. B. Kovsh, I. V. Kochetov, V. G. Pevgov
and B. M. ilrin, Physics Institute imeni P. N. Lebedev, USSR Academy of Sciences,
- Moscow]
~ [Text] A theoretical investigation is made of the way that the
lasing .^..haracteristics of a pulsed electroionization CO laser
using pure carbon monoxide depend on the fraction r1 of pumping
energy that is expended directly on heating the gas. A com-
parison is made with the results of theoretical research. It
� is shown that an increase in n over the theoretical value pre-
viously predicted gives good qualitative and quantitative agree-
ment between theoretical and experimental data with respect to
laser efficiency, lasing delay time and radiation spectrum.
In Ref. 1, experi.~nental research was done on stimulated emission in a pulsed electro-
ionization CO laser using pure carbon monoxide, showing that its efficiency (~3%)
in c~ntrast to that of electroionization lasers based on mixtures of CO-NZ and
CO-N2-He, is almost an order of magnitude lower than the calculated values [Ref. 2].
The discrepancy, as noted in Ref. l, may be due to the fact that the numerical
calculation of Ref. 2(with which the experimental data were compared) used an
overstated value of the eff iciency y of vibrational excitation of CO molecules
by electron impact (Y is the fraction of pumping energy expended on excitation
' of vibrational levels of CO molecules). Such an overstatement leads to under-
estimation of the heating of the working gas mixture during the pumping pulse as
a consequence af direct transfer to heat of the fraction r~= 1- y of the excitation
- energy, and accordingly to an overstatement of the lasing efficiency.
- In this article, a quantitative evaluation is made of the way that the energy,
time and spectral characteristics of radiation of a pulsed electroionization CO
laser using pure carbon monoxide~depend on the quantity r~, and calculated data
are also corapared with experiments. To ge~ the theoretical values of the laser
parameters, the system of equations of vibrational kinetics was solved simultaneously
with equations for intensities of stimulated radiation and gas te~nperature. The
calculstions were done by a method developed in Ref. 2, 3 for the conditions of
Ref. 1: particle density N= 0.5 Amagat unit, initial gas temperature T= 100 K,
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/ 3D
~ 150 j
ro j ~
tio
c~
~ fOD ` u ?0
i
~ ~
~ �U
50 ~ iD
~ w
'b 3 w
cE ~ ,_�p W
3-i
~~1DD ?DO JD0 400 p 0,1 G{2 L
4in ~ J/ ( Z �Amagat)
Fig. 2. Theoretical dependence
Fig. 1. Radiation energy Qrad aS of efficiency of pulsed electro-
a function of sgncific energy in- ionization CO laser on rt
put Qin: 1, 2--calculation at
n= 6(1) and 20% (2); 3--experi-
ment [Ref. 1, 5]
gun current density ig ~ 15 mA/cm2, pumping pulse duration Tp = 30 us, threshold gain
1'= 0.4 m 1. The energy input level changed in accordance with the initial value
of the normalized field stren~th in the discharge E/N, which was varied over a
range of (0.9-1.5)�10-16 V�cm ; during pumping the quantity E/N decreased by a
factor of approximately 1.5. The dependence of the radiation energy on the er~ergy
contributed to the discharge was calculated in two variants. In the first, the
~ fraction n of pumping energy expended directly on heat was assigned as a function
of E/N calculated in Ref. 4 on the assumption that the gas is heated due to rota-
tional excitation and elastic losses of electron energy. According to Ref. 4 in
the given range of E/N, r1= 5-7%. In the second variant, the calculatians were
done for a set of fixed values of r1 in the range of 5-30%.
Fig. 1 shows theorer.ical and experimental [Ref. 5] curves for rad~ation energy
as a function of specific energy input. It can be seen that an ir.crease in the
amount of energy going to heat leads to a considerable reduction of efficiency
and improves agreement with the experiment. This is also implied by Fig. 2, which
gives the theoretical dependence of ef f iciency on r~ (Qin = 300 J/ (Z �Amagat) , Tp = 20 us,
I'= 0.05 m 1 and other conditicns the same). The theoretical data show that lasing
should not arise at all at rl~ 0.3 even at a very high value of reflectivity of
- the output mirror (~90% for an active region 1 m long).
Since lasing was observed on pure CO in the experiment, it can be concluded that
~ r~< 0.3 in the investigated range of E/N. However, this conclusion contradicts the
results of Ref. 6, where E/N p 10-16 V�cm2 for pure CO gave r1~ 0.5. Therefore,
we feel that the question of the value of n for carbon monoxide remains open; ad-
ditional experiments must be done on determining the eff iciency of vibrational
excitation of CO in an electric discharge.
An increase in the fraction of energy expended on heat leads to an increase in
the time of the delay Tdel of the lasing pulse relative to the pumping pulse (Fig. 3)
since in our temperature range the rate of VV-exchange decreases with heating, and
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Tdel~ uS
~
~
BO
2~
` a
40 3 .
\
0
100 200 300 400
Qin, J/~Z'~gat) b
Fig. 3. Delay time Tdel as a function of
4in� Notation as in Fig. 1
consequently so does the rate of formation 7-6 9-B 1l-10 v-v-1
of inverse population. The departure of ~
the experimental curve [Ref. 1, 5] from Fig. 4. Emission spectrum of the
calculated behavior at n~ 6% also confirms pulsed electroionization CO laser
the fact that r~~ 6%. at Qin= 400 J/(Z�Amagat): a, b--
calculation for n= 6(a) and 20%
Comparison of the emission spectra of the (b); c--experiment [Ref. 1, 5]
pulsed electroion ization CO laser using
pure carbon monoxide as calculated for different values of r1 at fixed specific
energy input (Fig. 4) shows that an increase in th~ fraction of energy going di-
rectly to heat noticeably shifts the spectrum into the long-wave region, better
agreement with the experiment being observed for the spectrum calculated for high
values of n(in the experiments of Ref. 1, 5, the rotational structure of the vi-
brational ba�~zds was not resolved, and therefore in the calculation the energies
of the radia:ion on separate rotational transitions were summed for each vibrational
band) .
Thus the assumption of a greater degree of heating of the active medium of the
pulsed electroionization CO laser than previously predicted theoretically in the
excitation process leads to better agreement of theoretical and experimental curves
for efficiency of stimulated emission, delay time and radiation spectrum for pulsed
electroionization CO lasers using pure carbon monoxide. Comparative analysis ~f
the calculated and measured characteristics of the pulsed eiectroionization CO
laser shows that for E/N = 10-16 V�cmz the efficiency of vibrational excitation
of CO molecules by electron impact n= 85% (in any case no less than 70-80%).
REFERENCES
1. Basov, N. G., Danilychev, V. A., Ionin, A. A., Kazakevich, V. S., Kovsh, I. B.,
Poletayev, N. L., KVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 1208.
2. Basov, N. G., Dolinina, V. I., Suchkov, A. F., Urin, B. M., Preprint of Lebedev
Physics Institute, USSR Academy of Sciences, Moscow, 1976, No 1.
3. Konev, Yu. B., Kochetov, I. V., Pevgov, 4. G., ZHURNAL TEKHNICHESKOY FIZIKI,
vol 49, 197y, p 1266.
76
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4. Konev, Yu. B., Kochetov, I. V., Marchenko, V. S., Pevgov, V. G., Sharkov, V. F.,
Preprint of the Institute of Atomic Energy, Moscow, 1977, IAE-2810.
5. Ionin, A. A., Candidate's Dissertation, Lebedev Physics Institute, USSR Academy
of Sciences, Moscow, 1977.
6. Londer, Ya. I., MPnakhin, L. P., U1'yanov, K. N., TEPLOFIZIKA VYSOKIKH TEMPERATUR,
Vol 18, 1980.
COPXRIGHT: Izdatel'stvo "Radio i~vyaz "Kvantovaya elektronika", 1981
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OPTICS AND SPECTROSCOPY
WAVE FRONT SENSOR BASED ON TALBOT EFFECT
Leningrad ZHURNAL TEKHNICHESKOY FIZIKI i.n Russian Vol S1, No 7, Jul 81 (mantiscript
received 25 Apr 80, after revision 24 Feb 81) pp 1432-1438
[Article by A. S. Koryakovskiy and V. M. Marchenko, Physics Institute imeni
P. N. Lebedev, USSR Academy of Sciences, Moscow]
[TextJ A wave front sensor based on the method of multibeam
interferometry is considered that has a number of advantages
over conventional wave front sensors. A simple algorithm is
developed for processing the resultant interference patterns.
Phase distortions are measured with precision of ~5�10-3a.
1. A necessary component of active optical systems [Ref. 1, 2] is the wave front
sensor. The requirements for wave front sensors are formulated in the survey
of Ref . 2.
This paper analyzes the feasibility of developing a wave front sensor using the
method of interferometry worked out in Ref. 3, ~ and based on the Talbot effect
[Ref. S, 6]. From the standpoint of spatial resolution and admissible range of
messurement of phase distortions, such a wave front sensor has several advantages
over those described in Ref. 2. An algorithm is developed for calculating the
shape of the wave front.
io s
# An optical diagram af an interferometric wave
~ ~z�y,=corcstJ ~ front sensor is shown in Fig. 1. A wave with
~ M~~/p a~~ ~ a planar or parabolic front is directed toward
i ~
~ i a two-dimensional periodic grating (with geom-
~ z~ i etry satisfying the conditions of Ref . 6) lo-
_ ' a= cated in plane z= 0. It is further assumed
~ . that the lattice periods along the X and Y
~ axes are identical and equal to p. Then the
i ~ R ~ radiation passes thorugh a medium cliaracterized
0 ~ z, ZM z by the function of phase distortions �(xl, Y1) _
$r(X1, Y1) -~i(xl, yl) in plane z= zl, where
= Fig. 1. Optical diagram of an �r(xl, yl) and ~i(xl, yl) are the phase ad--
interferometric wave front sen- vances in th~ investigated medium and in the ref-
- sor based on the Talbot effect erence medium (of given form) respectively;
yl is the coordinate along the Y1 axis perpen-
dicular [o plane (X1, Z). Intensity distribution is recorded in plane z= zN that
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coincident with the plane of reproduction of the field. In the case of an initial
planar wave and ~(xl,Yl) = 0, zN = 2P2N/a, where ~ is wavelength, N= 1, 2,... is
the number of the plane oF reproduction, and radiation to each point of the plane
of reproduction ~.s from region 4MiNp of the grating; 2Mi+ 1 is the number of spa-
t~al harmonics (diffraction orders) that take part in image formation; Mi is de-
termined primarily by the geometric parameters of the grati.ng. For example, for
a sine-wave amplitude grating Mi= 1, and fo~ a rectangular grating with traris-
- mission factor rect (x/q) comb (x/p) [Ref . 7] , where q is the size of an opening,
Mi is very large and is limited by wavelength Mi < p/a. Actually, Mi is limited
by introducing a spatial filter or by the sensitivity level of the reception equip-
a ment, siY~ce the intensity the harmonics Im falls with increasing m. For example
for the above-mentioned rectangular grating
-sinG2 mc ,
'I o ~ f c ~ ~
- where Q= q/p, m=�l, �2,..., and Io is the intensity of the zeroth harmonic. Since
in practice we are deali:zg with gratings of finite dimensions 2a, reproduction
_ will take place in region ~x~ , ~Y~ ~ a- 2~Ii.~p, disre~arding diffraction by the
aperture.
2. If an optically inhomogener.us medium is placed between the grating and the
plar~e of reproduction, the reprociuction pattern is distorted as a consequence
of the fact that the spatial narmon.ics acquire different phase advances upon pas-
- sage through differen*_ regions ~f the medium. The optical quality of the medium
can be ju~iged from the distortion of intensit~~ distribution. ,
- In the general case �~(xl,yl) can be found from solution of the inverse problem
of reconstructing; the phase distribution from the known intensity distribution
[Ref. 8] .
~ Let u(xl, yl) be the distribution of the field in plane z= zl of the object. Then
immediately behit~.d the object the distributicn will be u(il, y,)e'~~s~~v!~. From mea-
surement of the intensity distribution in the plane of observation, we find
- IuP(x, y)~; a method of sr~ccessive approximations is used to get ~(xl, yl). Ac-
cording to Ref. 7, the field u(x, y) can be represented as a Four ier tr~r.sform
x ~ 2
'Jf the f~111Ct1Ai1 ~l ~~1, l~l~j C'4~z~' y~~C, 2~f~-f'~ i+y~), where k= 2~r/a . LE':L ~ p~X1 ~ yl) be an
_ arbitrary zeroth approx.imation of the unknawn function, then
k w
t~k~f~�_+~~ �r s (z;+y') p ~
_ ~o y) = t~ (z~,. - a,~ e~' j u�~~~ yi) X
_m.
' k ~=2+y1 ~ _ ( ~ f ~s (s,x+Yi!')
- x e~~o(=~, y,)e z(`x-�,) ~ e ( A'- dyldyi,
Leaving the phase factor in uo(x, y), we replace the amplitude part 1~y ~ue(x, y)~,
and find ~y inverse Fouxie~ transformation ul (sl,~yl)c'p'ts" y'~;. Tt~is cycle is re-
peated until we get the steady-state solution ~n(xl, Yi) =~n+i~Xl~ Yi)~ where n
r is the number of the Cteration. The number of steps n dep~nds on how close the
~o~Xi~Yi) is t~ ~h~ ar,tual value of ~(xl, Y1)�
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In the given interference technique the number of ineasurement points is determined
- by the parameter (4aMi/p)2= I04-106 {p/2Mi is the dimension of a minimum structure
of the image), and the problem of finding ~(xl, yl) is laborious and time-consuming.
3. It was shown in Ref. 3, that the reproduction effect takes place also in
cases of simple optical iahomogeneities such as a plana-parallel plate and a wedge,
and in the case of a parabolic lens is accompanied by a change of scale, i. e.
_ the intensity distribution rernains discrete and contrasty. Slight disruption
of optical homogeneity of such media leads to displacement of contrasing cells
in the plane of reproductian. In this connection, it makes sense to use the dis-
pla~_~ment of images of individual cerls in the plane of registration as measured
parameters, and to develop a simplifiedliutprecise algorithm for quantitative
processing of the resultant interference patterns. This automatically does away
with the difficulties involved in photometric measurement of resultant intensity
distributions since in this case the phase distortions are converted to displacement
of the contrasting images of points with respect to X and Y. To make the distorted
reproduction pattern sharp enough for measurement, rertain conditions must be
met with regard to the parameters of the grating and ~(xl, y�). To find these
conditions, let us expand ~(xl, yl) in a series with respectyto derivatives in
the vicinity of the point (xi~ Yi)=
.
~ ~xv y~) _ ~ ~x~, y~) d~ ( ~i=1 y?) ~2~ - x~)
+d~ ( d~~ y~) ~y~ - y~) ~ R y~), ~2)
where
m
~ ~ d~~ ~xl~ y!~ x- 2~ n d~-~~ ttt~ yi~ d~ ~Zt~ ~lll X
~(xi~ yi~ n dZi ~ i + d=1 1 d9i
~=z
a X ~~1 _ xi~~-~ - y~) . . . -j-- d~~ a
y; y`) ~yi - y?)"~ �
HerP the first term of the second member describes the constant phase shift in
Lhe vicinity of (xi, yi) that displaces the plane of reproduction along the Z
axis by Z= ~p(xi, yi)/k, ar?d the second term is the slope of the wave front that
shows up in displacement oi images of the cells in the vicinity o� point (xi~ Yi)
by an amount
~ ~x_d`P~=i, yi) ZN-=I , Q d5'~zi� yi) ZN-Z~ , 3.
dxl k . y= dyl k
These two types of distortions are distinguished by the fact that they introduce
phase shifts that are the same for all spatial harmon ics, and hence do not affect
the contrast of the reproduction pattern. Therefore in the given case the condition
~ of image contrast wi?1 be met if the displacement Z of the reproduction out of
the plane of registration is less th.sn the depth of f ield of the reproduction,
which is found as the distance from the position of reproduction where the advance
of'the Mi-~h harmonic changes by ~r relative ~o thz zeroth harmonic. From this
- condition, using the results of Ref. 3, 4, we get
~ ~ 2~ ~PI M~^)'� ~4)
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M'nR O~F'!~'EAi. i i~~' (1N1.1'
If we take into consideration that usually (p/Mi~)2~ 103-10``, condition (4) is
. met over a wide range.
- The quadratic term of expansion (2) and the terms of higher order describe dis-
tortions that introduce phase shifts in th~ vicinity of the point (x', y') of
� the expansion that depend on the number of the harn~onic, blurring the pattern
of reproduction in plane zN. Since radiation arrives at point (x', y') in the
lane of observation from the section of the investigated object ~xl- xi~,
~Yi- YiI ~ 2MiNp(1- zl/zN), the contrast will be preserved if in this region
~ ?Ji) ~5)
We note that distortion of the wave front due to the quadratic term of (2) shifts
_ the reproduction pattern without blurring it, and changes the scale [Ref. 3, 4]
zN i zi = Zp,i P� = P'f Z` , ~6)
~ _ Zl
where f is focal length. This enables the method to be used for studying the
optical quality of lenses and parabolic mirrors. In this case ~(xl,yl) is the
deviation ~r(xl, yl) that characterizes the actual object away from the quantity
assigned by the object with focal length ~i =(xi+ yi)/2f.
Thus by selecting the type of grating (p, Mi) and the position zl of the inve~ti-
gated medium, we can get a contrasting distribution of intensity in r~gistration
plane zN by satisfying inequality (5).
From the dependence of the position of the plane of reproduction on p we get the
condition for precisi.on (periodicity) and alignment of the grating. Assuming
that the pattern in the plane of registration is not blurred if displacement of
the plane of reproduction due to imprecision of the period ~p is less than the
depth of. field defined above, we get
~p ~ p/4M?N. (7)
Incli~ati~n of the grating at angle S leads to d cl~:;snge in the effective period
p' = p cos S= p(1 - SZ/2) . Then from (6) we get the condition for alignment
~ (3 ~ 1/Mi 2N.
- 4. The initial material for getting quantitative information on phase distortions
of the investigated medium i~ an interference pattern that is a set of contrasting
images of the grating cells shifted relative to the undisturbed initial positions.
The algorithm for processing the interference pattern i~ as follows: 1) the po-
sition of points of ineasurement of the function of phase distortions of the in-
vestigated object ~(xl, 1) is given by pro~ections of transmitting cells of the
grating on the object (x~, y~), where Z, s= 0, l, 2,... 2a/p; 2) at each point
(x~, y~), ~(xl, yl) is representQd as a series (2), and si.nce the interference
, patterns are obtained under. condition (5), we can limit ourselves to constant
and linear terms of the expansion; 3) from the displacement of ima~es of the grating
cells in the p1anE of. registration zN~xZ, ~yS (Fig. 1), in accordance with (3), we
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_ de~ermine a~(xi, y~)/axl, a~(xi,y~)/ayl; 4) beginning with an arbitrary point
(x y~�), we find over the entire aperture 2a
~P ~?i{~ ~ yi~ ~P ~~i+ ~i~ 2 [d ~f ~~z1 9i) d~P ~s~ii 9i) l ~
J
- p d~ yi) + a~ c=I. y;+~~
~P~~,~ yi )=~~~i~ yi 2[ dYi dUi J'
~ (~i+~, y;+') = 2 ~x~+'? y3) -f- 2 ~a~ (=ay~ y~) + -
a~~=i+~~ b~+l)~ ~t .+~~.L P a~f=~, ,4i+i)+a'P~yi+l� Ui+l)1l
+ dY~ 5' ~ i+ ~Ji . 2[ dx, dzi J1 ,
- In most cases errors by a constant phase shift due to arbitrary selection of
~(x~�, y~�) play no part since we are usually interested in the behavior of
~(xl, yl) rather than in its absolute value.
The error on one step will be 2R(p/2, 0). If it is assumed that the unknown
�(xl, yl) is a sufficiently smooth function, the main contribution to the error
will be from the ~uadratic term of expansion (2), and in accordance with (5}
2R(p/2, 0) S~rr/16MiN2. It may happen in practice that it is impossible or unneces-
sary to meet condition (51. Then error 2R can be estimated from the modulation
of the image in the plane of registration due to phase mismatch of harmonics.
If the intensity distribution in the cells of the plane of registration zN is
modulated with period T, thi.s means that the m= p/T-th harmonic is out of phase,
i. e. R[(2p;T)Np(1- zl/zN), 0] ~ n, and consequently the error on one step is
2R(p/2, 0) (~r/16N2) (T/p}2. Thus the sharpness of the interference pattern is
an index of accuracy of determination of ~(xl, Y1)�
The accuracy of determining ~(xl, yl) can be improved if it is averaged at each
computational point (x~, y~), i. e. if we take the average value between those
obtained in calculation by different routes, e. g. as is done in (8) ~(xi+', yi+~~-
(~pi cp~)/2, where ~ 1 is ob ta ined f rom ~~x~, by route ~(x~, y;) ~(x;+', y;) ~l (xi+~, y~+i~~
and �2 is obtained by route ~(x;, y;)-~~(a;, yl+l)=~; ~Z(xi+', y;+'). Averaging can be done
with respect to three, four or more values of ~(z;+'. y;+'), obtained from different
trajectories of coznputation, or for example around a ring ~p(xi+ yi)-"P~~i}'~ bi)~
p ~~i+l~ y~+~ ~ m (x~, yi+') ~ ~ ~~i+ yi)�
t
~ �
~
1 2 3 4. 5 ~ 6~
Fig. 2. Diagram of facility for measuring wave front distortir~ns
5. The facility for measuring wave front distortions shown in the diagram of
Fig. 2 is an example of realization of the described method. Radiation of He-Ne
- laser 1 is expanded by eyepiece 2 with spatial filter 3 placed at the focus. Ob-
jective lens 5 is set so that its central part received the incident beam so as
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to reduce ttie intensity differential over the cross section. Two-dimensional
periodic grating 4 is placed in the divergent beam, enabling variation of the
period of distribution in the plane of registration by longitudinal displacement
of the grating. The spacing 6 can be varied by relative displacement of two iden-
tical gratings superimp~sed on each other. The intensity distribution is regi-
stered by photographic plate 6 in the plane of reproduceion, the position of this
plane being defined by formula (6). Objects to be studied can be placed anywhere
between grating 4 and registration plane 6.
As an illustration of the possibilities of the method, measurements were made
of the distortions of a wave front by inhomogeneities modeled by a glass plate.

- On the interference patterns of Fig. 3[photo not reproduced] the unperturbed
distribution is shown on the left, and the distribution distorted by oprical in-
homogeneities of the plate is shown on the right. The photographs were obtained
for the same region of the plate (the period of di5tribution on the object was
1.3 ~n, N= 1) with grating spacings a1= O.lSf Q2= 0.5. In the former case, the
number of harmonics of comparable intensities is greater than in the latter case
[for example for ~1, according to (1), I3/Io= 0.5, and f or Q2, I1/Io= 0.41], and
more blurring of the image is observed as a consequence of violation of condition
(5). The one-dimensional nature of inhomogeneities introduced by the plate simpli-
fies processing of tt?e interference pattern, reducing this procedure to a one-
dimensional pre'~'.em. The interference pattern of the second photograph can be
interpreted as follows.
In the center of the photograph (in the vicinity of the 17-th line from the bottom)
the images of the squares are blurred, i. e. in this area R(xl) is large, and
the period of distribution is smaller than in the undistorted left part, indicating
a focusing convexity in the relief of the plate. In the region of the 8-14-th
lines, the images of the squares are fairly sharp, R(xl) is small, and displacement
of. the lines in case of the period of the image equal to the undistor~ed value
i;~r~i~ates an optical ~edge in this region. In the upper and lower parts of the
photograph the image is blurred, and the period of the distribution is greater
than the undistorteu period, which is an indication of a defocusing concavity.
For numerical processing of the interf~rence pattern in this photograph, the dis-
placements ~xZ of the squares, where Z is the number of the line, were m^asured
relative to the left part that had not been subjected to the action of the investi-
gated plate, Frhich to some extent eliminated the influence of nonideal~~y of optical
components of zhe system. Derivatives were found by the formula a~(X1>/aXZ=
2~r(~xZ) /az*, where Z* = ZO S~" Z56 -~Z05Z56~f~ , zos is the distance from the object
to the objective lens, 256 is the distance from the objective lens to the plane
of registration, f is the focal lzngth of the objective lens. Considering that
p(xl) = L,L(xl) (n- 1) �2n/a, where n is the index of refraction of glass, ~L(xl)
is the change in thickness of the plate along X1, we fir.d ~L(xl)(n - 1) (Fig. 4).
It can be seen that the resultant relation caincides with the Qualitative study
of the interference pattern outlined abQVe. The accuracy of ineasurement of ~xZ
was 0.1 mm, which in the given measurement system corresponded t~ 8�10-` a.
The. third photograph of Fig. 3[photo not reproduced] is the interference pattern
of a fairly smooth section of the pl.ate, the region ~xl--xil [see (5)] being re-
duced by a factor of 1.7 as compared with the preceding case. The change in tbe
phase front of the plate is shown in Fig. 4. In the given case, the initial
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s, MM 30 20 10 0'
~
_ Fig. 4. Change of phase front
in g.Lass plate as a function of i0.1
xl, obtained from processing
interference patterns 2 (upper 0.5~
scale) and 3(lower scale) of ,i0~
Fig. 3 [not reproduced]
p 1 S 10 z, MM
- interference pattern is fairly cont.rasty, whict; enabled measurement of ~x with
accuracy of 20 um, and accordingly the accuracy of determining ~L(xl)(n - 1) was
4�10-3 a.
- If anly the curvature of the wave front is of interest, the measurements can be
done with respect to the distorted right-hand part of the interference pattern.
In this case Oxi is measured zo within an unknown constant that corresponds to
a fixed optical wedge over the aperture.
6. This wave front sensor based on the method of multibeam interferometry has
certain advantages over conventional sensors. The optical system of the wave
front sensor is analogous to that of the Hartmann sensor [Ref. 2], is simple,
and is easily realizable. However, the sensitivity of the wave front sensor to
phase distortions is considerably higher [Ref. 4], and the accuracy of ineasurements
increases with their reduction. A wave front sensor with grating of small size
enables investigation of a medium with large apertures. The spatial resolution
defined by the parameter 4MiNp(I- z/zN may be considerably higher due to the
capability of reducing the lattice period. The range of phase distortions that
the wave front sensor registers is determined by the condition of contrast of
the intensity distribution in the plane of registration (5), and may amount to
many wavelengths. Studies have shown that the wave front sensor is not very sen-
sitive to nonuniformities in illumination of the aperture.
The wave front sensor is especia~ly convenient in use as an indicator of wave
front distortions, for example in systems of aperture probing or sharpness enhance-
ment [Ref. 2]. It is less sensitive to perturbations of equipment by vibrations
than other interference wave front sensors.
The capability of real-time use of the wave front sensor is determined by the
rate of computer input of information on ir~tensity distribution in the plane of
re~istration, which depend.s on the reception dev~ce, and by computi:~g time. The
= data processing algorithm developed in this paper is simple and permits rapid
computation of the shape of a wave front. '
In conclusion the authors thank A. M. Prokhorov for useful discussion.
REFERENCES
1. Bakut, P. A., Ustinov, N. D., Troitskiy, I. N., Sviridov, K. N., ZARUBEZH-
' NAYA ELEKCTONIKA., No 3, 1977, p 55.
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2. Hardy, J. W., PROC. IEEE, Vol 66, 1978, p 651; TRUDY IIER, Vol 6, 1978, p 31.
3. Koryaicovskiy, A. S., Marchenko, V. M., FIAN Preprint No 89, Moscow, 1979.
4. Koryakuvskiy, A. S., Marchenko, V. M., KVANTOVAYA ELEKTRONIKA, Vol 7, 1980,
p 1048.
S. Deckers, Ch. NOUV. REV. OPTIQUE, Vol 7, 1976, p 113.
G. Montgomery, W. D., JOSA, Vol 57, 1967, p 772.
7. G~odman, J. W., "Vvedeniye v Fur'ye optiku" [Introduction to Fourier Optics],
"Mir", Moscow, 1970 [New York, McGraw-Hill Book Co., 1968].
8. Bakut, P. A., Troit:kiy, I. N., Lemin, A. A., Safronov, A. N., ZARUBEZHNAYA
RADIOELEKTRONIKA, Nv ?1, 1978, p 3.
COPYRIGHT: Izdatel'stvo "Nauka", "Zhurnal tekhnicheskoy fiziki", 1981
66?0
- CSO: 8144/1798-A
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UDC 621.3.038.8
FEASIBILITY OF MAKING AN ABSORBING CELL FOR 1315 nm
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 6(108), Jun 81 pp 1315-1319
[Article by 0, B. Danilov, A. P. Zt~evlakov and I. L. Yachnev]
[Text] It is experimentally shown that a concentration of unex-
cited iodine atoms of (2-5)�1017 cm 3 can be obtained on the
pyrolysis phase of photolysis of perfluoroa~kyl iodides. The
velocities of pyrolysi~ and compressional waves are measured
in a thick layer of perfluoroalkyl iod3.de. It is found that
the velocity of the pyrolysis wave is much greater than that
of the compressional wave. The authors discuss the feasibility
of constructing a pulse absorption cell for 1315 nm in which
the absorbing medium is produced by a pyrolysis saave.
At the present time the amplif ication stages of a photodissociation iodine laser
are decoupled by using an absorbing cell [Ref. 1, 2] that works on the transition
I(52P ~2- 52P ~2). Unexcited iodine atoms are produced by thermodissociation of
iodine molecules I2. The cell is pl3ced in a thermostat with temperature of ~800�C.
The working temperature of the iodine atoms was ~1017 cm 3 Since the absorbing
transitir;n is the inverse oi the stimulated transition I(52P ~2- 52P ~2) and the
widths cf the lines of both are made equal, the iodine absorbing cell should work
with re~.uction of the cross section of the luminous flux of the preceding amplif i-
cation ~~tage. A weak point of the thermal absorbing cell is the windows that are
;lways in contact with iodine, which reduces their r.adiation strength. An absorb-
ing cel:. in which unexcited iodine atoms are formed upon flash photolysis of per-
fluoroalkyl iodides is free of this d{.sadvantage. The photolysis region in the
absorbin; cell can be localized at any distance from its windows, and therefore
the dime~isions can be selected in accordance with the admissible requirements for
radiatio;l loading. A pulse absorbing cell has been used for decoupling the master
laser ar~d amplifier [Ref. 3]. However, Ref. 3 contains no data on the transmission
factors and operating conditions of the absorbing cell that would help us to under-
stand whether such a cell can ~e used for decoupling powerful amplification stages.
In photolysis of perflu~roalkyl iodides, a concenrration of iodine atoms of 1017
per cc or more is difficult to achieve on the pre-pyrolysis stage of photolysis
even when a strong quenchant of excited iodi.ne atoms I* is used because of rapid
recombination of iodine atoms with radicals CF3, C3F~ [Ref. 4]. But such a con-
centration of iociine atoms is easily realiaed on the post-pyrolysis stage of
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photolysis. This has been es�ablished in experiment~ on transillumination of a
medium being photolyzed on a= 1315 nm that were done on the facility described
in Ref. 5. The source of transilluminati~n was a photodissociation laser operating
on one transition F= 3- F= 4. According to Ref. 6 the half-width of the emission
- line of such a photodissociation laser is 0.0015 cm 1. The half-width of the ab-
sorption line was calculated from the data of Ref. 7. Conformity to Bouguer law
was verified by varying the length of the absorbing medium. The experiments were
done on mixtures of CF3I, n-C3F~I with air and Xe. The oxygen of the air, a strong
quenchant of I*, prevented amplification of the ~ransilluminating signal on the
pre-pyrolysis stage of photolysis.
~J(SIP,,~Z)~�s016cM-' The time dependences af concentration of iodine
p atoms for different mixtures (curves 1-5) are
- 60 y given on Fig. 1. This figure shows that with
_ 40 3 photolysis of mixtures of CF3I, n-C3F~I with
ZD ' air we can get concentrations of iodine atoms
of about (2-5)�1017 cm 3. The region of fast
~0 5 formation of iodine atoms corresponds in time
to the region of intense photolysis [Ref. 8J.
6 The concentration of iodine atoms is 6�1016 cin 3
4 on the pre-pyrolysis stage of photolysis, which
- Z lasts for the entire pumping pulse in a mixture
6 of n-C3F~I:air:Xe= 1:5:20 (pn_C3F~I � 20 ~n Hg) .
S , , , , , Pa~~age of a nanosecond pulse through the ampli-
0 fOD 200 d00 40n t, us fier is accompanied by the appearance of a pede-
stal (pre-pulse) that is longer than the part
Fig. 1. Time dependences of the pulse in which the main energy -Ls concen-
of the concentration of unex- trated [Ref. 2]. The transilluminated absorbing
cited iodine atoms in the cell should maximally attenuate the radiation
following mixtures: CF3I:air of the pre-pulse, superluminescence and lumines-
= 15:75 (1), 30:75 (2), cence of the preceding amplifier (weak signal)
C3F~I:air = 15:50 (3), 30:50 and should pass the radiation of the main pulse
(4) and C3F~I:air:Xe = 15:75:300 (strong signal) with minimum losses. For ef-
mm Hg (S); 6--pumping pulse; fective decoupling of amplification stages by
standard error of ineasurements an absorbing cell, the absorption linewidth should
of concentration of iodine be no narrower than the amplification line of
atoms for curves 1-4 is �20%, the preceding stage. It is known [Ref. 3] that
and for curve 5--40% the amplification line is intentionally broadened
- by adding large concentrations (~1019 cm 3) of
t~uffer gas to suppress self-excitation of the amplifier. It is not advantageous
to use such a method of line broadening in the absorbing cell as it leads to a
reduction in the concentration of iodine atoms. It is suggested that the widths
of the absorption ac~1 ampliiication lines be matched by applying an inhomogeneous
longitudinal magnetic field on the absorbing cell. Broadening of the absorption
line of the absorbing cell by the magnetic field enables us to use a relatively
low concentration of the working mixture. This is important since a reduction
in thP. pressure of the medium increases its resistance to optical breakdown.
~ ~ A possible design of an absor.bing cell is shown in Fig. 2. Thin magnet coils
8 are placed at the"ends of quartz vessel 1 to set up an inhomogeneous longitudinal
$7
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S 6 B 3 2 1 4 6 ~
_ ~
:
~ - - - -
. -
. '
:
l~ lp ,
j Fig. 2. Construction of an absorbing cell
magnetic field. The working mixture is admitted to the chamber with bell mouths 6
as far as vacuum gate 4, and the rest of the absorbing cell is evacuated. Opening
the gate gives rise to a rarefaction wave at the gas-vacuum interface, this wave
- moves through the gas at the speed of sound c, and the gas begins to escape into
the vacuum. The velocity of the gas boundary is u=[2/(y - 1)]c, where y is the
adiabatic exponent [Ref. 9]. To eliminate th'e influence of both processes on the
operation of the cell, it is necessary to locate the gate at certain distances
both from the pumped region of the gas (Z1, see Fig. 2) and from the focal plane
of the input lens of the absorbing cell 5(Z2). Let us estimate the lower limit
of the values of Z1, Z2, after assigning the shutter opening time t3. At t3= 1 ms
[Ref . 10J , c= 160 m/s, u= 2.2 km/s, we get Z1= 16 cm, ZZ = 220 cm. Firing of pump-
- ing lamps 2 located in illuminator 3, estat~lishment of the magnetic field and trans-
mission of the monopu:.se through the absorbing cell up to input lens 7 of the fol-
lowing stage all take place before arrival of the gas in the regi.on near the focus
of lens 5 to preclude optical breakdown there. In determining the parameters of
the absorbing cell, we begin with the premise that the pressure of the working
mixture must ensure the necessary concentration of iodine atoms on the one hand,
and must ensure resistance of the mediurn to optical breakdown on the other hand.
A concentration of iodine atoms of ~4�1017 cm 3 can ~re obtained from a mixture
of CF3I:02= 1:1 (p~g3i= 20 mm Hg). Assuming that the breakdown threshold for this
mixture is the same as for air (~250 GW/cm2) [Ref. 11], we find that at a pulse
duration of 1 ns a beam can be sent throu~h the absorption region with energy den-
sity e= 250 J/cm2. On the gas-vacuum interface, the admissible energy density
is certainly greater than 250 J/cm2. For subsequent estimates, let us take the
energy density of the signal incident on the absorbing cell as e= 50 J/cm2. An
absorl?ing medium in a magnetic field that is inhomogeneous lengthwise of the medium
has a nonuniformly broadened absorption line. The problem of calculating the satu-
rated coefficient of absorption of such a medium transilluminated by a nanosecond
radiation pr~lse has not yet been solved [Ref. 12]. For estimates of the weak-
signal and strong-signal transmission coefficients of the absorbing cell, let us
assign the length of the pumped region (120 cm), and assume that its central region
with length of 20 cm is in a magnetic field H~+O. In the absence of a magnetic
field, the absorption line is uniformly broadened. According to Ref. 13, for the
- main pul~e (T1- 1 ns), the pre-pulse (T2>�~1) and the superluminescence signal
at a gas pressurP in the absorbing cell of 40 mm Hg we have the relation ~~2 < pvl ~
~vs1C ~~Lor ~~~1,2 s1,Lor are the half-widths of the main pulse, pre-pulse, super-
luminescence signa~ and Lorentz absorption line respectively). The strong-signal
88
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transmission coefficient of the given segment of the medium is
T1 = 1 - hvNl/ [ (1 + gl /$2) e) ,
where hv is the energy of a quantum of incident radiation, N is the concentration
- of unexcited iodine atoms, Z is the length of the absorbing ~redium, gl, g2 are
the statistical weights of the ground and excited states of the iadine atom. We
will assume that the rate of intermixing of sublevels of the hyperfine structure
i=4
of the ground state vm ~ T-1. At N= 4�1017 cm 3, Z= 30 cm, g1= ~ gF'=i 24' g2=gF=3-~
i=1
and e= 50 J/cm2, T1 > 0.99. Considering that the weak-signal transmission T2 is
determined by Bouguer law, and taking the absorption cross section Qab equal to
5.8�10-1` cm2 [Ref. 14], we get T2~ 10-3. Let us note that in the phototropic
filters used in photodissociation lasers for these same purposes [Ref. 15] at the
present time, values of Tl and T2 thdt are close to those obtained above are not
simultaneously realized.
The region of the absorbing cell medium that is located in the magnetic fie13 is
necessary only for suppressing the luminescence of the preceding amplif ication
stage. Assuming that over the entire length of the absorbing cell the minimum
cross section of absorption of iodine atoms is realized in a magnetic f ield of
0-8000 oersteds (Qa~,p 9�10-20 cm2 [Ref. 14]), ensuring the equality ~v4bs = ~vlum~
we get an upper limit for the coefficient of absarption of the luminescence signal
_ of ~10-`. When the entire length of. the worki~ng medium is taken into consideration,
T1 decreases to 0.97. It should be noted tha~ in a pulse absorbing cell, the values
of the coefficients T1, T2 may vary over rather broad limits due to the capability
of changing the length and concentration of the absorbing medium.
Simultaneous pyrolysis of the working gas throughout the active volume of a pulse
absorbing cell for a vessel diameter of 30-100 mm and working gas pressure of
30 mm Hg is impossible because of the large cross section of absorption of the
" pumping light by the perfluoroalkyl iodide molecul~s. Sufficiently intense pumping
in the medium of such an absorbing cell should give rise to a pyrolysis wave [Ref.
16] with velocity determined by the time of readiness of the ves~el for operation,
and a gasdynamic perturbation wave [Ref. 17] that leads to disruption of the opti-
cal homogeneity of the medium. The velocities of both waves were measured in a
cylindri.~al chamber 175 mm in diameter with flashlamp ~n the axis. This lamp had
- an outside diameter of 70 mm, and the length of the irlterelectrode gap was 1 m.
The lamp input energy was about 48 kJ. Duration of the half-period of the dis-
_ charge current was 40 us. The chamber was placed in a planar optical cavity.
Time-scan photography nf the radiation f ield in the near zone showed a lasing
cutoff wave on the fiela paetern, propagating from the surface of the lamp to the
wall of the vessel. This wave arose only in the pure rerfluoroalkyl iodide, and
was not present in a mixture of the iodide with buffer gas (SF6) during the pumping
- pulse. On ttiis basis, the effect was identified with the pyrolysis wave. The
gasd4-namic perturbation wave ~compressional wave) in a mixture of C3F~I-S~6 showed
up well on the field pattern of radiation in the near zone, and had the form of
a pronounced narrow zone of absence of lasing, but with lasing r~tained ir. the
region between the compressional wave and the lamp surface. Fig. 3 shows Rt plots
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of pyrolysis and campressional waves. It can be seen
_ that the pyrolysis wave (curve 1) ari:es prior to the
R,c'" compression wave (curve 2) and works tnrough the entire
4 active space of the chamber. The velocities of the
3 ~ pyrolysis and compressional waves under the conditions
- 2 of the experiments were 1.2 and 0.3 lan/s respectively.
2
~ The resultant d~.ta demonstrate the feasibility of an
~ absorbing cell with working vessel 100 mm in diameter.
20 30 4~ u s
In such an absorbing cell the diameter of the region
Fig. 3. Rt-diagram of of the absorbing medium undisturbed by the compression
pyrolysis and compres- wave will be 70 mm when the pumping that is used is
sional waves� 1--p~3F~I external with respect to the vessel of the absorging
- =23 mm Hg; 2--mixture of cell. A cell with such an aperture can b2 used to
C3F~I:SF6 = 23�92 mm Hg; decouple the target unit from the last amplification
R= 0 corresponds to the stage of a powerful monopulse photodissaciation laser
lamp surf ace; the bro~cen [Ref . 2].
line denotes the wali of
the chamber The authors thank S. A. Tul'skiy for assistance with
the experiments on observation af the pyrolysis wave.
REFERE:JCES
1. Gaydash, V. V., Yeroshenko, V. A., Lapin, S. G., Shemyakin, V. I., Shurygin,
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661U
CSO: 1862/242 ' ~D '
= 91
_ FOR OFFICIAL USE ONLY
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