JPRS ID: 8959 USSR REPORT PHYSICS AND MATHEMATICS QUANTUM ELECTRONCS

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~ ~
QUANTUM ELECTRONICS
29 FEBRUARY i988 CFOUO 3r80) 1 OF 1

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JPRS ~./8959
. 29 February 1980
- USSR Re ort
p
PHYSICS AND MATHEMATICS
(FOUO 3/80)
Qu~ntum Electronics
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JPRS L/8959
2~ February 1980
USSR REPORT
_ PHYSICS AND MATHEMATICS
(FOUO 3/80)
QUANTIJM ELECTRONICS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 6 No 12, 1979 pp 2517-
2524, 2533-2545, ?590-2596, 2606-2609, 2652-2653 -
- CONTENTS PAGE
Photon Branching in Chain Reactions and Chemical Lasers
_ Initiated by Infrared Radiation
(V. I. Igoshin, A. N. Orayevskiy).....,... 1
Prospects for Employing Porous Structures for Cooling
~ Power Optics Components
(V. V. Apollonov, et al.) .
. 12
Relation~ship Between the Statistics of Laser Damage to ~
Solid Transparent Materials and the Statistics of
Structural Defects
_ (Yu. K. Banile;ko, A. V. Sidorin) 32 -
Investigation of Limiting Operating Modes of a Lamp-type `
_ Pumping Module in the 'Mikron' Laser Unit
(B. V. Yershov, et al.)............ 13 is
reached with an average number of vibrational quanta per molecule of about
- three. The fact that such a level of the vibrational excitation of inethyl _
- fluoride can be actually realized under conditions of a high pressure me-
dium is demonstrated experimentally in [11]. -
The analysis made makes it possible to estimate an unknown energy gain,
defined as the ratio of the energy emit*_ed by a laser to the initiation
energy. Expenditures of photons for the formation of a single active cen-
ter equal m/2~ , and the number of emitted laser photons per single active
center equals f. Then for the energy gain, K, it is possible to write
.
K=2f
~lm. (13 )
8
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Substituting in (13) the values of all paramet,ers, we find that in the
. variar.t discussed K= 50 to 300 . Even for values of f severalfold
_ lower than the maximum, it is possible to create on the basis of the sys-
tem r~~iRgested a ctiemical laser initiatzd by IR radiation with.an energy
gain not lower than 10.
= The analysis made makes it possible to conclude that ander conditians of a .
= Photon-branched reaction when both zhe absorbed and emitted phot~ns have
- the same frequency, the energy gain, K y for a single amplif.Ler stage will
lie within the range of 10 to 103. Even with three-stage amplificatiorr
the energy of the "start" pulse will equal only 10 3 to 10 9 of the outnut -
energy, i.e., the energy requirements for the master oscillator will be
very low. This makes it possible to talk about the self-contained nature
of pulsed chemical lasers utilizing a photon-branched reaction. _
Let us note that in analyzing the kinetic system the burnup of CH3F was
disregarded in the process of the chain reaction -
� F~-CH,F-� HF-{-CH~F,
- CHZF-{-Fz-. CH~Fa-{-F,
taking place concomitantly with chain (5). The time for the burnup
ef CH3F caused by this reaction under the conditions considered is greater
than 30 us, which is an order of magnitude lor.ger than the length of the
laser cliemical proce~s. ~
An additional contribution to branching of the chain can b~ n:ade by the
dissociation of vibrationally excited molecules of CH F formE~d in reac- _
tion (2), the thermal ef.fect of which equals ap~roximately 80 kcal/mol.e,
= and the si~are of dissociated molecules of CH2F2 under conditions of low ~
pressures (1 to 10 mm Hg) according to [15] Iies within tl~.e range of
(2 to S)�10 2. Although the dissociation of CH2F � at high pressures has
not been studied, taking this process into accoun~ only increases the es- _
timated value of the energy g~in.
Of importance is the question of the stability of a mixture of inethyl _
fluoride with fluorine. ~xperimental studies have demonstrated that the
process of self-coinbustion of such mixtures under conditions of low pres-
sures of the reactants is completely suppressed by dilution of the reac-
tants with argon. Even more effective for this purpose is the add:Ltion
_ to the mixture of C02 and 02 [15]. This makes it possible to hope to
achieve stability of a high-pressure working mixture of CH F-D -F -CO -
-He-O for approximately 10 min, which is sufficient for conducting a2
laser2experiment. And if Zongterm stability of the working mixture at
high pressures is not achieved, then ror the purpose of realizing the
laser chemical process discussed can be used a reactor wit~ rapid turbu-
- lent mixing of componen~s (over a period of about 1 ms) admitted to the
working space via an ar.ray of jets. .
9
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Bibliography -
l. Basov, N.G., Markin, Ye.P., Orayevskiy, A.N. and Pankratov, A.V.
DAN SSSR, 198, 1043 (1971).
2. Semenov, N.fi. Preprint of IKhF AN SSSR [USSR Academy of Sciences In-
stitute of Chemical Physics], Chernogolovka, 1975.
- 3. Igoshin, V.I., Nikitin, V.Yu. and Orayevskiy, KVANTOVAYA ELFKTRONIKA, ~
~ 3, 2072 (1y76). ~
~
= 4. Igoshin, V.I., Nikitin, V.Yu. and Orayevskiy, A.N. KRATKIY~ SOOB- _
S1iCHENIYA PO FIZIKE, FIAN, No 6, 20 (1978). `
5. Akinfiyev, N.N., Basov, N.G., Galochkin, V.T., `Lavorotnyy, S.I., Markin,
Ye.P., Orayevskiy, A.N. and Pankratov, A.J. PIS'MA V ZHETF, 19, 745
- (1974) . ~
' 6. Galochkin, V.T., Zavorotnyy, S.I., Kosinov, V.N., Ovchinnikov, A.A.,
Orayevskiy, A.N. and Starodubtsev, N.F. KVANTOVAYA ELEKTRONIKA, 3,
125 (1976).
"l. Balykin, V.I., Kolomiyskiy, Yu.R. and Tumanov, O.A. KVANT011AYA ELEK-
TRONII:A, 2, 819 (1975) .
- 8. Lyman, J.L. and Jensen, R.J. J. PHYS. CHEM., 77, 883 (1973). _
9. Belotserkovets, A.V., Kirillov, G.A., Kormer, S.B., Kochema~ov, G.G.,
Kuratov, Yu.V., Mashendzhinov, V.I., Savin, Yu.V., Stankeyev, E.A.
and Urlin, V.D. KVANTOVAYA ELEKTRONIKA, 2, 2412 (1975). i
- 10. P1ant, T.K. and DeTemple, T.A. J. APPL. PHYS., 47, 3042 (1976). ~
.11. McNair, R.E., Fulghum, S.F., Flynn, G.W., Feld, M.S. and Feldman, B.J. :
CHEM. PHYS. LETTS., 48, 241 (1977).
12. Weitz, E. and Flynn, G. J. CHEM. PHYS., 58, 2679 (1973). ;
13. Ambartsumyan, R.V., Gorokhov, Yu.A., Letokhov, V.S. and Makarov, G.N.
: ZHETF, 69, 1956 (1975).
14. Frankel, D.S., Jr. and Manuccia, T.J. CHEM. PHYS. LETTS., 54, 451 ~ -
(1978) . -
15. Fedotov, N.G. Author's abstract of candidate's dissertation, MFTI,
1978.
16. Bokun, V.Ch. and Chaykin, A.M. DAN SSSR, 223, 890 (1975).
_ 10
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= 17. Stephenson, .T.C. and Moore, C.B. J. CHEM. PHYS., 52, 2333 (1970).
COPYRIGHT: Izdatel'stvo Sovetskoye Radio, KVANTOVAYA ELEKTRONIKA, 1979
_ [83-88311 .
CSO; 1863
8831
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_ UDC ~35.313 =
PROSPECTS FOR EMPLOYING POROUS STRUCTURES FOR COOLING POWER OPTICS COM-
PONENTS ~
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 6 No 12, 1979 pp 2533-`1545
manuscript received 17 Aug 79
(Article by V.V. Apollonov, P.I. Bystrov, V.F. Goncharov, A.M. Prokhorov
and V.Yu. Khomich, USSR Academy of Sciences Physics Institute imeni P.N.
Lebedev, Moscow]
[Text] The result~ are given of theoretical investigations of processes of
heat and mass transfer in structures with an exposed void content, as well .
as the results of calculation of thermal and heat-strain characteristics
of laser reflectors designed on the basis af powder and metal fiber struc- ~
tures, for the purpose of creating optimal designs for power optics com- -
ponents. The method suggested for predicting the char~lcteristics of laser
reflectors based on porous materials makes it possible to determine the
optima.l type and parameters of a structure gudranteeing dissipation of the _
required heat fluxes with permissible values of distortions of the reflect-
ing surface. -
.
The feasibility of employing structures with an open void content for the
purpose of cooling heat-stressed laser reflectors was established for the ~
- f irst time theoretically and experi.mentally in [1,2]. An increase in the
thresholds of optical failure of laser reflectors based on porous struc-
tures is made possible by the creation of a"mi.nimum" thickness for the -
dividing layer (dozens of microns), the intensification of heat exchange
by means of agitation of the heat transfer agent pumped through the struc- _
ture, and the effect of considerable development of the suxface [3]. In .
[4y5J it was demonstrated experimentally that the placement of sp~cial
porous inserts in the tube makes it possible to increase (approximately ~
ninefold) the effective coefficient of convective heat exchange, which
according to [4] has reached about 22 W/cm2�deg.
The results of tests of water-cooled laser reflectors created on the basis
of structures with an open void content pointed for the first time toward
- the possibility of the dissipation of high heat fluxes with insignificant
amounts of strain in the reflector's surface; the maximum value of the
I2
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density of the dissipated heat flux not resulting in failure is q =
= 8 kW/cm2 ; with q= 2 kW/cm2 the amount of heat strain equa].s approxi-
mately a/20 , where a= 10.6 u[3].
A further increase in the threshold of optical failure for cooled reflect-
ing surfaces can be ach~.eved as the result of optimizing the parameters of
_ the porous structure, appropriate selection of the heat transfer agent and
intelligent design of the system for supplying and eliminating it. Devel-
_ opment of such laser reflectors of an "optimal" design requires a detailed ~
study of the processes of heat and mass transfer in porous structures,
which at the present time have been inadequately investigated. Let us
- discuss cer.tain aspects of this problem. ;
~ 1. Temperature Field in a Porous Structure with Convective Cooling ;
We will calculate the temperature fields in a porous structure in a unidi- ~ ~
mensional formulation with the following assumptions: The incident radia-
tion is uniformly distributed over the irradiated surface; the thickness _
of the porous layer, is considarably greater than the depth of heatingy
which makes it possible to consider it infinitely great and to con-
sider a modei of a half-spa~e; the temperature and rate of movement of the ~
heat transfer agent through the thickness of the porous layer are constant.
T}len the heat exck~ange equation describing the distribution of temperature ;
over the tt~ickness of the porous layer can be written in the form
~Z = ~ S~ (t-tT),
- (1) ~
where x is the coordinate, t and tT are the temperatures of the ma- '
terial (she~11) of the porous structure and the heat transfer agent, re- :
sPectively; h is the coefficient of heat exc~ange between the material
of the structure and the heat transfer agent; a is the she11's heat con- _
duction along axis X; S~ is the heat exchange surface per unit of
volume. -
i -
Equation (1) can be represented in dimensionless form:
dae = N (0-1), � I
dz' ~
. ~2~ ,
ti i
wkiere 0= t/tT , x= x/ds and N= NuN' are the dimensionless tempera- _
ture, coordinate and parameter, respect,~vely; ds is the mean dia~eter of
particles of the structure; I~u = h d/a is a modified Nusselt number
characterizing the relationship between convective cooling and heat trans- ;
fer on account of the she11's heat conduction; and N' = SVdS is a dimen- '
sionless paramefier characterizing the structure. ~ -
13 �
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The boundary conditions of equation (2) can be written in the follawing =
manner:
x=0; d6/dz=-Nu q x--? oo; 9--~ 1,
_ where q= q/(h tT) is the dimensionless density of the heat flux; and
q is the densi~y of the heat flux transmitted through the dividing layer.
- The solution to equation (2) with the boundary conditions in (3) has the
f orm -
6(x~ =1 1- q Y:V u/N' exp N x~. -
(4)
From (4) it follows that the rate of .the drop in temperature through the
thickness of the porous structure is determined by the parameter ?~N .
Let us write out some relationships needed later for the purpose of calcu-
lating the thermal characteristics of lasPr reflectors. The temperature
of the dividing layer a~ the boundary of contact with the porous base
(x = 0) equals:
6p=1 +q Fiu/N'�
(S)
- The maximum density of the heat flux eliminated from the reflector in the _
convective cooling mode, from the condition for the equality of 0 and
the boiling point, 0, of the heat transfer agent, at the appropriate
pressure (0 ti 0 ) equals:
r- s
9~8:= ~68-1) N~~Nu, . (6)
= The degree'of intensification of heat exchange in a porous structure as
the result of agitation of the flow and development of. the surface is de-
termined by the coefficient K. , which charact~rizes the ratio of the
amount of heat dissipated by t~ie heat transfer ,agent in the structure con- _
sidered to the amount of heat which would be dissipated directly from the
cooled surface of the dividing layer by the heat transfer agent when flow- ~
ing in a slit channel of depth A:
- KA8=9~he~tx~o tT)~
where h~ is the coefficient of convective heat exchange when the heat `
- transfer agent flows in a slit-type gap of magnitude ~[6]. For example,
for a turbulent mode of flow of the heat transfer agent ~he equation for
determining the Nusselt number, Nue , has the form
14 ,
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Nue=0,023 Reo,epro,a~
where Re and Pr are the Reynolds and Prandtl numbers.
~ Let us introduce the coefficient of the intensification of heat exchange
- on account of agitation of the flcw, k,r = h/h , where h is calculated -
from the condition of constancy of the ratesof~flow of thesheat transfer
- agent circulating through the reflector. Then K, , depending on the type
and parameter~ of the structure, as well as on thenthermophysical proper-
ties of the heat transfer agent, is computed thus: _
K.,A=KoKT, ~ -
where K~ = q/hs(t- tT) _(N'/Nu)1~2 is the fin-effect cooling coeffi- -
cient of the coole~ surface of the dividing lay~r.
From equation (4) we find the depth of heating of the structure, determin-
ing the minimum possible thickness of the porous layer, assuming by a con-
vention that heating terminates at coordinate x/d , where the tem-
peratures of the shell and heat transfer agent differ ~by one percent:
~=N-%=1n 102q (Nu/N')'~=. ~8~
In the case of dissipation of maximum densities of heat f.lux the depth of
heating equals
, Omaz=N-'/= In lOZ (~e 1).
(9)
Thus, the equations obtained, (4) to (9), make it possible to calculate the
heat fields and thermal cb.aracteristics of cooled laser reflectors. In
combination with expressions describing the hydrodynamics of the flow,
they are the basis for optimizing the parameters of porous structures en-
suring minimum heat strains in the reflecting surface, or, if this is
necessary, the maximum heat fluxes dissipated in convective cooling.
2. Convect3.ve Heat Exchange in a Porous Structure
The mode of flow of a heat transfer agent in porous materials of interest
for power optics is an intermediate one between the laminar and developed
turbulent modes; here calculation of the coefficient o~ heat exchange be-
tween the shell and the heat transfer agent is very difficult in spite of
numerous experimental data. The most complete survey of experimental in-
vestigations of heat exchange in porous materials, chiefly for gaseous
heat transfer agents, is given in [7], where in addition to dimensionless
~ 15'
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- equations for calculating heat exchan~e coef~icients are presented a
procedure for processing experimental data and a form for the representa-
tion of decisive dimensionless numbers. -
But the lack of a unified agproach to processing experimental resul~~s and
the impossibility of a precise determination of such important charaTter- _
istics as Sp, d , etc. hinder the employment of the equations in [7]
for calculating t~ie heat exchange of trickling fluids in different types
of po.rous structures with ~eometrical parameters varying over a wide range.
_ Therefore these relationships can be recorumended.only as a first approxi- _
mation.for calculation of the volumetric coefficient of heat exchange in �
- ~tructures identica~ to the e~erimer..tal, and as applied.to gaseous cool-
- ants.
It has becom~ generally acknowledged that the dimensionless equation for
intrapore convective heat exchange for gases and trickling fluids has the
form [7] -
j Nu=c (Re Pr)R,
- (10)
wher.e c and n are constants depending only on the structural character- ~
~stics of the porous material. -
Based on the experimental data in [7-10], we made an analysis of the depen-
dence of c and n on the structural characteristics of porous materials
for which the latter were known with sufficient certainty; it was estab-
lished as a result that c and n depend chiefly on the volumetric void
content, P~ .
- Thus, equation (10) for the dimensionless Nusselt number taking into ac- -
count the correlation expressions c(Pp ) and n(PV) makes it possible
to calculate the ~oefficient of convecfive b:aat exchange in a porous ma- -
terial.
- 3. Hydrodynamics of Single-Phase Flow in a Porous Structure
The temperature field and heat straining'of the reflector are determined
to a considerahl~ extent by the rate of flow of the heat transfer agent
pumped through the porous layer, and this rate depends on hydrodynamic -
characteristics and the conditions for supplying and discharging the heat
transfer agent. A great number of experimental studies, a survey of which
is given in [7,8], are devoted to an investigation of hydrodynamic charac- -
teristics in the flow of a single-phase heat transfer agent in porous ma-
terials, chiefly in the region of P< 0.5 . The equations suggested by
different authors can be used ~or the calculation of the hydrodynamics of .
a flow in materials having a structure identical to that of the models.in-
vestigated. .
Generally the hydrodynamics of a flow in porous materials are described by _
a modified D'Arcy equation (a Dupuit-Reynol3s-Forcheimer equation [11-13]):
16 _
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- ~ = a�u ~pu2,
(11)
wriere p is the pressure of the flow; u is the filtering rate, equal to ~
- the ratio of the unit bulk rate of flow of the heat transfer agent, V, to _
the density, p; a and R are the viscous and inerti.al drag coeffi-
cients, respectively; and u is the coefficient of dynamic viscosity of
. the heat transfer agent.
- From equation (11) we get the equation for the coefficient of frictional
drag, Cf , in the form
Ci=2/Re-~2, ~12 ~
where Cf =-2(dp/dx)p/G2S and Re = G~/ua (S/a is the characteristic
dimension).
The practical utilization of equation (12) for the p~~rpose of calculating -
- the hydrodynamics of a flow in different types of porous materials whose
structural characteristics vary over a wide range is difficult because of
- the lack of necessary information on coefficients a and R, which as a
rule are determined experimentally.
In [14] is given a somewl:at different approach to the calculati.on of Cf :
Selected as the characteristic dimension xs where K is the pene- _
trability factor characterizing the hydrodynamics of the flow of a stream
in the D'Arcy mode (Re~ = G~/u); then
Ct = 2 ~1/ReyK c~/c. (13)
The relationship between coefficients a and S and~Parameters c and
K can be represented in the form a= 1/K , S= c/~K .
- As demonstrated in [14,15], parameter c is a univercal constant for por-
~ ous structures of the same type, e.g., for all ma.terials made of inetallic
` powders with particles of spherical shape or close to it, c ti 0.55 , and
for materials made of powders of random shape, 0.45 < c< 0.566 . There-
fore, below in calculating hydraulic characteristics of structures we will -
assume that c= 0.55 , although in our case this gives a somewhat too , ~
high value of the coefficient ot friction.
Studies conducted with fibrous materials, foam plastics and structures
consisting of layers of particles of random form [14,15] have demonstrated
17
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that parameter c for them is relatively low. This is exp].ained by the
fact that c, characterizing the percentage of inertial losses, depends
chiefly on the nature of the wake formed behind solid particles when
- streamlined by a f1ow, and the wake is determined b~ the type of porous _
structure. -
The presence in ~etal fiber structures of free ends which additionally -
agitate the f~ow results in an increase in c; thus, for relatively sh~rt _
= fib~rs, JC/d = 50 to 100 and c ti 0.132 [14].
The penetrability factor, K, being a structural characteristic of a porous
material, does not depend on the conditions of flow and is determined ex-
perimentally from D'Arcy�s law. In connection with the development of _
, studies in the area of heating pipes at the present time, thPre is a suf-
ficiently great number of experimental data for determining K both for -
powder and metal fiber structures [8,16].
From the experimental data in [17J the dependence of the penetrabili*_y fac-
tor of inetal fiber structures on the volumetric void content has the form:
K=AII~ , -
(14)
~ahere A and m are coefficients depending ou the relative length of
fibers, Q/d [16]. Similar expressions can be obtained for powder mater- _
ials, too.
- In addition, the penetrability factor is calculated from the well-known
Karman-Kozeny equation:
K=~II~ds/(1-I1v)z~IIy/5S~ ,
(15) _
_ where ~ is a constant depending on the structure.
The equations presented, (13) to (15), have been used for determining the
hydraulic characteristics of power optics components designed on the basis
_ of porous materials made of inetal powders and metal fiber structures. -
4. Influence of Conditions for Supply and Discharge of Heat Transfer Agent
on Hydraulic Characteristics of a Reflector
Usually in cooled laser reflectors the supply and discharge of the heat ~
transfer agent for the porous structure are carrie~ out via staggered
channels evenly distributed over the cooling sur~n~:., which are made in the
form of slits or holes. With the slit form of delivery are made possible
a more uniform velocity field for the heat transfer agent and a minimum
- drop in the pressure required to pump it, and with supply and discharge
of the staggered hole variety there can take place considerable nonuniform-
ity of the velocity field with spreading of the flow in radial directions.
18
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This results in considerable losses of pressure in circulation o,f the heat
- transfer agent, which are taken into account by coef.ficient Kg ; in this
case the total pressure drop in the porous layer equals
_ ep=opK~,
(16) -
_ where ~p is the pressure drop with a uniform velocity field.
On the assumption of uniform injection (flowoff) of the heat transfer agent
in radial directions in delivery (discharge) zones bounded by the region
rn< r< s/2 (where s is the spa~ing between staggered holes and r~ is -
tFie radius of the hole), coefficient K characterizing the influence of
_ collector effects on hydraulic drag in ~ovement of the flow in a porous
layer can be represented in the form:
F cG (1 /a - 1) /nnps~ -(v/'j/~ ln a
K~ nsan (1 - a) v/ 1~ cv .
(17)
Here G is the bulk rate of flow of the heat transfer agent; F is the
area of the irradiated surface; n is the number of channels for supplying -
(discharging) the heat transfer agent; and a= 2r0/s is the relative
spacing between holes. It is obvious from (17) that K depends both on
the geometrical characteristics of the system for delivering and discharg-
ing the heat transfer agent (on a) and on G; with an increase in a
and G coefficient K increases. Thus, K characterizes the structural
ideality of the systemgfor distributing and ~ollecting the heat transfer
agent of a coo~.ed reflector. ~ _
With known K the total pressure drop in the porous layer is calculated
- from equationg(16) taking into account the following expression for the _
calculation of ~p :
~p = vps (1-a) (vI~I( ; cv)/jrK,
_ (18)
where v= Gs/(PF~) is the filtering rate of the heat transfer agent.
5. Heat Conduction of a Porous Material ~
As applied to questions rel.ating to the cooling of power optics components,
it is of interest to investigate the shell heat conduction of a porous ma-
terial without taking into account the heat conduction of the heat transfer
agent pumped through. In [8,17] are generalized the results of numerous
experimental investigations of the heat conduction of materials of differ-
ent structures and it is demonstrated that the effec~ive heat conduction
depends not only on the volumetric void content, but also or. such factors
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as the material's tendency to cake, ti:e size and shape of the original
particles, the technology for compacting and sintering, etc., which re-
sults in a wide variance of data and hinders the generalization of re-
- sults.
ti
In practice data are generalized in the form of dependences a(PV) for
samples made according to a unified technology from the same type of ma-
terial. An analysis of experimental results has shown that for the purpose
of calculation over a wide range of values of the void content of powder
materials can be used Odolevskiy's equation [8]:
7~=~,x(1-IIv)~(1-~-IIv). (19 )
where ak 'is the heat conduction of a compacted material.
The effective heat conduction of inetal fiber felt structures can have con-
siderable anisot~opy depending on the 3irection of fplting. Thus, on the
basis of [17], a is generalized by the following equations:
, ~=~.x(1-IIv) exp (-IIv), (20a)
7~=~.~(1-lIp)'.
(20b)
ti
where a is the effective heat conduction in directions parallel (20a)
and perpendicular (20b) to the felting plane. In the latter case can be
used the equation
7~=?.~(1-IIy)'. ( 21)
Equations (20b) and ('ll} satisfactorily approximate the experimental data
and can be used in determining the thermal characteristics of cooled laser
reflectors designed on the basis of inetal fiber structures. Here equation
~ (20b) describes the upper limit of e~erimental data (the optimistic esti- .
mate) and ~21) the lower (pessimistic estimate).
6. Estima.tion of the Amount of Heat Straining of the Optical Surface
Generally, the heat strains of a reflector are calculated from the tempera-
ture field of the dividing layer and the porous base and the known condi-
tions for fastening them. A precise solution to this heat strength prob~-
lem under real conditions of the irradiation of a re~lector presents great
difficulties.
For the purpose of estimating slight distortions of an optical surface
_ characteristic of straining of power optics components, it is possible to
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make an assumption regarding the free expansion of the porous base and
dividing layer in keeping with the temperature fields. Then the heat
straining of a reflector surface, jd , is the sum of the expansions of the
dividing (thickness of Ar) and porous (thictcness of layers:
IV=apOptTli~z 191-i-Oz)-6o1-{-a�OtTI(1-6o)-f-qd,~(N~~)], ~2~~ ~
where a and a are the temperature coefficients of linear expansion
of the d~viding a~id porous layers, respectively; Oi = Ti/tT is the
dimensionless temperature; t~ is the temperature of the heat transfer _
agent at the inlet inta the reflector; and tt and t2 are the tempera-
- tures of the outer and inner surfaces of the dividing Iayer, respectively.
- From equation (22) it follows that the higher the rate of flow of the heat
transfer agent (0~ } 1), the lower is W. Maximum strains of the optical
surface are realized in the area of drainage of the heat transfer agent
from the porous layer, whereby the amount of heating of the heat transfer
agent when it is supplied through slit-type channels is
OtT=QFIGCT,
where CT is the heat capacity of the heat transfer agent.
i. R.e~ults of Calculations of Thermal Characteristics of Reflectors
The equations arrived at above, describing the processes of heat and mass
transf.er in a porous structure, were employed by iis for the purpose of cal-
culating the characteristics of cooled laser reflectors with a system for
- supplying and discharging the heat transfer agent in the form of evenly
(with a spacing of s) staggered holes; the distribution of the heat load
over the surface of the reflector was assumed to be uniform.
~
Tn fig 1 is given the qualitative dependence of straining on the maximum
_ density of the dissipated heat f1L: (variable PV with constant d)
f:or two isolated zones of a reflector corresponding to regions for ~he
injection, W1(q~X) , and outflow, W2(q~X) , of the heat transfer agent.
By varying tFie mean size of the grain, v,(or the diameter of~the fiber),
it is possible to plot a family of curves characterized by a constant
value of d and a variable void content, P, for reflectors with an
identical type of capillary structure. The curves are plotted upon the
condition of constancy of the pressure drop of the heat transfer agent and
taking into account its heating in the porous layer, and the temperature of
the heat transfer agent at the inlet is assumed to equal the temperature ;
of the final finish ot the reflector.
Straining of the optical surface in the zone of outflow of the heat trans-
fer agent equals W2 > Wl ; therefore, of decisive significance for selec-
- tion of the structural c~iaracterist3.cs of a porous material is curve 2,
and the difference between curve 1 and 2 characterizes the degree of
- 21
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- ideality of the cooling system. These curves represent envelopes of the
working heat strain characteristics af a family of reflectors with a -
specific type of structure.
W
2 1)
n~
~
i
~n {
N/.
~
I
i
� I
b n�~ i � -
I ,
~ I ~
o ~ "-O� ti
�Q Qnp2 2~ Q~P~ Q
- Figure 1. Qualitative Dependence of Heat Straining on Maximum
Density of Dissipated Heat Flux for ~o Zones of a
Reflector Corresponding to Regions of Injection (1)
and Outflow (2) of the Heat Transfer Agent
Key: ,
1. PV 2. qPr2
The working characteristic of a reflector with a predetermined void con-
tent of the structure, PV , is obtained by connecting by ~ straight line
point C with the origin. Point C corresponds to the maximuin density of _
the heat flux dissipated in the convective cooling mode, and straight line
segment OC rE~presents the dependence of heat distortions of the reflecting ~
_ surface on thc heat load. , ~ '
= Generally on curve 2 it is possible ~o isolate two points: A, correspond- -
- ing to the optimal void content, P�p1 , with which is ensured the dissipa- _
tion of maximum densities of heat ~Iux for a selected grain size, pressure
drop of the heat transfer agent and conditions for supplying and discharg-
- ing it, and B(the point of contact of curve 2 with the straight line ~rom ~
the center of the coordinates), corresponding to the void content, PVp2 ,
with which for a specific porous structure are realized optimal heat dis-
tortions of the reflecting surface.
Selection of the material and key parameters of the structure (d and P)
_ should be done on the basis o~ comparing family of curves 2 withs V -
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opportunities for producing porous materials of the required structure and
for creating the dividing layer with therr..
~ a - - - n~ - 900~0- T ,---~---~---r-- , .
- 1.. 80 ~ I ,
~ 70 I ` i ~ -
~ ~1,9\ \\~BD 1\ I 6D 50 4DI � ; j I -
~ ~
~ ~ ` 3p _ T ,
0, 3 ~ 7D~ ' : ` 1n . _ ; -
~ 90~~~\', ~10~ 60^~5D~~~40 i i I
~ , 8~J i ~r~.~-~.~~!` ~ . ~ ~
- ~ ZD~~C 120 ~p\~'~ ~ ~ ; I ~
_ ~ i `\60j~~'~'~5D ; ; ~
~ 90 `u
9~~__~
o p
~40~ ~ ; ~ , ~
0.1 ..-7Ci B0~ ~~~~6Dj 50 ~ -
~ ' ~ .
~ i1U ` ~'-~~i~ 60 I
- ~ ~90 3 ,i0 yp , a ' _ 60
I I~~ ~ 3D ; ~ 4D 7U ' S0 50 j ~
~ ~
1 ~
_ p, , , i ~ ' I i I
p 1 2 3 4 S 6 7 B 9 lU 11 11 13
a)
I - - - ( - - f-
5
~ , I I
r 1D ~
4, 0 ~p ---Y - -.1_ _ ~ - I
, ;
I
- 3~5 ! 1D3Q~4050 , I .
Z 10IOr 50 60 I I
z ZO 3 ~ ~ o , ; I
U'~ ~2D o 70 ' ~ ~
~~~3D I SD ~ -
2.5 ~ ~ 4D \ ~
! ~3D \ ~ o ~ 70
~ ! 30 ~ B~
2' ~ ' 4D ~ 5 : ~
! i ~4 j ; 70
~ ~ ' ~ 50 ~ �BO
i i ' 5D ~
I ; 70 90I6 60 ,BD
. a 9~
i ~ 8D '80 0
' i BO -
D, 5 n~~90%
90 90 ' ' 90
` 0 QS 1,0 1,5 2,0 1,5 3,0 3,5 4,0
b)
[Continuation and caption on following page) '
23 -
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O,1D ~ - ~ .
~ i
~ i
- ~ ~
_ qa9 - i o ~
~ n~=20 / ;
QOB ' 70 'S0 4D ' - - - � -
� ~ Dx ~D' ~
~ ~ ~ ~ ~ ~
407
~ ~ ~ `,7D~~ i~~~5D40
Q06 D~' , t~`'~�'.
F~ ~
05 ~.?d`?~ .~a.~`,6~5p' ;
Q o-.�.-, a?' ~~~7D~ -
10 ~ ' � ti, 70
a04 5 ~ ~
0 1 T 3,~ 5 6 7 B
C
1,1 ~p -r----- - T- - ~ -
. 0~ - I i
1,0 ~ 40 ~ - - ~ .
50 ~
- ` ~ ; ~ i
49 L-- - '
TO ~ ~ ~ ~ 60
~ ~ .i
qB 40 ~ ` -
i 20 ~ 30`~~`~\\ I~ 60 '
p ~ 20 ~ �
5I \
a6 \ ~~3 ~ 40 ~ ~
~ o --t--
~ ; ~ ~
~ ~ ~ ; ~ 7D
0,5 ~
_ I i 4D 5D~ ND
i
0,4 ' ~ ~ ~
I + 50 ~ � BD ~ .
Q3 ~ 50 6~
. ~ 906D~ p ~
Q2 -
~.9a ~ ~ ~o _
90 ~ BO i ~ -
41 nv'~ 90 ~ i ~ _
; '
0 QS f,0 1,5 2,0 1,5 3,0 ~
-
Figure 2. P:o~ograms of Heat Strain Characteristics ~or a Family of
Water-Cooled Reflectors Based on Porous Structures Made
fr~m Copper (a and b) and Molybdenum (c and d) Powders for
the In~ection Zone (a and c) and Discharge Zone (b and d)
[Continued on following page]
. 24
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- The puints in this and remaining figures correspond to the -
following diameters of particles or of the felt: white dots-- ~
20, black squares--30, white squares--50, white triangles--
- 100, black triangles--150 and white dots [as published]--200
microns
lly~10 0 ~ 010
- 1~ I ~o
- ~
D,y 10 .l ~ ~ 3~5~ lOD3
~ 50 4D ~ ~ I iD ~ ~ j
ZD
I ~ 50 60 ~ 50 ZO i ( 1 I Q o 40 5 , , _
~ I I~ ~ Z ~ j ~ ~ ZO 3a'~ 40 ~
BO 70e~ ~ 2D 40 3~I I ~ 15 I 2D ~50
~ 3 r- ' 6D ~
BD~ I10 70~c-~"~50 3D 4'0 ~ 10 0 ~ -
90 BO o�' ~ ~ i JD ~ ~
o~ ~ ~ I ~ ?,p ~ 50� 6D
_ y~o~ � I8D o~ ~50 ~ I , I~0 ~3D _
R 90 I~~ n ~ , ~,5 ~_70
? D d 70 I 4D
~ i 9 q~~ g � ~ �7
~~5D60 i i ~ Q7 0~ -
90 ( ~ 30 4~ 50 i ~,0 I I 6D Bp 6D SO
~ 7D oB ~6
� D,1 0, 5 , B0~-BD 70 B -
0 1 1 3 4 5 6 7 g� v=90% c BO
_ a~ 90 9
p 90 90 BO -
D 0,5 1,0 1,5 7,0 b~ 7,5 3,0 ,~5 4,0
[Continuation and caption on following page]
25
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l{14 !~,-lOX
q~
4a
Qll 10
q1
; .
' 2a
a ~ 3n
~ u,~~~o
~ f0 SD SSD `
I
a~ � TpQ
~ ~ -
~ 0
SUgp d O
~ ~ ap 4p70 50
/1~=90x ~
- ~ f. 1. 3 4 S B 7
c) .
. ~ � ,
_ 'r 0 ?D~U
a 9 IQ 40 _ I -
i 3p I ; ~ ~
a8llr=lOt 405
0 I i
~ q ~ ~ - ~
' ?D SD' '
q6 ~ 6D !
_ as ~ -
_ ,
_ q4 65Q ~
~ I
_ ' ~ D -
, yo ~
� � 7D 60
q2
~B SD i
B 7D~ ~ 060 i i
a~ yD_~~0 BO 70 BO
9To~
0 o,s ~,ad~ ,s 2,a z,s ,~o -
[Caption on following page]
26 ~ ~
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~
- Figure 3. Nomograms of Heat Strain Characteristics of Family of _
Water-Cooled Reflectors Based on Poruus Structures Made
from Copper (a and b) and Molybdenum (c and d) Felt,
for the Injection Zone (a and c) and Discharge Zone
(b and d )
Key: !
1. PV = 10 percent . ~
In figs 2 and 3 are given the results of numerical calculations of the
- heat strain characteristics of a series of water-cooled reflectors with -
porous structures made from the widely used copper (fig 2a and b} and ~
molybdenum (fig 2c and d) powders, illustrating the capabilities of the -
method. The mean grain diameter and volumetric void content varied over
the range of 20 u< ds < 200 u and 0.1 < PV < 0.9 . ;
From fig 2 it is obvious that the limiting densities of heat flux equ~led:
in the zone for supplying the heat transfer agent, q~l = 12.8 kW/cm ,
and in the zone for discharging it, qPr2 = 3.75 kW/c~i , whereby W1 = i_
= 0.1 to 0.4 u and W= 0.4 to 3.5 u. In the region of maximum densi- ~
ties of heat fluxes W
22 = 1.5 to 2 u, which in the majarity of cases is
substantially higher tFian the maximum permissible straining of reflectors '
for C02 lasers. ~
With an increase in the rate of flflw of the heat transfer agent (fig 2b) '
W2 can be reduced drastically by using ma.terials with a high volumetric ~
void content (0.7 to 0.8) and by changing to a larger grain size. Here !
q ti 2 kW/cm~ with W= 0.5 u ~ The creation of structures with P>
~m~x~5 frcm powder materials while observing the necessary requirements ~
for power optics is very difficult. With a reduction in void content to
realistic values of approximately 0.6, the dissipated densities of heat
- flux with deformation of approximately 0.5 u equal approximately 1.4 ;
kWJcmz . Let us note that an increase in the rate of flow of the heat
transfer agent is achieved also by means of an intelligent design for the " I
cielivery and discha~ge ~;Gt2m to ensur;: a more unit~im distribution of the ~
heat transfer agent over the cooling surface. ,
It is obvious from fig 2c and d that the employment of porous molybdenum
makes it possible to reduce approximately fourfold the level of heat
sCrains of the reflecting surface both in the first and in the secor.d zones, i
whereby q is somewhat lowered: q = 7.8 kW/cm2 and q = 2.8
kW/cm2 .~or this structure (fig 2c)pw~th the realization ofpmaximum dis- !
sipated fluxes the heat strains which originate lie below the characteris-
tic optical failure thresholds o~ reflectors for COZ lasers. For example, ;
a structure with P= 83 percent and d= 20 u enables dissipation of
q = 2.8 kW/cm2 ~aith W= 0.4:i u. Wi~h an increase in the rate of
f'~ow of the heat transfer agent (fig 2b) , W2 W1, but q~ is thereby ~
rpduced. In this regian the level of dissipated Fieat fluxes can be raised
~
27
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. ~
_ as the result of using materials with larger grain sizes; for example,
a molybdenum powder structure with Pv = 60 percent and vs = 20 u
makes possible dissipation of q~X = 2.1 kW/cm2 with W= 0.23 u.
In fig 3 are presented the heat strain characteristics of reflecr;~rs with
porous structures made from copper (fig 3a and b) and molybdezium 3c
and d) felt. It.is obvious from fig 3a and c that a change%?ver to`~~etal
fiber structures results in a substantial (approximately ~.7-fold) reduc-
tion in q , which is related to the reduction in the effective heat -
conductionPof these structures as compared with powder structures.
In zones for discharge of the heat transfer agent (fig 3b and d) the limit-
_ ing densities of heat flux lie at the same level as for reflectors with
powder structures, but an increase in the rate of flow of the heat trans-
, fer agent results in a stronger dependence of W on P and in lower sen-
sitivity of W to the diameter of the original fibers.V Here strains
corresponding to q prove to be approximately twofold less than with
_ powder structures: p~or reflectors made of copper W= 1.2 u with q =
= 3.9 kW/cm1 and of mol bdenum W= 0.3
, y , u with q_r = 2.6 kW/cm2 Pr
_p
For reflectors with a copper fiber structure the densities af heat flux
which can be realized with W= a/20 (where a= 10.6 u) equal 2.4
kW/cm2 , which is higher than the corresponding level of for powder
materials. Thus, the emplo}rment of inetal fiber structures ~or the purpose
of creating on their basis power optics components is quite promising;
for example, for a structure made of malybdenum fibers with a diameter of
- 100 to 200 u and a void content of 50 to 60 percent, = 2.2 kW/cm2
with W ti 0.15 u; in addition, the possibility of producing materials with
, high values of P= 70 to 80 percent makes it possible to create optimal
- designs of reflec~ors.
8. Comparison of Theoretical and Experimental Results
We compared the results of a calculation of heat straining of the reflect-
ing surface of a laser reflector based on a porous material made out of a
copper powder with the experimental data in [3]. -
In fig 4 are given the results of experimental investigations of heat ~
- straining of a water-cooled reflector as a function of the density of the
dissipated heat flux, as well as the results of a calculation of maximum
heat strain characteristics in the zone o,f discharge of the heat transfer -
_ agent for a series o~ reflectors with a void content~of 55 to 70 percent. ~
The straig}it lines represent calculated character~stics of the tested re-
flector for extreme void content values of 60 and 62 percent. It is ob- -
vious that there is good agreement o~ the theoretical a~d experimental
data. `
_ In fig 4b is illustrated a calculation of the heat strain characteristic
of this series of reflectors in the zone of delivery of. the heat transfer
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i
' ~
~
_ agent, which, as occurred in fig 4a, was arrived at on condition of equal-
ity of the temperature of the cooled surface of the dividing layer to _
- 100�C. From fig 4b it follows that qmaX = 8 kW/cm2 , which is in good ~
agreement with the experimental data.
,
Wy~ MHN ~ _
3,D ~ d=s % ;
I 6D 6~
1, 0 ~o ~
~
- W~, MHM ~ _
1,D 0,2 ~
a~s Av-70%~-�
~ ~SS '
3
0 2 q,KBm/caz 7,0 8,0, $D= 4
, , , . , , , , , q, KBm/cM ~
- 0~ 3 ~ 7 8 qmQx, xBm/cM 2 b~
a
i
= Figure 4. Heat Strain Characteristics of a Series of Water-Cooled ~ i-
Reflectors Based on Porous Structures Made of a Copper
Powder: Injection Zone (a) and Discharge Zone (b)
~ (black dots--theoretical; white dots--experimental)
i
Key: '
1. u 3. q, lcw/cm2 ~
2. P~ = 55 percent i
In conclusion, let us riote that the method discussed for predicting the ;
thermal and strain characteristics of laser reflectors based on porous ma- _
terials makes it possible to determine the optimal type and parameters of ~
a structure ensuring dissipation of the necessary heat fluxes with per-
missible values of distortion of the reflecting surface. The results of ~
_ theoretical and experimental investigations confirm that water-cooled laser i
reflectors with a porous structure have a high ~ptical failure threshold. ~ I
As new experimental data are accumulated on convective heat exchange and
on the hydrodynamics of flows in porous structures these can be incorpo-
rated sufficiently easily into the calculation algorithm. _
- ~ .
_ Bibliography ~
' l. Apollonov, y.V., Barchukov, A.I., Prokhorov, A.~. and Khomich, V.Yu. I
"Tezisy dokl. IV Vsesoyuz, soveshchaniya po nerezonansomu vzaimodeyst-
viyu opticheskogo izlucheniya s veshchestvom" [Theses o~ Papers at the ~
Fotirth All-Union Conference on Non-Resonance Interaction of Optical ~
. Radiation with Matfier], Leningrad, GOI, 1978, p 31. ~
~
I
i
29 :
i
; FOR OFFICIAL USE ONLY
- ~
, ~ -
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2. Apollonov, V.V., Barchukov, A.I., Borodin, y.I., BYstrov,
_ Goncharov, V.F., Ostrovskaya,~L.M., ~rokhorov, A.M., Rodin, V.N:,
Trushin, Ye.V., Khomich, V.Yu., Tsypin, M.I., Shevakin, Xu.V. and
_ Shur, Ya.Sh. KVANTOVAYA ELEKTRONIKA, 5, 1169 (1978).
3. Apollonov, V.V., Barchukov, A.I., Borodiu, V.I., Bystrov, P.I.,
, Goncharov, V.F., Ostanin, V.V., Ostrovskaya, L.M., Prokhorov, A.M.,
Rodin, V.N., Trushin, Ye.Ve, Khomich, V.Yu., Tsypin, M.I., Shevakin, _
Yu.F. and Shur, Ya.Sh. PIS'MA V ZHTF, 4, 1193 (1978).
4. Megerlin, F.Ye., Merfi, R.V. and Berles, A.Ye. TEPLOPEREDACHA, SER.
S, No 2, 30 (1974).
5. Polyayev, V.M., Morozova, L.L., Kharybin, E.V. and Avraamov, N.I.
IZV. WZOV, SER. MASHINOSTROYENIYE, No 2, 86 (1976).
6. Isachenko, V.P., Osipova, V.A. and Sukomel, A.S. "Teploperedacha"
[Heat Transfer], Moscow, Energiya, 1969.
7. Maqorov, V.A. TEPI,OENERGETIKA, No l, 64 (1978).
8. Belov, S.V. "Poristyye metally v mashinostroyenii" [Porous Metals in
Machine Buildingj, Moscow, Mashinostroyeniye, 1976. _
9. Keys, V.M. and London, A.L. "Kompaktnyye teploobmenniki" [ComFact Heat
Exchangers], Moscow, Energiya, 1967.
- 10. Lykov, A.V. "Teplomassobmen" [Heat and Mass Exchange], Moscow, -
Energiya, 1978.
11. Dupuit, J. "Etudes th~oriques et pratiques sur le mouvement des eaux"
[Theoretical and Practical Studies on the Motion of Water], Paris,
1863.
12, Reynolds, 0. �1Papers on Mechanical and Physical Subjects," Cambridge
= University Press, 1900.
13. Forcheimer, P. "Wasserbewegung 3urch Boden" [Movement of Water Through
Soil], Z. VEREINES DEUTSCHER INGENIEUR~, 45, (1901).
14. Biverz, G.S. and Sperrou, Ye.M. PRIKLADNAYA MEKHANIKA, SER. YE, 36,
_ No 4, 59 (1969). ~
15. Biverz, G.S., Sperrou, Ye.M. and Rodenz, D.~e. PRIKLADNAYA MEKHANIKA,
SER. YE., 40, No 3, 12 (1973). .
16. Semena, M.G., Kostornov, A.G., Gershuni, A.N., Moroz, A.L. and Shev-
_ chuk, M.S. TEPLOFIZIKA VYSOKTRH T~ERAT[JR, 13, 162 (1975). -
30
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- 17. Semena, Pi.G., Kostornov, A.G., Zaripov, V.K., Moroz, A.L. and
Shevchuk, M.S. INZH. k'IZ. ZHURN., 31, 581 (1976).
- COPYRIGHT: Izda~tel'stvo Sovetskoye Radio, KVANTOVAYA ELEKTRONiKA, 1979
[83-8831]
CSO: 1862
8831
_ ~ 31
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UDC 621.375.826
RELATIONSHIP BETWEEN TEiE STATISTICS OF LASER DAMAGE TO SOL3D TRANSPARENT
MATERIALS AND THE STATISTICS OF STRUCTURAL DEFECTS
- Moscow KVANTOVAYA ELEKTRONIKA ir~ Russian Vol 6 No 12, 1979 pp 2590-2596
manuscript received 6 Apr 79 _
~ [Article by Yu.K. Danileyko and A.V. Sidorin, USSR Academy of Sciences
Physics Institute imeni P.N. Lebedev, Moscow]
fText] The problem is discussed of the statistics of bulk laser damage
- under the effect of focused beams. A new method is suggested for an ex-
perimental determination of th~e defect distribution function from failure
thresholds in the low-threshold region. The method is tiased on an investi-
gation of fluctuations in the distance from the focal point of the lens ~o
~he fracture most remote from it. Experiments are performed on single
_ crystals cf silicon and gallium arsenide by utilizing the radiation of a
.pulsed CO2 laser. A concl~sion is drawn regarding the applicability of
the procedure to investigation of defects of condensed media.
1. Introduction
As is known, real optical materials possess a considerable amount of dif- -
ferent kinds of structural defects af the foreign-phase inclusion type,
cluster-type pile-ups, inhomogeneities in composition, etc. [lJ. These _
formations can initiate laser failure and result in considerable lowering
- of the threshold. The concentration of these defects even in highly pure -
, and ideal materials can be high--right up to.109 cm 3[1,2]. It is pre-
cisely the existence of such high concentrations of defects which results -
in the fact that high failure thresholds (1010 to 1011 W/cm2) character-
istic of critical failure mechanisms are realized only in volumes of ~
approximately 10 1U to 10 9 cm3. With an increase in the extent of inter-
action between high-power electromagnetic radiation and the material there -
occurs a lowering of the failure threshold, associat~d with an increase in
the probability of inclusions with a low failure threshold entering the
interaction region (the so-called dimensional effect) [3]. This reduction
depends on the features of the defects present in the opttcal material and -
can vary noticeably from sample to sample.
32
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_ Questions relating to predicting the laser resistance of materials con-
. taining inhomogeneities are complicated for two reasons. Tirst there is
the almost total absence of inethods of determining the dimensions, struc-
ture and chemical composition of microdefects. Second there is the im-
possibility of constructing quantitative theories of laser failure without
- complete information, including statistical, on the magnitude and mechanism
of the absorption of light radiati~n in the -region of inhomogeneities. It
is precisely for th3.s reason that it is of interPSt to investigate the sta- -
tistics of laser failure. This interest is based not only on obtaining
statistical data on the failure thresholds of a material, but also on the
possibility of obtaining information on the mechanism of failure and the
characteristics of defects.
Since the statistics of laser failure in defects are determined totally by
- the distribution function of threshold intensities of failure, f(I) , the
purpose of this study has been to develop methods of investigating it ex-
perimentally. Knowledge of function f(I) in the region of high intensi-
ties is important in connection with explaining the role of critical mecha-
nisms (cumulative or multi-photon ionization) in the failure of transparent
materials. Meanwhile the form of function f(I) in the region of low in-
tensities determines the real optical strength, i.e., not the local failure
threshold, but the threshold characteristic of a large volume. In this
study we will be interested only in the low-threshold portion of distribu-
tion function f(I) .
2. Choice of Investigation Procedure
Let us consider an optical material containing dPfects randomly distributed
_ over its volume. Let each defect be characterized by its own failure
threshold. In this case under the effect of laser radiation~the morpholo-
gical pattern of failure will have the form of individual foci the local
- concentration of which is determined by the intensity of radiation and the
~unction for the distribution of defects by failure threshold. However, -
it proves to be impossible to determine its form by the direct measurement
of the concentration of failures, since the spatial distribution of the
' intensity of radiation in the interaction region is unknown. This is asso-
ciated with the unknown law for the attenuation of radiation in the direc-
tion of propagation resulting from screening by the failures which occur.
Actually, as our experiments have demonstrated, in focusing the radiation ~
of a C02 laser with power approximately an order of magnitude greater than -
the threshold onto the bulk of a sample of silicon, in it originates a re-
gion of failure measuring approximately 10 ~ cm3 and containing about 100
individual microfoci [4]. In spite of the fact that the intensity result- -
ing from focusing should have increased as the focal point was neared, the
- reduction ~n the concentration of microfractures in the direction of pro-
pagation testifies to the opposite. ~his has been confirmed also by the
strong "cutoff" of radiation passing through the sample.
33
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- Thus, information regarding the distribution function of defects in terms
oE the failure threshold can be obtained only from magnitudes not aub~ect
to the influence of the "cutoff." As such a magnitude we will employ the
- distance from the focal.point of the lens to the seat of failure at the
- maximum distance fram it.
- 3. Theoretical Analysis
Let a cylindrical beam of power P with a uniform distribution of inten-
sity, I, in terms of cross section be focused on a medium containing
structural microdefects with a concentration of n and distributed ran-
domly and independently over the bulk of the sample. We will assume that
a great number of defects (Vn � 1) are contained in the region of inter-
action discussed, of length ~0 , and having in c~ur case the shape of a
cone (fig 1) with a volume equal to V=(1/3)Az (A =~r tan2 a aud 2a
is the angle at the apex of the cone). If it i.s~assumed that each of them
is characterized by its own threshold degree of failure, then it is pos-
sible to introduce function f(I) , representing the distribution density
for the magnitude of th~e threshold intensity and normalized in~the follow-
ing manner:
m
~ rf~l)d~=no� ' '
� o . .
.i .
~ ~Z ~ Z' 0
~ . ~ 70
I
- i
,
Figure 1. Geometry of Focusing of Laser Radiafion
In this case P(z)--the probability that between cross sections z and
_ z0 there will occur but a single seat of failure--is determined by the
equation [5J: _
. _ , ~ ~x~
' 1- exp Axadx f f(l) d~
p ~Z~ ~ , : o .
1 exp ( -noV) _
(1)
34 ~
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I
I
i
Utilizing the fact that the intensity of light in cross section z can be -
written in the form I(z) = P~/Az2 , we rewrite equation (1) in the follow-
ing manner:
i
3/2 So/Az~ s I
1- exp - 2~ X~2 I~(~) d~ ~ I
P (z) - Sf~~0 ~ '
1-exp(-noV) ' ~
~2~ i
where S~ = P~/I~ = I f(I~~) I/I~ ; and I~ is some typical ;
value of intensity in the dis~ribution f(I) , e.g., the mean or most pro- i
bable. Let us now determine random magnitude z. , equal to the distance
from the focal point of the lens to the seat of ~ailure at a maximum dis- -
tance from it. We will assume that zi � Qf , where Rf is the length ,
of the lens's focal region. In this case the distribution density of mag-
nitude z will be the function W(z) _ ~dE(z)/dz~ , and the values of ~
~ z and iz2 can be found from the equations ~
z, z. � ~
~ a=~P(z)dz, zz=2~~zP(z)dz. -
(3)
Equations (2) and (3) can be used to determine cextain characteristics of
distribution function f(I) . ~
~
Since in the case of Vn � 1 the magnitude of z, is determined by the ~
behavior of with Qow values of the argument,lwe will approximate it ~
in this region by power functions. Let us consider two cases.
1. = a~k . This approximatiun is based on th~ assumption of the ex- '
istence of defects with low failure thresholds. Substituting it in (2) ;
and with the tendency of z~ ~ we get the prob~bility density: ~
~
_ ~ ~z) = 2kz 1 l Zi )2k eXP ( z }2k- ~ ~
x ~4~ '
- f(k) ~0~ p~k-~-I l/(2k-1) . I
I
ZX- ki(k-}-1)(2k-l)Ak] .
~5~ ~
~
Let us note that distribution (4) represents the Weibull distribution [6] '
for the magnitude 1/z used for estimating the probability of electrical '
breakdown. ~
~
~
~
I -
35
~ i
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_ i
� i
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I:mploying (4), .Eor the values o,~ z and z2 we get:
. i= r( 2k-i ~zx~ Zz=r~ 2k-i }ZX~
- (6)
� where I'(x) is a gamma function and derivative ~~k~(0) is related to
coefficient a as follows:
- a = ID+l f (k) ~k ~ . . .
Far the root-mean-square fluctuation, (z - z)2 , from (4) we have
(z - z) 2 = Y2 (k) z2 , -
- where
Y(k)=~r~ ~-i ~-r~~ 2k-~ ~'r~ ~-i ~
With k� 1 we have y(k) ti 1.28/(2k - 1) . Let us note that equations ~
(6) can be used for an experimental estimate.of parameter k.
For a more reliable determination of magnitudes k and f~k~(0) we will
- employ the method of maximum plausibility [8]. Let there be a sample
_ zi...zn of capacity n with a random value of zi . Having determined
= for it the logarithmic plausibility function
_ ~ n
L = E ln W(zl,k,z~) ,
i=1
we find the most effective estimates of parameters k and f~k~(0) from
the system of equations _
aL =0' dk
x
-
It can be easily solyed numerically after transformation to the form
_ n _
- R u (lIl Zi~~Zj -2k
2k2n i- 2 ~ ln z~ 2n ~R = p~
~ ~~Zi-sk _
~
. ~ (g)
36 ~
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~
n~ 1-2k ~i?lk-~)
Zk - (n ~ I~Z~ ' -
i
Having found the root-mean-square deviations S(1~~ and S(F~k~) , of the
most effective estimates of parameter k and f~" (0) from the equation -
' in [7],
S(x) = E[-32L/ax2]-1/2 .
(E is the mathematical expectation arrived at by aver~~.ng in terms of j
- the combined prob ability distribution), for k and f (0) we get:
i
/t k f k^~~2 ~2 4k - 3) ' Zx - Zx ~ ZY
(2k-1)~/n ,
vn -
(9)
~
- where k~ and z` are solutin.ns to system (8). Thus, equations (9) within '
the scope of a f~rst approximation solve the problem posed of finding ;
parameters of distribution f(I) from the characteristics of samp~e zi .
2, = a(~ -~)k . Here ~ is the intensity normalized for I and ,
I, is the minimum value of the threshold below which failure is ~mn
possible.
Making computations similary to sec 1 and estimating the integrals in (3)
by the Laplace method, we get:
z= (1- 0) Y pa~~Almtn)+ z2= (1 -20) Pol~Almia) (10) ~
I' (1/(k-f- 2)) ( k-I- 2\1/(k+2) a ( Po \3~2 -
~--2~k+2~ ` D~ ~ , D= 2~k+1~.vA l fmio ~ �
(11)
In deriving equation (10) it was assumed that D� k+ 2. Equations (10)
with ~igh k can be used for approximate estimates of magnitudes Imin _
and a. ~mploying the method of maximum plausibility, we find more pre-
cise values of parameters I i , a and k similarly to sec 1 from the
system of the following equat3ons: ,
3 n 2 lk-}- 2 I
dL R ZmaxA ~ Zmax _ 1 I =
- da - a - 2 (k -f- 1) (k 2) ~ z2 j '
t=t ,
i
37 ~ ~
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I
. ~
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- aL n 1 3n .
=(k+ 1) ~
~max t~ 1 zi ~Zmaa ~2~ -1~ ?Zmax
n ~ ( 2 2 k i
, ~ z2 lZmax~2~ - 1) +
-n(k+2)'a~ ` =0; ~ -
~ ~Zmaa~Li - 1~k+2 -
~,.1
n 2 '
_ dk - ~j ~n Zm2z - 1 + n
r~ 1 z~ k-~- 2
n
- ~ lzmax~2~ - 1~k+2 In ~ZmaxrZ2- 1)
_ _n~_~
, n = ~i
' ~ (z2 ~22 _ i~k-f-2 .
~ max i
!=1 '
a ~12~ -
where zmax P6~~'Imin '
4. Discussion of Results Obtained
Let us discuss the applicability of the method described ab~ve for deter-
~ mining the parameters of distribution f(I) from characteristics of a _
sample of random magnitude zi . Let us note that fluctuations in the -
distance to the last fracture, z~", generally speaking, can be caused for -
~ two reasons: the finitene~s of ~he total number of particles in the space
considered, and the variance in the failure threshold in different defects. ~
Of course, the parameters of function f(I) can+be found from magnitude
z, onlg in the second case. Actually if f(I) = 8(I - I), fluctuations
in z, wi1] be caused only by the finiteness of the conc~ntration of de-
i
fects--
(6z~)1~2 = IP/n0~~ . ~ -
Consequently, the~problem of finding the parameters of ~(i) can be solved ~
~if the characteristic breadth, , of ~unction f(I) satisfies the in-
equality ~ -
38
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. d! 2A{~2~5/2 ~ ~ .
, dz Yoz2 = �1 0.8 ms) the maximum power
for IFP-8000-1 and INP-18/250 lamps differ insignificantly. The strong _
difference in the maximum power for IFP-8000 and IFP-8000-1 lamps is ex-
plained evidently by the difference in design and fabrication technology.
For the purpose of determining the reliability of operation of the entire
pumping system as a whole it is necessary to determine to what extent
W is lowered when going from a single lamp in free space to a multi-
l~amp system placed in a light source. Qne of the chief reasons for the re-
duction in W in a light source is thought to be the increase in the am-
plitude of th~rcurrent flowing through a lamp as the result of the absorp-
tion of the radiation of neighboring lamps and the radiation returned from
reflectors [3-5]. Experiments conducted have demonstrated that in our case
the current in a lamp, within the limits of ineasurement accuracy of 15 per-
cent, is identical both for a single lamp and when the same lamp is operat- _
ing in a group of 18 lamps placed in a Kh-122-PM light source. As a reflec-
tor was used aluminum foil with reflectance of r ti 0.6 . Measurements of
maximum power~make it possible to assert that W in this design of a -
light source practically does not depend on whet~ier one or 18 lamps is
working in the light source. As a result of these experiments it was found _
that the factor influencing W r in a light source is the existence of a
closely placed wall (at a dist~nce of 1.2 cm from the surface of the lamp).
In fig 3 is shown the W(T) curve with the presence of a closely placed
wall for the IFP-8000-1 ~amp (curve 2a). It is obvious from comparing -
curves 2 and 3 that the most substantial reduction in W takes place
with short pulses (T < 0.3 ms); this reduction practical~y disappears with
T ti 0.8 ms .
W�p,H~ 1) .
a jo'
_ .sa ~f~
~
.
Z _ ~ .
~ E Y: -
~o - ~/~3 ~~`v!~~
- ~%T~'' -
5
3 ? ~
0,1 0,3 0,6 ~ 2;nc
[Caption and key on following page]
- 45
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Figure 3. Dependences of Maximum Loads on Pulse Length for an
_ ~FP-8000 Lamp (1) ~rom the Data in [6] (:~Thite Dots)
and from the Data of Our Study (Black Dots), for an .
I~P-8000-1 I,amp in Free Space (2) and Near the Wall
of the Light Source (3), and for an INP-18/250 Lamp
ira Free Space (4)
Key: '
1. pr , kJ 2. T., ms
By utilizing curve 2, it is possible to estimate the operating li$etime
of a pumping system in this mode (T ti 0.35 ms and W= 5 kJ)--approximate-
ly 800 flashes. The data on the operation of a pumping system arrived at
over the course~of.two years of operation give a value of about 200 flashes,
" which in order of magnitude agrees with the estimate given. For INP-18/250
lamps thi:~ estimate according to the data in fig 3 gives about 104 flashes.
As the result of using an individual Rh-122-PM light source with two pump-
ing modules (36 lamps of the INP-1$/250 type), after 200 flashes in the
working mode no change was defiected in the parameters of the lamp, which
= does not contradict the estimate given. -
The data obtained ~ake it possible to speak of the high reliability of the .
pumping system of the "Mikron" unit and indicate the promise of developing
multi-Iamp pumping systems for high-power solid state lasers.
- Bibliography
1. Batanov, V.A., Bogatyrev, V.A., Bufetov, I.A., Gusev, S.B., Yershov,
B.V., Kolisnichenko, P.I., Malkov, A.N., Prokhorov, A.M., Spiridonov, _
_ V.A., Fedorov, V.B. and Fomin, V.R. IZV. AN SSSR, SER. FIZICHESKAYA, -
- 42, 2504 (1978).
2. Waszak, L. MICROWAVES, 8, No 5, 132 (1969). -
- 3. Mak, A.A. and Shcherbakov, A.A. KVANTOVAYA ELEKTRONIKA, No 5(17),
68 (1973). ~
_ ~
4. Basov, Yu.G., ~vanov, y.V., Ma.karov, V.N., Narkhova, G.I. and Shcher- -
bakov, A.A. OPTIK~ I SPEKTitOSROPIYA, 38, 608 (1975). -
- 5. Kizsanov, V.~., ~roshkin, S.V. and Bykov, I.V. KVANTOVAXA ELEKTRONII:A,
3, 431. (1976) . ~ ~
6. Kirsanov, V.P., ~roshkin, ~.V. and Bgkov, I.V. KVANTOVAYA ~LEKTRONIKA, -
2, 181 (1975). ~
7. Marshak,~I.S., editor. "xmpul'snyye istochniki sveta" [~ulsed Light
SourcesJ., Moscow, Energiya, 1978.
~ ~ ~+6. -
. ~ FOR OFFICIAL USE ONLY
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rux ~rr l~l~, U~~, UNLY
8. Podgayetskiy, V.N. and Skvor~sov, B.N. KVANTOVAYA ELEKTRONIKA,
No 4 (1.0) , 82 (1972 ) .
COPYRIGHT: Izdatel'stvo Sovetskoye Radio, KVANTOVAYA ELEKTRONIKA, 1979
[83-8831] ~
CSO: 1862
8831
~
~
I
- ~
. ~
_ 47
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UDC 621.383.8
INVESTIC.~: ~i1't~; CHA:RAClERISTICS OF NEW COtg'OSITIONS FOR PASSIVE SHUTTERS
FOR TODL~I~ f�r,;;~.rS
Moscow Kt1.t:N''_'~~lA'IA ELEKTRONIKA in Russian Vol 6 No 12, 1979 pp 2652-2653
manuscz~.~t ~e~e_i.vPd 12 Jul 79
[Article by S.,?'. Batashev, M,G. Gal'pern, V.A. Katulin, O.L. Lebedev,
Ye.A. Luk~yanets, N.G. Mekhryakova, V.M. Mizin, V.Yu. Nosach, A.L. Petrov
and V.A. Petuktio~~, USSR Academy of Sciences Physics Institute imeni P.N.
Lebedev, Moscow] '
[TextJ A report is given on the creation of two dye compositions which
clear under the :i.nfluence of the radiation of an iodine laser (a = 1.315 -
u) and have low residual absorption.
For the purnose of elirninating self-excitation in high-power iodine laser
units, as optical decouplers between amplifier stages are tised clearing
filters based on atomic iodine [1] and solutions of organic dyes [2]. '
Filters based on iodine are complicated to use, since in working with them
it is nec~ssary to maintain the temperature of the cell at about 8(l0�C.
Clearing f ilters based Qn solutions o~ organic dyes are simpler and more
reliable and can be used in laser beams with practically any aperture. �
An important parameter of clearing compositions influencing the output pow-
er of a laser. unit is the amount of residual absorption in the cleared -
state; therefore the creation of clearing compositions with reduced residual
absorption is a topical problem.
In this study a report is given on the creation of new compositions based
on dyes 1~61 and 1067 which clear under the effect of the radiation of a
photodissociatian i.odine laser with a wavelength of 1.315 u, and the re-
sults are g-ivF~,i of an investigation of their key characteristics. Measure-
ments of ri;e paramerers o~ solutions of dyes were made with an iodine laser ~
with a pow~x of approximatel.y 3 J and a pulse length o~ approximately 1 ns.
The transmittance o~ the compositions in determining its dependence on the -
power den~~ir_v c~F tre incident radiation was determined as the ratio of the -
power of t,e laser pulse having passed through the cell with the composition
and of tn~~t h:Ctta.ng the cell. The power density of the radiation hitting
48
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~ the cell (beam diameter of 1 cm) was varied b}� means of neutral filters
and the pulse energy be~ore and after the cell was measured by calorimet-
ers.
In fig 1 are given curves for the transmittance of solutions of dyes 1061,
1067 and 1057 (a report was given on the latter in [2]), having different
initial transmittance. From a comparison of these curves it is obvious
that compositions 1061 and 1067 have lower residual losses than the solu-
tion of dye 1057 developed earlier.
T
g6 . ~
2
0, 4 3
0,2 � 4
~ ~ i> ~
1/1-~' 10-3 10-1 >0"~ f,,Qxr/cM2 -
Figure 1. Dependence of Transmittance, T, of Investigated Composi-
tions with Different Initial Transmittance on Power Densi-
ty of Incident Radiation: 1--1067, T= 0.25; 2--1067,
T~ = 0.004; 3--1061, T~ = 0.006; 4--1557, T~ = 0.01 -
Key:
1. J/cm2
We also studied Sulfolan solutions of dyes No 1, 2 and 3, close in struc-
ture to dye BDN II in which good clearing was achieved in [3]. The best
_ clearing was arrived at with dye No 3, whose absorption spectrum is identi-
~ cal to the spectrum given in [3] for BDN II in Sulfolan, but it is much
worse than with dyes 1061 and 1067. In the table, for all the dyes stu-
died, are given ratios of the original optical density, D~ , to the opti-
cal density in the cleared state, Dpr , found from the clearing curve.
Table
x
pac~renb I n avanbxoe ( 3~ De1p I Kpacxreib I Haveneaoe I D D
panyctsenee np I npoaycKax~e ap _
1
Ns I 0,16 1,2�0,1 1061 0,085 6,9�0,7
N42 0,14 1,4�0,2 1061 0,006 6,8�0,7
Ns3 0,41 2,8�0,2 1067 0,25 7,7�1,0
1057 0,12 I 4,2� 0,5 1067 0,004 9,2 � 1,5
[Key on following page]
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Key:
1. ~ye 3. D~/DPr
2. Original transmittance .
Another important characteristic o.f a clearing composition is the time for
relaxation of the cleared state. ~'or the purpose of determining the relaxa-
tion time of a composition was employed a system with a variable optical
delay 13.ne (OLZ). Part of the radiation of the iodine laser cleared the
_ cell with the solution and another part of the radiation, after the OLZ,
was reduced by neutral filters and also passed through the cell. By mea-
suri~zg the energy of the delayed pulse before and after the cell, we de-
termined the. transmittance of the cell at different moments of time after
the clearing pulse passed through. The relaxation time for the cleared
state of sol�utions of dyes 1057, 1061 and 1067 determined from these mea-
- surements equaled 20 + lU ns.
By means of the compositions developed, passive Q switching of an iodine
laser was accomplished. The laser's cavity was formed by flat mirrors with
reflection coefficients of 100 and eight percent and the distance between
them varied from 110 to 220 cm. The design and parameters of the laser
head and the composit_.~n of the -~7orking mixture were the same as in [2] .
By selection of the key parameters of the laser and by employing as a
passive shutter a cell with a solution of a dye having an original trans-
r~ttance of Tp= 10 percent was achieved the generation of a single gi-
- ant pulse. Wifh a cavity length of 110 cm the pulse had a smooth shape
with a duration of 20 ns, and with an increase in the length there appeared
amplitude modulation, reaching 100 percent with a cavity length of 220 cm
(f ig 2). The shape of the pulse was recorded by a high-speed I2-7 oscillo-
- graph connected to a coaxial FEK-31KP photocell. In the case of 100-percent
modulation, the laser's radiation represented a chain of individual peaks,
as is usually observed in lasers with self-synchronization of modes. The
length of an individual peak was 4 ns. Such a long length of an individual
peak as compared with the ultrashort pulses of solid state lasers with
self-synchronization of modes is explained by the ~,narrow breadth of the
lasing spectrum of an iodine laser, which is approximately 0.01 cm 1 at the
- pressures employed for the gas mixtures. In Chis case with a cavity length
of 220 cm the number of lasing modes is not greater than three or four. The
length of an individual peak cannot be shorter than t~/m , where t~ is
the time for double passage through the cavity (in our case t= 15 ns)
and m is the number of excited modes; consequently, the leng~h of a peak
with sel'f-synchronization of this number of modes should equal 3 to 4 ns,
which has been observed experimentally.
The compositions developed by us, in addition to law residual absorption,
~ have high resistance to the influence of laser radiation and do not change
their properties during longterm storage, which makes them promising for
employment in iodine las~r systems.
Employment of passive shutters based on dyes 1061 and 1067 in a high-power
~ iodine laser unit at the USSR Academy of Sciences Physics Institute has
50
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made it possib],e substantially to improve emission parameters. With a -
radiated power of at+out 100 J a contrast o~ 108 was achieved [4]. ~
. -
Figure 2. Oscillograms of Lasing Pulses of an Iodine Laser with
Passive Q Modulation by Means of a Dye Solution (T~ _
= 0.10) with a Cavity Length of 110 (a), 145 (b) and
220 cm (c)
Key : -
Z . 10 ns
In conclusion the authors wish to thank V.N. Kopra:~enkov for his helpful
_ discussions and for offering analogs of BDN II. -
Bibliography
1. Gaydash, V.A., Yeroshenko, V.A., Lapin, S.G., Shemyakin, V.I. and
- Shurygin, V.K. KVANTOVAYA ELEKTRONIKA, 3, 1701 (1976).
2, Gal'pern, M.G., Gozbachev, V.A., Katulin, V.A., Lebedev, O.L., Luk'-
yanets, Ye.A., Mekhryakova, N.G., Mizin, V.M., Nosach, V.Yu., ~etrov,
A.L. and Semenovskaya, G.G. KVANTOVAXA ELEKTRONIKA, 2, 2531 (1975).
3. Beaupere, D. and Farcy, J.C. OPT~CS COI~dS., 27, 410 (1978).
4. Basov, N.G., Zuyev, V.S., Katulin, p.A., Lyubchenko, A.Xu., Nosach,
V.Yu. and Petrov, A.L. KyANTOVAYA ELEKTRONIKA, 6, 311 (].979).
COPYRIGHT: Izdatel'stvo Sovetskuye Radio, KVt~NTOVAXA ELEKTRONIKA, 1979
[83-8831]
CSO: 1862 END
8831
51
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