JPRS ID: 8801 USSR REPORT PHYSICS AND MATHEMATICS QUANTUM ELECTRONCS

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~
QUANTUM ELECTRONICS

S OECEMBER i979 CFOUO 6l79) i'OF i
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JPRS L/8801
5 De~ember 1979
USSR Re ort
~
- PHYSICS AND MATHEMATICS
CFOUO 6/79~
Q~uantum Electronics
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JPRS L/8801
5 ~December 1979
USSR REPORT
PHYSICS AND MATHEMATICS
(FOUO 6/79) �
~ OUANTUM ELECTRONICS ~
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 6, No 8, Auq 79
pp 1626-1638, 1690-1697, 1705=1711, 1773-~.777, 1816-1818
CONTENTS PAGE
LASERS AND MASERS
Theory of an Electron Phototransition Chemical Laser
With Thermal Initiation Behind ttie Shock Wave Front
(I. A. Izmaylov, et al.)~ 1 -
Optimization of Electron Beam Parameters and Choice of
Foil in Electron Beam Controlled Lasers
(A. I. Dutov, et al.) 22
Lasing Modes and Emission Characteristics o~ a Riro
Type Photodissociation Iodine Laser
(V. N. Kurzenkov) 34
Investigation of Properties of a LasEr With an Unstable
Cavity and Added Feedback ~
(Yu. A. Anan'yev, et al.) 44 ~
Some Results of Experiment� on a Gas Dynamical C02 Laser
(S. B. Goryachev, et al.) 48
Efficiency of a Selective CO Laser
(A. A. Likal'ter) 52 ,
II~I - USSR - 21H S&T FOUO] ~
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LASERS AND MASERS
UDC 621.3?3.826.038.823 -
~ TI~ORY OF AN ELECTRON PflOTOTRANSITION CHEMICAL LASER WITH THERMAL INITIATION -
, BESIND THE SHOCR WAVE FRONT
Moscow RVANTOVAYA EL~I~T'RONIKA in Russian Vol 6 No 8, Aug 79 pp 1626-1638
manuscript received 19 Oct 78
, [Atticle by I.A. Izmaylov, V.A. Kochelap, Yu.A. Kukibnyy and S.I. Pekar,
Ukrainian SSR Academy of Sciences Institute of Semic:onductors, Kiev]
J [Text] The theory is developed for a steady-state electron phototraneition
chemical laser initiated by a shock wave in a dense flow of reagents. A
calculation is s~de of the inverse population density behind the front of the
shock wave for th~~ case of photorecombination reactions. Proof is given of
the origin of a waveguide localizing the working mode of the laser in the
inversion zone. The light gain, a, in waveguide modes is calculated. For
- laser generation conditions in gas dynamics and chemical kinetics the light-
stimulated chemical reaction is taken into account, which alters the spatial
- relationships of the density, temperature, flow rate and concentrations of
reagents. A determination is made of the unit light power, P, drawn of~ from
the flow as a function of light losses. A number of specific gas mixtures are
discusaed and three of the most prnmising have been selected for use in lasers:
N02C1-Ar, 03-Ar and 03 C0. It is demonstrated that for these inversion origia-
ates over a broad wavelength range and the conditione for the origin of a
waveguide are compatible with the conditions for the formatian of inversion. -
For theae mixtures have been obtained a ti 10 3 cm 1 and a power of
approximately 100 kW per square centimeter of the gas flow.
1. Intrnduction
- The upper limit of the power of a chemical laser in the steady-atate mode ie
. determined bq the density of the ~lux of chemical energy aupplied to it. With
, ~this energq, eeparated in the elementary event of the reaction, the power
aupplied is propor*ional to the density of the gas mixture and its rate of
flow. With a supereonic flow rate of 3 km/s, a nornial gas densitq and energy
released in the elementary event of22 eV, the flux density of the chemical
energy equals approximately 3 MW/ an . In order for a laser to poasesa high
efficiency, it is sufficient that the energy of an emitted photon be comparable
' to the energy released in the elementary event of the reaction, which is
possible with electron phototransitions, and that the quantum qield of the
1
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- sti~..alated emi~sion be on the order of one.* The latter condition can be
fulfilled in lasers where the parallel reaction channels are a thermal and
radiation channel (cf., e.g., [1,2]). By stimulating the reaction's radiation
~ channel, its dominance over the thermal can be achieved even in the case when
the quantum yield of spontaneous emission is low. Then the velocity of the
laser process will be determined by the rate of exhaustion of reagents (for
a photorecombination laser, by the rate of exhaustion of atoms and radicals).
The theory of chemical lasers utilizing electron phototransitions at high
pressures was considered in [3-8], but such lasers have still not been impie-
mented experimentally.
In another group of studies devoted to the creation of chemical electron
phototransition lasers studies were made of exchange reactions between metals
and oxidants [9]. The quantum yield in these reactions is high (0.15 to 0.6)
even in spontaneous chemiluminescence. However, with an increase in pressure
beginning with a few mm H8 the quantum yield drops substantially. And in this
gro~p of studies it has still not been possible to achieve inversion [10].
In this pap~r the theory is developed for steady-state lasers operating with
an initial gas mixture pressure on the order of 1 atm and higher, when the
time for the occurrence of the thermal chemical reaction is not longer than
1 us and the length of the reaction zone along the flow is less than 1 mm.
It is necessary that the reaction not be able to take place during the relatively
long period of mixing and supplqing the mixture to the cavity. For this purpose
the temperature of the mixture in the supplying gas line must be so low that
a reaction does not occur at this temperature. The reaction must be stimulated
~ within the optical cavity itself during periods much shorter than 1 ms. This
can be accomplished by a sudden increase in the temperature of the gas (of
thousands of degrees in 0.1 ns) in the front of the ahock wave (W) created
inside the cavity [11].
Usually the length of the inversion and laser generation zone is shorter than ;
the thermal reaction zone. In particular, in a laser of the type in [1,2] the !
stimulated radiation reaction must outdistance the thermal and as a result of
this the length of its zone can equal a~rwdiffraction1losses of photonahand ~
With these thickn:esses of the active lay
losses associated with distortion of the active layer become substantial. As
a result of these losses generation generally couid prove to be impossible
[5,6]. However, behind the froand refractivekindicesnofhtheegasiowhichecanises
a layer of increased densitiea ,
act as a plane wavegu~de localizing the.laser's operating mode in the inversion
zone and eliminating these losses of photons [12].
Below are discussed onlq reactions of radiative recombination of atoms and '
radicals. '1'fl~e latter react rapidlq even at low temperatures; therefore they
*Another poss~bili~y ~o?' achieving hi~h e~~iciency of the laser process involves
the utilization of photons of not too high energy with a quantum yield of
' atimulated e~miss~ion per aingle reaction event o~ greater than one. For example,
a cascade o~ stimulated vibrational~notational phototransitions.
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cannot be present in the supplying flow. These radicals must be rapidly and
in great quantity created inside the optical cavity, e.g., by the thermal
d~ssociation of atable moleculea behind the front of the shock wave.
Tn thiy paper r.he theory of rhe ~hock wave i.a developed ancl of the unidimenAional
st~ady-state gas dynamica~ flow, taking into account the kinetica of chemical
reactions in the gas. Zt differs from the familiar theory in [13J by taking
account in kinetics of the light-stimulated radiation reaction, which alters
the spatial relationships of density, temperature, flow rate and concentrations
of components of the gas mixture. Then are calculated the spatial behavior
of the complex dielectric constant and the lowest modes of the plane waveguide
originating behind the shock wave front. A determination is made of the gain
(absorption) of light in these modes as a function of the pressure, velocity
and composition of the initial gas stream. The output light power is obtained,
derived from a unit area of the cross section of the incoming flaw. Tlie
theory developed is applied to 12 specific gas mixtures from which have been
selected three of the most promising: N02C1-Ar, 03-Ar and 03-C0.
2. Investigation of the Gas Dynamics, Chemical Kinetics and Properties of
the Waveguide, Taking Into Account the Laser Process
Of the 12 mixtures considered in this paper seven react according to the
following scheme. A gas consisting of molecules AX is thinned by inert gas M;
after a sudden rise in temperature the following reactions take place:
AX-;-Af--A-}-X~~ ~1S--Q~, (1�)
AX ; X-.A-~-~:, ~2~
( t~''~
a rI )C~ ,
l a4 c3~
� where Q equals the heat of the reactions. It is assumed that at the tempera- -
ture considered particles of A do not dissociate and do not form compounds of
A2. Reaction (3) takes place through competing radiation and thermal channels.
Designating the partial concentration of gases as [AX], [X], [A], [X2 ~ and
[M], the density of the mixture by p, the te~perature by T and tHe velocity
by v, we write the laws for the conservation of mass, ~momentum and energy
in the absence o~ laser generation:
Pv -povo, ~4) �
N-f-Pv2=Po-~-Povo, ~5~
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_ 1/~v=-}-(i= 1/~vu-f-/t~, (b)
where p is the pressure of the gas mixture; subscript 0 indicatea the
initial state of the gas flowing into the shock wave front; and h= c T+
~ +(1/p){Ql~g~ +~2R -Q )~R is the enthalpy (c is the specific h~~t,
depending on concen~ra~ion~. The specific heat o~ each component of the
mixture is considered constant. We disregard spontaneous emission in (3).
Equations for the b alance of matter have the form
[r,X l-f- [X I-i-2 [X21= [11X 1-~- [:11-(A~Po) [~~X 10. . ~
As a result it is sufficient to write kinetic equations for just two con-
centrations:
d
dx �X] v) lY/i -11%L-W9, ~8)
z~) ik%'., I~ 2 1~a~
(9)
where
l~'1=k,f1141([AX]-I~'~l[Y ]~K,);
W~-k:([AX 1 [X 1--[:~ ] [X.~ 1K~~K1);
1Y~3== [ Y 1 z--K, [ X�~ i) [~~i i; =
(io)
- kl 2 3 represents reaction rate constants; and K1 and K3, equilibrium
co~lstan~ts of reactions (1) and (3). It is assumed that altTiough the concentra-
tions of components are considerably unbalanced, thermal equilibrium exists
in all degrees of freedom of the motion of molecf~:es. Coordinate x points
along the flow. Plane x= 0 represents the front of the shock wave. In
_ the region of x< 0,[AXI~ and n=[~l0/LMlO are assigned and [X) ~
_ [A] _ [X2] = 0 .
Solution of Ga~ Dqnamics and Kinetics Equations in the Absence of Laser
Generatian
For the purpose of investigating the possibility of achieving high concentra-
tions of atoms and radicals, as well as an inverse population density in the
laser's initiatian o~ a shock wave, equations (4) to (10) have been solved
numericallyr ~or many vaXues o~ the parameters inc~luded in themil Em~loyed
_ have been values of kl A 10~ exp I-Q1/(RT)] cm /s ~ k2 = 10 cm /s ,
~4
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k= 10~33 cm6/s , K = 1025 exp [-Q /(RT)] cm 3, and K3 = 1024 exp
exp [-Q3/(RT)] cm 3 1 which is typical of fast reactions at high temperatures
[14]. As a result, e.g., with Q1= 35 kcal/mole , Q3 = 100 kca�1/mole ,
p0 = 5 atm , and TD = 300�K , ana
with a Mach n~mber o~ M= 5.5 , n= 0�1 , (11)
the dependences have been obtained which are shown�in fig 1, where curves
1 to 3 represent the spatial behavior of relative concentrations of components
determined from the equation cB = fB]/([M]n) . Curve 1 shows that dissociation
and ti~e disappearance of original molecules of AX take place in a zone whose
length is on the order of 1 u. Curve 3 shows that in the same zone are formed
atoms of R needed for working laser reaction (3); their concentration, CX ,
reaches a maximum value of 0.45, whereas its equilibrium value with x-~ ~
equals 0.014. CR is fairlq high in a zone 10 to 20 u 1ong. Curve 2 shows
the monotnnic growth in the concentration of products X2.
~e, ~u
~r
p,5 -
, 3
0, J -
a
~
0,~ ~
' 1),
O 1,5 S 7,S X,MKM
Figure 1. Dependences of Plow Characteristics on Distance to the
- Shock Wa~~e Front : 1-~1/2 C~; 2--CR ; 3--CR; 4--S2V
2
Key:
1. R, u
In lasers of the type con,sidered (if, e.g., radiative combination takes place
from a continuous spectriaa) it is feasible to term inverse the case when
- for a specific frequency o~ w per unit of time the number of radiation events
is greater than the number of absorption events. The test for this inversion
has the form [3]:
~Xl'>[XZ1Ks~T) e~P ~fcu/k7~. (12)
It is obvious �rom this equation that with assigned concentrations and tempera-
ture there exists a violet ~requencp litqit (~waximum frequency)~ wv ~ below
which inversion exists. ~1~th w= wv (12) i$ converted into an equal3ty.
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In fig 1 curve 4 represents the spatial behzvLor of the magnitude S2 =
-}"'~v~Q3 ' Fr�~ it it is obvious that inversion is possible with ~ ti 2 eV .
Fig 1 illustrates the .favarable possibility for accompliahment of the process
under conditions when the inversion zone is much longer than the zone for
initiation of the ~working reaction. For efficiency of the laser it is also
important that inversion exist in ~a zo~e on the order of 10 u and that the
concentration of reaction products R2 be still not too high. As a maximum
~ [g] ti 2�1019 cm 3 .
Curves similar to those presented in fig 1 were calculated for differen~ com-
binations of parameters Q,*1 , pp and M. Since it is impossible to
present the entire diversi~y of individual graphs, let us show onYy the
maximum ordinates of curves for C and SZ (fig 2) . It is obvious from
fig 2 that if with fixed M p0 is increased, then CX almost does not change
(is slightly reduced). With an increase in M, CX 3ncreases substantially,
as aZso with a reduction in Q1 and n.
po,vmM pn. cmM po. omr~
O,B 0,9 0,9 U,B 0,? 0,6 0,7 0,6 Q7 0,8 30 -;I,f 0.' J.6 !!7 0.6
1,~~,~~ 0,7j ~ I ' r/~
0,7{ ~0,8 I ~ y~,i p,y -I w'~ i
II I ~ / ~ ~ ~e~
1 i j 3~~ I ~ 10 . I ~ ,
~ I ~ ~ I ~ f I/~/~
, I ~ 05J , i I�
(~,3 ~ I i, i/ 1 I~~~ 3 ~:1~ ~/I I
i/:,~~ I I~~~/~ C3 I I
f I
' ' ~ _ 1~_
0 f ~i_ ~ ~J,3 ~1--- L- 1 I~JJ
i i J' 6/'4 -b i B r'1 7 d ,S
C.f U4 b~ C)
, a)
Figurp 2. Maxisqwn Values o~ CX and SZv for Q= 20 (a), 35 (b) and
50 kcal/mole (c)~ rt = 0.2 (solid line~', 0.1 (dotted line)
and 0.5 (dash-dot line); Q3= 100 kcal/mole; as well as for
different values of p~ and M. ~e nearly vertical lines
correspond to constant values of C , indicated above the
curves, and the sloping 13nes to constant values of SZ~X ,
indic~ted on the curves.
Key :
1. p~ , atm
The violet inversion boundary, S2 , increases with an ir.crease in p and
_ n and with a reduction in Q1 and M. In order, with assigned Q~ and
_ n, for ~ to be greater than a given value, it must lie in plan~ p~, M
to the rig t of the corresnonding nearly vertical curve. In oxder for St~
to exceed a given value it must lie above the corresponding sloping curve.
A comparison of fig 2a to 2c shows that for the purpose o# achieving favorable
values of CR and S2~ it is necessary to select low Q1 . With Q1~Q3 ~
> 0.5 process (1) to (3) becomes endothermic.
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According to the Chapman-Jouguet equatfon [13], for each value of heat release
in the exothexmic process there exists a lower limit of M with which the flow
� of gas from the shock wave can still be steady-state (in other worils a super-
crnapressed detonation wave is realized). This lower limit of M, when n a
= 0.1 , Q3 = 100 kcal/snole , and Q1 = 20 kcal/mole , equals 3.7 and with
Ql = 35 kcal/mole , 2.8.
Proof of the Origin of a Plane Waveguide in the Reacting Gas Behind the Front
of the Shock Wave
As shown above, the inversion layer can have a thickaess on the order of 10
to 20 u. With intensification of the light propagated along this layer,
diffraction losses of photons occur, as well as losses associated with possible
distortion of this layer. However, as we noted in [12], immediately behind the
front of the shock wave there originates a thin layer of compressed gas with an
elevated dielectric constant, e. This layer can act as a plane +�aveguide for the
intensified light. Compression occurs because with small x there takes
place intense dissociation of original AB molecules (cf. (1) and curve 1 in
fig 1) which draws off heat from the �low and reduces its temperature and
speed. With great x, an exothermic recombinr~cion reaction takes place
(cf. (3)), resulting in heating and acceleration of the f low and accordingly ~
3.n a reduction in its density. With great x the density can be reduced to
values lower than in the plane of x= 0 (cf., e.$., fig 3).
It has been assumed that a contribution to Lhe real half of e is made chiefly
bp a diluent gas in wh3:~ah there are no phototran3itions in the region of the
spectrum considered. Therefore below we disregard the variance of Re e(x)
- anc's assuffie that
R~~(x) -1-I-2~P~x)~ (13)
wh~re S is a constant. In the waveguide having originated TE mo~ies were
calculated, whose electric field is determined by the equations
Ey ~~~i~e~ ek:-m~), dx~ l
~
2 Re e(x) k~ 18 = 0. (14)
System of equa.tions (4) to (10), (13) and (14) has been solved num~ricalYy
w#th a computer; as a result the amplitudes of tl~e lowest modes, E(x) ,
E(x) , etc., have been obtaine~d. For S has been asaumed a value carres-
ponding to argon: S= 0.08 em /g [15]; ~w = 0.4Q3 . The verq existence of
solutions for E(x) tending toward zero as x~+~ proees the existence of
the waveguide. It is obvious from fig 3 that the zero mode is localized in
_ the inversion zone for this w. The number of TE modes, NW , is finite.
If N~ � 1, then it is determined from the equation -
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~
N~, = n yRe (e(x) - e(oo)) c1.r,
~ (15)
where tlne integral is taken for the region in which Re (e(x) - e(~)) > U. ,
For example, with the values o# parameters indicated, but with p~ ~ 3 atm ,
N ti 60 .
~�,~(x) ~(~y,~~:7,,
0,1 -
_ ~
t
~ a)
.
~ 1' �
, _
~ ~
~ -
~
~ ` ~
' ~
~
0
S1a;Cx
0,5
1 \ .
_ 1~\ b~ ~
0,3 ~ ~ ` .3
1; i
_ ~
~
i
~'0 10 40 7, MXM
$igure 3. Spatial Dependences o~ E~ (a, Straight Line), [p(x) p(~)]/ _
~p(0) (a, Dotted Line), S2 (b, StrSight Line) aad C -
- (b, ~lotted Line) #or palues~of ~arameters in (11) with X
Y~Y~ a 1 (1) , 0.7 C2) Snd 0(3)
Key : ~
1. x , u
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In certain cases a waveguide originates also with an endothermic nonequilibrium
reaction.
Light Gain in the Waveguid~ Mode
~ Let I(z) be the integral flux of light energy for plane xy in this mode.
Termed the light gain in this mode is the magnitude a=(1/I)dI/dz . If
~Im e~ � Re (s - 1) , then _
m -
dz (z) ~ z Im e(x) ~ dx a' (x) I~(x) I'
a = k-�' = ~
~ ~ ~
f dxRee(z)Ib�(X)I$ ~ dX~~(x?~'
-
(16)
where
~
a' (x)=a (w~ T'1 ~ [al" - [xal K, e
~r ~ _
(17)
is the light gain in an infinite spatially homogeneous mixture of gases;
a' and a(w,T) were camputed in j4,6,16].
In disregarding laser gemeration, (16) corresponds to amplification of an
~extremely weak signal., a= a81 eakJ ~ Which was computed for the zero3~nd _6
first mode~~(cf~6values of param~~ers in (11) and fig 3a): a = 1.3�10 cm
and -5�10 cm for the zero and first modes respectively. S~us, the zero
mode is intensified and the first damped.
Solution of Gas Dynamics and Kinetics Equations in the Presence of Laser
Generation
In this case equations (4), (5), (7) and (14) and formulas (10), (13), (16)
and (17) do not change. To the right half of (8) it is necessary to add the
decrease in the number of atoms of R per unit volume~per second on account of
light-stimulated events of radiative chemical reaction (3): -2WSt , where
W ~T ~X~ - c
f~~X> U~x~' ~18~ -
Here U(x) is the in~egral density of electrotnagnetic energy in the waveguide
for close ~requencies of generated waves. To th~ right half of (9) it is
neceasary to add the increase in the number o~ molecules o~ X2 per unit volume
per second as the result o~ the sa~e radiative reaction, i.e., Wat . To the
1ef t half o~ equation (6) it is necessary to add the tez~m
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A
li~(u ~'[fx 11%,
~ uT
{~ot~~ 0
asaociated with the energy gotng into radiation.
Then, in order for the system of equations to be ccm4plete, it is necessary
Go add also an equation determining the value of the steady-state energy con-
tent of the waveguide:
cu ~19~ -
where y is the energy decrement in the waveguide cavity resulting from
various losses of photons, e.g., on ar.count of the incomplete reflection of
mirrors, which is assumed to be specifi~d.
The self-consistent sqstem of gas dynamics, kinetics and electrodynamice
equations obtained in this way, in which e(x) depends on the concentration
- of gases and density, and tne latter depend on the generated radiation, has
been solved with a computer for diff erent values of parameters. _
In taking generation into account, i.e., terms with Wst and equat~.ons (19),
to the parameters previously figured ln the sqstem of equations are added two _
new ones: a(w,T) and Y. It is easy to see that the system of equations
is imrariant with a simultaneous substitution of a-~ va , Y-? vY and U(x)
+ U(x)/v , where v is an arbitrary number. Here the sought functions of x--
[XJ, [X ] and other concentrations, p(x) , and also (with an accuracy of s _
constan~ factor) E(x)--remain unchanged. Theq depend, consequently, not on
the two parameters a and Y, but only on the ratio of ~y/a .
For the origin of generation it is necessary that the damping constant, , ~
be below a certain threshold Va1ue o~ q. The latter.is chosen from the
requirement that equation (191 be ~ul~il~ed with U(x) n+ 0, i.e., with a, _
~ a . It is ol~vious that a/a depends only on the previous parameters of
thesproblem, but not on a an~l Y. Therefore, according to (19), Y=
m casl = a� const , where const depends only on the former paramete~s.
Hence it follows that the solution can be tabulated as a dependence on para-
meter Y/yp (and not on Y/a
As an example let us give the results o# a calculation performed for values .
of the parameters in (11) and of ~ew A 0.4Q3 . It ie obvioua from fig 3 that
= with a diminution in Y/^y there is an increase in the influence of stimulated ,
radiation on kinetics andpgas dynamics. Whereas for curves l and 3 the values
of p(~) agree, for curve 2, corresponding to the~'drawing off of energy from
the flow, the value of p(~) is greater (indicated bp the dot-dash line in
fig 3a). With a~diminution in Y/Y the spatial behavior of deneity changes -
so that curve E(x) becaaes in fo~m both lower and wider. The plateau on
dotted-line curve 3 in ~ig 3b shows that in the region of x A 20 to 40 u
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Cg is greater with an evolved stimulated process than in its absence, although
it would seem that stimulated radiation should annihilate atoms of X. Thie
_ is explained by the ~f~ct that the inversion zone is located in the region of
X< 10 u and *here C is actually lower than in the absence of stimulated
radiation. In the reg~on o# x= 20 to 40 u there is no inveraion and the
absorption of accumulated p'hottms predominates, increasing CX .
The pawer drawn off from 1 cm2 of the stream on account of all kinds of losses
of photons equals
~
,
, . ~I' _ ~ J U (x) d.r.
_
(20)
?'i�~'mnz
1~
_ 0,5 f
~ - ~ ~
0 t7 ZS J.r'' 0, 75 ~'~a'n
Pigure 4. Dependence o~ P/P~X on y/Yp ~or Values of Parameters in
(11)
If losses associated with the transa~ittance o~ the mirrors prpdominate, then
P is the power of the generated laser radiation. In �ig 4 is given the de-
pendence of P on Y/Y ~w~th the values of parameters in (11). The maximum
value of P ~ 18.3 k~'/cm is achieved with Y/Y = 0.37 . Here fnom one -
gram of the~gas mixture (including the diluent) an ~nergy of 12.8 J is derived.
It is obvious from fig 4 that when y; 0, P+ 0, unlike steady-state genera-
tion in a spatially homogeneous mixture of gases, where with a reduction in
Y, beginning with the threshold value, P increases monotonically [2].
3. Investigation of Specific Chemiluminescent Mixtures Reacting According to
System (1) to (3)
Having been selected are relatively stable initial compounds AX for which it is
possible to disregard the reaction AX + AX ~A * X2. Zn a11 cases the diluent
was argon. '~alues of s}~eci~ic heat were taken ~rom [17]. The equilibrium
11
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constants, K1(T) and K3(T), ~'or mixtures Nos 4 to 7~ given in table 1, were
also taken from [17]. ~or NOC1 and NO2C~g Kl was determined from thg6data
in [18,19] and equale~l ~~~per..t~vely 3�IO exp [-Q1/(RT)J and 3.85�10 exp -
exp [-Q1/(RT)]~(150~~T) cm~ .~ox NO~r, Ki was ca~puted ~rom the theoretical
equation K1 ~ 5�10 exp [~Q1/(RT)] cm^ , and Q1 was taken frosn [20].
Pa,a;nM 1~ / ~'J,`
i ~ ~ =
/
J ~ /
G,6~ ~~~F ~ /
~ , ,
~ s s f-~~r w5~ 5.-- f-y.-;~
~ ~ ~Q4 � 0,35
Q1 a~ b) '
e~,f,u
~,3,3' 4 ~~,D , p, ~f
. 'D,~i75
p,3 30 - l; 4P~ -
� ~ -
~-~42 O,,f7
~,o~~M f03'S --4 k,5 M -
lo~ ~ d)
o~ ' _
_ 30 e~ -
a~s ;
L
. 5 -
Pigure 5. Maxin~um Va].ues o~ i2 ~or Dif�erent , M and n for i
Mixtures with Axgon~-03: rt = 0.1 (straight line, a) and 0.2 ~
(a, dotted line~; N20 : r1 = 0.1 (straight line, b); COS:
n~ 0.01 (b, dotted line); NO C1: n~ 0.1 (c, straight line), ;
0.5 (c, dotted line) and 0.2 ~c, dash-dvt line); NOBr: n ~ '
0.1 (straight line, d); NOC1: n= 0.1 (d, dotted line) and I"
N~O~cSn = O.1 (e); for the bottom dotted line in fig a, t2~ :
Key ~
:
1. pQ , atm !
~6
In fig 5 are given the masimum values of ~unction S2v(x) in relation to p~
and M(similar to the oblique l:ines in �ig 2). ~o~c the ~requencies indicated ;
. with these curves inversion in the p~, M plane is not achieved below the ~
curves and is achieved (although in not too great a zone o~ in the plane t
above the curves.
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Table Parameters Used i~px Ca7.cul.ating Speci~ic ~ubstances
d
I . .
V
" ~ a o 3~ 4~ o
1~` ~ I, 2~ ~ r'{p1 ~'-1 ~
~ c~t'i(ainnb�c) ' ~
~ I ~ Y I B-~ _
W
t I CI I NO ~ 3Y,79 I 7,9�10~s (24] I l,7�iC'~ I 34.79
2 I Cl I NO~ i 27,5 I 6,3~10~a (32j I 2,~.10~~~ I:iu,3 (;ilJ
3 I Er I I~O I 25,04 I 1,1�1016 [2~!] I 2,3�10'a I 25,04
� 4 I O I O: I 22,7 ~ 10~~ [25) i 1,3� 101~ i?4,25 [23) -
5 I O I 1`~0 I 65 I 1,1 �(O1e [23] I 2� 10~' I 72 (`l3]
G I 0 I N: I ~S I 5�10" I 1,3�1011 I 59 [23j
7~ S I CO ( 60,7 I I,5� IOt'' ~ 3,7� 1011 I6S,3 [23]
; I ~ 5~ I j~~~
~ o kz.
� < C\I~%~M074~�l'~ eica~fn~on~ ~r~ i ..i~P
_ ;i ~ ~tic~~ ,
pn1~~ .R I
~ u ~ 1
I I. _
1~ ~,8�101= I 0[30j I 1,4�1Q~; [23] I 58 [17) I 1,3 i 0,38
~ - -
2 5,:3�10~~ i 0 I 1,4�10~~ [23J , 58 [l7] I 1.3 I Q,38
3 �1� Il)'Z I 0 I 2,9� IQ~~ [23] ( 9fi (F7J I 1,5 ( 0.�tt
4 l,?. !Oi~ I 4,7 (25] I 2,5� 10'~ (23~ , 120 [!7] I O,G I ~1,~}
~ '
5 i0~a I Q[27] I 2.5� 10~~ [2,i] ~ 120 [17J I O,G I 0,1 -
6 s".1G~:~ I'>S [30) I 2,5� 10~~ [23J I 120 [17j I O,G I 0,4
~ 7 s�to13 I 2~ (2E~ I~�~o~~ (2s~ I too (i~~ I o,~s ~ o,s~
Note:
0-1 E~/RT E�D/RT ~'1 , 0 E
ki� ~k~~ ~ -{-(IMl/koo) ~ ~ ~ ~ ki=~A~,e - ~iRT . -
7~kr is the red boundax~? o~ inyestigated wayelength xegions ~ox sppntaneous
chemiluminescence; S2~ ~ ~hl~kr~43 ' ~
IKey on following pag~]
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K~y:
1. Nwaber o~ n?fxture 5. cm6/ (mo1e2 �s)
2. kc~l/mole 6. Akr , u
3. ctn1/ (mole � s) 7. i2k
r
- 4. s
Fig 5 must be considered in comparison with the last column of table 1. For
exaaiple, in the case of an 03~Ar mixture (No 4 3n table 1) luminescence is
substantial in the spectrum region o~ S2 > 0.4 . To this mixture corresponds
fig Sa, from which it is obvious that with this S2 in the c~se of thinning of
n= 0.1 (solid-line curve) inversion is achieved already with a pressure of
p on the order of 1 atm and M= 5.5 to 6, because of which the unft con-
- centration of atomic opqgen, C~ , is on the order of one. With p ti 10 atm ,
inversion exists also for shorter wave radiation, right up to S2 = 8.6 , i.e.,
a=0.4u .
A comparison of fig Sb to e with table 1 shows that in the case of mixture
No 2(fig 5c) inversion and high unit concentrations of atomic chlorine are
also easily achieved. The situation is worse with the remaining mixtures.
Mixtures Nos 6 and 7 are characterized by low velocity of reaction (1), since
for them constant k~ is very low. Therefore in situations when inversion is
achieved in the necessary region of the spectrum CR proves to be low. Mix-
tures Nos 1, 3 and 5(fig 5d and e) achieve inversion in the necessaxy spectrum
region only with high pp. We give the resuTts of further calculations only
- for 03 and N02C1. Coefficient a(w,T) figuring in (17), unlike in [16], was
calculated on the assumption that with high pressures, because of the heavy
impact broadening of ltmminescence lines, the rotational structure of spectra
disappears. For a maximum of a(w,T) the following values are obtained:
~ O-f-O, ~=0,6 ~ a==5� 10-~~(1000/7~3~z exp (-14,800/T) cai5;
Cl-}�Cl, 7~=1,17, u a=2,4� 10-43(1000/T)~~2 exp (3300/T) cn~'.
The gain for the waveguide mode was calculated from equations (16) and (17)
for different values of p and M. Unlike in sec 2, where a value of S
was'assumed corresponding ~o Ar, here and below were taken into account con-
tributions to all Re e'of all components of the mixture, the polatizability of
, which was taken from [15]. Among calculated values for a81 the following
proved to be the highest:
a~�= 1,5� 10-3 cM-1 for 0: Ar-1 : 5, Po-17 aTnr, M-6,4. (21)
a~�=3� ]0-' cri 1 for NOQCI : Ar=1 : 20, po=8 aTri, At=3,9. (22)
Also obtained wexe dependences o~ on Y/hr of the type given in ~ig 4. 2
For the cases of (21) and (22), with ~r/~y =~/3 , P = 224 and 8.7 kW/cm ,
and the light energy obtained ~rom 1 g o~pthe mixture,~+l and 5.5 J, respectively.
14 -
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y!.. ~ . . , ~ . , . . - . . . . . . ~ ~ . . . ~ ~ ~ ~ . . ~
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4. ~nvestigation o~ Speci~;ic 1`~xtures in 4Jhi~h Ato~ts Recombine Radiatively
with Molecules of the Dfluent
Let us consider the more complex reaction scheme in which in addition to (1) ~
to ~3) the following reactions take place: ,
r ~
M-{- X-}- M= MX A4 j Q (23)
~
AX-}-M=A-{-MX, (24)
Xa-?-M=b1X-~-X. (ZS)
The radiation channel important for laser generation is made possible now by ~
reaction (23), and not by (3). _
Instead of (8) and (9), in this case it is necessary to solve three kinetic
equations, e..g., for [R], [X2] and [MX]. Wst has the previous form in (18),
but inst~ad of (17) we get
a'=-a(c~, 7~{[X]IM1--I:~~XI~;e~~'/k''},
(26)
where K is the equilibrium constant o~ reaction (23). In a corresponding
manner were changed the equations for the balance of matter and the expression -
for h in equation (6).
Be1ow are considered five specific mixtures in which % is always an atom of
hydrogen (Q = 120 kcal/mole), and M and AX are given in table 2. The
reaction ra~es o� re~ctions (23) to (25) have a te~perature0dependence of the
kind k= k exp [-E /(RT)] , and the values of k and E are given in
table 3. The equilibrium constants for these reactions and other thermodynamic
characteristics are taken from [17]. ~
Inversion regions in which a' > 0 are given in fig 6, similarly to fig 5.
Mixture No 12 is not given in ~ig 6, since in the actual spectral region,
according to calculation, inversion is not realizable for it. Mixture No 11
is unstable at room temperature; therefore for it was used a value of T=
~ 100�K [21], whereas for the remaining mixtures in calculation it was assumed
that TD = 300�R . Let us stress that if in ~igs 2, 5 and 6 along the X axis _
instead o~ M is plotted T ia~mediately a~ter the sudden ahock (cf., e.g.,
fig 6b), then the curves u~aintain their position and ~orm even ~or TD somewhat
different fxom thos.e e$tablished 3n calculations (stxona shock Weves). For all
the mixtures gtven in ~i,g 6 in the actua,l apectral region inversion is real-
izable at not tvo hfgh pxesa~uxes�.
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~
Table 2.
. __I q _
Il,~cc~i` _ I. _...1X ---I--' I,I'. Mh~.i --I !:rp
l~ ~L_
_ 8 I Cn I _
_ g I ~p I~_p ~~8 Q,3
10 I CO I ~VO.,
' Il I NO I p9 ~
1,4 0,17
12 I NO I \O._ '
Key :
1. Number o~ Mixture 3. S2k
- 2. 71~r, u r ,
Table 3.
PeaK~WN 1.~ I k: ~ Z~E=. 3'lurepa�
KK9~'~(0.7L~ rypa
~ ~
O' -I- CO I G� 10~~ I 22 I [29~
_ N_O CO I 1,1 � IOtI I 23 [5J ~ .
I
NOj CO I 2� IOi'- I 29 I ;
I ~
~a-I-NO ( 4,2�101" I 23 I (21] I
i
N20-}- NO 2,5� lUl; I 50 [~J :
I I ~
~ Oa-i-CO I 3�1012 I 5l I [30j i
I
CO O-}- M I 6, 2� 10~a I 0 I (30J
NU-}- O-}- M I 10" I ~ p (27j
;
i
Nofie: The xeaction rat~s g~ l~iaqp~ecu~,ax x~a,cCiqns axe giVen in cm3/ (mole �s) , I
and ot tri~olecular, in c~nq ~~mole �s:~ .
jRep~ on follm~.ng page] ~
' 16 i
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Key:
- 1. Reaction 3, Bibliography
2. kcal/mole ~
Pm./u~~~ 1~
lU
~'s ~
. ;
~ 6,~i r7 M
i
o,~ jf a)
g 9 f0 M
l'~~, 14U0 ~ ---T
----r--- ~
17u^0 1BC0
T, H
0,1 0, 3
u,~~ - a,2~ b)
pa,amM l;4i~ 0,5
~ Bf B,5 ~9 M
0, 3 ~ ~ py
/ '
i
i
G,1- ~
~igure 6. Maximum values o~ S2v ~pr the ~ollowing Mixtures: 03~C0:
n= 0.1 (solid line); 0.05 (dotted line) and 0.025 (dot--dash
line) (a); 03~T0 (b); NO2-CO (solid line) and N20-CO (c,
dotted line); for b and c, r1 = 0.01
Key:
1. p0 , atm
In order to give pre~erence to one of these mixtures it is necessary to con-
sider characteristics oP them not given in �ig 6. xn particular, important
are the values of gain in which totallq taken into account are concentrations
of atomic oxygen, the properties o~ the waveguide, etc. Gain w~s computed
for many values o~ p0 and rI .~n all cases it was assu~ed that n~ 0.1 .
The following maximum values of a~s1 were obtained for the zero waveguide
mode:
a.~�= 1,2� 10-3 cn~-1 for O,-CO, pu-1`2 a~rst, M�=6,
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u~�=~! � 10-5 cnt-1 for N ZU--CO, po-7 aTni, M= 7,6,
a~�-=2� lU-'' cn~~'' for NO.~-CO, po =13 a~rni, M=7,4, .
a~n-~3� 10'~ cn~-i for O~- NO, pn==0,1 aTn~, ]~1...~8,5. (27)
In the case of the last mixture were studied only pressures n~t greater than
0.1 atm, since for T~ = 100�R with great presaures the mixture is condensed.
It is obvious from the data given that asl is maximum ~'or a mixture of
03 C0.
It is obvious from the results of secs 3 and 4 that 03 is a better donor of
atomic oxygen than N20 and N02. This is associated with ~he fact that in 03
the activation energy for separation of an oxygen atam, E1_ e is lesa than 3n
the other molecules studied, and pre-exponential factor ~k.l is fairly high
(cf. table 1).
For a mixture of 03 CO = 1:10 and for the parameters in (27) the equations
_ were solved b}~ taking into account the stimulated radiation. Arrived at were
~ P= 155 kW/cm with y/~y = 0.22 , and the light energy equals 54 J from one
gram of the mixture. Th~s value of P is not, generally speaking, the maximum _
possible, since in this and the previous sections we selected p~ and M so
that as1 would be maximum, and not P~X .
We were conv~inced that in all the cases considered M corresponds to conditions
of supercampressed detonation, when steady-state flows with a shock wave exist
[13]. Checked also was the test for the stabilitq of unidimensionality of
the flow (of a plane front) [22]. A plane front of supercompressed detonation
can be accemplished either by means of a piston pushing the studied gas at
supersonic speed, as is done in a shock tube, or in a supersonic steadq-state
flow of this gas. The velocitq of the flow and its variable cross section can
be selected ~o that the front of the shock wave will be stationarq.
- The radius of curvature, caused by viscous layers near the walls, of the front
of a shock wave traveling through a tube 10 cm in diameter equals R ti 100 m.
At the same time losses of photons resulting frrnn distortion of the waveguide's
plane become comparable with the calculated values o� a onlq with R on the
order of a few centimeters. Because o~ the origin of a waveguide it is poesible
to accomplish feedback in a laser without mirrors, when in a non-unidimensional
' flow the front of the shock wave, the waveguide and the path of the light beam
form a closed circuit. _
According to estimates, with evolved generation in a wavegu~de the atrength
- of the electric field caa reach a value on the order o~ 10 MV/cm, which creates
the threat of a breakdowa o� gas even at ~requencies corresponding to viaible
13ght.
' 18
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Conclusion
With the exa~ntple o~ specific gas mixtures it has been shown that by L~eans of
a shock wave it is possible to trigger an electron transition chem~cal laser
with high flow density and speed, i.e., with high supplied chemical power.
A proof has been given of the possibilfty of the formation of a plane waveguide
behind the front of the shock wave, which eliminates losses of light associated
with slight thickness of the generation layer. The conditions for formation of
the waveguide are compatible with conditions for th~ origin of inversion and
intensification. For the types of reactions considered the positive role of
the diluent consists in acceleration of the useful reaction for the dissociation
of donors of R atoms, making it possible for this reaction to compensate the
consequences of harmful react~ans which destroy X atoms. Pnmping of these
lasers is accomplished on account o~ chemical and mechanical energy of the
- gas fl~w co~parable in magnitude. For specific gas mixtures a gain ~n the order
nf 10 cm has been achieved and a power on the order of 100 kW/cm of the
cross section of the gas flow, which exceeds the unit power of all known
chemical and thermal lasers.
Bibliography
1. Pekar, S.I. DAN SSSR, 187, 555 (19E'~).
2. Kochelap, V.A. and Pekar, S.I. ZHETF, 58, 834 (1970); UFZH, 15, 1057 (1970).
3. Kochelap, V.A. and Pekar, S.I. DAN SSSR, 196, 808 (1971).
4. Kochelap, V.A., Kukibnyy, Yu.A. and Pekar, S.I. KVANTOVAYA ELEKTRONIKA,
1, 279 (1974).
5. Tal'roze, V.L., Gordon, Ye.B., Moskvin, Yu.L. and Kharitanov, L.P.,
DAN SSSR, 214, 846 (1974).
6. Bashkin, A.S., Igoshin, V.I., Nikitin, A.N. and Orayevsk~y, A.N. "Khimi-
cheskiqe lazery" [Chemical Lasers], Moscow, VINITI, 1975.
7. Biryukov, A.S., Prokhorov, A.M., Shelepin, L.A. and Shirokov, N.N.,
ZHETF, 67, 2064 (1974).
8. Losev, S.A. ~~Gazodinamicheskiye lazery" [Gas Dynamical La~ers], Moscow,
Nauka, 1977.
9. "Electronic Transition Lasers" in "Proc. 2nd Swmner Colloq., Woods Hole,
Sept. Y7-19, 1975."
lU. Ekstrom, D.J., Barker, J.R., Haraleq, J.G. and Reilly, J.P. A~PL. OPTICS,
16, 2102 (1977).
11. Gross, R.W.g., Giedt, R.R. and Jac~bs, T.A. J. CHEM. PHYS, 51, 1250 (1969).
19
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_ 12. ~ekar, S.I. ! Zz~yloy~ Z.A. , Kochel.ap, ~'.A. and KLkiL-nyy, Xu.A.
DAN S~SSR, 241, 80 (1Q78) .
13. Zel'dovich, X`a.B. and Rayzer, X`u~~. "~izika udarnykh voln i vysokotempera-
turnykh gazodinamicheskikh yavlenig" [Phqsi~s o~` Shock Waves and High-
Temperature Gas Dynamical Phenomena], Mosco~a, Nauka, 1966.
14. Kondrat'yev, ~1.N. and Nikitin, Ye.Ye. "Kinetika i mekhanizm gazofaznykh
reaktsiy" [Kinetics and Mechanism of Gas Phase Reactions], Moscow,
_ Nauka, 1974.
15. "Tablitsq fizicheskikh velichin" [Tables of Physical Magnitudes], editied
by I.K. Rikoin, Moscow, Atomizdat, 1976.
16. Izmay~lov, I.A., Kochelap, V.A. and Kukibnqy, Yu.A. IJPZH, 21, 508 (1976).
17. Glushko, V.M. "Termodinamicheskiye svoystva individual'nykh veshchestv"
[Thermodynamic Properties of Individual Substances], Moscow, Izdatel'atvo
AN SSSR, 1962.
_ 18. Ashmore, P.J. and Spencer, M.S. TRANS. FARADAY SOC., 55, 1868 (1959).
19. Ashmore, P.J. and Burnett, M.J. TRANS. FARADAY SOC., 57, 1315 (1961).
20. "Energiya razryva khimicheskikh svyazey. Potentialy ionizatsii i srodstvo
k elektronu" [Energy ox Breaking of Chemical Bonds; Ionization Potentials
and Electron Affinit~~], edited by V.N. Kondrat'yev, Moscow, Mir, 1974.
21. Izmaylov, I.A., Rochelap, V.A. and Rukibnyy, Yu.A. In the collection
"Kvantovaya Elektronika" [Quantum Electronics], Kiev, Naukova Dumka,
No 14, 1976, p 26.
22. Shchelkin, R.I. and Troshin, Ya.R. "Gazodinamika goreniqa" [Gas Dqnamics
of Combustion], Moscow, Izdatel'stvo AN SSSR, 1963.
23. "Fizicheskaya khimiya bystrykh reaktsiy" [Phqsical Chemistry of Past
Reactions], edited by I.S. Zaslonko, Moscow, Mir, 1976.
24. Maloney, K.K. and Palmer, A.B. INT. J. CHEM. KINET., 5, 1023 (1973).
25. Center, R.E. and Rung, R.T. J. CHEM. PHYS., 62, 802 (1975).
26. Hay, A.J. and Bel~ord, R.L. J. CHEM. PHYS., 47, 3944 (1967).
27. Dushin, V.K. and Losev, S.A. NAUCHNYYE TRUDY NII MEI~IANIKI MGU, No 43,
102 (1976).
28. Thrush, B.A. and Fair, R.W. DTSC. FARADAY SOC., 44, 237 (1967).
20.
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29. Garvin, D. J. ~SER. CHENi~ SOC., 76, 1523 (1954).
30. Kondrat'yev, y.N. "Konstanty~ skorosti gazofaznykh reaktsiy" [Reaction
- Rates of
Gas ?hase Reactione], Moscow, Nauka, 1971.
31. Martin, H. and Knauth, H.D. BER. BUNSENGES PRYS. CHEM., 73, 922 (1969).
- 3?... Cordes, H.F. and Jonstan, H.S~ AMER. CHEM. SOC., 76, 4264 (1954). -
= COPYRIGHT: Tzdatel'stvo Sovetskoye Ra.dio, KVAN7'OVAYA ELEKTRONIKA, 1973
[23-8831] -
, CSO: 1862
8831
' 21.
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LASEltS AND MAS~RS
UDC 621.373.8.537.533
OPTIMIZATION OF ELECTRON BEAM PARAMETERS AND CHOICE OF FOIL IN ELECTRON BEAM
CONTROLLED LASERS _
Moscow RVANTOVAYA ELERTRONIKA in Russian Vol 6 No 8, Aug 79 pp 1690-1697
manuscript received 20 Nov 78
[Article by A.I. Dutov, S.V. Minayev and V.B. Nikolayev]
[Text] By the Monte Carlo method a study was made of the transmission of
relativistic electrons through the foil-gas-anode system in an electron beam
controlled laser (EIL). The influence is discussed of beam parameters, the
cdmposition of the active medium and the electric field in semi-self-maintained
discharge, as well as of the design features of the laser on homogeneiGy of
ionization in the discharge gap and on uniformity of the electric field in it. ~
Questions are discussed relating to selection of the beam's energy and design
elements of the laser when using light foils.
1. Introduction
In an electron beam controlled laser the electron beam, accelerated to relati-
vistic velocities, passes through a vacuum-tppe foil and ionizes the active
medium, whi~ch makes it possible to contribute considerable energy to large
volwnes of the active material [1,2]. At the present time considerable atten-
tion is being devoted to problems of spatial homogeneity and stability of a
semi-self-maintained discharge in laser mixtures [3-6]. A number of suthore
have noted that nonuniformity of ionization over the cross section and length -
of the discharge gap contributes to instability of the discharge [4,5,7,8j.
Obviously associated also with inhomogeneous ionization of the laser cavity
and with subsequent nonunifona excitation are inhomogeneities in gain and
in the final analysis in the medium's refractive index [9]. The limiting
characteristics o~ an E~L of both the continuous and pulsed periodic type
depend not only on these ~actors, but also on the heat reaistauce and trans-
mitting capacity of i~oils [lOJ. _
These problems are responsible ~or the considerable interest in investigationa -
of the tranamission o~ electron beama through ~oils and active media in EIL's.
In addition, in the utajority~ o~ studies on the theoretical plane important
factora influencing the pattern o~ the process have not been taken into
account. ~or example, in so~e studies the electron bea~ on its entrance into
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the gas was considered monochxoiqatic, i~e., the consequences q~ scattering of
electrons in the ~oil, were nofi taken into account [13]. In studies [5,13]
the distribution o~ ionization losses in laser~n2ixtures was studied only with
nitrogen as an example~ Often not paid attention to has been the presence of
the anode of the primary~ discharge, although it is known that electrons reflected
back can effectively ionize part o~ the gap [12]. Tt is also necessary to take
into accounfi the structural arrangement o~ the cathode, usually executed in the
form of a grid, since there is no electric ~ield between the ~oil and cathode.
This exerts an influence on formation o~ energy an~ angular distributions
in the flow of electrons arriving at the cathode. An investigation of laser
~ construction has been made in ~ust one study [12]. Here a study was made of
the influence of the anode's material on the distribution of ionization lossea
in the gap, but calculations were made only for a single specific combination
of parameters.
' In this paper a study is made of the transmission of electrons with energy of
100 to 250 keV through the foil-gas-anode system in an EIL and an estimate is
made of homogeneity in ionization of the ~.~orking material in relation to the i
height of the discharge gap. Discussed are standard foils, typical laser
mixtures at atmospheric pressure and electric fields in a semi-self-maintained
discharge. Of course, the energy and angular spectra of relativistic electrons
depend on the type of electron gun; in particular, for systems with a field
emitter the energy spectrum is of a rather complex nature, which together with
broad angular distribution results in considerable losses in passing through
the foil [15]. Pulsed pawering of an electron gun with a cathode of any type
also results in added losses in the foil as compa~ed with a gun ope~ating
" with a steady power supply. Therefore in our calculations it was assumed that
in the EIL is employed a grid-controlled electron gun operating with a steady
acceleration voltage [16,17] and making possible monochromaticity of electrons
= and orthogonalization of their paths to the emitting foil window.
In this study are calculated distributions of ionization losses, D(x) , and
of the electric field, E(x) , over the height of the discharge gap. Further-
~onore, the energy of the monochromatic electron beam, Ep, hitting the foil was
- ~raried, as was also the magnitude of the electric field, E, averaged in terms
of the length of the discharge, and applied between the ca~t?ode grid and anode. .
A study is made of the influence o~ the thickdess and material of the foil, as
well as of the composition of the active medium and of thQ anode's material,
on these distributions. The calculations made make it possible to draw certain
conclusions regarding optimization of the parameters of electron beams and
foils, as well as to specify requirements for the design of EIL's.
2. Calculation Procedure
- These distributions and characteristics were calculated by the 1~Ionte Carlo
_ method ~rl.th ref erence to a model o~` continuous deceleration [ 1~] . Zn each
case were considered the paths o~ travel o~ not less than 2~10 electrons _
hitting the ~oil. Hexe iqean ionization losses per unit length o~ the electron's
path in the ~qaterial o~ the ~oi1 and a~ the laser ~aaedium were determined from
Bethe's equation, and tfie angulax distribution o~ electrons was calculated
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with Moli~!re's ecJuatiQn~, [].8] ~ 7,'he ~h~ckness p~ the ~(o~.iL~e ],a~*ex was chosen _
so that 20 to 25 collisions would occur in it~ CAnsideration p~ the thtee~
dimensional tqotion o~ sn e~.ectron in the medium ceased when its enexgy dropped
to 10 keV. Let us� note that ~ox the purpose of reducing the ealculation time
it is possible to consider tY~e two~dimensional path o~ an electron. An analyais
has shown that here acccuracyr is reduced ~i~ye percent in calculating the trana~
mia~aion oP foils [19] and 10 to 15 percent in calculating losses in the gas.
The original electric field in the discharge gap was considered homogeneous
and constant at the initial stage of the discharge. Zn all figures, except
- specially stipulated cases, the ~oil is located in plane x= 0, and the
cathode grid wtth 100 percent transmittance, in plane x= 2 cm . Based on
distributions of losses, D(x) , obtained in the foil-gas-anode system, the
function of the secondarq electron source was computed, i.e., the rate of
formation of electron-ion pairs in the gap [20]. Then, according to a procedure
similar to [7], were calculated local changes in ~the electric field, E(x) ,
in the discharge gap. The cathode drop was not taken it~to acco~nt, since in a
typical EIL its spatial spread equals approximately 10 to 10 cm [21]. For
a mixture of C02�N :He = 1:2:3, the distribution of E(x) was calculated by
taking into accoun~ the dependence of the recombination coefficient on the
electric field [22]. -
For the purpose of checking the correctness o~ the pracedure, variants were _
calcula�ted, data on which were available in Che literature. The discrepancy
with the results of studies [10-12, 14, 23] proved to be less than 10 percent.
3. Results of Calculations
In figs 1 and 2 are given unidimensional distributions of ionization losses, -
D(x) , in keV/cm, over the length of thE discharge gap taking into account
different factors influencing the homogeneity of ionization. Here it was
assumed that the anode is an ideal absorber of electrons, which made it
possible to isolate its influence from other effects. In f ig 1 are shown
distributions for four values of the energy of the electron beam, ED , hitting '
- an aluminum foil 25 u thick (curves 1 to 4). From this figure it is possible '
to estimate to what extent the degree of homogeneity of ionization depends on , ~
the length of the gap selected for each energy value. For example, at a dis-
tance of 10 cm frrnn the cathode the decline in ionization relative to the
maximum equals 38, 20 and 10 percent for beams with energy of 130, 150 and ,
200 keV, respectively. At a distance of 18 cm from the cathode for these
same energies the decline in ionization reached 66, 40 and 30 percent (and
only seven percent ~or EQ= 250 keV Calculation of similar relationships
with a foil thickness o~ 50 showed that the value of the ionization maximum
was reduced ~or low E and grew ~or high. The homogeneity of ionization
worsened considerably,~especiallp ~or beems with energy of 130 and 150 keV, '
for which the mean free path o~ electrons was drastically shortened. '
Curvea 1 to 4(.~ig 1) xelate to the typical laser mixture C02:N2:He = 1;2:3, ~
which ie relatiyel~r light b.eca,uae o~ its. strong helium content. ~n working ;
_ ,
24
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with more inexpens�iye He�,~ree laixtu~es� it is necessaxy to take into account
their strong retardin~ capacity~~ Cuxves 5 and 6(~ig 1) s~ow�the behavior
. of the dependence o~ ionization losses, D(x) ,~or nitrogen and the mixture
C02:N = 1:3, respectively, with E~ ~ 150 keV . Obviouel~r, in changing to
dense~ gases ie observed a sudden increase in the degree o~ tonization~ as
well as in inhoffiogeneity (c~. curves 2, 5 and~6 in ~ig 1).
11~ K3H~C.M
I
d ~ 6
I
I 5
6 ~
I
1
~ 3
I
I
~~~i
2 ~
I
I
I
I
L ~ ~L- i ~
0 S 10 I5 29 x, cM
k'igure 1. Distribution of Ionization Losses Over the Length of tlte Gap
with EX = 5 kV/cm for Mixturea of C02:N ;He = 1:2:3 (1 to 4),
CO2 �N ~ 1:3 (6) and for Pure Nitrogen (S~j; E~ = 130 (1),
15v.(~1,5,6), 200 (3) and 250 keV (4)
Key :
- ~ 1. D, keV/cm
D, K~B/cM
, ~
B ; ~
i
6 ~
- ! 2, Ex = BIfB~CM
4 ~
. i
Z ~ 0 3 S
~
0 S 10 15 10 X, Ch~
~'igure 2. Distxil~utipn p~ Ionization Lpsses Oyer the Length a~ the Gap
as.~ a~uncti,qn p~ the E~.e.ctxic ~ield ~ar the l~ixture C02:He ~
1:3
[Key on followiag page~
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_ . ~ , , ,
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Key:
1. D, keV/c~q 2. EX ~ 8 ky/cm
As early as in the first s�tudy,on the calculation u~ losses [14] it was noted
that it is necessary to take into account the in~luence o~ the electric field
on the travel o# electrons in tlie gap. Tn ~ig 2 are shown distributions of
losses, D(x) , in taking into account several ty~pical values of the electric
field E (E = 150 keV aluminum ~oi1 25 u thick). Obviously, an electric
field~applied~collinearly~to the dixection o~ travel of electrons considerably
extends the mean free path o~ electrons in the gas, but the magnitude of the
field has a but slight in~luence on tiie degree of inhomogeneity in ionization
of a gap 10 to 15 cm long. It is significant that curves for EX = 5 and 8 kV/cm
are very close in the gap considered.
For the purpose of approximation to a real EIL system, calculations were made
by taking into account electrons repelled from the anode. In fig 3 are shown
dependences of losses D(x) and fielde E(x) for two specific laser units
described in [16]. In both cases were used identical acceleration voltages
(E~ = 150 keV), foils and discharge gaps. The difference consisted in the
composition of the gas mixture and the strength of the electric field in the
discharge. Obviously for the mixture C02:N2 = 1:3 there is a considerable
decline in ionization near the anode (approximately 50 percent), and electrona
repelled by an a~uminum anode improve homogeneity but slightly. The diatribution
of ~he electric field in this case is strikingly inhomogeneous. For the light -
mixture CO :NZ:He = 1:2:3, the homogeneity of ionization is fairly high
(approxima~ely five percent) and the role of the anode in equalizing ic,nization
and the electric field is substantial. From comparing figs 3a and b it becomes
understandable why in the case of a light mixture in the experiment it was
possible to realize a higher enexgy contribution and energy output in spite
of ~the great ~ difference in electric f i.elds in f avor of the heavy mixture [ 16
With an increase in the beam energy, EQ , to 200 keV, the contribution of
electrons repelled from the anode to ionization of the gap can have e consider- ;
able influence not only on homogeneity, but also on the degree of ionization
(fig 4). In the same figure it is shown that with an increase in density and
atomic number of the anode's material the share of repelled electrons in ion- ;
ization grows and reachea 50 percent at the anode, which is in agreement with
the results of study [12].
- A role o~ no slight importance in the interaction of an electron flow w3th an '
active gaseous mediwn is played by the energy and angular distributions of
electrons formed after the beam passes through the foil. We calculated the
energy and angular spectra for beaa~s wlth an initial energy o,~ EO = 150 keV' ,
having passed through various #oils. Tt is obvious ~:rom ~ig 5 that ~oils with
low unit density~ di~~;ex advantageou~ly ~rout heavier ~oi1s in the sense of ;
preserving the monochxrn4aticity~ and directivity o~ the beam. Especially dis- ~
tinguished is a Lavsan film. ~
The distrihutions o~ ionization ~osses.~~ D(x) ~ gtven in ~igs 1 to 3 were
obtained on tl~e b~aeis o~ a s~in~7.e electxon hittin$ tlie fQf~.. ~or the purpose '
o~ es�timating tt~e ~unction o~ tYie aecondary electxon souxce and the distribution ~
26 ~
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of the concentratiQn Q~ e7,e.ctxons: in ~he disch~r~e this is su~~;icient,
but ~or the purpase o~ c&1,cu7.a~i;t~~ heat ~el,ease in ~ctils~ a1,s0 required is
knawledge o~ energy~loases�pe~ sia~le el,ectxon in passing thxpugh the ~ilm,.
The table gives $n idea o~ the txans~nission coe~~icien~s o~ standaxd ~'oils in
relat3on to energy, T, and current, T, on tt~e assumption o~` monochromaticity
of the electron beam qnd normal inciderice on the ~oi1. C~lculatione ~or
current agree well with experi~ental a~tudy [23], and ~or coefficienta T and
TE , with theoretical study~ j11] (with an accuracy ot one percent). There _
is also agreement with the reaults of studies [12,14], if it is taken into
account that contributing to coefficient TE are both ionization losses of
the primary beam and the energy o~ electrons repelled from the foil. Actually,
- in the final analysis repelled electrons basically return to the foil and are
absorbed 3n it because o~ the braking field of the electron beam._ A1so indicated
in the table are calculated values o~ the mean scat~tering angle, a, and the
mean energy of an electron, E, passing through the foil. Thus, the table
supplements fig 5.
D, H3B~CFI E, HB.~CM
ll! ~ I~ 1)\, i0 I~~,
~ ~ 8 i 6
~ i ~ i 5
6 i 1 4
5 I 3 5 ~
I ~i
I 2 i
0 2 4 ar, cM 0 Z 4 6~r, cM
~ b~
Figure 3. DisCribution of Ionization Losses (1) and Electric Field
Strength (3) in the Discharge Gap According to the Data of
[16], as Well as Contribution to Tonization of Electrons
Repelled frrna the Anode (2) for Mixtures of C02:N2 = 1:3
with E= 6.6 kV/cm (a) and CO :N :He = 1:2:3 with E_
= 4 kV/cm (b) 2 2 X
Key:
1. D, k.~V/cm 2. E, kV/cm
~ ti~36fcrf
i 1)
. ,7
~ . ~
L '
~,.,'~i
. C 1 3 6 a', cFJ
~igure 4. Distributfcm a~` Tonization Losses, D(x) ~ in the Discharge
Cap (So1id Lines) and Contribution to Tonization oP Electrona
[Caption continuation and key on ~ollowing page]
.2~ .
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Repelled ~rqp{ tRe ~node (~Qt~]?ash ~,tnes.) ~`Gr ~nodes ~ade o~
Copper , 3tee~. (_2~ and ~1.uu~inu~4 (3~ t = 2D0 kev ~
~'oi1, ~1us~,in~, 25 ~ Tliick; ~i~cture o~ CQ21N2 ;He a~,; 2; 3;
E 5 ky/c~q
Key: -
1. D, keV/cm
N(fl, am~~ ed. 1~
0,9 ~ N~a~/N~~~ ~
_ 0,3 1 ....___.i
2
3 4 1 ~ .
0, 7 O,S j
. a ~
I
~ 0 3U 60 90a �
a ~ 24 3 .
2) .
~7S 100 175 E~ K3B
Figure 5. Energy (a) and Angular (b) Spectra o~ Electrons Having
Passed Through goils of.Different Thickness: 1--aluminum,
50 u; 2--,aluminum, 25 3-- Lavsan, 20 u; 4--titaaium,
13 u
Key: .
1. N(E) , relative units 2. E, keV ,
4.-Discussion of Results and Optimization of Unit
The calculation routines which have been developed make it possible to select
the optimal energy of the primary beam with a specified set of parameters:
the material and thickness of the foil, the cmnpositiion of the mixture, the
length of the discharge gap and the strength of the electric field in it. _
For example, for an EIL with a discharge gap approximately 20 cm long and
- an aluminum foil 25 u thick, increasing the energy of the beam, Eo, about
150 keV is not advisable in the case of light mixtures. Calculat3ons which
we.have made showed that increasdng the energy of the beam bq 50 keV, other
conditions being equal, practically does not change the level of ionization
in the gap and even slightly worsens homogeneitq. It was indicated in [2]
that increasing t.e energy o~ the beam higher than 150 key did not reault in
the experiment in a noticeable increase in contributions o~ energy to the
discharge. Wlth a~urther inc~cease in lieam energ}r there will be an increase
28.
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in the share gpi~g i~tp heax ~nd x~adiatipn in the. ~ri~qarY discharge anode,
and the mea,rt ~ree pa.~h. Q~ repelled e~,e.ctron~� wi.1,~. a~,so be incxe~sed. Con-
sequently~, ioniza~ion near t~e enode wi1,1, ~rowy which can res~u~t in strengthening
of the ~ield near the cattiode and in ttle appearance there o~ discharge instability.
Table
~ ~ ~:,~~u~~~:,, I J g -
1~ Tnn c~~r:n,ri~_..._. ~ ~~,/r:.~~ I 1.`.. "~u I rN, ou I rE~ I t. p~ i L�'~ r.aA
~ -
-laioauwF+it 50 13,? 150 62 40 0,79 9fi
2~ 2U0 85 G7 0,76 157
A,~i~aiuu?ttt 25 fi,SS 150 I 91 77 0,72 123
I I I 200 ~ 9G I 88 I O,G! I 183 _
TIIT~H I 2~ I ~~0 I' 1~~ I 7h I 5~ I ~,R~ I ~~l)
3) ~ 200 88 77 0,76 175
TFiTau 13 5,6~ t50 88 77 0,77 131
_ I ( 200 I 95 I 88 ( 0,67 I ISG
Jlaecau 20 2,8 100 98 87 0,56 88
4~ I I 150 I 99(,7) I 94 I 0,41 I 142
Key :
1. Type o~ foil 5. Thick~ess, u
2. Aluminum 6. mg/cm
3. Titanium 7, keV
4. Lavsan 8. Radians
Of no slight importance also is the fact that with an increase in acceleration
- voltage the high-voltage power supply o~ the gun becames complicated and the
requirements for its insulation are increased, the biological shield becomes
heavier in proportion to the energy and the like, i.e., the cost of the unit
increases and its reliability is reduced.
On the other hand, reduction of the electron heam's energy is advantageous
only to a specific limit, related basically to ~the foil chosen. Actually it
is important to ensure low losses in the foil, as well as to form behind the
foil the required energy and angular distribution in the beam (cf. table and
fig 5). Then by proper sele.ction o~ tlie position and material o~ the anode it
is possible to crnttpensate the natural decline in ionization in the gap.
An optimal material for the outlet window is obviously poly~mer films, e.g.,
Lavsan. Actually~~ it is obvious ~rum tlie table that the transmission coeffi-
cients of aluminum ~oil 25 thick and of titaniu~a 13 u thick ~'or E~ = 200 keV
are very~ close to the transieis~s~i.qn coef~icient of a Lavsan ~i~.m 20 ~ thick
29
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as soon as ~Q~~,OQ ~~Y ; 7,'l.i~s� is� s~u~~i~ie~t ~Qx ensurfn~ insigni~`icant
heat release in the ~i1,~~
It is obvious ~raa~ the tatile that in changin$ ~xc~n1 aluminum ~oil 50 ~ thick
to a Lavsan ~`ilm 20 u thick the t~ransmiasion o~ energy* ~or E~ ~ 150 keV
increases ,front 40 to 94 percent, and the tranamiesion ln terma af number of
particles frotn 62 to almost 100 percent. ~or a laser o~ the continuous or _
pulsed periodic type this suiistantial di~`~erence in trans~mitting capacity
of light and heavy #oils is intens~ified more so by the fact that in a real
electro-optical system o~ a gun it is impossible to count on the fact that
the paths of all electrons~ striking the ~oil Frlll be orthogonal to it. This
resulta [19] in drastic worsening of the ~ransmission of foils with angles
of incidence o~ electrons $pproximately greater than 60 degrees, which in turn
entails an increase in heat release in the foil and can cause additional in-
_ homogeneities~in ionization in the gap.
Let us consider a few examples.of optimizing the energy of the electron beam
and the parameters of the discharge gap on the basis of using a Lavsan film
20 u thick and of an assigned value of the mean electric field in the gap
of 5 kV/cm. In fig 6 are shown the distributions of ionization losses and
the electric field in a discharge gap 20 cm long for the mixture C02;N2:He =
= 1:2:3. Homogeneity in ionization at a.level of a few percent (curve 1) is
achieved here by employing an acceleration voltage of E= 150 kV , as well
as bq drawing the cathode grid 4 cm back from the foil. From fig 6 it ie
obvious what an important role is played by electrons repelled from a steel
anode (curve 3) .
j if3~~C'f 1~ 'Z~ f, Nf~~CM
ti j 4 fi~
i' ,
4- p
~ T~ S
~ 3
1~ ~ /
~ ~ u ~ 0
U 4 ~Y 12 16 x, cM
Figure 6. Distribution of Ionization Losses (1,2) and Electric Field
(4) in the Discharge Gap ~or a Cathode Grid Distance of
4 cm (1,4) and 2 cm (2): 3,~Contribution to Ionization of
Electrons Repelled frrnn a~teel Anode
Rey:
1. ke'~i/cm 2. kV/cm
For a g,ap 10 ct4 long the ppti~l calcu~.ated tze~q enexgy~ is k~ 1X0 keV
for the saiae ~nixture and ~npde ~t~atexi~].~ but here ch~nging the beam energy
a total of ~F 10 ke~V rea.atlted in a decicease in ionization at the anode or :
- catiiode o~ 30 percent.
30
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With the s.ame desi~n pax~e.~e~s; p~ tY~e ~i�~,i ~ox ~he purpQse g~ achieying
homogeneous~ioniz~tiQ~ in he~~~qi:x~ures�, e,~.~ CQ2fN2 ~~i3# it i,s necessarY
to deal ~tli high.e.r be~q ene,r~t~s�~ ~`n ~ig 7 is~ shQwn an exa~qp].e o~ achieying
uniformity i~n the ahsox~ed dos.e by s~e~ecting ttle acce~eration valta~e (E~ R
180 to 200 keV) and position o~ tY1e cathode grid. ~t is obvious that in this
manner it is possible to acliieve a reduction in homogeneity of approximately
15 percent (curve 2)~ ~or a discharge gap 10 cm long with the sa~ne mixture
an optimal beam energy o~ En= 150 keil was obtained with a cathode-to-foil
distance of 3 cm. Varying tTiis distance over a range o~ t 1 cm resulted in
a decrease in ionization near electrodes o~ 20 percent.
~ , E, rcB/cr~
HJBI~'~ 1 2
I
~ ~
I 1 ~
6 3 5
4
I 5
y ` ' ' ~ J ~F
0 ~ 8 >2 16 10 x, CM
Figure 7. Distribution of Ionization Losses (1-3) and Electric Field
(4) in a 20 cm Gap for E~ = 180 keV and a Cathode Grid
Distance of 2 cm (1); 200 keV and 3 cm (2,4) and 200 keV
and 2 cm (3)
Key:
1. keV/cm 2, kV/cm
Calculations made with discharge gaps 30 cm long when using aluminum �oil
25 u thick demonstrated that it is possible to achieve uniformity in ionization
on the order of 10 percent with a beam energy of E= 250 keV both for light
and for heavy mixtures. Here the decisive role in ~he formation of ionization
near the cathode is played by the position o� the cathode grid, and in equali-
zation of the absorbed dose at the anode, by the material of the anode.
T!zus, the utilization of light foils wl.th a simultaneous reduction o� the
energy of the electron beam makes it possible to increase the concentration
of secondary electrons in the plasma, to reduce the cross section of the dis-
charge (because o~ a reduction in scattering angles in the foil), as well as
to facilitate the biological shield and to sintpli~y the unit. Light �oils are
distinguished also by~ reduced losses with respect to energy and the number of
particles, which makes pos:sib7,e the txansmission by them o~ gxeater mean power
- of the electron f1ow~ Tn the ~.iteratuxe there is ia~`ormation also regarding -
the employ~qent of an a.7.um.inwq ~Qi1 12 u thick fn a pulsed C02 laser [22] and
of a syathettc ~i~.m o~ tfi~ s.~e thickness in a continuous pxvduction process
laser [24], whicli tes~~i~fes� to the sux~qountal3il,ity~ of the technfcal di~ficulties
asaociated with caaipacting ttii7t ~oils� and removing heat,
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In opezation unde~ PpKi~~. ~o~ditiQn~� ~t is neGes~~ a~.s.V tp keep in mind
that i~ duxing the, p~xiQd P~ a pu7.s.e the be~ ~nex~~ q~rt~s: b~* a~o~?X p~ ~
10 to 20 k~V this. catl ~esu~.x in 7~edis:trihution 0~ ipniza~ion ~Q9e,es o~v~ex the
iiischarge gap and i~n i+ntens~,~ic~ti.Qn o~` the e~,ectrtc ~ie1d in the cathode or
anode rebion.
In conclusion the authors~ wish to express their thetnks� to A.A. 1~1ak ~`or his _
hlelpful discuss~ions and to 3Cu.A. Anan~yev and N.N. Rozanov ~or their constant
attention and ass~istance in this paper.
- ~ihliography
1. Basov, N.G., Belenov, E.M., Danilychev, V.A. and Suchkov, A.g. U~N, 114,
213 (1974).
2. Danilychev, V.A., Rerimov, O.M. and Kovsh, I.B. TRUDY FIAN, 85, 49 (1976).
3. Boer, K., Henderson, D.B. and Morse, R.L. J. APPL. PHYS., 44, 5511 (1973).
4. Yevdokimov, O.B., Mesyats, G.A. and Ponomarev, V.B. ~IZIKA PLAZMY, 3, 357
- (1977) .
5. ~`evdokimov, O.B., Ryzhov, V.V. and Xalovets, A.P. ZHTF, 47, 2517 (1977).
6. Theophanis, G.A., Jacob, J.H. and Sackett, S.J. J. APPL. PHYS., 46, 2329
(1975) . ~
7. Jacob, J.H., Reilly, J.P. and Pugh, E.R. J. APPL. PHYS., 45, 2609 (1974).
8. Bychkov, Yu.I., Genkin, S.A., Korolev, Yu.D., Mesyats, G.A., Rabotkin, _
V.G. and Filonov, A.G. IZVESTIYA WZOV SSSR, SERIYA FIZIKA, No 11, 139 ;
(1975). !
9. Pugh, E.R., Wallace, J., Jacob, J.H., Northam, D.B. and Daugherty, J.D. I
APPL. OPTICS, 13, 2512 (1974).
10. Denholm, A.S. and Quintal, B.S. I~ASER FOCUS, 10, No 7, 41 (1974). ,
- 11. Seltziar, S.M. and Berger, M.J. NUCL. INSTR. AND METIi., 119, 157 (1974). ~
12. Smith, R.C. APPL. PHYS. LETTERS, 25, 292 (1974). !
13. Yevdokimov, p.B. and ~'a~avets, A.P. ZHT'~, 44, 2~.7 (1974)~
14. Smith, R.C. AP~L. ~H'XS,. LE7,'TS., 21, 352 (1972). ~
15. Ahlstrout, Ii. G. , Zngles,akis~, G. , Holzichtex, , Kan, T. ,,7enaon, J.
and Kolb, A.C. A~PI,. PAY~. I~ExTS~., 21, 49~ (1972).
32 -
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16. ~vanes~n~ V.S~~= Rt~tav~ T,~,1thnQ= yu.V. and ~a],akhoyi ~,.Nf
KYAN'~ITV~~`~{ k~k~QNiKA, 4.t ~,827 ~~,977~ .
17. Dutov, A.~. ~rid Nik~l~ay~e~, ~'.S. ~~~ezi~}~ dqk~,adov ~ vsesp~uz~ kon~.
~ 'Optikr~ lazexov~'" [~'heses~ o~ Pape~s��.a~ the ~i7cs�t t~17,~Unipn ~FOptics of
Lasers'~ ConferenceJ, Leni~ng~ad, GOi~ 1977, p 108,
18. Baranov, V.~. ~~Dozimetriyia elektronnogo izluchenipa" [Electronic Radia-
tion Dosimet~y], Moscow, Atamizdat, 1974.
19. Nikolayev, V.B. ZHTF, 46, 1555 (1976).
20. Fenste�rmacher, C.A., Nutter, M.9., Leland, W.T. and Boyer, K. APPL.
PHYS. LETTS., 20, 15 (1972).
21. Mills, C.B. J. APPL. PAXS., 45, 2112 (1974).
22. Douglas-Hamilton, D.H. and Mani, S.A. J. APPL. PHYS., 45, 4406 (1974).
23. Dipony, G., Perrier, F., Verdier, P. and Arnal, F. C.R. ACAD. SCI.,
PARIS, 258, 3655 (1964).
24. Yoder, M.J. and Ahous, D.R. APPL. PHYS. LETTS., 27, 673 (1975).
COPYRIGHT: Izdatel'stvo Sovetskoye Radio, RVANTOVAYA ELEKTRONIKA, 1979
[23-8831]
CSO: 1862
8831
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LASERS AND MASERS
UDC 621.373.826.038.823
LASING MODES AND EMISSION CHARACTERZSTICS OF A RING-TYPE PHOTODISSOCIATION
IODINE LASER
Moscow KVANTOVAYA ELERTRONIRA in Russian Vol 6 No 8, Aug 79 pp 1705-1711
manuscript received 27 Nov 78
[Article by V.N. Kurzenkov]
[Text] An experimental investigation is made of the energy, space-time and
polarization characteristics of a photodissociation atomic iodine laser with
a four~m3.rror ring cavity. It is shown that a key role in the formation of
lasing directions is played by weak return signals which can arise in the
absence of additional mirrors because of parasitic reflections or scattering.
Under conditions of tube pumping a recording has been made of the influence
of dynamic waves of inhomogeneities on the lasing threshold, which is evidenced
in the space-time structure of the pattern of the close-range field. The
. linear nature has been established of polarization of the output emisaion in the
absence of external magnetic fields. The feasibility is demoastrated of the
employment for investigations of amplifying sqatems of a ring-tqpe oscillator
- arrangement making possible suppression of the self-excitation of an amplifier
employing cavitq mirrors.
Theoretical and experimental investigations of the lasing modes of ring lasers
(cf., e.g., [1-4]) have demonstrated that an important role in the lasing
mechanism is plaqed by the parameters and form of the amplification circuit,
dete'rmined by the type of active medium, the amount of pumping and the level
of return signals. In studies published up to the present time information
is lacking on the properties of the ring circuit of an atomic iodine photo-
disaociation laser (FL), which is of great interest because of the wide range
of possible variation of its parametera. In this paper an experimental study
is made of a number of characteristics of such a laser and measurements are
made of energy conditions and properties of the output emission.
Experimental Setup
Measurements were made for the arrangement of a ring laser with a four-mir:or
cavity (fig 1). Serving as the active element was a quartz ce13. with Brewster
windows with an inside diameter of 2.5 cm and an active aection length of 25 cm,
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p laced in a two-lamp elliptical light source. The cell was filled with gaseous
C F J or wit~ mixti~res of it with Xe at various pressures. The cavity was
f o~rmed with three flat mirrors, M2 to M4 (R = 86 percent), and a glass plate,
M1 , with a coated back surface. In one of the arms of the oscitlator's outlet
was installed an additional mirror, Mdo , whose reflection coeff~'.cient deter-
mined the lasing modes. Recordings wer~ made of the energy (with calorimeters
K to K), time (with an FEU [photomultiplier]), polarization (wi~t~ calorimeters
K1 and angular and spatial (with an EOP [image converter tube] and cameras
Fi and F32) characteristics of the emission field. The emission spectrum was
monitored individuallq; in the absence of a magnetic fietd lasing was performed
~long th~ single line F= 3-~ F' = 4 of the hyperfine structure of the
pl/2 P3/2 transition.
1) K, ~12)
~ ~ tr:
_ qan ~~QiT~ ~
~ (3--7
I'll ~ N4
~ ~14i:' 4 Yr
Mi .~_~/~iq~
~-0- ~'f--�.--~
9U11
Figure 1. Sketch of Experimental Setup
Key:
1. Md~ 3. FEU -
= 2. F2 p 4. EOP
Experimental Results; Energy Characterist3cs
Measurements of the energy characteristics of a ring FL revealed the existence
of stable single-wave and two-wave modes and ~n unstable mode with a change
in lasing direction with a change in pressure of the working gas (fig 2).
Dependences, characteristic of the stable single-direction mode, of the output
energy on the pressure of alkyl iodide are shown in fig 2a. The distribution
, of energy by direction in the absence of additional mirrors is of a fairly
one-waq nature (cf. W and W' The install~tion o~ an additional mirror
with R~o ~~ddi~~ona~d - 4 percent counter to the direction of W1 changes
the las n~ rec on the opposite (cf. W2 and W2' A reduction in Rdop
results in a growth in W2 and simultaneously in a decline in W2 . A dis-
tribution close to an equal~energy distribution (W and W3 ) was observed
with Rd ti 10 3. A smooth redistr3bution of in~ensity between directions
in the d~~ection of an increase in WZ and a reduction in W2 occurs also
by gradual tilting of M . It should be mentioned that in a number of cases
the lasing direction wit~o~t Md changed to the opposite after read~usting
the arrangement, but in series w~~h fixed ad~ust~aent the mode was stable and
was reproduced well.
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_ ~
W, omy ea Wr
q9 1) . wz
U,6 - g~
. n w3
Y. - r
0~3 ~ ~-O''~ W3
- ~~~~;ZW,
0
IV, omy. ed.W '
~o~ '
n,a wz
. b) ~
qa ~vz ~
w; ;
~ t`L1_L_L
4V, J/i
~N. G'~ .
,
O,G -
x
P, 3
~ 2~ ,
~ 4-~. A -
p 1J 30 4,S rtM ;~irf. cm.
Figure 2. Dependences o~ Output Energy on Pressure of Alkyl Iodide
in Stable Single-Direction Mode (a) , in Mode with Unstable
Lasing Direction (b) and in Stable Two Wave Lasing Mode (c).
In fig Zc are ahown the following values:
~s�, ~ ~c~~
f,ll. IV~ (Y,)~ 1~': 11"~ (~b 1G'~3(~1 ~ .
w'~ (r~!)�
IC~y? f
1. W, relative units 2. p, mm H$
In the mode with an unstable lasing direction energy ratios had the form showa i
in fig 2b. The values of W1 and Wi represent the ratios of the output
energy in the forward and reverse directions to the total energy. Instability
is expressed in the redistribution of energq by direction (cf. W1 and Wi )
- with a change in pressure of the alkyl iodide. When the arrangement,wa~ i
readjusted the nature of the distribution changed samewhat in form (cf. WZ
and W' By adding a return mirror to arm W1 with p~ F J a 30 mm Hg
- equali~q o~ energies was achieved with R ti IO 4. 3 7
dop -
Energy dependences relating to the atable two~wave mode are shown in fig 2c.
~ In the presence o~ an additional mirror (Rdo ~ 4 percent , R~, [o tput ~ '
a 10.7 percent } the generation is of a sing~e~-direction natur~~~c~. ~1 ~d '
Wi wherebg energetically it is equivalent to the variant with a plaae
cavitq (W2 in fig 2c) with R
ry~ = 8 percent . In the absence of Mdop ' ~
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in each direction is contained about half the total energy (c~. Wg and W3
Of definite interest is the fact that increasing the pressure of tTie active
medium by the addition of a buffer gas (Xe, 150 mm Hg) for the purpose of
achieving an amplification circuit of a purely homogeneous nature does not
influence the lasing mode both without Mdop (W3), and with Mdop ~W1~'
Thus, the results of an experiment with an iodine FL have proven the possibility
of the existence of all energy mddes tygical of a ring arrangement. It has
been demonstrated that a substantial role in the formation of different modes
is played by slight return reflections, and a change in modes is as a rule the
consequence of a change in the system's parameters (a change of cells with
Yeadjustment of the cavity, or changes in the registration system).
Space-Time Characteristics of Emission
The shapes of lasing pulses were recorded integrally from the entire cross
section of the active mediwn, and for the purpose of comparing typical modes
they are given in fig 3. The high-amplitude pulse in fig 3a corresponds to
an arrangement with Rd~ = 4 percent , and the second pulse was recorded under
the same conditions wi~Fi~ut M in the stable two wave mode. The parameters
- of pulses in the M ring ari~ngement and in an arrangement with an ordinary
two-mirror optical ca$ity practically did not differ. With the elimination of
M and a changeover to the two wave mode, in addition to a reduction in the
pu~~e's amplitude, there was evidenced slight modulation of its peak. A
comparison of pulses propagated in opposite directions in the mode of practically
single-direction generation without Md shows a drastic difference in their
shapes (fig 3b). The lasing time is de~~rmined by the length of emisgion in
the forward direction (the bottom pulse); in the reverse direction (the top
pulse) in this interval were observed a single little peak or a series of
several relatively short little peaks. The difference in the shapes of pulses
demonstrates that the return signal is not a result of reflection of the forward,
but is formed independently. In experiments with a return mirror were observed
a slightly pronounced correlation, resulting from the great difference in am- -
plitudes, in the origin of small peaks in the reverse direction and a slight
- r~eduction in amplitude in the forward direction, which possibly indicates the
presence of the effects of competition.
A typical feature of the lasing pulse regardless o~ the type of cavity is its
peak structure, partially observed on oscillograms and distinctly evidenced in
the dynamics of the picture of the close-range field (fig 4). Measurements of
the structure of the field in the close-range zone, made by means of a slit
scan of the image on the EOP, demonstrated (fig 4a) that the modes studied are
observed under conditions of fairly homogeneous pumping of the active medim
(pressure of alkql iodide less than or equal to 75 mm Hg). At the initial and
final stages of the pulse are clearly pronounced pulsations in intensity with
a period of approximately 1 us. The period is variable over time and depends
on the pu~ping level. Scanning o~ pulse sections with ~aster sweeps showed
- the presence o~ pulsatfons wri.th a 100 percent modulation depth and a period -
of up to 10 na (fig 4h), arising under conditions o~ a more than twofold
excess in pumping over the threshold, synchronously wlth regard to cross section.
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; ~ -
-
,r ~ ,
_ ~
Figure 3. Oscillograms of Lasin~ ~ulses: Sweep of 10 ms/division.
, 'X.~~
`:~~x
~
~
. I
~
~iguxe 4~ S1iX Sca~ o~; I~as.~,ng Zone with a Scanning Duration of 50 us ~
(a? and Scan o~ $ecti,on o~ I~as~ng Zone (b)
x~y:
1. 1 us
In the scan of the eulission field giyen in fig 4a is observed a zone of ~
" weakened intensity mov3ng ~xotn the wa11s o~ the cell to its center at a rate
of approximately 200 ~p/s~. A&:t~1ax pattexn was cleaxly xecoxded in casea j
when the pressuxe o~" C3~ Z~ ax a~xtuxe o~ ~.t Fr.ith %e equa7.ed appxox~mately :
greater than 6Q tmq Hg ~ Th~a ~act ca,n be expla~.ned by the presence o~ 3ynamic
- waves o# inhomogenetty of an actfve medium ~n an gL wi:th tube pumping [5,6] :
~
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and directly demonstrates the~x in�luence on lasing powex, occasioned by a
~ growth in the threshold in the shock zone.
It must be mentioned that the nature of the change in the width of the direct-
ivity diagram over time corresponded to the dynamics of the development of
- shock waves; this fact was ev3denced in a growth in the width of the diagram
over time with an increase in pressure of the active medium above 15 mm Hg.
With lower pressures and the same pumping level the dispersion and emission
_ remained practically constant for the period of the entire lasing pulse.
This pattern was typical to an equal degree of both ord3nary and ring cavities.
In experiments with a ring cavify in individual instances was detected instability
in the direction of the diagram s maximum over time, as a rule falling in line
with the plane of the cavity, which is most probably related to conditions for
the formation of lasing in an out-of-adjustment cavity with an inhomogeneous
active medium. In the course of ineasurements of the width of the diagram
while focusing the emission and comparing the dimensions of a spot at different
distances from the focal plane was observed a distinctly pronounced hyperfocal
focusing effect [7]. A spot of minimal dimensions with time-integrated radiation
density practically an order of magnitude greater than the density in the focal
plane was recorded (without optimization) at a distance of 30 to 50 mm beyond
the focal plane of a lens with a focal length of 750 mm installed at a distance
of 4 m from the outlet mirrWi~~ a cavitythavingfplane~mirrors~in the presenceicity
of the wave front in an FL
of aptical deformation of the active medium.
Polarization of Emission
An analysis of polarization of the output emission was made by comparing the
energy of signals reflected frnm two mutually perpendicular Brewster's bands,
M3 and M4 (cf. fig 1). The orientation of these bands corresponds to
. two separate directions: parallel to and perpendicular to the cavity's plane.
In an FL with an ordinary optical cavity the nature of polarization of the
~.emission is determined wholly by the presence inside the cavity of a cell with
Brewster windows. The polarization is in this case linear, its direction is
determined by the orientation of the wi~dows, and the measured ratio of com-
ppnents with regard to energy equals 10 and more. Another pattern is observed
in an arrangement with a ring cavity. Regardless of the orientation of the
Brewster windows, radiation was lineaxly polarized in relation to H in the
cavity's plane. This fact demonstrates that the nature of polarizat3on is -
determined t~y the ratio of amounts of feedback through the outlet mirror,
which is confirmed by estimates of the corresponding threshold conditions.
The reflection coefficients at an angle of 45� from the surface of a glass
plate (the outlet mirror) for mutually orthogonal camponents equal R= 10.7
and 1.1 percent . A campL~tation o~ threshold values of unsaturated gain forl
two orientations of the windows givgs in the first instance 0.1 and 0.13 cm ,
and in the second, 0.~ and 0~22 c~t" .~xom comparison o~ these resulta one
can understand the constanc}* in the dixection v~ e~mission polaxizatiion in a
ring FL wl.th a glass plate nscane roveeto bervery important in aenumber ofhat
- this feature o~ polarizatfo p
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instances. ~or example, in the presence a~ external magnetic fielda there I
can be evidenced a dependence ot lasing parameters on orientation of the field,
and obviously in the most complex way in the case o~ a apectrally and polari-
- zationwise inhomogeneous active medium,
Ring-Type Photodissociation Laser with an Amplifier
This arrangement makes possible optical bypassing with regard to reflections
~ and makes it possible to el3minate self-excitation of an antplifier employing
cavity mirrors, at the same time itaproving storable inversion in operation in
the slave mode and making possible registration of the amplified signal in
synchronous pumping. Tn exper3ments conducted these ideas were tested experi-
mentally, whereby as the amplifier was used the active element of the FL de-
~scribed, and as the oscillator served a similar element with a cell of somewhat
smaller diameter (1.5 cm). The typical pattern character3zing the operation of -
a system in the slave mode with an ordinary two-amirror cavity is shown in
fig Sa. ~ao pulses were observed, the first of which relates to self-excitation
of the amplifier with the oscillator's cavity mirrors and the second re~resents
the amplified s3.gna1. The energy of the self-excitation pulse equaled, depending
on the pumping level of the amplifier, from 20 to 50 percent of the stored
energy,. Se1f-excitation of the amplifier was practically totally eliminated
when usfng in the system a ring cavity with an additional mirror fixing the
lasing direction (R = 4 percent). In this case in the emisgion is observed
only an amplified puQ~e (fig Sb). Thus, it was possible either completely to
eliminate the influence of the mirrors or to reduce it substantially, while -
maintaining the level of the input signal. '
I
, ~
~
~
;
;
'
~
~'igure 5~ Qscil.logxa~na o~ ~ut~p~ng Cu7cxent o~ A~ap~.f~~;ex ~nd Oscillator ~
(Top 8e2~tqs~) and o~ F~qission ~ulses in the A~tplt~iex~s Output '
(Bottosrt Beams�) . 3weep o~ 25 us/div3sion. ,
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Discussion o# Results and Conclus3ons
The Yesults given demonstrate that in a ring-type iodine laser a practically
single-direction lasing mode can be accamplished and can be steady without
additional mirrors and barrier-layer devices. Of course, one of the possible
reasons for its occurrence can be the effects o~ competition between counter
waves, the simultaneous generation of which near the threshold at matching
frequencies is impossible with expansion of the l~inescence boundary of a
uniform nature [2]. gor an iodine gL with tube pumping these conditions can
be assumed to be fulfilled [8,9], taking into account the fact that the pumping
level is variable, i.e., a single-wave mode is possible at the moment of the
origin of generation, when the pumping rate is not too high. It is known also
from experiments with a ruby laser that single-direction generation is realized
also with a sufficiently high excess in pumping over the threshold with the
presence inside the ring cavity of an external control signal [10]. This
provides a basis for asswaing that a similar mechanism for the origin and
evolution of single-direction generation is possible also in an iodine riY:g
FL. However, the randomness in the generation direction characteristic of
this variant has practically not been observed.
As demonstrated by experiments with an additional mirror, quite important to
the formation of energy distrib~utions is the influence of weak return signals,
whose role for conditions closest to the experimental was analyzed in [4].
It was demonstrated in [4] that with the presence of slight feedback in one
direction a counter wave evolves, if its initial amplitude is sufficiently
great; otherwise a single-wave mode is stable. In the experiment for this,
obviously sufficient is the presence of parasitic reflections or scattering,
which additionally supply the counter wave, in confirmation of which can be
given the experimental result of [3], where reflection from the faces of the -
active element, having arisen when their tilt was eliminated, resulted in
a two-wave generation mode. With the presence of an additional mirror genera-
tion according to [4] must be of a single-wave steady-state nature with a
direction determined by this mirror, in the case when R > Rk , where
is the critical value depending on the pumping leve~�.p Under the conditions
~rthe experiment the excess in pumping over the threshold equaled 2 to 2.5
and with R1~= 0.107 and RZ_4 = 4.86 the calculatinon gives ~r = 3 to 4
percent, which is in total agreement with the experiment: With ~
= 4 percent was observed a stable practically single-direction gene~ation
mode. Taking these facts into account, the hypothesis regarding the features
o~ the formation of energy modes realized in experiments with a ring-type
iodine FL can be formulated in the ~ollowing manner.
1) The reason for the origin of a specific mode is difficult-to~monitor
redistributions, characteristic of a specific arrangement, in the magnitude -
and ratios of weak return signals, which in the absence of additional mirrors
can be formed as the result of parasitic reflections or scattering, e.g.,
in wtndows o~ a cell contatninated by photolysis products,
- 2) The extstence o~ a st~ble single~direction ~node ~s appaxently asst~ciated
with the presence o~ return sigaals Which are weak (approxi~atatelyr 10 ) but
different in magnitude.
41
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3) The presence o~ an unstable mvde with a change in genexation directi~n with
a change in pressure o~ the act3ve mediwn is possibly caused by return signals
which are weaker as co~mpared with the preceding case and close in magnitude,
and by the ci.multaneous effect oi~ variable ampli~ication parataeters.
4) The stability of the two wave mode, as in [3], can evidently be explained '
by the presence of parasitic reflections which are considerable and comparatively
close in magnitude. Thus, the results presented demonstrate that the kinetics -
of the generation of a ring--type iodine TrL depend substantially on the preaence
in the syste~a of parasitic sign~l8 whose influen~e has been recorded experimentally
at a 1eve1 of approximately 10 ; therefore, for the purpose o# isolating in
pure form controllable effecta in the competition of counter waves it ia necessary
to take special measures for the suppression of these signals. Of definite -
- practical interest is single-direction generation without additional mirrors,
as well as with an additional mirror with Rdo � 1, which can be used as a
var3ant o� optical bypassing with regard to re~lections in amplification systems
f or the purpose of eliminating self-excitation. The suppresaion of generation
in the dynamic shock wave zone detected in measurements of space-time charac-
~teristics of the emission demonstrates the direct influence of these waves on
the generation threshold of an PL under conditions of pumping with pulsed tubes,
which must be taken into a~count in a detailed discusaion of generation kinetics
in addition to features of polarization specific to a ring-type FL syatem and
evidenced in the most complex manner in the presence of external magnetic fields.
In conclusion, the author expresses his gratitude to N.N. Rozanov for his
helpful discussion of several questions in this paper, and also to I.M.
Belousova for a number of practical valuable recom~endations.
- Bibliography
1. Tang, G.L., Statz, H., de Mars, C.A. and Wilson, D.T. PIiYS. REV., 136,
1 (1964).
2. Zeyger, S.G. and Fradkin, E.Ye. OPTIKA I SPEKTROSKOPIYA, 21, 386 (1966).
3. Bonch-Burevich, A.M., Petrun'kin, V.Yu., Yesepkina, N.A., Kruzhalov, S.V.,
Pakhomov, L.N., Chernov, V.A. and Galkin, S.L. ZHTF, 37, 2031 (1967).
4. Ruzanov, N.N. OPTIKA I SPERTROSKOPIYA, 38, 340 (1975).
5. Golubev, L.Ye., Zuyev, V.S., Katulin, V.A., Nosach, V.Yu. and Nosach,
~ O.Yu. KDANTOVAYA ELERTRONIKA, edited bq N.G. Basov, No 6(18), 23 (1973).
6. Danilov, O.B., Novoselov, V.V. and Spiridonov, V.V. O~TZKA I SPEKTROSKOPIYA,
39y 680 (1975).
7. Mala}rev, V.V. and Kaliteyevskiy~ N~x~ ~n ~~~izika gazayy~kh lazexov~~ -
[Phy~sics o~ C,as Lasera�J, I~enfngrad, xzdatel~stvo LGU~ 1969, p 5. -
~ 42. .
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- 8. Zuyeyev, y.S., Katulin, y'.A. ~ Nosach, V.X'u. and Nosach, O.Y'u. ZHETIA,
62, 1673 (1972).
9. Belousova, T.M., Kiselev, V.~1. and Kurzenko~v, V.N. OPTIKA T STEKTROSKOPIYA,
33, 210 (1972).
10. Antsiferov, V.V., Derzhi, N.M., Kuch.'yanov, A.S., Pivtsov, V.S.,
Ugozhayev, V.D. and ~olin, R.G. KVANTOVA'~A ELEKTRONxKA, 2, 57 (1975).
COPYRIGHT: IzdaCel'stvo Sovetskoye Radio, KVANTOVAYA ELEKZ'RONTKA, 1979 ~
[23-8831]
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i
_ ~
~
I
~
LASERS AND MASERS
_ ~
UDC 612.378.325
, ,
INVESTIGATION OP PL~~PERTIES 0'F A LASER WITH AN UNSTABLE CAVITY AND ADDED +
FEEDB~ACK '
Moscow KVANTOVAYA ELERTRONIRA in Russian Vol 6 No 8, Aug 79 pp 1773-1775 !
manuscript received 9 Jan 79 ~
[Article bq Yu.A. Anan'qev, D.A. Goryachkin, N.A. Sventsitskaya and I.M. '
Petrova] ~
[TextJ An experimental study is made of the properties of a laser with an !
unstable cavi~y and an added mirror covering part of the cross section of the ;
light beam for the purpose of lowering the lasing threshold. The.results are ~
compared with the case of an ordinarq unstable cavity of low magnification.
It is shown that in a laser with an unstable cavity~and added feedback it is
impossible to achieve low angular divergence of the radiation.
I
If to a laser with an uustable cavity is added an additional elemeat (mirror j
or semitransparent plate), as the result of reflection from which a converging '
wave is farmed, this reaLlts in an increase in the radiation density in the ~
zone near the axis and in loweriug of the lasing threshold [1,2]. Both can ;
prove to be useful in different practical applications. ~
Increasing the density in the zone near the axis facilitates control of the j
lase"r by means of intluencing the small central area of its cross section, ;
which can be used in particular,for accrnaplishing the spectral selection of ~
~radiation [2]. The effect of lowering the lasing threshold in principle makes
it possible to use unstable cavities, least critical with regard to accuracy
of fabrication, ad~ustment and the lik.e, with high magnification, M, not only
in ordinary cases, but also for lasers w~.th not too great amplification in the
activs medium. At the same t~me in alI previous experiments [1,2] the addition
of a supplementarq element caused, in addition to desirable conaequeaces, also .
an increase, completelp unacceptable from the viewpoint of practical application,
in the angular divergence of the radiation. In [2] this was explsined by the ~
existence of an entire series of rap trajectoxies which became "lociced" be-
ceuse the added re~lectox cavered the entire cross sectton o~ the cav~ty.
This paper is de~?oted ta a studq~ o~ tY~e #ntexes~tf,n~ c~se when hhe etdded re-
flector covers� on1~* auch a poxt~,an o~ the crosa~ section ~hat the exi~tence of
1'ocked txa~,~ectoxies~ w~tfiin the ~~mqework o~ a gean~etxicr~l ap~xox~ttton becomes .
impossible.
. 44
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Experiments wexe pex~oz~d wl.th a, neody~,um gla~s. las.ex (dia'Aleter o~ ~ctiqe
element 45 mm, length 600 m~), operating in the ~ree gener2~tion ~qQde. In
order to imitate the case o~ media with 1o~r ampld~~cation, only a part of
the active element 200 mm long was sub~ected to pumping. Under these con-
ditions the optical magni~ication, M, of an ordinary telescopic cavity
(without an added reflector) equaled 1.2 to 1.3; the use of such a cavity
with M= 1.26 made possible an output enexgy of approxitttately 30 J and
angular divergence of the radiation (in terms of the hal~-energy level) of
approximately 1.5'. With an ordinary cavity with M= 2 the lasing threshold
- is barely reached.
In experiments with a flat supplementary reflector inst311ed at the outlet
of the telescopic cavity, both the reflection coefficient of the reflector,
p(ti 100 and ti 10 percent), and the magnification of the cavity (M = 2, 3.8
and 8.3) were varied. By moving the reflector transversely it was possible
to change the area of the covered portion of the cavity's cross section
(the boundary of the reflector located wlthin the working cross section was
a straight line). The majority of ineasurements ~aere performed with a reflector
covering half or not much less than half of the cross section; the "geometrical"
iuodes described in [2] hereby certainly were not able to be formed.
It was shown that the addition of a supplementary reflector lowers the lasing ~
- thresshold quite heavily. Not only with M= 2(p ti 100 and ti 10 percent)
but even with M= 3.8 (p ti 10 percent) the output energy was even somewhat
greater than 30 J, and only in the case of M= 8.3 and p ti 100 percent
did it drop to 12 J. Moreover, the amount of angular divergence did not once
drop below 2', s~metimes reaching 4.5' (M = 2, p ti 100 percent). From this
follows the main conclusion that it is obviously impossible to achieve satis-
factory results in unstable cavities with a forcibly formed converging wave.
Even very simple unstable cavities with not too high M prove to be more
advantageous from the viewpoint of angular divergence of the radiation; it is
not necessary even to speak of investigations in [3,4] of unstable cavities
with rotation of the field.
Let us relate some more useful information on the behavior of lasers with a
supplementary reflector. In fig 1 is shown a picture of the angular distri-
bution of radiation in the case when M= 2 and p ti 100 percent (the
reflector covers slightly less than one half the cross section). If this
picture is compared with the similar one for the case of a cross section
totaLly covered by a semi-transparent reflector [2], then it can be seen that
the first of these represents, as it were, one half of the second--in the
angular distribution are seen the same rings with the diameter of each
succeeding one M-fold greater than the diameter o~� the preceding one.
Similar patterns of angular distribution were observed also in a passive
~xperiment, a sketch of which is shown in fig 2. A parallel beanr.of light
from an auxiliary gas lasez = 0.63 u) was dixected through dividing plate
3 onto concave mixxox 1 0~ the telescope ~oxmed by totall.y xeflecting mirrors
1 and 2. At the outlet o~ the telescope ~n the xemote zone (through telescope
~ 4) is seen a system of rings whose diameters, as be~ore, increase successively
45
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M-fo1d. Tf one hal~ the cross section o~ the original beam is covered, then
the aperture around ~he convex inirror in the telescope's outlet is all the
same illuminated completely, whereas in the remote zone only half of the
original pattern remains.
Figure 1. Angular Distribution of Radiation of a Laser with an Unstable
Cavity (M = 2) and a Supplementary Mirror in Part of the
Cross Section
~r
~
, 2 3
~w6:.~.
,
~
1~ a,=D,63~lKH ~
Figure 2. Sketch of Passive Experiment
Key:
1. a = 0.63 u
All this testifies to the fact that the attempt made in [2] to explain
phenomena arising in add-~ng a supplementary reflector oli the basis of notions
of purely geometrical optics was illegitimate. When the converging wave pro-
duced by the reflector (or external source) completes several passes through
the telescope system and its cross section is reduced many times, diffraction
takes on a decisive role. Diffraction "spreading" of the beam (conducive to
which can be the influence of inhomogeneities in the medium) results in the
fact that part of the radiation goes back and part penetrates from one half
of the cross section into another. These processes are completely similar
to the processes, considered in [5,6], o~ reflection ~rom a caustic and of
the passage through it o~ converg~.ng wayes pxodueed by di~~raction at the
edge of the cavitp. As a xesult in pxecisely the same way is evidenced the
~ degeneration oi' modes ~f,th re$pect to losses, a tendency towaxd utultimode
generation, and, as a xesult, a gxowth in diyergence o~ the radiation. Of
course, with the addf,tion o~ ~ re~lector, on aceount o~ the high intensity
of converging wavea, a11 these undesixable consequences turn out to be
. 46
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immeasurably gxeater than in the case when tl~e on~y aouxce o~ converging
waves is edge di~~r:action.
From the results of pasaive experiments can be concluded also the lack of
promi~se o~ attempts to control the radiation~of a laser with an unstable
cavity by introducing converging waves from an extexnal source (a suggestion
of this kind was wade, in particular, in [7]). Requiring a quite cautious
attitude is also the question of using multi-pass telescopic amplifiers in
experiments with return of the wave front; in the performance of passive
experiments according to the diagram in fig 2 the systetn of rings in the
remote zone is visible even in the case when in the concave mirror there is
an opening whose diameter is greater than the diameter of the convex mirror.
Bibliography
1. Anan'yev, Yu.A., Vinokurov, G.N., Koval'chuk, L.V., Sventsitskaya, N.A.
and Sherstobitov, V.Ye. ZHETF, 58, 786 (1970).
2. Anan'yev, Yu.A., Grishmanova,-N.I., Petrova, I.M. and Sventsitskaya, N.A.
KVANTOVAYA ELEKTRONIKA, 2, 738 (1975); 2, 1952 (1975).
3. Zavgorodneva, S.I., Kuprenyuk, V.I. and Sherstobitov, V.Ye. KVANTOVAYA
ELEKTRONIRA, 4, 1383 (1977).
4. Anan'yev, Yu.A. PIS'MA V ZHTF, 4, 372 (1978).
5. Vinokurov, G.N., Lyubimov, V.V. and Orlova, I.B. OPTIKA I SPEKTROSKOPIYA,
34, 741 (1973).
6. Anan'yev, Yu.A. and Sherstobitov, V.Ye. ZflTF, 43, 1013 (1973).
7. Buczek, C.J., Frieberg, R.J. and Scolnik, M.L. PROC. IEEE, 61, 1411 (1973).
COPYRIGHT: Izdatel'stvo Sovetskoye Radio, KVANTOVAYA ELEKTRONIKA, 1979
~23-s83i~
CSO: 1862
8831
~47
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LASERS AND MASERS
UDC 621.373.826
SOME RESULTS OF EXPERTMF.NTS ON A GAS DYNAMICAL COZ LASER
Moscow KVANTOVAYA ELEKTRONIRA in Russian Vol 6 No 8, Aug 79 pp 1775-1777
manuscript received 21 Jan 79
[Article by S.B. Goryachev, B.A. Tikhonov and V.F. Sharkov, Institute of
Atomic Energy imeni I.V. Rurchatov, Moscow]
[Text] The results are given of preliminary experiments on a COZ GDL [gas
dynamical laser] with heating of the working mixture of gases N2-C02-He in
_ a plasmatron. In tti~e continuous operation mode arrived at experimentally are
a unit power outpu~ of 20 J/g,~nd an efficiency of approximately 1.2 percent
with a~stagnation temperature of To= 1700 + 100�K, a value of parameter
- p h* of approximatelq less than 0.5 atm�cm and a total gas mixture flow rate
o~ approximately 0.5 kg/s.
Up to the present time in numerous experiments with homogeneous CO GDL's [1]
not too high levels have been obtained, as compared with those pre~dicted by
the theory, in such key laser characteristics as efficiency and unit power
output. In the stagnation temperature range of practical importance, T~ _
= 1700 + 100�R , instead of the calculated efficiency of greater than oae
percent and unit power output of 20 to 30 J/g, obtained experimentally have .
been an efficieneq of approuimatelq 0.1 to 0.5 percent and a unit:power output
~ of approximately less than 10 J/g.
In this paper are reported some results of experiments with the unit in [2],
the modernized arrangement of which is shown in fig 1. This is a stationary
wind tunnel with the separate delivery frow high-pressure cylinders of techni-
cally pure nitrogen, helium and carbon dioxide. Part of the nitrogen pasaes
through a three-phase plasmatron [3,4]., where it is heated to approximately
400�K. The prescribed stagnation te~tierature with a certain percentage com-
position of the w~orking~gas mixture is obtained by mixing in the gas channel
~behind the pleamatron the requfred quantities of cold nitrogen, helium and
carbon dioxide. Purthexmo~;e, aface the area o~ the npzzle~s cxitical crose
section is #ised, ie aet a apeci~ic ~tagnatiot~ pXessu~e, p.3 7,'he spent gas
. mixture is exhausted into a vacuv~4 taak w~th a~volume o� 5~ ~q , which has been
preliminarilp ev~cuated to 0.1 to 1 aoa�Hg. ~
~ 48.
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'1'he throat unit :La assembled ,~xom 52 ,~1at profi.].ed ,~ins eimilar to thoae
described in [1.,2), which ~orm 51 supersonic thxoats with a critical cross
section of 0.047 X 5.1 cm and an expansion ratio of 22 each. The dimensions
of the supersonic vacuum channel are 50 X 50 cm with a height which varies
along the stream from 5.1 to 7 cm ~or the purpose of compensating the growth
of the boundary layer. A cavity of the stable type is formed by an opaque
concave copper mirror (diameter of 15 cm and radius of curvature of optical ~
surface of 15 m) and by a plane-parallel semi-transparent germanium mirror
(diameter 15 cm and thickness of 2.2 cm). The distance for the flow from the~~.y
critical cross section to the axis of the cavity is 25 cm. The semi-transparent
mirror on one surface has a dielectrie transluceut coating, and on the other,
facing the opaque mirror, a dielectric reflecting coating wl.th a reflection
coefficient of 80 + 3 percent. For the purpose of relieving the semi-trans-
parent mirror of atmospheric pressure, the beam is led out through a plate of
KC1 2 cm thick. The cross section of the extracted beam at a distance of 20 cm
from the outlet plate has dimensions of 14 X 5 cm. The length of the working
pulse is 1.2 s+ 2 percent. The time for the buildup and release of pressure '
is 0.1 s for each. The laser energy derived during the time of a working pulse
was measured by a calorimeter with a thermistor. The duration and shape of
the lasing pulse were monitored with an FSG-22-3A2 photoconductive cell.
d ~a�7Kf~~ro.y~Ni ~~�irn~a~n
R ' ~ h
1
y J; ~ I
~ ~..5
� I70c~~ ,4
- 1 - - -
, ~
~ ~ i A.Km~iBi;nn ~
- -
~ I ~ C-n-+e-', ' ~
. v~ I I N~ ~I
~ 50C~1 1 Ni
3~.~~------ e I
R ~.//(~t;muuer,KCe}~ ~~6~~~:~~� "`vC~~~~~~~---.-.Y
-~~7 ~ ~z~~~~iu~ \
~ � � + + + � 3
~ Mecma 3a~~cpa
~a 4~ Pa l u ro
i
Y I
cot~ ~ ~ `2
N2>~ I ~F--He
1
N2
' I ~n2'
5~ ,
Un anenrr,~r,%4!'CH~7l! CB/f1/~
~igure 1. Sketch o~ Experimental Unit: 1--plasmatron; 2-~mixer-reducer;
3--throat unit; 4--ad~usting unit with opaque copper mirror;
[Caption continuation and key on following page]
49
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5--supexsonic vacuum channel. wlth exit cone; 6--exhaust manifold;
7--ad,~usting unit with semi~txansparent germanium mirror; 8--KC1
vent plate; 9--calorimeter with thermistor; 10--photoconductive cell
Key :
1. To t~a~cuum tank 4. Points ~or measuring p~ and TD
2. Active taedium 5. ~rrnn electxical main
3. Critical cross section
As a result, with T~ = 1700 -F 100�R , p~ = 6.5 to 8.5 atm , a working gas
mixture flow rate of S50 to 750 g/s, and a molar composition of the gas
mixture of NZ:He:C02 = 45:45:10, the unit power output averaged per second
equaled 20 + 3 J/g, and the effic3.ency approximately 1.2 percent. The total
number of experiments for which statistical processing of the resulta was ~
carried out equaled approximately 300. '
While varying the reflection coefficient of the outlet mirror (the remaining
parameters of the unit remained the same), an experimental t~easurement was
made of the value of the unsaturated gain: R~ = 1+ 0.3 m . '
~t,ro series of experiments were also per~ormed in which, while maintaining the
specified composition o~ the working gas mixture and identical operating para-
meters of the unit, in the plasmatron was heated either a molecular gas--
nitrogen--or a monoatomic gas--helium--and the remaining components of the '
mixture were mixed in the mixer-reducer. The m.easured values of the unit power
output in both series of experiments proved, with an accuracy of not worse than
20 percent, to be identical, which indicates the equilibrium nature of heating :
of the gas in the plasmatron (for our conditions) and, consequently, the possi-
bility of extending the data obtained to a C02 GDL with an arbitrary method of ~
heating the working mixture. ~
- ;
Thus, in our expeximents energy charactsristics were obtained for a C02~ GDL ~
which exceed the values obtained under comparable conditions in [1]. The key ;
physical reasons responaible for obtaining rather high values of unit power !
output are apparently the following: ~
i
1) The organization of the gas atream both in the supersonic section of the
throat unit and in its subsonic part, especially the elimination of overflows
of small quantities of the heated gas working mixture past critical cross
sections of throats.
2) Elimination o~ the influence o~ heating o# throat ~ins and cav~ity mirrors
by employing relatively short-duration working staxtu~s for the unit (approxi-
mately 1 s),
3) The employ~qent aa com~on~nts o~ the Working m~xtuxe o~ technically pure !
gases, N2, C02 and He. . ~
4) Ensurf,ng fn a~l experiutent~ value~ of parameter p~.h o~ not, greater than ~ '
0.5 atm�cm.
~
50 ~
- . ,
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5) Placement of the opticai ca~vity at an opti~ual distance ~rom the throat
unit (approximately 20 cm), i.e., beyond the zone o~ companion traces [1]
of the throat ffns. "
6) High quality o~ the cavity's mirrora (the opaque mirror, e.g., had a
reflection coefficient of noC less than 98.5 percent).
In addition, as preliminary numerical studies demonstrated, the composition -
of the working gas mixture, C02:N2:He = 10:45:45, and the reflection coefficient -
of the outlet mirror, R= 80 percent, are quite close to the optimal parameters
enabling maximum unit power output.
It is necessary, however, to emphasize that only after comprehensive experimental
and theoretical optimization of the unit's parameters, which it has been proposed
to carry out in the future, possibly, will it be possible to refine the energy
balance in the GDL and determine unambiguously the quantitative influence of
the numerous operating parameters on the specific power output of a C02 GDL.
The authors wish to mention the constant attention to this paper of Ye.P.
Velikhov and V.D. P~s'mennyy, the participation of M.Yu. Orlov, E.G. Rutberg,
M.A. Grigor'yev and Yu.F. Suslov in the creation of experimental equipment,
_ as well as the valuable comments of G.V. Abrosimov, A.A. Belokon', A.M. Dykhne,
A.N. Kukhto, A.P. Napartovich and E.L. Spektor, made in discussions of experi-
mental results and wish to express their thanks to them.
~
Bibiliography
1. Losev, S.A. "Gazodinamicheskiye lazery" [Gas Dynamical Lasers], Moscow,
Nauka, 1977.
2. Abrosimov, G.V., Vedenov, A.A., Vitshas, A.F., Napartovich, A.P. and Sharkov,
V.F. TVT, 13, 865 (1975).
3. Glebov, I.A., Kasharskiy, E.G. and Rutberg, F.G. "Sinkhronnyye generatory
v elektrofizicheskikh ustanovkakh" [Synchronous Generators in Electro-
physical Uriits], Leningrad, Nauka, 1977.
4. Brantsev, A.N., Grigor`yev, M.A., Kiselev, A.A. and Rutberg, F.G.
"Moshchnyye generatory nizkotemperaturaoy plazmy i metody issledovaniya
ikh parametrov" [High-Power Low-Temperature Plasma Generators and Methods
of Investigating The3r Parameters], Leningrad, Txudy yN~ZElektromash, 1977.
COPYRTGHT: Zzdatel'styo Sovetskoye Radio, KVANTOVAXA.ELEKT~ZQNZKA, 1979
[23-8831]
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LASERS AN~J MASERS
~
UDC 621.375.826;539.196.5 ~
EFFICIENCX OF A SELECTIVE CO LASER
Moscow KVANTOVAYA ELEKTRONTKA in Russian VoZ 6 No 8, Aug 79 pp 1816-1818
~ manuscript received 17 Jan 79 -
[Article by A.A. Likal'ter, USSR Academy of Sciences Institute of High Tempera-
tures, Moscow]
.[Text] For a CO laser with a selective cavity are found the generating trans- '
ition efficiency and the gain saturation law. The efficiency of selective
lasing is limited by the transfer by molecules of quanta to the upper portion ~
of the vibrational spectrum in eluding the lasing transition. ~
A CO laser generates simultaneously in several vibrational-rotational bands
f rom 5 to 8 u. In order to isolate radiati~n at a single frequency, a
selective cavity is employed. The efficiency of a CO laser with a selective
cavity was studied experimentally in [1] and a theoretical estimate i~ given
in [2]. In this paper the specifics of selective generation are taken ~nto
account more campletely. A?~imiting factdr for efficiency is ahown to be the
transfer by molecules of quanta into the upper portion of the vibrational
� spectrimn in eluding the lasing transition.
A study has been made of the flow of excitation quanta in the vibration$1
spectrum, corre~ponding to localization o~ pumping in hhe Xower half and of ~
quenching in the upper half of the.spectrum [3,4]. The flow of quanta is
carried by the vibrational-vibratio~}al (~IV) transf.er CO(R) +�CO(u + 1) +
CO(~ + 1) + CO(u) , enabling the transfer of excitation from transition (u) -
-(u + 1) to the transition (R.) -(R + 1). The flow o~ quanta in the section
- passing through level is determined by the equation
nD~ ~Qi.l+~uln~nu+i--e 'nU-n)n~T~nu1~ .
uu),
wh~ar~~ Q and ~S rtre parametera. :L~ the charactcr~.etic 1ei~gth of the vnri.n~ion
in popul~ation densiCy on the Vibrational numbex axis is much greate~r than the
mean free path o~ a quantum, then the ~low o~ quanta is expresaed in differential
form:
1[-('lQ/8~~)u=n"-(2b--d~!n ni:ta=].
~2~
The distribution satisfying the boundary conditions and consistent with constant
P has the form [5]:
no c:cp 2baa br.~=), u~u;
r~ ri ~.c; uj ex ba= - l 2 a
_ ( o P(~ i a .
Beyond the lasing transition at point Y(fig 1) the flow of quanta is
reduced to a finite value equal to the number of de-excited l~ser quanta.
It is necessary to relate the discontinuity in the flow to the derivative
d ln n/dv at point Y; this is expressed through t~he gain.2 The discontinuity
in the flow causes a discontinuity in derivative d 1n n/dv . Tn connection -
with this, diffusion representation (2), generally speaking, is not valid,in _
the vicinity of point y~ with a radius less than the length o� the quantum's
mean free path. Tn extending equation (2) to this vtcinity, it is necessary
to add a certain e~~ective boundary condition. Zts role is played by an
additional relationship obtained from (1). Abbreviating in di�~erence P~ - -
- P te~cros making a contribution to the ~low in both cxoss sections,
andvgoing to a di~~ex~nti.~1 ~:ep~e~entation, We ~ind
_ c1II= (~Si2jr~l7n, ~5~
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where Q~' and A~D t~xe the xea~ and di~#uston d~~cqntinuities in the f1ow,
respectively, in tFie laeing tranel~ion; ~actox d/2 ti 1/3 , equal to the
inverse mean ~ree path o~ a quanfiwp, takea into account the txans~er of quanta
~ to the lasing tra~nsition bypass.
~ . . I ~ _ . ~ .
_ I
j~
~
+ II
I
~
- , ~ ;
' ot, N u _
Figure 1. Vibrational Distribution in Vicinity of Lasing Transition
In computing the diffusion discontinuity in the flow we asaume that the re-
duction in the level of the plateau aesociated with it is not too great.
Regarding y~ 1n n as a coozdinate, and vibrational number v as t3me, we
write (2) in the form o~ an equation of motion of a particle above a potential
barrier, depending on P as on a parameter:
y __~u~au,
u(z~,y)==-2ny._~rts~~~aQv~~~-~~~.
The distribution satis~ying the conditions of a non-negative character in this
region and o~ diminution with high v corresponds to the tra~ectory of a particl~
.almost entrapped by the peak of the barrier. (Since equilibrium at the peak of
the barrier is unstable, other trajectories deviate heavily from the latter
beginning with a certain v; therefore they cannot satisfy the necessary
conditions.) Near the peak of the barrier the equation of motion has the form
~-~b(y--yr), (6,
where
~ ~d~
, Jp - 2 ln 41iQt'~'
The general solutioa to equa,tiun (6) ~
yP Ae-2 1 bv T BC2 Ybv,+ ~(2l - 1)I
~2 ~v~21
~7~
~ 54 ,
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describes the vibrational disfixibution near the 7.eve7, o~ the plateau to which
corresponds y ~ y ,
~ r
ConAideri.ng lasing At a t~ranait~,on 1.oca~ized w~,th a.~aix7.y high v~.brational
number, we wi11 assume that 2~~ � 1 and we w:111 1ee th~ Aeym~totic aeries
descend in relation to the inver~e powers of this parameter in (7). Coefficients
A and B are ~ound fraq the boundary conditions for each of the regions
a< v< Y and Y< v E N, whereb}~ with 2?~b(~y - a) � 1 and 2~(N - y) �
� 1 fulfillment of the boundary condition at the left end of each region is
made possible by a term with a descending power, and at the right, with an
ascending. In the vicinity of point y the distribution has the form
1~. I1S_~_ exp I.u-'_ ~'�~_e2 ti`b (v-V)I
96Qv- 2 b J, U l Y;
~ v-
9b'Sv- ~x~~ U~~_l iy ~_2 r'6 (L~-v)~, v~Y~
Y- ~ y ~
~8>
where y= y(Y) and P and P' are the flows o~ quanta with v< y and
v> y, respectively. Joining equations (8) with v= Y, we find the relation-
ship of diffusion flows:
17' I7 cap [2 (J I- 1/v)/vb) . ~9)
From (9) and (5) follows the expression for the efficiency of the transition:
- r~ (b/2) ~ 1 exp [2 (u 1/1')/1/hj i � ~10~ -
The limiting value of the efficiency, d/2 , is caused by the transfer of quanta
into the lasing transition bypass. With a relatively not too great diffusion
discontinuity in the flow
,I _ _.'fi ~~,.~~~E~L, (11)
Derivative y is expressed via the gain '
,ti"=�ay(I)n.,!:?l11 ~~~;-!l1,
~12~ .
where v(~) is the cross ~ecti,pn of the xad~,ation gain in fieruls o~ the _
populati~n denaity* q~ the ~ribx'ational l.evel.; B is the 7:otation$1 c~onstant;
and ~ is the xotational motqent. Hexe it is assumed that B,j/T a< 1.
With not too high transftion ef~iciency
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K ?!il%!' ; p ,
tin'~v ~213jr7' I%Y' ~13~
where K~ and K are the ~ain o~ a weak signal and the threshf id ~ain,
respectively. Expressing jr ~rom (].3) and subs~itut~ng it in (11), we find
the relationsh3p between the transition e~#iciency and measured values of
K~ and K :
8 ~ 213i 1 ' Y
I -
- 1/b l T y l 1Co .
(14) -
The relationship between tti~ ga3n and the intensity of radiation in the cavity
is determined by the energy balance:
- , r~iIa~y-=Kl, ~
where I is the intensity of radiation and w is the laser quantum. �
Utilizing (14) we get the typical saturation l~w
Kd (1..~-/!!,)~
where
K~ J~ ~ na~ la; ~ z~,~,.y 7/ QR
Y~-1bQ T Y I~ s.. Q'
In a non-selective cavity thF. change in the flow of quanta in the region of
lasing transitions can be considered continuous and the ef~iciency of a single
band can be defined as rl,~ _-(d ln P/dv)v . Utilizing equation (4) we
have
i~y=~-2(q-E-i;p) . . . ,
(15)
This equation must be avexaged on a length on the order o~ the mean free path
of a quantuiq. Zn [2] an appx'oxiul~tion sitqilar to (15.) (in a di~~erence repre-
_ sentation) is used also in se].ectiye l~sing. ~qustion (11) ~ox transition~
efficienc~* in selectiYe lasing di~~exs ~rom (15) by the ~actor d/(2~b) ,
depending on tea~peratuxe.
In a sequence o~ lastn$ txan~ft~,ctns a~].ow~ o~ quanta can be de-excited prac-
tically totall~r, wh#ch exp7.ains tRe high e~~iciencp o~ a CQ 7.aser. On the
other ha+ad, lasing e~i'fciency in a selective laser cavity~ 3s lintified. Estimates
according to equatioa (14) make ~.t poaai.ble to explain the reduction observed .
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in [1] in the ef~iciency o~ a se7,ective CO ~ase7r as compazed with an ordinary
one. The growth noted Chere in the xadiated powex o~ bands in the upper
portion of the lasing spectrum in a~elective cavity is xe7.ated to an increase
in the inflowing ~low of quanta in the absence o~ 1a~ing at lower-lying trans-
itions, as we11 ~ts to an increase in the transifiion ef~ic~ency.
The electro-optical efficienc}r of a laser is represented by the product of
factors taking into account losses o� energy at various stages. In addition
to the losses taken into account by equation (14) they include the following:
the excitation of electronic degrees oP ~reedom; radiation, diffusion toward
walls and VT exchange o~ molecules at vibrational levels below the lasing
tran~itiqn; dissipation in W exchange, described by the quantum efficiency,
w/w ; rahere. ~ is the vib~rational quantum of CO (or of NZ if pumping takes
p~ace through ri~troge~i~; and radiative losses in the cavity. Taking these
losses into account for a selective CO laser is non-specific, i.e., is of a
fairly general nature and therefore is not considered here.
Bibliography
1. Avtonomov, V.P. et al. KVANTOVAYA ELEKTRONTKA, 5, 1896 (1978).
~ 2. Napartovich, A.P., Novobrantsev, I.V. and Starostin, A.N. KVANTOVAYA
ELEKTRONIKA, 4, No 10 (1977).
3. Likal'ter, A.A. PMTF, No 4, 3(1976).
- 4. Zheleznyak, M.B., Likal'ter, A.A. and Naydis, G.V. PMTF, No 5, 11 (1976). -
5. Brau, C.A. PHYSICA, 58, 533 (1972). _
COPYRIGHT: Izdatel'stvo Sovetskoye Radio, KVANTOVAYA ELEKTRONIKA, 1979
, [23-8831~
CSO : 1862
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