JPRS ID: 10155 USSR REPORT PHYSICS AND MATHEMATICS

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JPRS L/ 10155
~ 2 December 1981
- USSR Re ort
p
PHYSICS AND MATHEMATICS
(FOUO 10/81)
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JPRS L/10155
2 December 1981
~ USSR REPORT
_ ~HYSICS AND MATHEMATICS
(FOL'0 10/81)
CONTENT~
- LASERS AND MASERS
- Numerical Study o~ C02 Process Laser W~*_~~ Closed Gasdynamic
J
Cycle
Copper Vapor Laser With Transverse Discharge 9
Physicochemical and Electrop?~ysical Properties af Iiigh--
Temperature Insulating Ceramics for Elemental Vapor
Lasers 21
_ Energy and Spectral Characteristics of CO Gasdynamic Laser
Working Media 27
Copper Atom Laser Level Excitation Efficiency in Electric
Discharge 33
Active Media for C02 Gasdynamic Lasers Uaing Combustion
Products of Low-Nitrogen Fuelr~ 38
Spectroscopy and Primary Phatolysis Processes of Iodides for
Phc~todissociation Iodine Lazere (Review) 43
Tuhable Carbon Mon~xide Laser 80
Efficiency of Li-Nd-La Pt~osphate Glass Laser in Low Pumping
_ Power Range: Free-Running Operation 93
Requirementa Placed on Pumping X-Ray Laser With Ionization
Source 98
Dynamics of Hydroelastoplastic Systems 101
a- [III - USSR - 21H S&T FOUO]
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Calculating Energy Characteri~tics of Electron--Beam Controlled
- CO Proceas Laser With Turbocompre~sor Cooling 108
Theoretical Study of Wavefro~it Reversal Efficie~cy in
Inverted Carbon Dioxide 114
0.5 GW Electr.on--Beam Excited ReCl Laser 120
Dynamic Compensatioa of Iodine Laser Optical Inhomogeneities..... 123
PLASMA PHYSICS
Possible Mechanism of Instability of Glow Discharge Arising
_ After Pulse Action o~ External Ionizer 126
Particulars of OFtical Discharge Slow Burning Initiation in Air
on Optical Breakdown Inoculation Pl~asma 130
Interaction of Strong Electromagnetic Waves With Co3lisionless
Plasma.......~ 133
Influence of Laser Emission kTavelength on Plasma Formation
Threshold With Irradiation of Opaque Materials....e........~..? 138
_ Theory of Steady Optical Gas Breakdown Close to Metal Surface.... 143
OPTICS AND SPECTROSCOPY
Analysis of Absorption Sp~ctrum for D20, ~0 and H20 Vapor in
1.06 um Region.~.~ 152 ~
Power�ul Laser Probing of Physicochemical Parameters of
Atmosphere~ 157
OPTOELECTRONICS
Characteristics of Temperature-Sensitive Phoaphor Screens for
IR Phot~registration 162
. Properties of Incoherent Fourier-Transforming Optical Systems.... 169
Light Beam Amplification by Dynamic Holograms in LZT-La Ceramic.~ 174
Correcting Image Sharpness in the Case of Unknown 'Smooth`
Defocusing 177
MATHEMATICS
:
Integral--Transform Method in Wave Problems of Hydroacoustics....~ 180
_ Problems of Analyzing Resource Distribution.....,.~ 184
- b -
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~
L.ASERS AND MASERS
UDC 621.373.826.038.8L3
NUMERICAL STUDY OF C02 PROCESS LASER WITH CLOSED GASDYNAMIC CYCLE
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 8(110), Aug 81 (manu~cript re-
ceived 8 Sep 80, after revision 23 Feb 81) pp 1656-1662
[Article by V. V. Breyev, A. V. Gubarev, A. V. Kazhidub, A. T. Kukharenko, F. V.
Lebedev and V. P. Panchenko, Institute of Atomic Energy imeni I. V. Kurchatov,
MoscowJ
[Text] The article briefly describes a mathematical mod~;l de-
veloped by the authors for complex calculation of a COZ elec-
tric discharge laser including discharge chamber, ogtical reso-
nator amplifier, radiation focusing system, nozzle, diffuser,
coolers, compressor a?zd connecting tubing. A numerical study
of a 10 kW C02 process laser is done on the basis of the devel-
oped set of programs.
The outlook that has been noted in recent years for using C02 electric discharge
lasers in technology [Ref. 1-S] has brought to the forefront problems of design
calculations and optimization of the parameters of such facilities. These prob-
lems can now be resolved, as the physical processes o~curring in C02 electric dis-
charge lasers have been fairly well studied. Methods are also known for engineer-
ing calculation of all components of the gasdynamic circuit of the facility: com-
pressor, heat exchangers, tubiiig and so on.
Ref. 4 gives a detailed description of a mathematical model of a C02 electric dis-
charge laser with closed gasdyiiamic circuit. Our paper discusses the results of
an engineering study using this mathematical model of a COZ process laser w~th
power of about 10 kW [Ref. 3].
The mathematical model of the electric discharge C02 laser includes algorithms
for the following calculations:
flow of active medium in external electrir field and in radiation field;
multiple-pass unstabie amplifier cavity with arbitrary mirror arrangement;
distortions of r.adiation wavefront by inhom~geneities of the medium;
propagation and focusing of output emission;
1
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pressure losses on different sections of the gasdynamic circuit and its hydraulic
and thermal closure.
To describe the flow of active medium in the gas dfscharge gap and on the secr_ion
of stimuiated emission of light, we have used a quasi-one-dim2nsional approximation
for independent streamtubes, which enables us to get a nonuniform distribution
of the gain and density of the medium in accordance with the distribution of the
radiation field. The flow in a stream filament is described by the known system
of differential equa~ions [Ref. 6]
dF/dx=-N, (1)
where
F=~pu; Pu2-{-p~ Pu (e-}'P~p-I-u'/2)~ PuEi~ PuE:~ puEN~;
H=~�; F~u~ �~s-I-p~p-}-u=~2)-~Qo~ �E~-~-p~~ �Es-f-p:~ '�E,v ~'P. v~�
Here u= pudA/Adx, A is the area of a stream filament proportional to the flow sec-
tion, E1, E2, EN are the energies of the lower and upper vibrational modes of the
C02 molecule, and of the vibrational mode of nitrogen respectively. The remaining
notation is obvious, and the expressions for volumetric sources are given in Ref. 6.
The geometric-optics approximation [Ref. 7J was used to determine the radiation
field in a multipass unstable cavity amplifier and the energy characteristics of
the laser facility. In doing this calculation it is necessary to assign the radii
of curvature of the opaque and output mirrors of the cavity, the dimensions of
the output mirror of the cavity, and also the coordinates of the centers of all
mirrors and of the output aperture. These data are sufficient for defining the
path of ra;-s in the optical system f illed with hamogeneous medium (with constant
value of the index of refraction). The change of intensity of the light wave in
this case is
R-'d (R'~1dR=ky1, (2)
where R is the distance from the fo~us of the spherical wave, I is the intenslty
of the wave, ky is the gain of the medium. The formulation of the boundary value
problem for equation (2) and algorithm for its solution are described in Ref. 6.
Theoretical studies and estimates have shown that the inhomogeneity observed in
C02 13sers has a weak distorting effect on the tra~ectory of rays. This enables
us to reduce the problem of determining the wavefront at the output of the optical
system to calculation of the phase advance due to the difference in optical paths
in homogeneous and inhomogeneous media. The change in the index of refraction
determined by the density of the medium is found from the solution of system of
e~uations (1), (2).
In considering comparatively short-focus and low-power.systems that are convention-
ally used in process lasers, nonlinear effects of the light propagation in atmos-
phere can ger.erally be disregarded. Therefore the distribution of light intensity
in the focal plane of the lens is determined by the Kirchhoff integral written
for the complex electric field amplitude E(x,y,z) in the paraxial approximation:
2
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E~X, y~ f) = k e2nijk~ E~~+''~1~ ~0) ex~p ~k Gr i(U-+lY d~.d~,. .
~-e ~ ~ ~3~
where i=~, a and b are the dimensions of the rectangular aperture of the out-
going radiation.
The initial function
, 0)=Y1 exp fik~p-~-i/r (~?-{-~~12f], (4)
where I(~,r~), ~,(~,n) are intensity and phase (eikonal) of the radiation emanating
from the optical system. Considering function E(~,rt,0) periodic with respect to
~ and n with periods 2a and 2b respectively, we can use the algorithm of fast
Fourier transformation [Ref. 6] to find the intensity diatribution in the focal
plane.
To check out the mathematical model described in Ref. 6, we calculated a C02 laser
with closed gasdynamic cycle with test results described in Ref. 2-4. The gas-
dynamic circuit of this facility includes two parallel channels and a common dis-
charge chamber combined with the optical cavity. In the calculation, consideration
was taken of the experimentally determined coefficients of pressure losses in the
coolers, and the head characteristics of the comp;ressor. The optical diagram of
the laser is shown in Fig. la. The four-pass unstable cavity consisted of opaque
mirror 1 with r3dius of curvature R1= 26 m, three flat rotating mirrors 2-4, feed-
back mirror 5 with R5= 13 m, and output flat mirror 6 with rectangular hole of
4.5 x 2.5 cm. The static pressure of the working mixture N2:C02:H2O:02= 0.874:0.~5:
0.006:0.07 at the inlet to the nozzle was 3.3 kPa, and the temperature at the outlet
~�e ~ ky~M r
4 ~2
4 ~ ~ 2 B Y'~
4
c d~1
3
a+~
y ti d
~ ~Y O
q~ .Qt 43 z,M
~ t~~ 6 ~ A b
p R8'
- ~ne
S ~o~ J
!
A
$
Fig. 1. Optical diagram of laser (a) and the gain behavior
lengthwise of the discharge chamber in the midsection and on
the ends
from the coolers was 290 K. An electric discharge with fairly uniform energy input
over the volume of the discharge chamber was realized on the section from x-= 0.8 to
3
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x= 0.38 m. Vibrational efficiency of the discharge based on experimental data
[Ref. 3, 8~ was tak.en as equa~ to 0.85.
For purposes of illustration, Fig. lb shows the distribution of the calculated
gain of the medium along thc flow at three levels with ~espect to the Y axis.
We see considerable nonuniformity of the field of ky. According to calculations
at an energy input Ne = 62.5 kW (this corresponds to the maxi.mum energy input in
the experiment), the flow is accelerated in the discharge chamber by about 40%,
and its temperature rises by about 35~6. At the output from the zone of stimulated
emission, about 28% of Ne remains in vibrational degrees of freedom of COZ and .
NZ molecules. The maximum nonunifarmity of pressure and velocity of the flow in
the transverse direction reaches 3% and 2% respectively. This result coniirms
the admissibility of the filament flow model. Notice should be taken of good agree-
ment of the calculated values of flow velocity and pressure at the output from ~
the lasing zone with the experimental data.
t6, k s x N,y ki~J
A ~
- m
4~ ~ ~ 2p ` � '
e,: t� 2
1S
4~ . ~
o ~o ~c a�Ne, kW .
f0
Fig. Gas flow m in the dis-
charge chamber as a func-
tion of supplied electric s
power (o--experiment) and
required degree of com- ~
a
pression ~rK in the com- 'l~
pressor as a function of 3
supplied electric power at g~
canstant gas flow ~
4~ ~ 2
_ Fig. 2 and 3 show the calculated
curves for output power N~, elec-
tric eff iciency of the laser n~, O,os
and gas flow through the discharge
chamber as functions of the power p
Ne invested in the discharge. The ~ do f2o e~
b
results of experiment as shown on
the same figures agree well with Fig. 3. Emiaeion power (a) and electro-
the calculated curves. optical efficiency (b) as functions of
The distribution of gas density supplied electric power: gas flow variable
found in the calcu:lation in the ~1, 2) and conatant (3); coefficient of
losses in the mirrors q= 2(1,3) and 4% (2);
cavity zone enables us to calcu- o--experiment
late the distribution of the
phase of the radiation at the output of the facility (cross section 7-7 on Fig. la),
and to find the structure of the radiation intensity distribution in the focal spot.
4
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For the electro-optical laser scheme shown in Fig. la, at a power of 62.5 kW in-
vested in ~he discharge the phase difference of the outgoing beam does not exceed
3n. The calculated intensity field in the focal spot of a lens with focal length
of f= SO m is shown in Fig. 4. The broken line shows the intensity distribution
for the case of a plane wavefront (without consider-
N~ ~ ation of dlstortions). In the center of the prin-
~ i~ cipal maximum the intensity reaches about 16 kW/cm2;
~tt i~ however, this maximum contains only about 301' of
the emission power of the facility. Angular devia-
~ ~j tion of the light beam fro~ the optical axis (about
6 i i 2� 10-'') is approximately zqual to the angul ar di-
i i vergence of the radiation with respect to half
~ i power level. Under real conditions the radiation
~ ~
_ a i~,,, divergence was about 10- 3[Ref . 2], which was caused
-y,s -2,2s` o z,2s x,cM by considerable phase distortions in the output win-
dows.
Fig. 4. Radiation intensity
distribution in focal cross Good coincidence of all calculated relations with
section for plane (broken experiment over a fairly wide range of variation
line) and distorted (continu- in working conditions of the laser shows adequate
ous line) wavefronts description by the mathematical model [Ref. 6]
of processes in the C0~ laser, which provides the
basis for applying this model to numerical inveatigation and optimization of the de-
signs of such facilities.
Let us mention the principal results of tt~e theoretical analysis of the C02 process
laser [Ref. 3] with optical diagram shown in Fig. 1.
The main pressure losses in the circuit of the facility are due to the hydraulic
- drag of the coolers (about 50%), the drag of ~ections witr higt! flow velocity
(nozzle, diffuser) and of the discharge chamber (about 20 and 12~ respectively).
The drag of the discharge chamber increases with increasing energy input.
As the energy input increases on the discharge gap, the flow of the working mixture
in the circuit decreases, and at Ne = 120 kW it falls to about one-half.
The change in the coefficient of losses in the mirrors from 2 to 4% (curves 1,
2 on Fig. 3) leads to a reduction in emission power by about 10%.
Stimulated emission of light arises only wi th a power input of more than 20 kW
to the di.scharge.
As the power invested in the discharge increasea, the electro-optical efficiency
rises rapidly, and at Ne > 60 kW it reaches ~15%.
As the power invested in the discharge increases, the radiation power at first
rises monotonically, reaching a maximum of 15-19 kW (see curves 1, 2 on Fig. 3)
at Ne = 140 kW, and then drops sharply. The reduction of radiation power at Ne
greater than 140 kW is due to the reduction in gae flow (see Fig. 2) and its strong
overheating. At constant gas flow through the discharge gap the maximum radiation
power reaches about 25 kW at input power of about 200 kW and is limited by gas-
dynamic suppression.
5
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~
~ i~S ~ i 4 7 2 2 4 7
~--ICI j ;Q ~ ~
~4 ~ 4S~
?
_ ~ p 4~ ~ ~ 42 ~~s e
a e f 6 3 �3 S 6
~~S i ~s ~ ~ 2 7'a 4 ~ d 4
~0 ~ j ;0
I ~
xu 1 ~ I
4t 4~ 4AS � 4ts 4~s e a
b f 3 65 6 f J
~;o ~ ~;a ~ 2 ~ 4 s~.
~ i = i
O ~
4~ 4~ to ~ Q75 f
c g e
~ 2,SI ~ f J .sb f 3
~,g + C f
~;5 ~ ~ ~s j I
s~~ ~ ~~o ; + Fig. 6. Influence that location
Z~ . ~ ~ ~ ~ of optical pafasages has on the
~ output power of the laser (region
~ 02 on,c~c,. ~ Q1 ~~~M of energy input is shaded) :
d h N~= 10 (a), $.5 (b), 10.8 (c),
Fig. 5. Influence that the 8�9 (d), 10.5 (e) and 10.7 kW (f)
location of the energy input At constant energy input to the discharge
zone has on laser output
power (region of energy gaP ~Ne ~ 62.5 kW), a reduction in molar
input is shad~d, the broken concentration of C02 from 5 to 3y is ac-
lines show the extrPme companied by a drop in emission power
limits of the light beams): by ~20~6. Upon an increase in C02 content
Output power N~ = 10 (a), from 5 to 10% the outputvemission power
10.6 (b), 11.4 (c), 12.3 (d), at first increases by ~8/, and then mono-
tonically decreases.
9.6 (e), 13.3 (f, g), and
13.6 kW (h) Theoretical power of the facility r~aches
maximum at water vapor concentration of
0.6-1Y.
A change in oxygen concentration from ~7 to ~20~ has almost no effect on tYie output
radiation power and electro-optical efficiency of the laser. This means that air
that has been dried to the necessary moisture concentrationa w~.th addition of C02
can be recommended for use as a working mixture. However, the final solution of
this problem must take consideration of plasma-chemical procesaes.
The above-described results of_ the theoretical study have been directed at investi- .
gation of a specific C02 process laser [Ref. 3J. Obviously most of these results ,
can be obtained experimentally as well. The advantages of mathematical modeling
and numerical study show up most completely in solving problmes of design selection
of the parameters of the facility as a whole, and in particular in optimization
of the electro-optical system of the given facility. Experimental solution of
such problems requires large material investments and time.
6
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To illustrate this, let us give the results of calculation of different designs
of the electro-optical system for the facility inveatigated above. It was assumed
that the outside overall dimensions of the electro-optical system, its flow section
and the joining components are retained unaltered, and coincide with tlle regular
system (see Fig. 1), as does the total energy input to the positive d.isc'r~arge column
Ne = 62.5 kW. Let us note that these studies together with the development of the
methodology took a total of about six man-months, while the machine time of a BESM-6
computer was approximately 10 hours.
Fig. 5 shows some investigated variants of the distribution of energy input in
the electro-optical system of the facility. The desigri of the optical system re-
mained unchanged (see Fig. 1). The situation shown on Fig. 5e was realized under
experimental conditions. In this case the output power of the radiation was
- 9.6 kW (electro-optical efficiency rl~ = 15%). Change in the form of distribution
of the ener~y input has a weak influence on the output power (see cases a, b, e
on Fig. 5). More significant is the upstream shift of the zone of energy input
relative to the cavity (cases c, f, g on Fig. 5). The calculations show that an
upstream displacement of the energy input zone by 8 cro should lead to an increase
in output power by about 30y. A similar result ia realized when the length of
the discharge zone is shortened due to an increase in specific energy input and
when its "c~nter of gravity" is shifted upstream (cases d and h on Fig. 5).
The results of investigation of different designs of the optical system with un-
changed distribution of the energy input in the positive column (see Fig. 5a) and
c:avity magnification are shown on Fig. 6. The resultant data show that the geometry
of the cavity passages used in the experiment is near optimum. A tendency can
, be seen toward an increase of output power as the center of gravity of the radiation
field is shifted downstream. Let us also note that when the cavity is located
in the lower z~ne of the energy ingut, the output power should remain practically
unchanged even when the number of cavity passages is limited to three (see Fig. 6f).
The mathematical model of the process laser that was used in this paper does not
reflect such important point~ as the limitation o:t maximum energy inputs of a stable
discharge and t:~e influence of plasma-chemical processes on vibrational kinetics.
- Nonetheless, the modeling method that has been developed is very useful and can
be applied on the stage of design and development of process laser systems.
REFERENCES
1. Hoag, E., Pease, H., Staal, J., Zar, J., APPL. OPTICS, Vol 13, 19%4, p 1959.
2. Abil'siitov, G., Artamonov, A. V., Velikhov, Ye. P., Yegorov, Yu. A., Kazhi-
dub, A. V., L~bedev, F. V., Sidorenko, Ye. I., Sumerin, V. V., KVANTOVAYA
ELEKTRONIKA, Vol 7, 1.980, p 2467.
3. Abil'siitov, G., Antonova, L. I., Artamonov, A. V., Golubev, V. S., Drobyazko,
S. V., Yegorov, Yu. A., Katsuro, N. I., Kazhidub, A. V., Lebedev, F. V., Sena-
torov, Yu. M., Sidorenko, Ye. M., Sumerin, V. V., Turundayevskiy, V. B.,
Frolov, V. M., KVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 204.
7
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4. Artamonov, A. V., Yegorov, Yu. A., Kazh.idub, A. V., Katsuro, N. I., Lebedev, ~
F. V., Sidorenko, Ye. M., Sumerin, V. V., Frolov, V. M., KVANTOVAYA ELERTRONIKA,
Vol 5, 1978, p 920.
5. Letokhov, V. S., Ustinov, N. D., "Moshchnyye lazery i ikh primen~niye" [Power-
ful Lasers and Their Applications], Moscow, Sovetskoye radio, 1980.
6. Breyev, V. V., Gubarev, A. V., Kazhidub, A. V., Kukharenko, A. T., Mamzer,
A. F., Panchenko, V. P., Rikenglaz, M. M., Preprint, IAE, Moscow 1980, No 3319.
7. Anan'yev, Yu. A., "Opticheskiye rezonatory i problema raskhodimosti lazernogo
' izlucheniya" [Optieal Cavities and the Problem of Divergence of Laser Radiation],
Moscow, Nauka, 1979.
8. Artamonov, A. A., Breyev, V. V., Kukharenko, A. T., Samokhin, A. A., "Trudy
vtoroy Vsesoyuznoy konferentsii po fizicr,eskim protsessam v gazovykh OKG"
[Proceedings of Second All-Union Conference on Physical Processes in Gas Lasers],
Uzhgorod, 1978. ~
COPYRTGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
6610
CSO: 1862/14
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UDC 621.373.826.038.023
COPPER VAPOR LASER WITH TRANSVERSE DISCHARGE
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 8(lI0), Aug 81 (manuscript re-
ceived 11 Nov 80) pp 1686-1696
[Article by A. V. Sokolov and A. V. Sviridov]
- [Text] The paper gives the results of a study of a copper vapor
- laser with radially transverse discharge at pressures up to 1.5
_ atmospheres. It is shown that when the parasitic inductance
of the laser discharge circuit has been sufficiently reduced,
_ hig'n efficiency can be realized. A physical efficiency of 5.3~
is attained in the copper vapor laser. It is also shown that
the use of vaporizers enables appreciable improvement of the
output parameters of a laser with radially transverse discharge.
It is established that circulation of the active Cu-Ne mixture ,
~ overcomes the restriction imposed on the pumping power bq heat
release in the active meditun of the Cu-laser. Lasing of copper
. vapo~. is achieved in a pulsed discharge ~a3.th hollow cathode.
Lasing power was 1.2 W, physical efficiency reached 53~, and the
specific energy output was 15 uJ/cm3.
1. Introduction
The possibility of realizing efficient lasing and attaining economic working con-
ditions in lasers with transverse discharge on vapors nf copper and other metals
- depends to a great extent on the resolution of two important questions.
The first is the question of transferring pumping energy to the active zone of
a laser with minimum losses. Studies on optimizing copper vapor lasers were begun
in Ref. 1, 2. This paper examines the influence that parasitic inductance in the
chain of transfer of p~nnping energy to the active zone has on laser operation.
Results achieved with lasers with transverse and longitudinal discharges are com-
- pared with respect to the attained efficiency. The considerable difference between
lasers with transverse and longitudinal dischargPs is due to the great difference
in discharge currents. Operation of a laser with transverse discharge requires
pinnping currents more than an order of magnitude greater than longitudinal dis-
charge currents. Because of this, the influence of the supply inductance is quite
appreciable in a laser with transverse discharge.
9
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The second question is investigation of different methods of producing the work-
ing mixture based on vaporizing metal. We have examined the following methods:
heating the walls of the active zone of the laser by a special heater [Ref. 3]
or by the heat released in the electric discharge [Ref. 4]; producing metal vapor
by usin g vaporizers; producing the working mixture by forming a flow of inetal vapor
and inert gas without entrainment and losses of inetal vapor (in contrast to the
method used in Ref. 5).
2. Experimental Facility
The research was done on an experimental facility based on a coaxial laser with
cylindr ical metal electrodes between which a transverse discharge was produced.
The discharge zone ~:~J cm long was bounded by the walls of the outer electrode
- (anode) 6 cm in diameter and the cathode 2 cm in diameter. The working mixture
of the laser consisted of neon and copper vapor [Ref. 6].
The laser was pumped by an oscillator with cable transformer described in Ref. 1.
Pulses of 200 ns duration at the base with amplitude of 0.8-2 kV were transferred
to the laser cell through cables uniformly distributed between the lead-ins. Ths
outpLit impedance of the pumping oscillator, depending on the number of cables con-
- nected to the cell, was 0.15 or 0.4 S2, and the transformation ratio ntr = 10. The
- excita t ion pulse recurrence rate was 2-6 kHz. Fig. 1 shows a diagram of connection
- of the discharge gap to the pumping oscillator and to the sensors for registration
of pump ing pulses.
The registration sez~sors for voltage and , pumping .
curren t pulses were voltage dividers based oscillator
on low-inductance resistors and a Rogowski cables to
loop . Provisions were made for monitor- ~ ~ ~ ~ ~ ~ ~ ~ ~ oscilloscope
ing voltage pulses directly ar_ross the ~ ~
electrodes of the discharge gap. To do 2
this, the inner electrode was connected
to one of the voltage dividers via a sepa- J
rate h igh-voltage lead-in (see Fig. 1). ta
- This eliminated the voltage 3roF across osci~lloscope
the p arasitic inductance of the high-
voltage lead-in transferring the pumping
pulses to the discharge gap, and enabled Fig. 1. Diagram of connection
regist ration of the true shape and ampli- of the discharge gap of the co-
tude of the voltage pulse across the laser axial laser to the pumping oscil-
electrodes. E'rom the sensors, the pulses lator and to the ~innping pulse
were sent to a two-beam oscilloscope with registration sensors:
nanosecond time resolution, enabling phas- 1--high-voltage lead-ins; 2--anode;
ing of the current and voltage pulses, 3--cathode
as well as the laser light pulse obtained
by a coaxial photocell. The mean output luminosity was measured by a calorimeter.
The electrode temperature in the discharge zone was measured by an optical micro-
pyrometer and a thermocouple with signal operating a chart recorder.
3. Influence of Supply Inductance on Laser Efficiency
Because of the large currents that are realized in the discharge of a transverse-
discharge laser, it is impossible to disregard the supply inductance, which has
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impedance with a large reactance component. The supply inductance is an energy
- reservoir that has a considerable effect on the fraction of energy released in
the plasma resistance in different time intervals of pumping pulse action. Thus
the efficiency of a laser on vapors of copper and other metals is intimately related
to the processes that take place in the electrical part of the laser, an equivalent
circuit being shown in Fig. 2.
As has already been stated, the measurement
Re ~s from part of the experimental facility enabled
pulse voltage recording of oacillograms of the currents
R~ ~ generator and voltages on different parts of this cir-
cuit. In this way oscillograms were obtained
- of the pulses of currents and voltages on
the ~chamber, as well as of the voltages
Fig. 2. Equivalent electric circuit across the plasma resistance. A typical
of laser chamber: oscillogram of the pumping pulses is shown
U--voltage across lead-ins of laser in Fig. 3. This same figure shows the lasing
- chamber; LH--parasitic inductance; pulse phased with the current and voltage.
RB--lead-in resistance; Rn--plasma Graphic integration was used to determine
resistance; Un--voltage across dis- the energy supplied to the chamber and re-
charge gap of laser chamber leased across the plasma resistance over
any time interval of pulse action.
~ The equivalent electric circuit of the laser
2 is described by the equation
~ L tRe-}- iRII=U. (1)
3 Multiplication of this equation by idt and
0 ns integration transforms it to
Fig. 3. Typical oscillograms of fLid~~-J~~R,dt~-~-. fi~Rndt=f~Udt. ~2)
pulses of voltage acr~s~ the
_ lead-ins of the laser c~~.^~mber (1), The resultant equation characterizes the
discharge current (2), voltage energy balance in the electric circuit of
across the electrodes (3) and the laser, where j~Udt= WH is the energy
lasing (4) supplied to the chamber input without con-
sideration of reflections;fi'R,clt= W, is the energy released across the lead-in
resistance; ft"`IZndt=Wo is the energy released across the plasma resistance;
J;Lidi = WL is the energy that is stored and returned by the inductance. During
- the entire pumping pulse, fLidi~O in view of the reactive nature of the inductance
that stores energy E in the first half of the pulse (E = Li~X/2 at maximum current
~max~ and returns it to the discharge circuit in the second half of the pulse when
di/dt < 0.
The advisability of accounting for the resistance of the lead-in when examining
the electric circuit of the transverse-discharge laser was confirmed. The results
of graphic integration of oscillograms of the pulses of current and of voltage
across the inlet to the celr and across the plasma r~sistance showed that the energy
. released across the resistance of the high-voltage lead-in reaches 30% o,f the energy
supplied to the cell input. The results of calculations of energy losses across
_ 11
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the lead-in resistance as measured by an R-333 DC reaistance bridge with shorted
electrodes with consideration of the temperat ure behavior of this resistance showed
- good agrePment with experimental data. The 1 ead-in resistance of the investigated
- laser was comparable with the output impedanc e of the pumping oscillator, amounting
to ~0.1 S2 with respect to order of magnitude.
Despite the fact that the parasitic inductance in the discharge circuit does not
consume energy during a pulse, it has a detr imental effect on lasing. With suf-
ficiently powerful pumping, the lasing pulse is observed in the first half of the
excitation pulse. Specifically, during the f irst halt of the pumping current pulse
(when di/dt ~ 0), the lead-in inductance takes from the discharge circuit an energy
of Li~X/2, which it returns in the second half of the pulse when lasing has termi-
nated, and therefore this energy is expended only on harmful heating of the active
mixture. In the given experiments at the max imiun attainable currents the induc-
tance took up to 50% of the energy of the f irst half of the pulse.
Efficiency can be increased by shortening the duration of the pumping pulse before
the instant of lasing termination. The diff iculty in this method is in the problem
of making a pumping oscillator that shapes a pulse with duration of the order of
10 ns, and a laser chamber with parasitic inductance of the order of 1 nH.
Taking consideration of the losses on inductance in the first half of the pumping
currer~t, we can get a criterion for determining the permissible parasitic inductance
of the laser discharge circuit. In the f irs t half of the pumping pulse, which
_ is taken as triangular for the sake oi simpl icity, the pumping energy W~ without
consideration of losses in the pumping oscil lator during commutation, as well as
during transfer to and reflection from the cell, is CU~/4, where C and U~ are the
capacitance and voltage of charging of the c abl:: line. for a reasonable magni*_ude
of losses of ~10% of this energy, we have CUC /40. Setting this expression equal
to the energy stored by the inductance and equal to Li~x/2, we get a~, expression
for the permissible inductance:
L =CUc/(20imax~ = W c,'~lOtmax~�
Using this relation, let us determine the permissible inductance under some real
conditions. For example at a pumping energy of 1 J and maximum pumping current
pulse amplitude of 10 kA, the inductance in the laser discharge circuit should
not exceed 1 nH.
This reasoning implies that when considering the problem of the potentially at-
tainable efficien~y of a transverse-dischar ge metal vapor laser, one should take ~
account of losses on supply inductance and on the lead-in resistance. With con-
sideration of these losses, the efficiency of the laser is
~ � Wou t ~ ~Wx - Lj-max ~ 2 - WB ) ,
where Wout is the lasing pulse energy [Ref. 1]. The efficiency defined in t~~is
way enables us to evaluate the potential capabilities of transverse-discharge metal
vapor lasers, and to compare them with longitudinal-discharge lasers. It should
be noted that in longitudinal-discharge lasers the losses on parasitic inductance
and lead-in resistance are insignificant in virtue of the fact that their operation
requires pumping currents several orders of magnitude lower than in a transverse
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discharge, while the plasma resistance, being tens and even hundreds of ohms, far
exceeds the lead-in resistance.
- The maximum attainable efficiency of a transverse-discharge laser is 3~ [Ref. 7].
In experiments on getting high efficiency in a coaxial laser, a method was used
that was suggested in Ref. l, where it was shown that the physical efficiency of
- a laser with respect to the energy supplied to the cell increases with a reduction
inthe voltage across the laser chamber and the output impedance of the pumping
oscillator (we reduced the latter to 0.15 S2). At a voltage of 0.8 kV across the
cell, the physical efficiency of the laser re~ched 2.5%. The pumping energy was
= determined, as in Ref. 1, by graphic integration of the pulses of current and volt-
_ age across the cell.
Such a determination of efficienc:y does not permit evaluation of the potential
capabilities of the investigated laser due to technical difficulties in making
a low-inductance laser chamber. Therefore, to determine the efficiency that can
be attained with transverse excitation of copper vapor: it is necessary to take
consideration of losses in the electric circuit of the laser.
In the experiment under discussion, the lasing pulse was located on the current
pulse front, where di/dt ~ 0, and therefore part of the useful energy was released
on the inductance. Losses on inductance reached ~50%, which was confirmed by graph-
ic integration of the pulses of current and voltage across the electrodes of the
discharge gap carried out up to the instant of lasing termination. Losses on the
lead-in resistance were disregarded, as steps were taken in these experiments to
reduce this resistance.
_ Thus the potentially attainable, but apparently not maximum possible efficiency
of the coaxial laser (efficiency with respect to energy supplied to the cell after
deducting losses on inductance) was 5.3%. The obtained efficiency is almost twice
that of a longitudinal-discharge laser, and even greater than that theoretically
predicted for excitation of copper vapor in an electric discharge [Ref. 8].
The results show the considerable promise of lasers with transverse di~charge of
copper vapor, and apparently of other metal ~apore.
4. Influence of Methods of Producing the Working Mixture on Laser Efficiency
To increase the practical efficiency of the laser, we muat reduce energy expendi-
tures on producing metal vapor in addition to overcoming the difficulties associ-
ated with energy losses in the electric ptnnping circuit. Considered below are
various methods of producing the working mixture from the standpoint of increasing
practical ef.ficiency and achieving effective stimulated emission of the coaxial
laser. These studies were done with the described laser fed from a pumping oscil-
lator with output impedance of 0.4 S2.
The most widely used method of producing copper vapor in a transverse-discharge
laser is heating up the entire electrode zone with special heaters. An external
cylindrical heater was used in the laser that we investigated. ProvisiQns were
made for controlling the heater temperature by varying its power consumption. This
made it possible to establish the re~uired temperature of the wall of the active
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zone nn which the copper to be vaporized was located irrespective of pumping power.
Such a heating method i~ very convenient in physical research, and extends the
range of study as compared with the mode of self-heating due to 3ischarge heat
that has been used in work with longitudinal tubes, where it is necessary to change
the pumping power associated with wall temperature.
An investigation of the output power of the coaxial
- ~ i laser as a function of wall temperature of the active
~
� zone (Fig. 4) sr~owed that lasing arises at a copper
- ~ R~ vaporization temperature of 1200-1250�C. As the tem-
perature increases, the output power of the laser
�S rises, reaching a maximinn at 1450�C. Then lasing power
~
falls, and stops almost entirely at about 1600�C.
~'1i2on ~aoo u.aa ~sa~ r.~c At the optimum temperature and a pulse recurrence
rate of 3 kHz the laser output power was 10.5 W at
- Fig. 4. Laser output power a laser efficiency with respect to the energy of the
as a function of wall tem- pumping oscillator accumulator of ~1%. The practical
perature efficiency of the laser with consideration of the
power expended on heating the electrodes was consider-
- ably lower (?0.1~).
These results show the necessity of looking for ways to reduce the overall electric
supply power ~f the laser. Experiments were done in which the electrodes were
- heated via the pumping energy. To do this, the energy and recurrence rate of the
excitation pulses were increased while simultaneously reducing the heater power.
At a pumping pulse recurrence rate of 6 kHz the heater was crnnpletely disconnected, �
and the laser operated in the self-heating mode; however, the wall temperature
was below optimum. We were not able to achieve efficient stimulated emission by
using the energy released in the discharge to heat the electrodes. The output
power was only 1-2 W with yellow emission predominating, whereas a green line was
mainly excited at the optimwn excitation rate of 3-4 kHz. Apparently effective
self-heating can be realized in coaxial tubes of smaller diameter with appropriate
heat insulation.
~
,
To find the second optimum with respect to neon pressure reported in Ref. 2, ex-
periments were done in which a heater was use3 to raise the temperature of the
~ entire zone, and the pressure in the cell was reduced from a starting point of
1.5 atm. In view of the instability of laser operation due to breakdowns of the
high-voltage lead-in at low pressures, we were unable to detect the second optimum.
At the same time, in the range of neon pressures below 5 mm Hg (measured in the
cold region of the chamber), breakdown in the lead-in had almost no effect on the
stability of the hollow-cathode discharge described below.
Laser operation at low buff.er gas pressures or without buffer gas is of particular
interest and opens up definite prospects for realization of one of the principal
advantages of copper vapor lasers: high lasing pulse recurrence rate. A number
of causes have been suggested for the limitation on lasing pulse recurrence rata.
Among the most probable is the insufficient rate of the process of deionization
of the gas-discharge plasma of the laser in the interpulse period.
To establist-~ the nature of the deionization process in the las~r plasma decomposing
in the space between pulses, a third auxiliary electrode in the form of a grid
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(collector) was inserted into the active zone. This grid had its own separate
current lead through which a certain potential could be applied relative to the
main electrodes. For constant voltage, the main electrodes were held under ground
potential in view of design particulars of the cable transformer of the pimmping
oscillator. The collector was located at the same distance from anode and cathode.
Exper unents showed that in the absence of a potential across the collector, the
latter had no influence on either the occurrence of the pulse discharge in the
chamber or the lasing parameters.
A positive potential was applied to the collector relative to the main electrodes
of the laser. In the absence of a pumping pulse, a semi-self-maintained discharge
could be set up between the collector and the main electrodes, and monitored from
its currer.t-voltage characteristics. At the instant of the p~mmping pulse, there
was a sharp change in the number of charged particles in the dtscharge gap which
collected on tne main electrodes and on the collector in the space between,pulses
during plasma decomposition. The amplitude of the collector current and its shape
in different time intervals showed a reduction in the number of charged particles
as a result of plasma deionization. The time behavior of the collector current
was recorded by a resistor connected in the collector supply circuit; the signal
from this resistor was sent t.o an S1-54 oscilloscope.
Fig. 5 shows time dependences of collector
uK current for different mixture pressures
~ and pumping voltages. They all were ob-
- tained at a collector voltage of +300 V,
- 2 excitation rate of 0.5 kHz and electrode
temperature of 1500�C. In the pressure
range frum 100 mm Hg and up, the collector
- ~K current remains practically unchanged, and
3 degends only on the pimmping voltage (curves
1, 2). Apparently the process of volumetric
_ recombination predominates at these pres-
20 us sures. Whan the pressure falls below 100
u mm Hg, the time behavior of the collector
K current changes sharply (curves 3, 4).
_ 4 There is an increase in the rate of plasma
decatnposition. Wtien the pressu:e of the
working mixture decreases to a few mm Hg,
2p us processes of charge recombination on the
wall as a result of diffusion of charge
~v 500 us carriers to the wall of the discharge cham-
s ber begin to predominate. The role of volu-
metric recombination begins to fall off
t [Ref. 9].
Fig. S. Behavior of deionization
procESS during pause between pump- This technique, which was used by gas-
ing pulses (5) for different pres- discharge clasaicists in various versions
sures po of Cu-Ne mixture and vol- at the dawn of research on recombination
tages Uacc across the accumulator phenomena [Ref. 10], enables quantitative
(UK--collector voltage; Up discharge detez~nination of parameters of the investi-
gap voltage: Uacc � 16 (1, 3, 4) and gat~ld effects, but on the first stage in
8 kV (2); po= 1000 (1, 2), 100 (3) this work this problem was not raised, and
and 1-3 mm Hg (4)) an express method was needed that would
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enable keeping qualitative track of the deionization process in the active zone
of the pulse laser during the experiments.
The experiments done with the three-electrode laser show that metal vapor lasers
with low pressure of the working mixture may be quite promising. At low pressures
(1-10 mm Hg), effective plasma decomposition is possible in the period between
excitation pulses due to diffusion of electrons [Ref. 11], ions and metastable
atoms to the walls with subsequent deionization of the ions and quenching of the
metastable atoms.
We were unable to achieve efficient lasing at low pressure in lasers in which trans-
verse and longitudinal discharges were used. Pressure reduction leads to a reduc-
tion in the discharge current, and thus to deterioration of the conditions of
excitation. This effect is especially pronounced with cransition to the ra~ge
of pressures in which we are interested from a few mm Hg to a fraction of this
pressure unit, where multiple reduction of the discharge current occurs. Thus
the excitation of inetal vapor in a laser chamber of about 1 mm Hg in conventional
types of discharges (longitudinal and transverse) is ineffective in view of the
low electron concentration.
There is a way out of this situation. For pulsed excitation of inetal atoms at
low pressure it is advisable to use a hollow-cathode discharge [Ref. 10). The
discharge with a hollow cathode is characterized by an anomalous current rise in
just the low-pressure region of interest to us at comparatively low voltages applied
to the discharge gap. In other words the hollow-cathode discharge most completely
satisfies the conditions necessary for metal vapor laser operation.
It should also be emphasized that in view of the possibility of using longitudinal
current components for pumping in the hollow cathode, the overall pumping current
is slight, perhaps an order of magnitude less than the pumping current in a trans-
verse discharge for the same active volumes. This circumstar.ce relaxes requirements
for the supply inductance and thus simplifies the design of the discharge chamber,
minimizes inductive losses, and enables high physical efficiency.
Pulse lasing of copper atoms excited in a hollow-cathode discharge has been previ-
ously reported in Ref. 12.
The electrode configuration in the investigated laser enabled reaZization of the
hollow-cathode effect and stimulated emission of copper atoms without particular
difficulty. To do this, the inner electrode was made as a tube 0.8 cm in diameter
and 40 cm long with a slit made in the center. This electrode acted as a hollow
~ cathode. A planar cavity was formed by an opaque mirror with dielectric coating
and a glass plate.
Pulsed lasing of copper atoms in the hollow cathode was observed on both character-
istic lines: green and yellow at a cathode wall temperature of about 1500�C. At
an excitation pulse voltage amplitude across the electrodes of 1.2 kV and pulse
recurrence rate of 0.5 kHz, the output power was 100 mW. Increasing the excitation
frequency to 4 kHz l.ed to an increase in the mean output power to 1.2 W. Specific
energy output was 15 uJ/cm3 at pumping current in the pulse of about 100,A. The
~hysical efficiency of the laser (calculated with respect to the pumping power
absorbed in the plasma without reflections [Ref. 1]) reached 4.8-5%. The effect of
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superlinnineacence was observed in this mode. Increasing the excitation rate was
limited by the capabilities of the pumping oscillator, but we are assuming that
the optimum lasing frequency is considerably higtier and may be tens of kilohertz.
The characteristic:s obtained in these preliminary experiments are on the level
of the best results achieved with copper vapor lasers. All this shows that the
hollow-cathode laser has a good outlook for operation with metal vapor.
A considerable percentage of the electric power in operatior. of transverse-discharge
lasers on copper vapor is expended on heating of the active zone from the external
. heater.
Experiments with vaporizers without additional zone heating enabled a considerable
increase in the practical efficiency of the coaxial laser with consideration of
power going to the production of copper vapor, and also yielded efficient lasing.
In this case the copper vapor source was provided by vaporizers like that described
in Ref. 13. The vaporizers were placed in the lower part of. the anode at a length
of 20 cm. The total area of the moltien metal speculum was 6 sq. cm. With optimum
excitation, the output power was 8-9 W. The temperature of the metal melted in
the vaporizers was more than 1600�C, and the temperature of the electrodes heated
by the energy released in the vaporizers and in the discharge reached 1000-1100�C.
_ While raising the temperature in the vaporizers above the indicated value did lead
to a further increase in output power, there was a concomitant sharp drop in the
service life of the vaporizers because of intensive destruction of heating elements.
Some r.eduction in laser output power as compared with the case of zone heating
from an external source can apparently be attributed to intense condensation of
copper vapor on relatively cool electrodes. A confirmation of this assim?ption
is the presence of a considerable copper layer uniformly sputtered over the entire
surface of the electrodes, which was observed upon disassembly of th~ laser cell.
The power consumed by the vaporizer heater was r~educed by an order of magnitude
as compared with the power required for heating the entire zone, and the luminosity
of the laser changed insignificantly. This led to an ~ncr~ase in the practical
efficiency of the laser, which was about 0.6% (with consideration of the power
= or the vaporizers).
An investigation was also made of the working conditioi,a of the laser with simul-
taneous activation of the overall heater and vaporizer~,. In the authors' opinion,
this somewhat increased the copper vapor concentration in the active zone as com-
- pared with the laser operating conditions considered above, keeping the wall tem-
perature of the anode close to optimiun (1400-1500�C). Results found in the course
of these experiments and reflected in Fig. 6 show that increasing the concentration
above that corresponding to the optimum temperature leads to an increase in output
power. As can be seen from the figure, there is a considerable region where the
lasing power in operation with a single heater, is 2-3 times lower than the power
when the heaters are engaged with retention of temperature on the 1600�C level.
The saturation of laser luminosity when working with vaporizers can apparently be
attributed to disruption of the temperature conditions of the active zone of the
laser upon additional heating of the mixture by the energy released in the vapori-
zers, which is comparable with the heat from pumping. .
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In the authors' opinion, the optimum copper vapor
concentration is considerably higher than that
~ q~ corresponding to the optimum temperature of the
electrodes of the zone, i. e. higher than 1015 cm`3.
~ q~ ~ Therefore the temperature dependence of output
power shown in Fig. 4 does not define the region
~ qs of optimum concentration, but characterizes the
2 change of temperature conditions in the active
a g4 zone. Although there is an increase in copper
vapor concentration as the electrode temperature
43 rises, the gas temperature also rises beyond the
limiting ~alue, which may lead to deterioration
~e.� t~ o of lasing conditions. Gas superheating can also
Uacc~ k~ explain inefficient laser operation in the self-
heating mode, as well as the nresence of an optimum
Fig. 6. Laser output power as pumping power bey~nd which the lasing power begins
a function of accumulator vol- to fall. The optimum pumping pawer referred to
tage with vaporizer (1) and the length of the active zone was 40 W/cm.
without it (2)
In addition to gas superheating that leads to metastable states of copper atoms,
there may also be other causes leading to deterioration of lasing conditions as
there is an increase in the zone temperature, rate and energy of excitation pulses,
such as prolonged time of plasma deionization, discharge contraction and so on.
: Determination of their contribution is a complicated and important problem.
One of the effective ways of cooling the active mixture of gas lasers is circulating
the mixture through a closed loop from the active volume to the heat exchanger
and back. We did experiments with circulation of the Cu-Ne working mixture due
to natural flow of the heated gas in a gravitational field in the direction perpen-
dicular to the optical axis (Fig. 7). The gas heated in the discharge gap entered
the heat exchanger, and after cooling was again returned to the active zone. To
avoid metal vapor condensation, the temperature
of the electrodes and heat exchanger was main-
, tained on a level of 1400-1500�C. The gas heated
in the discharge to higher temperatures gave
up heat during motion to the relatively cool
_ ctive Heat heat exchanger and electrodes.
olinne e chang
The use of such a method of circulating the mix-
_ ture in lasers on copper and other metal vapors
�Flow of is ~ustified by the presence of a high temperature
head determined by the difference in temperatures
Cu-Ne mixture of the gas in the active zone and the heat ex-
- Heater
changer, which may be greater than 1000 K, al-
Fig. 7. Diagram of circulation though it is difficult to expect greater gas
of Cu-Ne working mixture circulation velocities in view of the technical
difficultiPS of making large vertical dimensions
of the laser and its cr~mponents that are to be heated to high tempera~ures.
Despite the low velocities of gas flow (of the order of 10 cm/s), which are very
difficult to measure and estimate correctly [Ref. 14], the luminosity of the laser
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was increased to 15 W instead of 10.5 W(i. e. by a factor of 1.5) as compared
to a laser without circulation, all other parameters being equal. There was also
an increase in the maximum pumping power, which was about 60 W/cm ~Fig. 8).
rp These experimental studies reinforce the confidence
,
in the advisability of cooling the working mixture
N of the copper vapor laser, and show that an effective
_
q~s f inethod of doing this may be to circulate the mixture
~ through a closed loop. An appreciable effect should
~ 2 be expected as the velocity of gas circulation is
~ a,s increased. This is an indication of the necessity
for further development of this area of inetal vapor
a Q? laser physics.
10 30 50 70
5. Conclusion
PH/L, W/cm
Fig. 8. Output power as a 1. In a pulsed transverse-discharge laser at currents
- function of linear pumping of 1-10 kA, and also when the discharge currents
power with circulation (1) are increased to 1 kA in a laser with longitudinal
and without it (2) discharge, the influence of parasitic inductances
in the discharge circuits and its resistances is
quite appreciable, leading to a reduction in the physical efficiency of the laser.
- A criterion is established for determining th~e admissible parasitic inductance
in the laser discharge circuit.
2. It has been shown that a physical efficiency of 5.3% can be attained in a trans-
verse-discharge laser when the lead-in inductance is minimized.
3. Copper vapor lasing has been accomplished in a hollow-cathode pulsed discharge
at low pressures of the mixture and insignificant inductive losses. Physical ef-
ficiency reached 5%, and the specific energy output was 15 uJ/cm3.
4. It has been shown that the insertion of a third electrode for an auxiliary
constant semi-self-maintained discharge enables monitoring the the deionization
process in the decomposing plasma in the interval between pulses.
5. It has been shown that the use of vaporizers in a transverse-discharge laser
makes it possible to raise the practical efficiency to 0.6~.
6. It has been established that circulation of the working mixture overcomes the
limitation on pumping power and improves the characteristics of the copper vapor
laser.
_ The results lead us to conclude that the possibilities of the copper vapor laser
- are far from exhausted, and their study is a topical problem.
REFERENCES
1. Babeyko, Yu. A., Vasil'yev, L. A., Sviridov, A. ~1., Sokolov, A. V., Tatarin-
tsev, L. V., KVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 1102. ,
19
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2. Bokhan, P. A., Shclieglov, 9. B., KVANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 381.
3. Walter, W. T., Solimene, N., Piltch, M., IEEE J., Vol QE-2, 1966, p 474.
4. Isayev, A. A., Kazaryan, M. A., Petrash, G. G., PRIBORY I TEKHNIKA EKSPERIMENTA,
No 1, 1973, p 188.
5. Russell, G. R., Nerheim, N. M., Pivrotto, T. J., APPL. PHYS. LETTS., Vol 21,
1972, p 565.
6. Babeyko, Yu. A., Vasil'yev, L. A., Sokolov, A. V.a Sviridov, A. V., Tatarin-
tsev, L. V., Y.VANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 2041.
7. Bokhan, P. A., Gerasimov, V. A., KVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 451.
8. Yeletskiy, A. V., Zemtsov, Yu. K., Rodin, A. V., Starostin, A. N., DOKLADY
AKADEMII NAUK SSSR, Vol 220, 1975, p 318.
9. Granovskiy, V. L., RADIOTEKHNIKA I ELEKTRONIKA, No 3, 1966, p 371.
10. Leb, L., "Osnovnyye protsessy elektricheskikh razryadov v gaze" [Principal
Processes of Electric Discharges in Gas], Moscow-Leningrad, Gosudartsvennoye
izdatel'stvo tekhnicheskoy i teoreticheskoy literatury, 1950.
11. Gabay, S., Smilanski, I.s IEEE J., Vol QE-16, No 6, 1980.
12. Fahlen, Theodore, J. APPL. PHYS., Vol 45, 1974, p 4132.
13. Ferrar, C. M., IEEE J., Vol QE-9, 1973, p 856.
i4. Harnett and Irvine, eds., "Uspekhi teploperedachi" [Advances in Heat Transfer],
Moscow, Mir, 1970.
COPYRIGHT: Izdatel'stvo "Radio i svyaz"', "Kvantovaya elektronika", 1981
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TTDC 546.27+621.315
PHYSICOCHEMICAL AND ELECTROPHYSICAL PROPERTIES OF HIGH-TEMPERATURE INSIJLATING
CERAMICS FOR ELEMENTAL VAPOR LASERS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 8(110), Aug 81
(manuscript received 13 Nov 80) pp 1697-1701
- [Article by 0. I. Buzhinskiy, V. V. Lopatin and V. P. Chernenko, Scienti�ic Re-
search Institute of High Voltages, Tomsk Polytechnical Institute]
[Text] The paper gives the characteristics of high-temperature
ceramics that are widely used in the construction of elemental
vapor lasers. It is shcswn that ceramics based on pyrolytic
boron nitride have the best characteristics with respect to a
set of selected indices.
A facility is described for measuring low-voltage and high-voltage
electrophysical ct~aracteristics of dieiectrics in a variety of
gases at pressures of 1-105 Pa and temperatures up to 2500 K.
The first experimental results are given on high-voltage elec-
tr~physical characteristics of pyrolytic boron nitride.
Elemental vapor lasers are currently in wide use as they cover a broad spectral
band and have high efficiencies and gains. It would he impossible to increase
the efficiency, emission energy and other technical-economic parameters of such
� lasers without using insulating materials that retain their dielectric properties
up to temperatures of 2000-3000 K. The choice of dielectric materials for various
structural components is dictated by their temperature conditions, by the complex
of physicochemical and electrophysical properties of the material, and also by
the characteristics of the medium.
At present, structures capable of operation in weakly aggressive atmospheres (air,
nitrogen and commercially pure noble gases at pressures up to 1 kPa) utilize com-
ponents of lnigh-temperature ceramics based on widely available and fairly well
studied oxides and r_arbides [Ref. 1-3], as well as nitrides that are not yet so
widely available [Ref. 4]. The literature contains reliable low-WOltage electro-
physical characteristics of oxides: volumetric pV and surface pg resistivities,
loss tangent tand and pe~ittivity e. What we do not have are the high-voltage
properties at high temperatures (electric strength Ebr, surface arcover gradient
Earc~ ~ich significantly determine the emisaion characteriatics of las~rs. And
despite the publication of considerable research, we do not even have reliable
21
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low-voltage electrophysical characteristic~ for nitrides. This is because items
made of BN and A1N powders are not series produced, and their properties are de-
termined to a considerable extent by che impurities of the powder, and by the pro-
duction and sintering process. In addition, the differences between electrophysical
characteristics can be explained by the lack of a generally accepted method of
measurements at high temperatures. This is particularly important for measuring
the electrophysical characteristics of anisotropic polycrystalline materials such
- as pyrolytic boron nitride.
In this paper a critical analysis is made of the properties of high-temperature
ceramics both from data in the literature and as measured by the authors.
Among the large number of high-temperature dielectrics, the best insulating proper-
ties are shown by corundum a-A1203, zirconium dioxide Zr02, brokerite BeO. nitrices
of aluminum A1N and boron BN (hereaf.ter the a-~modifications will be called simply
BN and A1203). Oxides of aluminum and beryllium, nitrides of boron and altmminum
are made in the form of powders, and itema are produced from them by hot pressing.
In recent years [Ref. 5] a technique has been developed for making items from boron
nitride by the method of gas-phase deposition: so-called pyrolytic boron nitride
(PBN);despite identical chemical composition and microstructure, items made from
powdered BN and PBN have different physicochemical and electrophysical character-
istics (Table 1, Figurel. An advantage of powder materials is the capability of
p~~ ~.~m molding "thick-walled" items. PBN can be used to make
"thin-walled" (down to 5 mm) items with large overall
dimensions and complex shape in the form of plates,
tubes, boxes and the like. A distinguishing feature
of BN and PBN is anisotropy of their properties in mu-
~oa 5 tually perpendicular directions, which is a consequence
4 of the graphite-like hexagonal lattice. With respect
3 to selected physicochemical properties (see Table 1)
~p4 2 and especially with consideration of the temperature
~ dependences of thermophysical and mechanical ~arameters,
_ ~oo the most s~uitable dielectrics for making items f or work
4~0 ~200 200o r,k at temperatures up to 2000-2500 K are ordinary and pyro-
lytic boron nitride.
Temperature dependence
of volumetric resistiv- High melting point, slow vaporization, fairly high me-
ity of ceramics� 1--Zr0 chanical strength at high temperatures and a number
[8, 10]; 2--BN [6, 10]; of other properties enable successful use of these ma-
= 3--Be0 [8]; 4--BN [15]; terials in high-temperature devices. PBN has high ther-
S--PBN, from measurement ~1 conductivity and diffusivity in the direction paral-
results for 10 specimens lel to the plane of deposition, and low values of these
parameters in the perpendicular direction. In addition,
because of its high thermal diffusivity, PBN has excellent thermal stability: items
made from this material can withstand about 100 heat cycles of 300-2000-300 K with-
out cracking or peeling (the experiments were done with nitrogen cooling under
' a pressure of 100-1000 Pa). The best oxide ceramic, brokerite, withstands 25 such
cycles [Ref. 9] (hot-pressed--12 cycles with heating to 1500 K[Ref. 6, 8J). In
contrast to other ceramics, PBN is very resistant to heat shocks: in the thermal
- stability tests, the specimens were heated to 2000 K. within 15 minutes. �
22 ~
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M'OR O~FIGIAi. U~~ pNl.1f
TABLE 2
T, K 800 I 1000 I~bO 1600 1800 I 2100 4500
_ p S, ~ ( 4�101' I 1019 7�109 8�10~ I 5�]O6 I 4�10~ 8�109
The authors have developed a high-temperature facility for measuring low-voltage
~pV~ pS~ e, tand) and high-voltage (Ebr~ Earc~ electrophysical characteristics
of dielectrics. The facility with resistive graphite heater can be used for mea-
surements in a variety of gases at pressures of 1-105 Pa and a temperature of up
to 2500 K. Techniques have been developed for preparing specimens and carrying
out measurements of low-voltage and high-voltage characteristics at high tempera-
tures. In measuring the temperature dependence of pp and pg of PBN, we observed
the standard technique approved for low temperatures (State Standard GOST 6433~2-71).
The electrodes were applied to flat specimens by smearing with grade MPG-8 graphite
or ~y platinum sputtering. The measurements were made with a guard electrode at
constant fi.eld strength of E= 50 V/mm after settling of the absorption current.
The electric strength Ebr was measured on oscillat~ng pulses with amplitude of
up to 40 kV, period of oscillations of 0.18 us, and logarithmic decrement of 2.
The permittivity of the ceramics is nearly independent of temperature, and the
- loss tangent increases by about three orders of magnitude when the temperature
is increased to 1000 K.
_ The Figure shows temperature dependences of volumetric resiativity pV for BN an3
PBN in the direction perpendicular to the plane of pressing (curves 2, 4, 5).
Table 2 summarizes the results of ineasurements made by the authors of the surface
resistivity pg for PBN in the direction parallel to the plane of deposition. Un-
fortunately, the measurements of ps for BN and PBN [Ref. 6, 8, 11, 15, 21] were
made in a two-electrode system, in which a combination of pV and pg is measured
rather than each one individually due to the anisotropy of the material. Besides,
these papers do not state the voltage and f ield strength at which the measurements
were made. This is apparently one of the reasons for the considerable divergence
of the results (for example, see the Figure, curves 2 and 4). It has been estab-
lished that the function pV = f(T) remains practically unchanged in air, nitrogen,
argon and heliiun in the pressure range of 1-105 Pa.
The electric strength Ebr of PBN flat s~ecimens 0.25 mm ttiick ~n the temperature
range of 800-1900 K was 160-200 kV/mm. The electric strength of PBN under repeated
pulse action (multipulse Ebr) is considerably lower than for a single pulse, the
- determining factors in reduction of Ebr being the repetition rate and number of
the acting pulses. For example at a rate of 1 Hz and T= 1800 K, Ebr decreases
by 20-30% with breakdown occurring as early as the 100-th pulse.
From our research, we can draw the following conclusions.
1. The literature does not give the high-voZtage electrophysical characteristics
of high-temperature insulating ceramics.
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TABLE 1
Characteristic I PBN BN ei~o, ~ A!N I s~o I zro,
I
Crystal Hexagonal Hexagonal ~etrag-
- structure I (graphite-like) (Wtlrtzite) onal
Mel t ing p oin t, K 3270 [ 5] 3270 ( 6} 2320 ( 7 J 26T0 ( 6j 2720 [ 7 J 2970 [ 7]
- Heat conduction 65-~~ 27 [6] 6[8] 8(6) 30 (8] 2[8)
at 1300 K, W/(m�K) [5, 20j
2-1
(5, 21]
Temperature coef- 2,6 -It
ficient of linear [5. t9)
expans~on_~t 1300 42-1, 0,8 [6) 8,b [9) 4,8 [6J 9,2 ~[9J 11,5 J8]
K, 10- K [2Ij
Specific h t at 1,8-2,5 2(IOj 1,1 (8] 1,~6 [6J 4(tOJ 2,7 [t0]
1300 K, kJ~j~k~ �K) [5~
- Vaporization rate2 4. ~p-6 l0-+ - - 10-' [10] 6� t0-6 [ 10]
at 2500 K, kg/ (~'m �s) (
Vapor pressure ot l0 [5J 108' ( 0~~ 10-' ~ 10) 10-1 (6] 3� 10-' -
2000 K, Pa ( lOj
Tensile s~rength at l8-(6. 8] '
1300 K, N ~2
stretc ing 49 (5] d- [6] 78 (l3] 177 [1~J 34 [9] -
bending 90-~( 4,9 ~6,8] - 128 [9J -
[ 11 ] 1;6.. .IDass
Oxidizability (ma~s 1p-s [5) 8,5�10-~ - on r? - -
lost in ox gen trgam ~6~ o~2~3
in 10 hours), g~cm
Permittivity at 4,0 4,1-4.510 (7,17J g,5 [14,6] ?,35 [l7] .12,3 (18]
LO6-LO9 flZ (ll, 2l] (6~
Dielectr,;ic losses, 2--4 (20~ 4-10 b[7] U,35-b~ [19J 2-5 3fi-5t [18~
tan 6 � 10 1171 [7~1T1
Note: II,l is the direction parallel and perpendicular to
the plane of deposition.
The mechanical strength of PBN (tensile, bending and compression) at low tempera-
tures is lower than for cther ceramics, but at 1Q00-1400 K it becomes comparable
to or even considerably greater than their strength. Table 1 gives the physico-
chemical characteristics of BN and PBN with density of about 2 g/cm3 (theoretical
density is 2.28 g/cm3), which should be considered the optimum from the standpoint
of both the process of item manufacture and resultant properties. Reducing the
density of PBN to 1.7-1.8 g/cm3 cuts mechanical strength approximately in half
~ [Ref. llJ, reduces chemical stability and increases the probability of peeling
of itema. PBN has higher chemical stability than other ceramics, shows almost
no tendency to react with most elements right up to temperatures of 2000-2500 K,
does not dissolve in water, and dissolves poorly in acids and alkalis. It is also
quite resistant to oxidation [Ref. 5] as the boron oxide (8203) film that forms
on the surface protects it from further oxidation. PBN is easily machined, has
fairly high vacuum properties, and forms vacu~mm-tight seals to titanium and copper
by the method of contact-reactive soldering with titanium-containing solders
[Ref. 16]. ,
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2. The use of ceramics like these in facilities that operate in multipulse con-
ditions requires measurements ofthe lifetime of insulation.
3. In insulation components that operate at temperatures up to 2000-2500 K, items
made from PBN can be unambiguously recommended for use with respect to a number
of characteristics. Where thick-walled insulators are necessary, hot-pressed BN,
' brokerite or aluminum nitride can be used.
REFERENCES
1. Petrash, G. G., "Spravochnik po lazeram" [Laser Handbook], edited by A. M.
Prokhorov, Moscow, Sovetskoye radio, Vol 1, 1978, pp 183-197.
2. Isayev, A. A., Petrash, G. G., Kazaryan, M. A., PRIBORY I TIIZHNIKA EKSPERIMENTA,
No 1, 1973, p 1880
3. Bokhan, P. A., Nikolayev, V. N., Solomonov, V. I., KVANTOVAYA ELEKTRONIKA,
Vol 2, 1975, p 159.
4. Buzhinskiy, 0. I., Kolganov, A. S., Krysanov, S. I. et al., KVANTOVA.YA ELEKTRONIKA,
Vol 4, 1979, p 2040.
5. Sharupin, B. N., in: "Khimicheskoye gazofaznoye osazhdeniye tugoplavkikh ne-
organicheskikh materialov" [Chemical Gas-Phase Deposition of Refractory In-
organic Materials], edited by V. S. Shpak and R. G. Arvabe, Leningrad, 1976,
pp 66-101.
6. Samsonov, G. V., "Nitridy" [Nitrides], Kiev, Naukova dumka, 1969.
7. Kikoin, I. K., ed., "Tablitsy fizicheskikh velichin" [Tables of Physical Quan-
tities], Moscow, Atomizdat, 1976.
8. Samsonov, G. V., "Fiziko-khimicheskiye svoystva okislov: spravochnik" [Physico-
chemical Properties of Oxides: Handbook], Moscow, Metallurgiya, 1978.
9. Belyayev, R. A., "Okis' berilliya" [Beryllium Oxide], Moscow, Atomizdat, 1962.
10. Kotel'nikov, R. B. et al., "Osobotugoplavkiye materialy" [High RefractoriesJ,
_ Moscow, Metallurgiya, 1969.
11. Bershadskaya, M. D., ELEKTRONNAYA TEKHNIKA. SERIYA MATERIALY, No 4, 1978, p 68.
~ 12. Libovits, G., "Razrusheniye" [Fracture], Moscow, Mir, 1976, p 7.
13. Lukin, Ye. S., Sysoyev, E. P., Poluboyarinov, D. N., OGNEUPORY, No 12, 1976,
p 34.
14. Repkin, Yu. D., OGNEUPORY, No 2, 1965, p 41.
15. Poluboyarinov, D. N., Shishkov, N. V., Kuznetsova, I. G., IZVESTIYA AKADEMII
NAUK SSSR: NEORGANICHESKIYE MATERIALY, Vol 3, 1967, p 1828.
25
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16. Batygin, V. N., Kruchinin, V. P., Kylasova, T. M., ELEKTRONNAYA TEKHNIKA,
SERIYA ELEKTRONIKA SVCh, No 3, 1977, p 71.
17. Koritskiy, Yu. V., ed., "Spravochnik po elektrotekhnicheskikm materialam"
[Handbook on Electronics Materials], Moscow, Energiya, Vol 2, 1974.
18. Tareyev, B. M., Lerner, ,I. M., "Oksidnaya izolyatsiya" (Oxide Insulation],
Moscow, Energiya, 1975.
19. Andreyeva, T. V., Barantseva, I. G., Dubnik, Ye. M., Yupko, V. L., TEPLOFIZIKA
VYSOKIKH TEMPERATUR, Vol 2, 1964, p 829.
20. Novikova, N. A., Vlasov, Ye. G., Nepomnyashchiy, L. B., OGNEUPORY, No 10, 1971,
p 54.
21. Bershadskaya, M. D., Avetikov, V. G., Sharupin, B. N., ELEKTRONNAYA TEKHNIKA,
- SERIYA MATERIALY, No 6, 1978, p 61.
_ COPYRIGHT: Izdatel'stvo "Radio i svyaz"', "Kvantovaya elektronika", 1981
6610
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1~`(1R (~F1('IA~, l?SF. (3~YX~.\'
UDC 621.378.33
ENERGY AND SPECTRAL CHARACTERISTICS OF CO GASDYNAMIC LASER WORKING MEDIA
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 8(110), Aug 81
(manuscript received 8 Jan 81) pp 1797-1801
[Article by B. S. Aleksandrov, G. A. Andronov, V. A. Belavin, B. M. Dymshits,
Ya. P. Koretskiy and V. F. Sharkov]
[Text] The paper gives the results of ineasurement of the power
and spectral composition of CO gasdynamic laser emission. Good
agreement between the results of calculation and experimental
data justified the confidence of the math.ematical model of the
CO gasdynamic laser and of the earlier prediction based on this
model of an attainable specific energy output of 50 J/g for a
CO gasdynamic laser using a CO-Ar mixture.
Recent years have seen the publication of research dealing with CO gasdynamic lasers.
None of them expresses any 3oubt as to the good outlook and high energy efficiency
of this system. Of course, there is a realistic basis for the optimistic prospects
of CO gasdynamic lasers: 1) high quantum yield of the CO molecnle; 2) the thermal
- stability of the molecule, and consequently the capability of storing a large amount
of vibrational energy; 3) low vibrational-translational relaxation rate. However,
the mere fact of a large store of vibrational energy that can be retained during
gas flow through a nozzle does not in itself ensure high output characteristics
of the laser: the stored energy has still to be converted efficiently to emission.
The efficiency of (;0 gasdynamic lasers still remains low, which is entirel_y natural
as experiments have been done only on small-scale facilities using shock tubes
under conditions that are obviously far from optim~mm. Suffice it to say that for
exampie the maximum specific energy output that has been experimentally attained
is no more than 2.2 J/g for a CO-N2-Ar mixture [Ref. 1], and 5.4 J/g for a Co-Ar
mixture [Ref. 2]. These values are clearly far from the true capabilities of the
CO gasdynamic laser. Therefore theoretical predictions of the capabilities and
eff iciency of this kind of laser should take on particular significance.
Same theoretical research has been done [Ref. 3-5] in which an investigatfon has
been made of kinetic processes in supersonic expanding flows leading to the forma-
- tion of inverse population in media containing C0, and calculations have been done
on the energy and spectral output characteristics of the laser. However,, it cannot
be said that we have yet achieved unanimity of views on the energy capabilities of
27
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CO gasdynamic lasers. �redictions of the energy efficiency of CO gasdynamic Lasers
given by various authors differ by about an order of magnitude [Ref. 3-5]. Such
a discrepancy of results can be attributed both to the difference in mathematical
models used f or the calculations, and to incompleteness of information on the l~inetic
constants appear.ing in the equations. In this connection, the 3ob of substantiating
the confidence of the mathematical model of the CO gasdynamic laser is of particular
urgency.
In Ref. S, the first attempt was made at substantiating the conf idence of the mathe-
matical model of a CO gasdynamic laser by comparing experimental and theoretical
data. However, this comparison was not sufficiently complete. Comparison of calcu-
lated and experimental data at isolated points may be insufficient for the absolute
value of lasing power. More convincing would be agreement between several para-
metric relations, assuming that the calculations were done ~aitlt the same set of
semiempirical constants.
This pager gives the results of a study of spectral and energy characteristics
of a CO gasdynamic laser using a more imporved experimental method. The spectral
composition of radiation, the most important characteristic of a laser, so far
has remained practically uninvestigated for the CO gasdynamic laser. Ref. 1 gives
the results of ineasurement of the relative intensity (weak, moderate, strong) of
individual lines; the emission spectrum of the CO gasdynamic laser given in Ref. 5
was recorded by a thermophosphor, i. e. it corresponds to the time-integrated radia-
tion over the entire pulse. The resturcturing of the spectrum that we observed
- when tt~.e experimental conditions were varied has enabled us to refine the theo-
retical model.
The experimental studies were done on a facility described in Ref. 5. A mixture
of CO:Ar = 37:63 was heatQd and compressed in a shock tube. A supersonic tapered
nozzle was used with half-angle of 10� and an interchangeable critical section,
enabling variation of the degree of expansion of the nozzle from 200 to 6400. The
nozzle diameter in the vicinity of the optical cavity was 200 mm. An external
cavity was used, formed by an opaque metal mirror and a semitransparent mirror.
Lasing involved about 1/10 of the gas flow close to the axis of the nozzle bounded
by the aperture of the windows set at the Brewster angle. Emission power was mea-
sured in the standard way: simultaneous measurement of pulse shape and total energy
_ Qave the time dependence of power. The duration of the quasi-cw period of stimu-
lated emission was about 1 ms.
An investigation was made of the way that lasing power depends on the transmission
factor t of the output mirror of the cavity. Flat dielectric mirrors (t = 0.15
and 0.35) and a germanium plane-parallel plate (t = 0.53) were used as the output
mirror. The curve for output radiation power Wout as as a function of transmission
factor (Fig. la) has a maximum in the vicinity of t= 0.15-0.35 f or the given spe-
cific conditions of the experiment.
The radiation power was also measured as a function of the degree of expansion
~f the nozzle F/F~r (Fig. lb). The output mirror with t= 0.15 was used. These
- results cover a different range of variation in F/F~r (200-800) than in Ref. 3
(400-3600). The level of Wout in our research was considerably higher due to the
use of a more efficient optical cavity.
28
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Fig. 1 also shows the results of
Wout~ calculations of the output radiation
W Q.Q01 power of the CO gasdynamic laser
for the given conditions. The method
W out, of calculation is given in Ref. 5.
Rns The calculations were done at dif-
a�o.ot rso ferent loss factors a on one mirror.
It was asstmmed that the value of a
~ a~f iao o a~ includes not only the losses imme-
- a diately on the mirror (thermal,
~so ~ diffuse scattering, etc.) that may
o s~ be determined with satisfactory
~ao - accuracy, but also possible absorp-
o tion in the boundary layer where
_ n,~ Q2 0.~ n.a �s t tou ~oo d00 F/F~r the gas temperature is high and the
a b state is close to equilibrium, losses
Fig. 1. Emission power as a function of on the mirrors, losses on inhomo-
transmission factor t of the output mir- geneities of the medium distributed
ror (a) and a function of the degree of through the volume and so on. Obvi-
expansion of the nozzle F/F~r (b)� ously it is impossible to measure
mixture CO:Ar = 37�63; po = 90 atm; To= the value of this quantity directly;
2050 K; o--experiment; o--calculation however, comparison of the results
with different values of the loss factor of calculation for different a with
a on one mirror; F/F~r = 800 (a); t= 0.15 (b) experiment gives a satisfactory
indirect estimate of a.
In comparing experimental and calculated data, it is also necessary to remember
that the cross section of the output window in the experiments had the shape of
an ellipse with axes of 30 and 15 mm, as did the working section of the mirror
surface, whereas the calculations were done for rectangular mirrors measuring
30 x 10 mm with gaussian field distribution in the direction of gas flow and con-
- stant distribution in the perpendicular direction. Clearly under such conditions
we cannot expect complete correspondence of values of the output power Wout observed
in the experiment to the calculated value. The best confirmation of the correctness
of the computational method might be agreement of qualitative dependences of Wout
on various parameters of the experiment.
The calculated behavior of the function Wout~t) satisfactorily reproduces the de-
pendence found in th2 ~xperiment (see Fig. la). Obviously there is no question
of coincidence of absolute values in the given case since the value of a is arbi-
trarily chosen, and one can always select a such that absoluCe values will agree
at one point. However, if we consider the fact that the best agreement is observed
at a= 0.03-0.1, and examine the results of comparison of the calculated dependence
Wout~t) with the experimental curve as an indirect method of determining a, then
in calculations of other dependences at predetermined a, co3ncidence of the curves
and in particular of absolute quantities is a strong argument in favor of the confi-
dence of the mathematical model and the assumed kinetic constanta.
We can see from Fi~. lb that the theoretical model also correctly describes the
dependence of Wout on the geometric degree of nozzle expansion. It should be taken
into consideration that in calculation and experiment, F/F~r increases due to a
reduction in F~r while F remains constant, which reduces the gas flow through the
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optical cavity. For the given conditiona, the calculation, like the experimental
data of Ref. 2, gives a maximum value of Wour in the vicinity of F/F~r = 800. The
less abrupt fall-off in experimental values of Wout as F/F~r decreases in comparison
with the calculated curves can be attributed to the fact that with decreasing ~/Fcr
there is a reduction in the thickness of the boundary layer and in its role in
absorption. The results shown in Fig. lb also confirm the assumption that the
loss factor is close to a= 0.05-0.10.
The occurrence of the maximum on the curve for Wout~F~F~r) (see Fig. lb) accompanied
by a reduction in gas flowrate G is due to a monotonic increase in specific energy
output Wout~G as F/F~r increases in the given interval. This result agrees with
- the conclusion of Ref. 1 on an increase in eff iciency of the CO gasdynamic laser
(a quantity that is obviously~proportional to the specific energy output) with
increasing F/F~r found experimentally.
The spectral measurements were made with a spectrograph with diffraction grating
of 200 lines per mm with intensity maximum at 4.3 um. A d.�.gram of the device is
shown in Fig. 2. The collimator ob~ective was a system comprising LiF lens 6 and
concave spher ical mirror 7. The spectrum was re-
corded by 10-channel IR receiver 9 with reception
� area of 3 x 30 mm built up of 10 Ge-Au cells measur-
r ing 3 x 3 mm. The IR receiver was operated at the
6 I~f temperature of liquid nitrogen. A wavelength band
of 4.7-5.4 um could be recorded. The parallel
~ laser beam was focused on the reception area of
the IR receiver by relative shifting of the mirror
~ and lens in the collimater ob~ective. Wavelength
z tie-in was with respect to high orders (7-9) of
~ a helium-neon adjustment laser emitting on a wave-
~ length of 0.6 328 um. This same laser was used
Fig. 2. Diagram of spectro- for alignment of the entire optical system. A
graph: diaphragm 4 was placed in front of the collimator
1--cavity mirrors; 2--nozzle; objective to reduce radiation intensity.
- 3--Brewster windows; 4--dia-
phragm; 5--flat mirror; 6-- The described system for recording the spectr~n,
LiF lens; 7--concave mirror in contrast to the system that we had previously
of collimator ob~ective; 8-- used based on a thermophosphor [Ref. 5), enabled
- diffraction grating; 9--IR us to record the spectral distribution of emission
radiation receiver energy as a f unction of time.
The random error in tie-in with respect to wavelengths, due mainly to the finite
dimensions of the He-Ne laser beam in the plane of the IR receiver we estimate
at 8a =�4 cm 1= t0.01 um.
The relative sensitivity of the cells of the IR receiver was calibrated by a heated
nichrome filament by focusing the filament image on the reception cells. The rela-
tive error of ineasurement of the signal amplitude from each reception cell according
to our estimates was 15-20%.
Measurements were made of the spectral compos ition of emission of a CO gasdynamic
laser on a mixture of CO:Ar = 37:63 at p= 90 atm and To=2050 K for nozzles with
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,
F/F~r = 200, 400, 600 and 800. Fig. 3 shows oscil-
~ ~ lograms of signals obtained from the IR receiver.
5 It can be seen from the oscillograms that the
2
duration of quasisteady lasing is about 1 ms.
3
- On the whole, the reproducibility of the results
~ should be considered satisfactory: the boundaries
5 of the spectrum and position of the maximum were
completely reproduced. The general shape of the
s--` envelope curve of the spectrum was also constant
� _ ` from experiment te sxperiment: a single maximtmn
Q in the short-wave part of the spectrum and a long
declining "tail" in the long-wave part. However,
Fig. 3. Oscillograms of sig- the rate of decline of the tail as well as the
nals from IR receiver. Con- ratios of intensities in different parts of the
ditions the same as in Fig. sPectrum underwent considerable deviations from
experiment to experiment (Fig. 4).
la: 1) 4.85-4.91 um; 2)
4.91-4.98 um; 3) 4.98-5.04 um; Fig. 5 shows experimental and calculated spectra
- S) 5.10-5.17 um; 6) 5.17-
of radiation for different values of F/F,,r at
5.23 ~rm; 7) 5.23-5.29 Ilm; 8) times corresponding to steady-state emission.
5.29-5.36 um The intensity of the maximum line in each case
. . ~,i ~i
a
s-a ~-a l?3 r~ r.-.
v(i) nN) ?A1 A7) AU) Afl) v(rl %s~ ~
b T T .
I
~
3-rt ~ s-+ ~ rr n
K~J ) A'~)~ Af~) ~ v(~ ~
- c
~�2 MJ S� e-s~ a-t a~!-t m-~~~1D rt-n
4,d 4,9 S,O ~1 3,2 um ~l~) X�/ ~13) v(s) P(s) a(S)
d
Fig. 4. Results of inea-
surement of the spectrum ~e ;e tr tt x~ a, um
of a CO gasdynamic laser Fig. 5. Experimental and
in ser.ies of experiments calculated spectrina of CO
with fixed conditions: gasdynamic laser at F/Fcr
F/F~r = 400 ~ 200 (a) , 400 (b) , 600
(c) and 800 (d). Remain-
ing conditions as in Fig. la
was taken as equal to unity. Fig. 5 illustrates on the basis of individual examples
the degree of agreement between the results of experiments and calculation done
at a= 0.05.
31
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With a simultaneous increase in F/F~r and the degree of cooling of the gas in the
optical cavity, there is an expansion in the overall limits of the spectrum, the
main fraction of emission energy is shifted into the short-wave region and there
is a transition to lower vibrational transitions. As F/F~r changes from 200 to
800, the gas temperature in the cavity changes from 75 to 40 K. A comparison of
calculation and experiments shows that the calculation satisfactorily reproduces
the range of wavelengths and the behavior of the spectrum with a change in the
degree of expansion. In evaluating the reproducibility of the exper:lments and
comparing them with calculation, it is necessary to consider first of all that
the tie-in of crystals recording IR emission to a certain wavelength range was
done with accuracy of �0.01 um, and secondly that defocusing o� the collimator
objective of the spectrograph due to the dispersion properties of the lens caused
focusing of the spectral ltnes on the receiver surface in spots of finite dimensions
so that some of them could be registered by two ad~acent crystals.
In addition to their independent interest, these results have confirmed the confi-
dence of theoretical prediction of the attainable specific energy output of a CO
gasdynamic laser based on a mixture of CO-Ar (~50 J/g), which was made in Ref. 5.
REFERENCES
1. McKenzie, R. L., PHYS. FLUIDS, Vol 15, 1972, p 2163.
2. Andronov, G. A., Armer, A. G., Belavin, V. A., Dymshits, B. M., Koretskiy,
Ya. P., Sharkov, V. F., KVANTOVAYA ELEKTRONIKA, Vol 4, 1977, p 1799.
3. Kukhto, A. N., TEPLOFIZIKA VYSOKIKH TEMPERATUR, Vol 14, 1976, p 1281.
4. Vasilik, N. Ya., Vakhnenko, V. A., Margolin, A. D., Shmelev, V. M., ZHURNAL
PRIKLADNOY MEKHANIKI I TEKHNICHESKOY FIZIKI, No 5, 1978, p 16.
5. Aleksandrov, B. S., Andronov, G. A., Belavin, V. A., Sharkov, V. F.,
TEPLOFIZIKA VYSOKIKH TEMPERATUR, Vol 16, 1978, p 1112.
- COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
6610
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UDC 621.378.33
COPPER ATOM LASER LEVEL EXCITATION EFFICIENCY IN ELECTRIC DISCHARGE
Moscow KVANTOVAYA ELEKTRONIKA in Russia:l Vol 8, No 8(110), Aug 81
(manuscript received 11 Dec 80) pp 1842-1845
[Article by 0. I. Buzhinskiy and M. L. Petrov]
[Text] On the basis of numerical solution of Boltzmann's equa-
tion for the energy distribution function of electrons, the au-
thors determir.e the rate constants of excitation of laser levels,
and the electron energy balances in a discharge in a Cu-Ne mix-
ture for different relative compositions corresponding to copper
vapor lasers with a heating method of producing copper atoms.
It is found that as the relative concentration of copper atoms
increases, the region of most effective excitation of laser lev-
els shifts toward larger values of E/N--the ratio of electric
field strength in the discharge to the total number of particles
in a unit volume. An examination is ma~e of causes for the
change in specific energy output at high temperatures in lasers
with thermal method of producing copper atoms (heating by the
discharge, forced independent heating~.
One of the ways to increase energy output in copper vapor lasers is to increase
the density of copper atoms in the working vol~e. However, experiments have shown
that energy output increases with rising temperature of the active medium only
up to =1900 K[Ref. 1]. As temperature rises further, there is even a reduction
in energy output [Ref. 2J. On the other hand, when copper atoms are produced by
using the mechanism of explosion of conductors, an increase in energy output is
observed up to concentrations of -1018 cm 3[Ref. 3], which corresponds to ~'thermal
population" temperatures much greater than 2000 K. As yet there has been no expla-
nation for the causes of the difference in specific energy output of a copper vapor
laser as a function of copper atom concentration for the thermal population and
the explosive mechanism. Therefore it is of interest to determine the electron
energy balance in a Cu-Ne discharge on the basis of numerical solution of Boltz-
mann`s equations for the electron distribution function and ascertainment of the
rate constants of laser level excitation for different relative compositions of
the Cu-Ne mixture, and to analyze the results as a basis for explaining the exist-
ing differences in the behavior of specific energy output of copper vapor lasers.
- The electron energy distribution function was determined from solution of the iso-
_ tropic compondnt of the Botzmann's equation:
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1 ( E~ u d/ l 2m d kT d `
3\ N l\~i91Qm/ du 1+~ �I .y~ du ( u=Qm1f -F' e usQmJ du f-f-
i
~I- ~ 91 ~u u~l) f ~u -I- utl~ Q~J ~u + ~t1) - uI ~u) ~ yJQt1 ~u) = 0, ~ 1)
t. / t. ~
where y~ is the relative concentration of atoms of the 3-th type; Qm� is the trans--
port cross section of collision between electrons and atams; Q i is ~he excitation
cross section for the i-th level of an atom of 3-th type; u is the mass of an
atom of the ~-th component; ui~ is the corresponding loss o~ electron energy; f is
the symmetric component of electron energy distribution.
This equation is valid under conditions of spatial homogeneity and weak anisotr~py
of the distribution function, where the frequency of elastic collisions of electrons
~ with atoms considerably exceeds the frequency of inelastic collisions. The first
term in equation (1) corresponds to the energy acq~ired by an electron in the f ield.
The second and third terms are the electron energy losses in elastic collisions
in the diffusion approximation. The last two terms of the equation describe the
losses of energy by the electron in inelastic processes. Equation (1) was numeri-
cally solved by using a method developed in Ref. 4. The transport cross section
and sixteen cross sections of lower levels of the neon atom were taken into consider-
ation in the calculations. The cross sections of processes of colli~ions between
electrons and neon atoms were taken from Ref. 5. At present there are no reli3bly
measured excitation cross sections for xesonant levels of the copper atom. Experi-
mental results found in Ref. 6, 7 differ by an order of magnitude from the results
in Aef. 10. Calculation of these cross sections by oscillator strengths [Ref. 8]
and by the Bethe formula [Ref. 9) gives values approximately half the level quoted
in Ref. 10, and higher than those of Ref. 6, 7. The authors of 10 normalize the
results of absolute cross sections of the excitations by a factor of two, holding
the relative accuracy of the results to 30y. Our calculations used cross sections
of excitation of resonan,t, metastable levels, as well as the transport cross section
of collisions of electrons with copper atoms from Ref. 10 with normalization by
a factor of two toward reduction. For the copper atom levels that have allowed
transitions to the ground state, the excitation cross sections by electron impact
were calculated by the Bethe formula in terms of the oscillator strengths of these
transitions [Ref. 9]. In addition to the above-mentioned levels, seven others
excited from .the ground state of the copper atom were taken into consideration.
The ionization cross section of the copper atom was taken from Ref. 11.
After numerical solution of equation (1) and determination of the distribution
function f(~~) of electrons, the following were found:
rate constants of the investigated processes
2c t / 2
Wr~ _ ( m ) ~ uQ~At ~u) du~ ~2)
electron drift rate .
v ~ 1/2 1 E W(~ ur ?J1Qm1 ~u)l ~ df du 3
np = - ( m ) 3 ( N ) ~J L~ J du ~ )
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and the relative energy inputs (energy balance) to the various processes
~ ~1
Zt~ _ ( N � VAP ~tk: k Ztk = ~ � ~4~
K, cm3/s
4 V~p, cm/s
3 ~ �
- y X-101
-s m~ ~-i
7t'I . ~ ,
. lU
_ ~
~ 10
I �
m
0,1 (E/N)~r~ m ,
~
(E/N) �1016, V�cm2 Q1 f ~o
Fig. 1. Constants K as a func- (E/N)�1016, V�cm2
tion o2.E/N in Cu-Ne mixture at Fig. 2. Electron drift rate in
X= 10- . 1, 2--metastable levels Cu-Ne mixture as a function of
- of lines 510.6 (1) and 578.2 nm E/N
, (2); 3, 4--resonant levels of
lines 578.2 (3) and 510.6 nm (4)
Fig. 1 shows rate constants K for excitation of laser levels of mixture Cu:Ne =
1:100= X as a function of ratio E/N of electric field strength to the total number
of particles in 1 cm3, and Fig. 2 shows curves of electron drift rate for different
relative compositions of the Cu-Ne mixture as a function of parameter E/N. As
we can see from Fig. 2, the drift rate increases with increasing concentration
of the mixture (or with increasing concentration of copper atoms) from X= 10-``
to X= 10-2 (at fixed E/N), and then falls at X= 10-1.
The specific energy invested in the discharge can be determined from the relation
W= Een~VAp~ ~5)
where E is the electric field strength in the discharge, e is the electronic charge,
V~p is drift rate.
Relation (5) implies that a reduction in drift rate with increasing concentration
of copper atoms leads to a reduction in energy input to the discharge at the same
values of electron density.
Fig. 3 shows curves for energy balance of electrons in the discharge as a function
of E/N for different relative concentrations af the Cu-Ne mixture. As comparat3.ve
characteristics of the given variants we take the values (E/N)~X where the great-
est effective energy contribution is made to the resonant levels, and (E/N)~r where
the rate constant of excitation of the upper laser level for the green line (510.6
nm) becomes g.reater than the rate constant of excitation of the metastable level
for this same lasing line (see Fig. 1). The results are su~arized in the Table,
which shows that the quantities (E/N)~r and (E/N)max increase with increasing copper
35
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z;.~z ,
a,7s. Zo/z
1
~ .
0,1 ~
8 I Z 3
Q1S ~ 3
6
I ~ d~ 7
- 1 I 9 ,~70 g !
0
Q/ ~f~Mlmar 1 10 Q1 f � M
(E/N)�io16, v�~m2 (E/N)�iola, v�~m2
a b
z,� /z
o.~s '
Fig. 3. Electron energy balance as a function
d of E/N in Cu-Ne mixture at X= 10'`` (a), 10'1 (b)
and pure copper (c): fractions of energy expended
�S on excitation of inetastable levels of lines 510.6
~ 2 s (1) and 578.2 nm (2), resonant levels of lines
o,~s , 578.2 (3) and 510.6 nm (4); fractions of energy
8 lost in elastic collisions with atoms of Ne (5)
9 and Cu (10); fractions of energy expended on ioni-
zation (6) and excitation of electronic levels
~ ii , 2 of Ne (7), and also on ionization (8) and excitation
(E/N) �10 , ~ �cm
of electronic levels of Cu (9)
atom concentration. For example (E/N)max is
equal to 2�10-16 and 10-15 for X= 10'2 and 10-1
respectively. Consequently at X= 10-1, five times
the electric field strength compared with the X (E/N~;x (E/N)m~xx
x10- ~ x10- ,
case of X= 10-2 is required to attain values V~ 2 ~ 2
of E/N that maximize the energy expended on ex- ,
citation of resonant levels at the same density 10-' ( 0,04 I 0,2
of atoms. Thus, as the temperature of the active
medium in copper vapor lasers with neon increases, I 0,08 I 0,6
there is an increase in the requirements for
- electric field strength as a consequence of the i
increase in (E/N)~r and (E/N)max~ and there is ~0-~ 0,25 I 2~
also a reduction in the energy input to the dis-
charge due to the decrease in electron drift 10-1 I 1'2 I 10
rate with increasing X. In all probability,
it is these factors that lead to an optimum in pure
the relation between specific energy output and copper 10 80
temperature of the medium in a copper vapor laser
with buffer gas. This effect is not observed
_ in copper vapor lasers without buffer gas. Ac-
cording to calculation of the energy balance of electrons in pure copper (see Fig.
3c), the fraction of energy exp~ended on excitation of resonant levels first in-
creases to values of E/N = 10-1 V�Em2 as the copper atom flensity increa~es (at
constant voltage across the discharge capacitance in this case, E/N is decreasing),
36
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and then begins to fall, approaching zero at E/N = 10-~6V�cm2. For example, at
_ a voltage across the discharge gap of ~10 kV and interelectrode spacing of ~2.5 cm,
such a value is realized only at a copper atom density of 4�1019 cm 3. Beaides,
in the case of exploding conductors the atoms are dispersed and the vapor tempera-
ture drops, possibly below the temperature corresponding to thermal population
of the metastable state, which has been observed experimentally specifically in
Ref . 12.
Thus the results of calculations of electron energy balance show that in a discharge
in pure copper right up to copper atom densities'of ~lO1e ca~ 3, the upper laser
levels can be effectively excited, and the absence of appreciable population of
the metastable level is conducive to an increase in the specific energy output
in the copper vapor laser at vapor pressure close to the atmospheric level.
- Our calculations did not take consideration of m~ny pracesses responsible for the
emission characteristics of the laser. Therefore the results can only be used
to estimate the limiting copper concentration in the copper vapor laser.
REFERENCES
1. Buzhinskiy, 0. I., Krysanov, S. I., Slivitskiy, l~. A., PRIBORY I TEKHNIKA EKS-
PERIMENTA, No 4, 1979, p 274.
2. Smilanski, J., Kerman, A., Levin, L. A., Rez, G. E., OPTICS COMMS, Vol 25,
1978, p 79.
3. Isakov, I. M., Leonov, A. G., PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 2,
- 1976, p 865.
4. Sherman, B., J. MATH. ANALYT. APPLIC., Vol 1, 1960, p 342.
5. Pevgov, V. G., candidate's dissertation, Moscow Physicotechnical Institute,
1977.
6. Aleksakhin, I. S., Borovik, A. A., ~tarodub, V. L., Shafran'osh, ZHURNAL PRI-
= KLADNOY SPEICTROSKOPII, Vol 30, 1979, p 236.
7. Borozdin, V. S., Smirnov, Yu. N., Sharonov, Yu. D., OPTIKA:I SPEKTROSKOPIYA,
Vol 43, 1977, p 384.
8. Corliss, C., Bosman, W., "Veroyatnosti perekhodov i sil ostsillyatorov" [Proba-
b ilities of Transitions and Oscillator Strengths], Moscow, Mir, 1968.
9. Sobel'man, I. I., "Vvedeniye v teoriyu atomnykh spektrov" [Introduction to
the Theory of Atomic Spectra], Moscow, Fizmatgiz, 1964.
10. Trajmar, S., Williams, W., Srivastava, S. K., J. PHYS. B., Vol 10, 1977, p 3323.
11. Pavlov, S. I., Rakhovskiy, V. I., ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY
FIZIKI, Vol 52, 1967, p 21.
12. Shukhtin, A. M., Mishakov, V. G., Fedotov, G. A., Ganeyev, A. A., OPTIKA I
SPEKTROSKOPIYA, Vol 39, 1975, p 785.
- COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
6610
CSO: 1862/14
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UDC 621.375.82+533.601
ACTIVE MEDIA FOR C02 GASDYNAMIC LASERS USING COMBUSTION PRODUCTS OF LOW-NITROGEN
FUELS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 8(110), Aug 81
(manuscript received 18 Dec 80) pp 1846-1849
[Article by N. V. Yevtyukhin, Institute of Chemical Physics, USSR Academy of Sci-
ences, Chernogolovka]
[Text] An experimental study is done on the way that optical
_ gain Ko depends on stagnation parameters in a C02 gasdynamic
laser using combustion products of model fuels with low nitrogen
content: atomic fraction of N in the composition ~N = 0.4. The
experiments were done in the following ranges of variation in
the pressure a~d temperature of the gas in the prechamber:
p= 4-25 atm, T= 1300-2300 K. It is shown that as the stagnation
parameters increase, there is a considerable reduction in the
range of working media with ~N = 0.4 that show active properties.
The compositions of combustion products that are characterized
by comparatively high values of Ko are formed wfien fuel is burned
with an excess oxidant ratio different from unity.
1. Introduction
In Ref. 1-3 an experimental and theoretical study was done on the amplification
and energy characteristics of multicomponent active media of C02 gasdynamic lasers
that are produced by burning different fuels with C-, H-, 0-, N-elemental compo-
~ sition. These papers determined the major principles governing the behavior of
laser character istics with a change from one composition of combustion products
to another f.or fuels with fixed fractian of N in the composition ~N = 0.6. A value
of f,N = 0.6-0.7 is typical of compositions produced by diluting nitro compounds
and hydrocarbons with air. In this case the concentration of molecular nitrogen
in the working medium is approximately 60-75 mol.% [Ref. 4, 5]. To evaluate the
effectiveness of using high-enthalpy fuels that contain nitro groups and other
nitrogen compounds and are undiluted by nitrogen or air, it is of interest to study
the change in the way that the weak-signal gain Ko depends on composition and stag-
nation paramet?rs for working media with a lower value of ~N in the composition.
This paper gives the results of an experimental study of amplification o,f resonant
emission in multicomponent active media with ~N = 0.4 done in accordance with the
approach and techniques presented in Ref. 1, 4, 6.
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i
2. Method of the Experiment
The experiments were done on a gasdynamic laser with combustion chamber operating
in the quasi-cw mode. To produce and study high-temperature laser-active media
of predetermined composition and temperature, a method was used that is based on
igniting model mixtures of C2H2, H2, C0, 02, N20, OZ and NZ under isochronous con-
ditions [Ref. 6]. The combustion products expanded~througYt a flat profiled nozzle
with height of the critical cross section of 0.03 cm, degree of expansion of 50,
and width of 40 cm. The active media were probed at a distance of 5.3 cm downstream
from the critical cross section of the nozzle by a cw C02 electric discharge laser
operating on transition P18. Processes of combustion and discharge of the gas
through the nozzle were monitored by two inductive pressure sensors located in
the wa11 of the combustion chamber (pl) and preceding the nozzle inlet (p2).
- 3. Results of the Experiments and Discussion
The initial data and major results of the experiments are presented in tables 1
y and 2 and in figures 1 and 2. Table 1 shows the compositions of ten model fuel
mixtures used in the work, initial pressures in the chamber pH before initiation
TABLE 1
~ Model fuel mixture om o~ i n vK. Tr . Tra~.
C~H, I H~ Cp p, I N~p I Cp, I N~ I+r~ I Kp K
I 1,03 - 2,06 16,48 - - 13,73 4,4� 2500 2160
2 1,01 - 3,18 18,71 - 0,86 13,46 4,4 2500 2370
3 1,05 - 3,49 11,20 - 2,82 14,01 4,2 2500 2320
4 1,05 - 3,67 8,13 - 4,81 14,13 4,2 2500 2320
5 1,07 - 2,32 - 8,74 8,38 5,52 4,0 2500 2240
6 1,08 - 7,25 - 7,25 5.68 7,12 4,0 2500 2330
7 1,09 12,62 - 6,11 2,57 8,42 4,0 2500 2300
8 1,76 1,64 - 5,76 - 7,82 15,09 4,2 2500 2270
9 1,21 4,80 - 6,02 - 7,20 16,05 4,0 2500 2150
- 10 - . 12,38 - 6,88 - 5,15 18,32 4,6 2500 2280
TABLE 2
in com onents o equ r um compo-
~ sition o~ combustion products, mol.~ pop~~ T K Komez.
T= 1500 Y = 10 atm erM opt~ ~-i
N, I CO~ I H~O I CO O~ I H~ I NO
1 43,2 13,0 3,2 - 40,5 - 0,1 10 1670 0,52
2 44,6 20,1 3,3 - 31,~ - 0,1 7,1 1620 0,66
- 3 46,2 27,7 3,5 - 22,2 - 0,1 6,5 1590 0,62
4 47,9 35.9 3,6 - 12,5 - 0,1 6,0 1570 0,49
5 49,7 44,7 3,7 - 1.8 - 0,1 6,l 1500 0,25 �
- 6 47,1 32,4 2,9 17,0 - 0,6 - 7,4 1620 0,64
7 44,0 18,0 1,8 34,R - 1,5 - 10 1740 0,63
8 49,7 37,3 11.2 - 1,8 - - 5 1440 0,36
9 49,7 29,8 18,6 - 1,8 - - 5 1400 0,27
- 10 49,7 t4,9 33,5 - l,8 - 4 133(1 0,02

~~,A~ .
39
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~0'~ ~
n a,~b ~ carbon
a.~ black
Q4
a
, 4~ Q06
0 QD6 0,f1 Q16 l{~4 D~ QJ6 M
a
K~ ~ ~
b M-i e
_ as ~6 carbon
black
Q4 ~ 14
- ' I R1 Q06
~ ~ Q06 0,11 0,36 ~n
0
~ � -41 ~ b
c
_ Fig. 2. Optical gain Ko in C02
. gasdynamic laser using combustion
40 ns products as a function of the ele-
Nig. 1. Recordings showing mental composition of fuels with
the change in the probing relatively low nitrogen content
radiation signal in active in the composition (~N = 0.4):
media with ~N = 0.4 for dif- P= 5 (a) and 15 atm (b) ;
ferent ratios of C02 and 02 T= 1450 (a) and 1950 K(b)
(compositions 1(a), 3(b) of the combusfiion reaction, calculated Trp
and 5(c) of the tables): and average experimental TP3 values of
Io--zero signal level; pl~ the maximum combustion temperatures.
p2--profiles of signals It is clear from Table 1 that the values
from pressure sensors in the of Tr3 are an average of 7% lower than
chamber walls and prenozzle the calculated values. This systematic
space respectively deviation is the result of two major fac-
tors: heat transfer to the wall, and somewhat premature opening of the diaphragm
- that separates the combustion chamber from the prenozzle space. The latter factor
has a direct influence on the completeness of combustion of the fuel mixtures.
However, taking into consideration that the characteristic combustion times in
the given case are ~10 ms (see Fig. 1), it should be assumed that the degree of
undercombustion decreases considerably during the equalization of perturbations
throughout the space in front of the nozzle after the instant of opening of the
diaphragm (period of settling to quasi-steady flow).
Table 2 shows the concentrations of ma~or components of equilibri.um compositions
of the combustion products of the fuel mixtures. These compositions are given
for a temperature of 1500 K, which characterizes one of the quasiequilibrium states .
of the working medium in the chamber preceding the nozzle. Also given there are
40
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the maximum values of gain Ko~X that were found in the experi.ments, and the corre-
sponding values of the temperature Topt and pressure poPt in the chamber.
The diagrams of Fig. 2 illustrate the principal trends in the behavior of gain
in media with low N2 content with a transition from relatively low to higher values
of stagnation parameters in the prechamber. Here Ko is plotted as a function of
the elemental composition of the model fuel mixtures at fixed values of T and p
in the prechamber. The elemental compositions corresponding to the compositions
selected for the study are located on two characteristic lines of the diagram:
1) a line on which the atomic fraction of the element H is fixed in the composition
~H = 0.03 (compositions 1-7 of the tables); 2) a line that corresponds approximately
to the stoichiometric proportion of fuel and oxidizer in the model fuel--the line
of ternary mixtures N2-C02-H2O [Ref. 1-3] (compositions 5, 8-10 of the tables).
The transition from composition 5 to compositions 8-10 is characterized by an in-
crease in the fraction of water vapor in the combustion products from 3 to 35 mol.%
and a simultaneous reduction in carbon dioxide content from 45 to 15 mol.%. In
turn, movement along the line ~H = 0.03 from composition 5 to different sides from
the line of ternary mixtures also corresponds to a reduction of C02 content in
the combustion products, chiefly due to an increase in the concentrations of 02
or C0. Let us note that on the basis of the results of Ref. 1-3 it can be stated
that the behavior of Ko along the given lines upon the whole determines the relief
structure of gain over the entire range of fuel compositions in which we are inter-
ested.
Typical recordings showing the behavior of gain in the gasdynamic laser operating
in the quasi-cw mode on combustion products of model fuels are given in Fig. 1.
The results of processing of these recordings and the way that they are distributed
on Fig. 2 show that for high-temperature working media of C02 gasdynamic lasers
that contain approximately 40-50% N2 there is much less evidence of the peculiari-
ties noted previously in Ref. 1 in the dependence of Ko on composition and stagna-
tion parameters. As can be seen from a comparison of the diagrams of Fig. 2,
there is an appreciable reduction in the ranges of working compositions with ~N =
0.4 that show active properties as the stagnation parameters increase. And compo-
- sitions with the highest values of Ko are situated farther and farther from the.
line of ternary mixtures N2-C02=H2O. Let us note that in our experiments the rms
error that characterizes variance of the reproducibility of KQ is approximately
equal to 0.05 m'1 on all levels of values of the measured quantity. The result
of estimation of the error of ineasurements of p and T showed that the error in
determination of pressure does not exceed 10%, and for pressure--15~6 of the true
value.
Generalizing the experimental data found in Ref. 1 and in this paper, we can con-
clude that for the entire aggregate of fuel compositions with C-, H-, 0-, N-ele-
mental composition that yield a high-temperature medium (T ~ 1500 K) upon combustion
with nitrogen composition insufficient for C02 gasdynamic lasers (~N < 0.8-0.9),
preference should be given to compositions both with low hydrogen content (~H =
0.02-0.06) and with ratio of combustible �nd oxidative components in the fuel dif-
ferent from the stoichiometric composition. The excess oxidan~ ratio should differ
from unity (to either side) increasingly with decreasiiig nitrogen concentration
in the composition in the fuel mixture and with increasing stagnation parameters.
41 ~
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- REFERENCES
1. Yevtyukhin, N. V., Genich, A. P., Yudanov, A. A., Manelis, G. B., KVANTOVAYA
ELEKTRONIKA, Vol 5, 1978, p 1013.
2. Genich, A. P., Yevtyukhin, N. V., Kulikov, S. V., Manelis, G. B., Solov'yeva,
M. Ye., ZHURNAL PRIKLADNOY MEKHANIKI I TEKHNICHESKOY FIZIKI, No 1, 1979, p 34.
_ 3. Genich, A. P., Kulikov, S. V., Manelis, G. B., ZHURNAL PRIKLADNOY MEKHANIKI
I TEKHNICHESKOY FIZIKI, No 4, 1979, p 11.
4. Genich, A. P., Yevtyukhin, N. V., Manelis, G. B., FIZTKA GORENIYA I VZRYVA,
No S, 1975, p 755.
5. Kozlov, G. I., Ivanov, V. N., Korablev, A. S., Selezneva, I. K., ZHURNAL EKS-
PERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vo1 68, 1975, p 1647.
6. Yevtyukhin, N. V., Genich, A. P., Manelis, G. B., FIZIKA GORENIYA I VZRYVA,
No 4, 1978, p 36.
COPYRIGHT: Zzdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 198Z
6610
CSO: 1862/14

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~ UDC 541.141.4
SPECTROSCOPY AND PRIMARY PHOTOLYSIS PROCESSES OF IODIDES FOR PHOTODISSOCIATION
IODINE LASERS (REVIEW)
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 7(109), Jul 81 (manuscript
received 4 Dec 80) pp 1397-1424
[Articl4 h_y A.M. Pravilov, Leningrad State University imeni A.A. Zhdanov]
[Text~] The general laws governing diatomic and polyatomic iodide
spectroscopy in the ultraviolet and f ar ultraviolet regions of the
spectrum are treated. The spectroscopic properties are compared
with the existing data in the literature on their primary photolysis
processes; the major attention in this case is devoted to alkyl
iodides and perfluoralkyl,iodides. An attempt is made to interpret
the observed laws.
Introduction
_ Lasing was produced for the first time more than 15 years ago based on the transi-
t ion
J ~2p~i~)-~ J (2P~~s)+hv, 7~=1315 xM ~1~
with tl~
The classificatinn of electron motion in a molecule according to types of symmetry
in the case of a large spin-orbital interaction depends on the molecule geometry,
the nuclear charge, etc., and for this reason, it is necessary to become familiar
with the classification of various types of coupling in molecules for the group
theory analysis of equations (7) -(11) in the case where the electron states ar?
described in terms of the A-s coupling.
_ The spectroscopy of diatomic molecules with large spin-orbital interaction (includ -
ing diatomic halogens) has been developed primarily in ttte works of Mulliken [10,
11, 17-21) (also see [22-25]).
As is well known, in the case of snin-orbital interaction in even one of the atoms
incorporated in a molecule, the axial electrical field, if it exists in the mole-
cule, ~ay not break the coupling of the orbital mament I of an electror? to spin _
moment s. In this case, the total electron moment of momentum ;=,I + s precesses
about the axis of the diatomic molecule Z, and only a quantum n~ber corresponding
to the projection S2 of the total moment of momentum f~ F~~i onto the Z axis is a"good"
quantum number. The projections of the total Or~~.t$~ moments of momentum = E.T~ and
the spin of the molecule S= Esi onto the Z axis (A and E respectively) beGOmei
meaningless: the correspondin~ quantum numbers A and S also become meaningless along
with them. This rough description of the coupling of the moments in a diatomic
molecule in the presence of strong spin-orbital interaction correspo~d+a~ ta Hund's
case C[7, p 165; 10].
Mulliken treated several variants of cases of Hund's C coupling in a series of
papers.
Case "C with eZose nucZei" [11, 17]. Because of the closeness of the nuclei, the
axial electrical f.ield camponent is small, the precession of the orbital mament
about the Z axis is weak and L, S, Ja (J in the atom) and SZ are "good" quantum
numbers (admittedly, the first three are not completely so). This case has no
direct bearing on the Following presentation,
SZ-w coupZing [11, 18, 21, 24]. If the molecule can be represented as a charged
core, characterized by quantum numbers A~, E~ and S2~ with an electron sufficiently
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remote from it (so th~at the interaction is weak), then the state of the molecule
can be described by considering the projections of the orbital and spin moments
of the core and this electron on the internuclear axis. For example, for the Ryd-
berg states of diatomic molecules R'I, where R' = H(2S), X(2P), the electron con-
figuration of the valence shell has the form [18]: ~
R'J l~Q2nRnJ~~II3~2v~]2,~, ~12)
R~J ~~v2nRn~~ 2n~ /s6~~o, i; (13)
and the electron configuration I2 in this case is:
. ~ 3 2 c~4~
~2 U87Lu7i8 II3i2uQR 2.Iu,
Jz ~~66nynB~ 2n i ~zuQa~a. ~u (15)
(The configuration of the R'J+' ion is written in the parentheses). The state
R'J is characterized in this case by the quantum numbers S~, A~, E~ and 5~~,
S2 = SZ~+1~2; the spin quantum number of the molecule has no meaning. The~states of
the molecule having identical quantum numbers n= n~ and SZ, and naturally also
the parity g, u and the properties with respect to reflection in the plane pas-
sing through the Z(+,-) axis, the same type of symmetry, they "mix" and "are
repelled". In other words, the "true" wave functions, i.e., those obtained in a
sufficiently good approximation, of the states belonging to the same type of
symmetry are the linear combination of "old" unperturbed states. This applies in
particular to the 3n1 and lII states (in terms of the A-s bond) of heteroatomic
molecules. For this reason, as compared to the case of the A-s bond, the intenaity of
the lII + X1E'~' transition falls off~ while that o~ the trans~tion 3II1 X1E+ increases.
The fact that the R'I states described by configurations (12)-(r5) form doub let
pairs ZIIp, lII and 31I1, 3II2 (in terms of the A-s bond) with an energy interval
between these pairs on the order of the spin-orbital interaction energy EsZ~
equal in this case to ~E2n3~2~ 2n1~2, is also significant in this case; the
splitting in the doublet is on the order of the singlet-triplet splitting energy
~E3~~1~; which is a great deal smaller here than ESZ (Figure 1).
Case "C urith distant nucZei'; tz~pe I, tz~pe II. [11, 17, 21, 23, 24] . If the
interatomic spacing in the molecule is sufficiently great, while the dissociation
energy is small (for example, I2), then the spin-orbital coupling in the atams
~ camprising the molecule can be preserved because of the axially molecular field
and tfi e totai moment of the atom Ja does not become meaningless. In this case,
the electron state of the molecule is characterized by only one of the quantum
numbers St (S2 is the sum of the projections of Jal and Ja2 onto the Z axis) ;
the quantum numbers A, S and E are meaningless. Naturally, the properties of
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- symmetry (g, u; are preserved. Mulliken breaks the "C with distant nuclei"
case down into "C, type I" and "C, type II". In the first case, the states with
same type of syu~netry belonging to different molecular configurations, but which
are formed from identical atamic configurations or having the same types of sym-
metry within the framework of the A-s coupling "interact" and "mix"; in the second
case, states formed fram different atomic configurations and not having the same
types of symmetry within the framework of the A-s coupling can interact. We will
consider the details of these coupling types in the discussion of the I2 molecule;
we will only riote here that in the case of the "C, type I, type II" coupling, the
3IIp state splits into 3II0 and 3II0 (0+ and 0 in terms of the 3C" coup~ing) and
there is a change in the mutual arrangement of 3II2, 3II, 31I~', II~ and II(in terms
of theA-s coupling; 2~,1, U+,O and 1 in terms of the "C" coupling) as compared to
the SZ1,~ cflupling because of the interaction of these states with higher states.
' ' f 1 'p ~E _ ~E. E E ` E
? Q~ 0 A~ A A~
~,h{ ~t ~--_,.i ~+h
~
.
,~~3~ ~E - ea
a~ E .E e
.=E~~Qt . }~h
lacv~,t �C, C, S1-GI- ~ ~ A-s-c~r+~b ~ ~'Gl ~ ~C, G�cat .
Ca.l lL2 C3) C5~ ~ ~.:C3) l2) ~ll)
- C~ v CS?
Figure 1. The mutual arrangement of the molecular energy letr.els for an
electron configuration of a2.~4~3Q1 1,3n ~S~etry group C~)
and ...e3a11,3E(C3v) for the ca~e of large and small spin-
orbital interactions (based on the data of [8, p.348; 24, 43]).
The positioning of the levels is approximate; the spin-orbital
interaction increases in strength from the center towards the
edges.
Key: 1. Ion state;
2. C, type II;.
- 3. C, type I;
4, S2-w coupling;
5. A-s coupling.
It is also important for us that in the case of the "C, type I, ~ype II" coupling,
the possibilities are increased for the "interaction" of states, since of the
quantim? numbers, only it has any meaning.
49
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Thus, the difference in the S2-w and "C, type I type II" couplings reduces to a
different classif~cation of the electron states, and consequently, to different
prohibitions on "mixing", as well as to a different mutual arrangement of theae
states. What this leads to will be seen in the review of the spectroscopy and
photochemsitry of specific iodide molecules. We will only note here that the
various bond types ~an be realized not only in different molecules, but in differ-
ent states of the same molecule or in one state of a molecule, but with different
- interatomic spacings [24].
To estimate the probability of a radiation transition in various R'I molecules,
it is necessary to first of a11 establish what type of coupling describes the given
molecule in the Franck-Condon transition region or (when considering polyatomic
moZecules), which of the types of couplings of diatamic molecules is most suited
to the description of the R'-I coupling in this molecule. One must further
establish which states can "mix" with states entrained in the radiation transition,
and to estimate, or if possible, calculate the effect of this "mixing".
As will be shown below, the consideration of just this aspect of thz photodissoci-
ation process is insufficient to describe the photodecomposition of R'I and
estimate the quantities ~I* and ~I. Nonadiabatic processes of state interaction
are also of great importance, where these states correlate with R' + I* and R' + I
in the F.ranck-Condon transition regi~n as well as in the case of large values of
r~_I, i.e., processes, the influence of which can be manifest when the R' radicals
and the I, I* atoms break up (see below for the theory of semicollisions).
The theory of photodisinzegration of polyatomic molecules has as yet been quite
poorly developed. In principle, any such theory should answer three interrelated
groups of questions which to some extent apply to the topic under discussion:
1. How do the spectral functions of the total or partial absorption cross-sections
of a molecule depend on its photodisintegration mechanism; what information can be
derived from these spectra? How is a molecule absorption spectrum to be resolved
into partial cross-sections corresponding to a transition to molecular states which
disintegrate via one channel or another?
= 2. How does the probability of molecular disintegration via any channel in~the
presence of nonadiabatic processes of state interaction of the molecule depend on
the Photon energy?
3. What should the distributions of the photodissociation products of a molecule
be via a given channel in terms of the kinetic energy, ~~ibrational-rotational
excitation of polyatamic photofragments, and the angular distribution of the
dispersal of a11 the photofragments with the absorption of a light quantiun of
any energy throughout the entire absorption spectrum of this molecule?
The approaches to the solution of these problems which have been developed at the
present time do not make it possible to resolve them even in the case of the
photodissaciation of triatomic molecules. Some of the literature known to us has
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been devoted to attempts to obtain answers to the first of the questions considered
here. A critical analysis of this literature does not came within the scope of
our task, and for this reaon we will discuss only its applicability to the study
of iodide photochemistry.
As is well known, the absorption spectrum of a diat omic molecule in the case where
_ it corresponds to a transition to the repulsion branch o� the upper state or to a
purely repulsive state is approximated quite well by a gaussian distribution or a
gaussian distribution corrected by a frequency factor [7~i p. 282] . Since the first
absorption band of alkyl iodides and perfluoralkyl,iodides likewise has a bell-
shaped form, while their photodissociation process~i s basically described by
reactions (2) and (2'), it seems enticing to employ the diatomic approximation
(ass~ning the mass of R to b e concentrated in a p o int and neglecting the vibra-
tional-rotational excitation of R) tc~ describe th e photodissociation of these
molecules and to resolve their absorption spectr~ into partial cross-sections
corresponding to the dissociation of these molecules via the channels (2) and (2')
[3]. However, this model is too rough; naturally, it cannot yield any inf ormation
on the vibrational-rotational excitation of the R radical. The limited natrzre
of its application to polyatomic molecules also follows, if only from the fact
that in the case of certain properties of the upper repulsive states, at least of
linear triatomic ABC molecules, the vibrational e~c itation of the AB radical
ABC+hv--~AB*+C (16)
can lead to oscillations in the ABC absorption spec trum [27, 28]. It is therefore
not surprising that no successful attemgts to apply the diatomic model to the
photodissociation processes of polyatamic RI molecu 1 es have been described in the
literature, as far as we know.
As far as the second of the questions under consideration is concerned, there have
been successful attempts to calculate the relative yield of photodissociation
products in the presence of nonadiabatic processes ~ or th~ photodissociation of
diatomic molecules [29-31]. We ~hall touch upon th is question later in the
discussion of the photodecomposition processes for IX, X= F, C1, Br.
A discussion of the techniques of calculating the vibrational-rotational excita-
tion and angular distribution of the dispersal of the photo fragments with the
photodissociation of the molecules does not came within the scope of this review,
since we are directly intereated here only 3n the spectral functions of the
absolute quantum yields of the atoms in the case of molecular photodissociation.
We will note only that neither the quasidiatomic mo del (for example, see [32])
nor the "semicollision" model (for example, see (33]) provides satisfactory agree-
ment with the experim~ntal data on vibrational exci tation of R' in the case of
photodissociation for even ICN [33, 34j, not to mention CH37. [32]. Satisfactory
qualitative agreement between the~ry and experimenz has been obtained only in the
more precise models of the photodissociation of 1:Inear triatomic molecules, in
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particular, ICN [35-37]. One can become familiar with the various camputational
models for the photo fragment excitation energy, for example, in [26, 37-39].
We shall now discuss how the general governing laws for iodide spectroscopy we
considered above ar~ manifest in specific diatomic molecules; this will aid us
in the discussion of questions concerning polyatamic iodides.
2. The Photochemistry of Diatomic Iodides
An enormous amount of literature has been devoted to the study of the spectro-
scopic properties of diatomic iodides, especially I2. However, we will be
interested here only in those papers which deal with the photadisintegration
processes of iodides, i.e,, the processes of photodissociation and predissociation.
Hydrogen iodide HI [11- 21, 40, p. 159; 41-51]. The absorption spect~r~. of hydrogen
iodide were studied in [41-44, 50, 51]; quantitative data for the spectral region
_ of a< 200 nm, according to the data available to us, were obtained only in [44].
The photochemistry of HI and DI has been poorly studied, and the only more or less
_ reliable data that we have are for only a few wavelengthe in A band (see the Table).
The spectroscopy of HI in the first absorption band was discussed in detail for
the first time by Mulliken [11, 21J; essentially no substantial changes have
taken place in the interpretation of this band since that time (see, for example
[49]). Mulliken demonstrated that tk~e type of coupling and the mutual arrange-
ment of the first excited states in the HI molecule should be described by means
of S2-w coupling, possibly with a slight addition of "C, ~ype I" coupling [11].
Consequently, `he first exicted states of HI should comprise two groups of
doublets 3II2, 3II1 and 3IIp1II (see Figure 1). Transitions from the ground state of
HI ~g lE+)to state3nl~ln should'be observed, where the intensity of the latter
transition should "be pumped across" to the 31T1 X1E+ transition; if there is
actually a slignt addition cf "C, type I" coupling, then the transition 3TT~'f
f X lE+ should be observed (0+ 0+ in terms of the "C" coupling) as a consequence
of the "mixing" of these states with higher states of this same symmetry type
(see [11, 51]). The latest experimental data have completely confirmed this
interpretation. The resolution of the HI absorption spectrum in partial cross-
sections, corresponding to transitions to the 3]il, 31Ip and 1TI states, carried out
by Wilson and his coworkers based on experimental data on the values of ~I*
~I*(a)[~I*(a) +~i(a)] at a= 254, 266 and 279 nm confirmed Mulliken's predictions
of both the mutual arrangement of potential energy curves for these states and
(qualitatively) tt~e intensities of the radiation transitions to these states
[21, 49] (Figures z, 3; see the Table).
The photochemistry of HI and DI at a< 254 nm and 214 nm respectively, if the
erroneous data of Martin et al. is not considered [47, 49], according to the
information we have, has not been studied at all; it is only known that some of
the rotational lines in their absorption spectra are predissociated [43]. Transi-
- tions to Rydberg states are observed in this region of the spectrum, starting
with the B band [50] (am~ = 180 nm), where these states converge to the doublet
components of the HI~- ion (21I3~2 and 2II1~,2) . An interpretation and analysis of
52
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54
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55
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d xl0 ;~ca1 dx/oarMr
3aB6420 ,~p i i
f+~10
,CN . 1 4j
~ i
~ 50 i i
10 ~
~
~ Jn~ Hl=s~+~(tp,h) , ~
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~o ~ C~Z ,o ~
X f ~ ~ /J i .
!0 i oi ~
0 ~
- D,1 0,2 0,3 0,4 r, NH r NM r~ ~
o,a
_ Figure 2. The absorption spectra and ; ~
the calculated potential 6 ~'np~) i~
curves for HI [49] . (b) 4
0,4 ' , : B'n(a~) ~ :
`
rPJ~ ~ tP~ '~4'
0,5
n ~s ie ~ 1i F~vo~; cM ~
6x10~CM1 y ~
B 5 Figure 4. The total (4) and partial
absorption cross-sections
4 of I2 in the spectral
region a> 400 nm, corres-
p ~1 ponding to tr~nsitions to
- dx/01�u~z a the s~ates 3IIOu ~1~ ~ 3nlu
s , (2) , IIu (3) (a) and a
~ schematic of the levels of
= 4 I2 (b) [24, 61].
~
~ - . _ _ _ _ _
~ 1 EtlOJCM~~
JD. d5 40 4f ~xIO?cM"~ p,~ 11
a cb>
~ \(to,~)~dr~rP;~t~ .
Figure 3. The total (4) and partial
absorption cross-sections of Bo.~ ,(~P,~)~Br('P,h)
- HI (a) and DI (b) in the �
- spectral region a> 214 nm, , e(~~o)
corresponding3t+ trans3tions ~y t~~ ~~f~~,).Er(tPJ~t)
to the state 1I~ (1) , IIl (Z) I~
and 11i (3); 5 is the sum of ~ ~ x'F' r, nm
2 and 3[ 49 o,~ ~o qJ q4 r~MM
drlOycMt
Figure 5. The absorption spectrum and
potential energy curves
of IBr (based on the data
of [29, 67]) . �
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- FoR o~F~c~ni, us~ ~tvt.~~
the vibrationaZ-Yotational structure in the 42.5 - 1$0 r~m region were made in
[43, S1], an3 also presented there are the spectroscopic constants of the abserved
electron states. We will note that the nature of the HI absorption spectrum in
- the 220 - 1`30 nm :~pectral region is altogether unclear.
MoZecuZar -iod~ine [21, 23, 24, 40, p 147, 181; 52-62]. As has already been mentioned~
considerable res~arch has been devoted to the studp of molecular iodine spe.ctroscopy
(for a bibliograFhv of the early.literature~ for example~ see j23, 24]). However,
only those aspect-~ of I~ spectroscopy and photochemistrp which have a bearing on
_ polyatomic i~c~ides will be of interest to us here.
The absorption spectra of I2 have been studied, for example, in (52-54J (also see
[23, 24]). There is sufficiently reliable data on the photochemistry of I2 for
certain wavelengths in the region a> 266 nm in [55-59]. Based on these data, the
I2 absorption spectra in the visible and IR regions were resolved into partial
cross-sections in [54], where these cross-sections correspond to transitions to +
lower excited states with a configuration of a2~ru~rgag 2431 1 u(3IIlu) , Du ~3~Ou~
1 u(lIIu) (Figure 4). Of these states, only 0~ correlates+with I+ I*, being a
coupling state, in contrast to the similar sta~e of HI (3]Tp). There is a detailed
expansion in [60] which was made on the basis of magnetic circular dichroism
spectra with measurements in a solution of I2 in hexane. A comparison of the
data shown in Figure 3 and 4 shows that for I2 as compared to HI, the contribu-
tion of the transition to a state which correl~fi es with I+ I* is significantly
higher in the initial absorption bands. Simple calculations performed by Mulliken
[21, 23], assim?ing the f~asibiliCy of "C, type I+ type II" coupling, demonstrated
that this effect is due primarily to the "mixing" of. the singlet ground state
(within the framework of Pi-s coupling) 2440 XOg (lE+g) with the "triplet" state of
2441 0+ (3IIpg) lying 4.1 eV above it (this is the "C, type I" "mixing" effect,
since ~he data on the state correlate with identical configurations of iodine
atoms p5 � p5). This effect is also due to a certain extent to the "contribution"
to the "triplet" state 2431 Ou of the "sing~et" ion state 1441 Ou (lEu), which is
realized through the "triplet" 1342 Oil (3IIu) state, i.e., the 1441 Ou "mixes" with
the 1342 Ou, while this "new" state mixes with the 2431 Ou. This is an effect
within the framework of the "C, type II" coupling, since the 1441 Ou and 2431 Ou
states have different types of symm~etry within the A-s coupling framework, and
= moreover, are formed fram different iodine atom canfigurations (the 1441 Ou and
1342 Ou states correlate with I+ + I- iona, the p4 � p6 configuration).
Thus, wQ see that the presence of "C, type I, type II" coupling leads to "mixing"
- of the "singlet and "triplet" states of symmetry Ou~q in IZ and an increase in
the value of ~I* a.s compared to the case of S2-w coupling .
A review and bibliography of literature devoted to the study of absorption and
fluorescence with the exicitation of vapors in the ultraviolet and far ultraviolet
regions of the spectrum can be found in [23, 62].
The interhaZogens IF, ICZ, IBr [18, 24, 29, 31, 63-70]. Just as for the I2 mole-
cule, the probability of a transition to the B0+ (3np) in the first absorption
band of the interhalogens is significantly higher than the probability of a
- 57
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transition to the state Al (3TI1) [18, 24, 63, 64]. Thus, there is apparently
"C" coupling in IX molecules (X = F, C1, Br). Unfortunately, IX spectroscopy
_ and photochemistry have been studied unsatisfactorily in the second and subsequent
_ bands, and it is therefore difficult to establish the energy and electron config-
uration of the states which perturb the B state.
The photodisintigration products of IC1 and IBr in the first absorption band should
be I+ X or I+ X*; in a zero order approximation, the coupling A1 and epulsive
0+ st3tes correlate with the first pair, and the coupling state B0+ (3lIp) corre-
lates with the second (Figure 5). In the IF molecule, the B0+ state correlates
_ with I* + F[65, 66]; the authors of [67] suppose that yet another state can
converge to I+ Br* for the IBr molecule (see Figure 5).
- However, here the nonintersection rule is manifest and in the IBr absorption
spectrum, for example, there is a system of bands corresponding to the transi-
tion to a"new adiabatic" coupling state B'0+. At the same time, in the case of
absorption in a continuum, corresponding to the transition B0+ XO+, the major
photodissociation channel is (17), and not (17'):
J + Br*, (17)
JBr (X0+) -F hv~
~+J gr,
- - (17')
as follows f rom the nonintersection rule. This effect is well explained both
semiclassically (within the framework of the Landau-Zener model [29]) and quantum
mechanically [30]; the calculations are in excellent agreement with experimental
data [31, 64], No states have been detected experimentally which correlate with
I* + X or I* + X*; according to the data of [67J, with the photodisintegration of
IBr, ~I*(a) < 10-4 in the region a> 300 nm. In the opinion of the authors of [67],
the~,reasons for this can be either the small relative values of the Franck-Condon
coefficients or the "repulsion" of states which converge to I* + Br and I+ Br*
(see Figure 5). At room temperature in the gas phase, along with the vapors of
IC1 and IBr, there are always I2, C12 or Br2 which are in thermodynamic equilibr-
ium with IX (the IF molecule is generally chemically unstable [65]), and f or this
reason it is difficult to obtain quantitative data on the absorption spectra of
IX, We do not have such information on the ultraviolet and far ultraviolet
regions of the spectrum, and can mention only the papers [68-70] in which the
_ absorption spectra of. IC1 and IBr are graphed, and the Rydberg bands are refer-
enced to them.
3. The Photochemistry of Polyatomic Iodides
The major goal of this ~eview is to consider the spectroscopy and photochemistry
of polyatomic iodides, primarily alkyl iodides and perfluoralkyl iodides, since
it is specifically these which are the working materials of photodis~ociation
- iodine lasers. Along with the presentation of the experimental data, we will
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- devote as much attention as possible to attempts to tie together the spectroscopic
and photochemical data so as to understand the faetors which govern the value of
@I,t with the photodissociation of various RI's. The treatment of diatomic iodide
spectroscopy and photochemistry presented above, as we shall see, will be very
- useful in this case.
Cyanogen iodide ICN [28, 33, 34, 71-81]. A rather large quantity of both e~peri-
mental [34, 71-79] and especially theoretical [28, 33, 35-37, 76, 77, 80, 81]
literature has been devoted to the study of ICN spectroscopy and photochemistry.
The theoretical interest is due to the relative "simplicity" of analyzing the
photodisintegration processes of a linear triatomic molecule in the presence of
a certain quantity of experimental data on the vibrational-rotational excitation
of the CN radical, which is formed with the photodissociation of ICN in a rather
wide spectral range. Least well known of all is the spectral function ~I*(a) with
the photodissociation of ICN, which is not surprising if one considers the diffi-
culties which arise with the quantitative recording of these atoms. Reviews of
the latest achievements in the study of ICN are found, for example, in [37, 76,
77, 79).
It is well knawn that with the absorption of a photon in the first absorption
band of ICN (a =?.90 to 220 nm), transitions are made to two states (both 0+ in
terms of the "C" coupling [37]). One of them (a linear one) correlates with
CN (X 2E+) + I*, and the other (bent or linear, but predissociated through the
bent one) r_orrel~tes with CN (X 2E+) + I(see the Table) [34]. At a= 266
- approximately 99 percent of the CN radicals (X 2E+) are formed primarily in the
vibrational state. The quantum ~I*(1~) has been measured suff iciently xeliably
only for 266 nm (see the reference to the pxivate cozxespqndence from
Baranovskiy and MacDonald in [37]): ~I*(a) = 0.6 - 0.3 at a= 266 - 280 rnn. An .
analysis of the reasons for the observed distribution of partial cross-sections
in the A band is extremely diff icult because of the sparse information on LCN
spectroscopy. Recent calculations show satisfactory agreement with experimental
data on the spectral functions of vibrational excitation of CN radicals, but are
either not completely satisfactory or unsatisfactory as regards the spectral
functions ~I*(a) and CN rotational excitation (for example, see [37]). The
photochemistry of ICN in the far ultraviolet spectrum has been studied, for
example, in [76, 79) and the absorption spectra in [71-74, 79] (Figure 6).
~~p/~MOqp'CM) ERIO~n~~MOAb�CM~ (1~
IQO -
40
40
10
10
10 0
J6 ~ 40 45 +10',cti' 60 70 ~0 9x10"~uw''�
Fi,gure 6. The absorption spectrum of ICN (34].
Key: 1. 1/{mole � cm).
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_ AZkyZ iod~des and perfluoralkyl iodides. RI spectroscopz~. [2, 3, 8, 9, 19, 20,
82 - 103]. The spectroscopy of alkyl i~dides and (to a le~ser extent) perfluoro-
alkyl iodides has been studied rather well at the presenti time. The absorption
spectr~ of numerous compounds have been measured [2, 82-89] (see references to
other papers in [83, 88]) and the vibrational structure and association of bands
in the absorption spectrum in the far ultraviolet region of the spectrum have been
- analyzed for CH3I, CD3I [90-92], C2HSI [93] and CF3I [94] (al.so see [8, pp. 132,
536, 540; 95, 96].
Data on the bond lengths and the sizes of the valence angles in RI are given in
[97-98] and the spectroscopic constants of the ground and excxted states of RI
are given in [8, pp. 634, 639; 90, 93, 99-102J.
The configuration of the ground state of CH3I (and CF3I), according to the
data of Mulliken [19], without taking into account the electrons of the inner
shells of the iodine atom, has the form: (ls~)2[sal]2 (5sIa1)2 [~e]4 [val]2
(5 p~rtIe)4 lA1 (the noncoupling electror_s are given in the parentheses, while the
ones in brackets are coupling electrons), where [sal], [~re] and [val] extend over
the entire molecule, but [neJ is practically completely localized while [sal] is
partly localized at the CIi3 radical. The C~I coupling.is provided for the
greatest part by the [Qal] orbital with the slight addition of the (salJ orbital.
Absorption of CH3I, at least up to the first ionization potential (taking spin-
orbital splitting into account) ir.clusively; is due to the transport of the one
of noncoupling electrons frotn the (5 p~rl e) orbital, the major contribution to
which is made by the SpX and 5py electrons of the iodine atam, to higher orbitals.
Mulliken has convincingly demonstrated that in the first absorption band of CH3I
there is the transition (5 p~rie) 3[Qai] 1,3E f,,, (5 p~rI e) 4 lAl, where
_ [Qa~] is the antibonding orbital[19, 20], in which case, just as for other iodides,
the state 3E 3.s split into E+ E+ Ai + A1 because of the strong spin-orbital
interaction, of which, only A* correlates with CH3 + I*. The nature and similarr
ity of the initi.al absorption bands of the various alkyl iodides and perfluoro-~
- alkyl iodides (Figure 7) [83-86, 88-89] allow for the assumption that the I~3E
states are repulsive, while the [Qa~] orbital is localized near the C-I bond.
These circumstances allowed Mulliken to classify the lower excited tates of
these molecules as camponents of Q complex [19] 1Q, 3Qp, 3Q1 and ~Q2, similar
to the 31I, 3IIp, 31I1 and 3n2 states of diatomic molecules (see Figure 1). Mulliken
came to the conclusion based on an analysis of the data of Porret and Goodeve
[3] that the most intense shortwave component of the first absorption band of
CH3I corresponds to a transition to the 3Q~ state [20], s,~ that the type of
coupling in CH3I is similar to "C, type I, type II" coupling in diatomic molecules.
The absorption spectrum of CH3I in the far ultraviolet region of the spectrum
has been studied quite well [82, 90-92, 95, 96J. In a spectral range of
a> 130 nm, it consists of intense bands which fall in the Rydberg series, super-
imposed on the continuum, where these bands converge to the first two states of
the CH3I ion formed with the separation of the 5 p~rI electron (S pnt e)3
CH3I+ (E3~2, E1~2) (ionization potentials of 9.49 and 10.11 eV respectively [95)).
- The first terms of these series form the well-known B, C, D, etc. bands of CH3I
and correspond to transitions to states just as for the A-states, with
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configurations of (5 pnI e)3 (nval)3,1 E, where n= 6, 7, 0- 0 transition
to the B state (type E symmetry), corresponding to the 3II2 state with a lin~ar
configuration, occurs at 203.13 nm; in the C state (E, 3II) - at 201.16 in
the D sate (E, lIi) - at 183.07 nm) [90]. There are also transitions to the
(A1, A2, 3IIp) states and the 0- Otitrans,~tion at a= 185.05 iun (see Figure 7).
The difference in the energies of C and D states and all subsec~uent pairs of
similar states with identical values n, which converge to different states of
the ion E3~2, E1~2, is ap~roximately constant and close to the value of spin-
orbital splitting in CH31 = 4,900 cm-1) [8, p. 538; 83, 84, 90]. We will note
that there is also similar effect in other iodides (for example, see [83, 84]).
The intensities of the strongest vibrational ban~s in these transitions have the
following ratio: = 44 (3II2): 500 (31I1): = 30 (3IIp): 540 (lII) [90J. A similar
intensity distribution in similar transitions occurs in HI: 0.01 (3II2): 1.(3II1):
0.1 (3np): 2.4 (lII) for the 0- 0 transitions [43]. All of this is evidence of
the closeness of the nature of th2 coupling in the Rydberg states of CH3I to the
S~-w coupling in diatomic iodides, with a slight tendency tawards a"C" type
coupling (see section 1).
Transitions to states which are closer to the CH3I+ (E3~2, E1~2) ion states are
placed in the Rydberg series, which, as a comparison of the absorption spectra of
CH3I and Xe has shown, correspond to the transition of 5 pX~y electrons of the
iodine atom not only in the ns-orbital, as at lower photon energies, but also in
the nd and even the np orbitals [83, 91, 104]. The continuum in the far infra-
red region of the spectrum for CH3I and other alkyl and perfluoralltyl iodides, as
Boschi and Salahub propose [83, 84], is due to the absorption of radiation by the
C-C and C-H bonds (this does not contradict our d~ta [88]).
d~a",cMt
- Is
12 +100
e
p ~�IO JCM ~
JO 40 50 6P 70 EO ~,cN ~ J
a (.a)
1~~ p
70
JO ~
~ J70 J00 2~0 ?6P 740b ~?70 ?Gn ~t, ~ pn ,50 f60 Mro AD ,i~ NM ~
6 ~ (c) e
Figure 7. The absorption spectra of CH3I (a) [82] and
CF3I (b, c) [88] .
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The absorption spectrum of C2H5I in the far ultraviolet, which is slmilar in nature
to the absorption spectrum of CH3I, has been much more poorly studied because of
the vibrational-rotational structure which is considerably richer than that of CH3I.
Assignment of some of the transitions in tfie first terms of.the Rydberg series of
C2HSI (a > 175 nm) though has been done successfully [8, p 553; 83, 93]. We will
ncte that as campared to CH3I in ethyl iodide, the relative intensity of the trans-
itions to states similar to the 3II2 and 3II~ of the HI molecule is significantly
higher, something which in the opinion of the authors of [93] is due to the delocal-
ization of the nonbonding electron of the iodine atom and the reduction of the sym-
metry from C3~ down to CS.
According to data available to us, an analysis of the vibrational structure and the
assignment of the bands in ~he absorption spectrum of CFgI in the region of a>
> 130 rnn were most completely carried out by Sutcliffe and Walsh [94]. In their
opinion, this spectrum is sim ilar to the CH3I absorption spectrum. The B-band (a =
= 174 nm) apparently corresponds to the C-band of CH3I, i.e., is due to the transi-
tion to the E(31I1) state; the C-band is complex and is due, in all probability, to
transitions to states A1 and E E3li�~ lII). The relative intensity of the ~
transitions to these states is u~nown because of the impossibility of resolving
the vibrational structure of the C-band; to all apparent extents, the relative pro-
bability of a transition to a state similar to the A1 state in CH3I is higher in
CF3I [94]. Just as for CH3I, these and the subsequent bands fall in the Rydberg
series [83, 84].
An analysis of the vibrational structure and the assignment of the absorp~ion
bands of the more complex alkyl iodides and their perfluoro analogs have not been
carried out because of the f act that the vibrational-rotational structure cannot
bc resolved ~83, 84, 88]. Th ere is all the reason to assume that the nature of the
absorption spectrum of these compounds is similar to CH3I.
- Procedures for stud~ing primary iodide photoZysis processes [2, 5, 32, 67, 88, 106-
-120]. The rather high deactivation rate, the relatively low excitati~n energy of
I* and the forbidden nature of the transition (1) (the radiation lifetime of iadine
atoms is TI* = 0.1 sec [104, 105]) makes it very difficult to obtain quan*itative
information on the values of ~I*(a) with the photolysis of RI. Obtaining suffici-
ently large monochromatic rad iation fluxes in the ultraviolet and far ultraviolet
regions of the spectrtm? is a complex task, and for this reason, a considerable
_ portion of the data on the values of ~I* and the reaction rate constanzs with the
participation of I* has been obtained at the present time by kinetic spectroscopy
techniques with �lash photolysis of RI in a broad spectral range > 200 mn)
[4-6, 106-108J. The incorrectness of this approa~:h to the study of photoprocesses
has been discussed in detail in a paper by the author on the technique for the
measurement of the quantum yields of photoprocesses [109] (also see [88, 110]). The
reason for the incorrectness consists of the following. If the quantum yield of
I* atoms, for example, is measured in a wide spectral range, al - a2, ~hen only a
- certain value can be measured:
' ~
_ ~~'M = ~aorn ~d~ ~ ~il nora d~~
_ where Iabsorp. - ~norn _ ~o l~ - eXP [ - QRJ ~RJ1J} is the spectral func-
tion of the radiation absorbed by the RI molecule; cJRI(a) is the spectral function
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i~~c~1t ti~'1F1~C'~ ~ t 1~#' t101`I
of the absorption cross-section; nRi is the concentration of RI; Z is the cell
length. The integral absolute quantrum yield of the I* atoms in the range al - a2
is
x,
_ m~. ~ ~.a~. dx ~ vR~ ~ = m~� QRJ 1~~~
, x,
which is equal to ~m*as only if in the region 1~1 -~2, ~I*(~) = const., or the
measurements are made for the case of an optically thin RI layer and a constant
_ spectral composition of the light source (Ip(a) = const.). It is practically
impossible to realize the latter condition with flash photolysis of iodides in
the 320 to 230 rnn range. For this reason, the data obtained in [4-6, 106-108J
for ~I*(a � 1 or 0 throughout the entire A band are~.~not comparable and are
meaningful only for the experimental conditions realized in this literature. This
remark also fully applies to papers [45, 74, 78) (see the Tab le).
Kinetic spectroscopy of photodissociation fragments [~2], a unique kinetic method
developed in [111] as well as the optical-acoustical effect [112] have also been
used to study RI photodissociation processes; results of ineasuring ~I*(a) were
recently published for the photolysis of HgI2, obtained by observing I* lumi-
nescence with the photolysis of HgI2 by the radiation of dy~e lasers [67]. We will
- also mention papers [113] (the resolution of the CH3I absorption spectra into
partial cross-sections by means of magnetic circular dichroism) and [114] (the
measurement of the angular distribution of RI photodissociation fragments). Inform-
ation on the value of CI*(a) +~I(a) and a 0 photodissociation channel of RI,
dif�erent from (2) and (2'), was also obtajned by classical photochemical tech-
niques (for example, see [115, 116]).
Work has been underway for a number of years in our laboratory of the photon
studies department of the Scientific Research Institute of Physics at Leningrad
State University on the study of spectral functions of the absolute quantum yields
of the photodissociation channels for RI into R+ I*, R+ I, etc. [2, 88, 89, 11~J,
117-120]. The method which we have developed numbers among one of the variants of
the classical technique of [109], in which the yield of atams and radicals is
measured based on the outPut of stable photolysis products fram mixtures of the
compounds being studied with acceptors of these particles and with other gases
and vapors. The essenc~e of the technique used by us is set forth in detail in
[2] (also see [88, 118]). The basis for it is the strong difference (no less than
- a factor of 104 times [2]) in the reaction rates of the I* and I atams with
- nitrosyl chloride:
I* + NCC1 NO + ICl ~18)
I + NCC1 NO + ICl (19)
and the presenc of activation energy in the reactions of R with NOC1:
R + NOC1 NO + RC1 (20)
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FY)R nFFIC'!A[~ I~SE ONt>Y
By thermalizing zhe hot radicals formed in the photolysis process with the intro-
duction of a thermalizer for the M radicals, for example, C02 molecules, and
bringing the intesity of the radiation absorbed by the iodine, IIh~ up to levels on
the order of 1014 quanta/(cm3 � sec), condi~ions can be created in the photolysis
of an RI-NOCI-M mixture where only the I* atoms react with the NOC1, while the
I and R are expended in the following reactions:
2I+M-?I2+M (21)
R + IC1 RC1 + I (22)
as well as (3) and (4). The absolute quant~.im yield of NO (~p(a)) under these
conditions is equal to ~I,t(a).
In the case where R is poorly thermalized or the reaction rate constant (3) is
_ small (.tv .
Figure 1. The output energy as a Figure 2. The average output power as a func-
_ function of the pumping tion of frequency for a pumping
energy for mirrors with energy of 2.6 J/pulse (1), 3.6
r~flection f actors of J/pulse (2), 4.9 J/pulse (3), 8.1 ,
R= 83 r= S m(1) J/pulse (4), 10 J/pulse (5) and
and R= 96.5 r= 12 J/pulse (6); R= 96.5% (1-3) and
= 3 m (2). 83% (4-6).
The pumping was accomplished with a Xe lamp (gas pressure of about 800 mm Hg) with
discharge dimensions of 4 mm in diameter by 60 mm long. The illumination source
was a quartz monoblock 40 mm in diameter by 60 mm long with a silver coating.,
cooled with distilled water. Th e discharge circuit of the pulse tube was formed
by a 20 uFd capacitor and an ind uotance of 33 mHy. A slaved arc mode with a
current of about 0.7 amps was employed.
The laser emission energy in a one-shot pulse m ode is shown in Figure 1 as a func-
~ tion of the pumping energy for two values of the reflection factor of the output
mirror: 83 and 96.5%. It should be noted that the utilization of a slaved arc made
_ it possible to obtain a gain in the output energy (for example, with a pumping
energy of 10 J, a gain by a factor 1.7) . It can be seen from Figure 1 that wi~h
10 J pumping, the effeciency is 2.G%. The threshold pumping when the denser of
the mirrors was used amounted t o 1 J.
The results of ineasurements of the lasing characteristics of a CPG laser operating
in a pulse-periodic mode are shown in Figure 2. The family~iof curves is plotted
which show the average emission power as a function of the pulse repetition rates.
The pumping energy is fixed along each curve.
Of the greatest interest here ar e the results obtained for high pulse repetition
- rates. Thus, at a frequency of 20 Hz and with an average pumpir~g power of 240 W,
an average output power of 4.2 W was obtained (efficiency of 1.75%). In the region
of low pumping energies (2.6 J/p ulse), the average output power was 0,5 W at a
repetition rate of 25 Hz (effic iency of 0.77%). In an almost fully enclosed reso~
nator with the same frequency an d a pumping energy per pulse of 1.2 J, the average
emission power (in one direction ) was 3.3 mW,
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It should also be'noted that the emissio~ energy with pumping of 10 J/pulse for
a frequency of 25 Hz is only 40% less than the energy obtained in the one-shot
pulee mode (see Figure 1). Preliminary inves~igations showed that the ~hajor
reason for this reduction is the thermo-optical distortions of the active element
during i;ts p~nnping, which can be extremely effecltively compensated for fixed
operating modes.
The internal resonator losses can be determined fram the slopes of the curves
plotted in Figure 1[5], as well as the ultimately passible differential laser
efficiency (i.e., the laser efficiency in the absence of internal resonator losses).
An expression was used for this which relates the lasing energy W to the para-
meters of the resonator, tMe active mediinn and the pumping energy Eg for a free
running laser. We shall wrtte this function for a four-level medium [6], taking
- into account the finite pumping pulse width, asauming it has a rectangular wave-
f orm :
~1 I ln R ~ ( .._.._T
x-tnREH-EOIt~" T ~ (1)
where R is the output mirror reflection factor; K is the internal resonator
losses; T is the pumping pulse width; T is the lifetime of the upper lasing
level; n is the efficiency of pumping energy conversion to the inverse popula-
tion; E~ mS~1nR~/2cr; Q is the lasing transition cross-section; S is the
cross-sectional area of the active element; ~ is the lasing quantum energy.
Included in K are the losses due to absorption and light scattering in the
resonator elements, as well as diffraction losses and losses related to inaccuracy
in aligning the resonator. In particular, if only the absorption losses are
considered, then K= 2yZ, where Y is the coefficient of absorption in the active
element at the lasing wavelength; Z is the length of the active ~lement.
Formula (1) is quite well observed where the threshold is suffi~iently exceeded
and where the lasing pulse width practically matches the p~ping pulse width.
When a sufficient amount of experimental data is available, this expression can
- be used to f ind a number of laser parameters: ?c, n, Ep and even R. The latter
is necessary when interference effects between the end faces of the active
element and the resonator mirrors have a strong impact on the effective trans-
parency of the output mirror.
From the differential laser efficiency
dl~ ~ln RI (2)
~d=~~~ x-lnR
using two experimental curves for W(EH) for different Ra an~. Rb, one can find
K and rt. Thus, designating x= na/rlb, y= 1nRa/1nRb, and assuming that K does
not depend on R, we derive the following from (2):
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- ~ 3)
x=(z-i) ~ InRQII(y-x)�
The quantity y can be found as the ratio Wa(0)/Wb(0), extending the function
W(Eg) until it ir~teresects the axis of the output energy on the side of its
negative values.
We have the following for ~ur experimental dat~ from (1) and (2) (see Figure 1):
- K= 0.04 + 0.024 and n= 5+ 1.2 (The effective reflection factars taking
into account the influence of the end face of the active element were used in the
calculations),
Thus, an inverstigation of the lasing characteristics of a CPG laser in a pumping
energy range of 1 to 15 J has sh~wn that a CPG active element of a comparati~e~.y
small dia~r~eter (6.3 ~n) efficientYy intercepts the pu~nping radiation (n = 5%).
- A CPG laser also has a rather high effi~iency in a pulse-periodic mode, right up
to a repetition rate of 25 Hz.
The low internal losses of the resonator attest to the rather high optical qua~!ity
of the CPG active element. The numerical values oi K and n can be utilized
i.n the design of lasers operating not only in a free running mode, but also in a
Q-switched mode.
BIBLIOGRAPHY
1. S.Kh. Batygov, Yu.K. Voron'ko, B.I. Denker, A.A. Zlenko, A.Ya. Karasik,
G.K. Maksimova, V.B. Neustruyev, V.V. Osiko, V.A. Sychugov, I.A. Shcherbakov,
Yu.S. Kuz'minov, KVANTOVAYA ELEKTRONIKA, 3, 2243 (1976).
~ 2. Yu.K. Voron'ko, B.I. Denker, A.A. Zlenko, A.Ya. Karasik, Yu.S. Kuz'minov, G.V.
Maksimova, V.V. Osiko, A.M. Prokhorov, V.V. Svchugov, G.P. Shipulo, I.A.
Shcherbakov, DAN SSSR [REPORTS OF THE USSR ACADEMY OF SCIENCES], 227, 75
(1976). ~
3. A.G. Avanesov, Yu.G. Basov, V.M. Garmash, B.I. Denker, N.N. I1'ichev, G.V.
Maksimova, V.V. Osiko, A.A. Malyutin, P.O. Pashinin, A.M. Prokhorov, V.V.
Sychev, KVANTOVAYA ELEKTRONIKA, 7, 1,120 (1980).
4. A.G. Avanesov, I.V. Vasil'yev, Yu.K. Voron'ko, B.I. Denker, S.V, Zinov'yev,
A.S, Kuznetsov, V.V. Osiku, P.P. P~shinin, A.M. Prokhorov, A.A. Semenav,
KVANTOVAiiA ELEKTRONIKA, 6, 1,586 (1979).
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5. Yu.A. Anan'ye:�, A.A. Mak, B.M. Sedov, ZhETF jJOURNAL OF EXPERIMENTAL AND
THEORETICAL PHYSICS], 48, 7 (1965).
6. A.A. Mak, Yu.A. Anan'yev, B.A. Yermakov, UFN [PROGRESS IN THE PHYSICAL
SCIENCES], 92, 373 (1967).
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika.", 1981
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_ UDC 621.373.826
REQUIREMENTS PLACED ON PUMPING X-RAY LASER WITH IONIZATION SOURCE
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 7(109), Jul 81 (manuscript
received 28 May $1) pp 1606-1607
[Paper by F.V. Bunkin, V.I, Derzhiyev and S.I. Yakovlenko, Physics Institute
imeni P.N. Lebedev of the USSR Academy of Sciences, MoscowJ
[Text] It is shown that when pumping a mediv~m with an atomic
number of Z= 30 using shortwave electromagnetic radiation with
a wavelength of Yp~p ~ 0.1 nce and an. intensity of =(1015 - 1p16
W/cm2 over a time of cp~p ? 30 nsec, it is possible in principle
to achieve lasing with the ni = 5.4 ng = 3 transitions between
hydrogen-like states of multicharged ions ~alas = 1-2 nm). The
active medium can be produced during the irradiation, for example,
using a copper or brass wire with a length of 1,~ = 1 m and an
initial radius of r~ ~ 0.3 mm.
As is well known [1], � 16), the recombinational nonequilibrium of a plasma can
be maintained in the steady-state by an external ionizing source (for example, an
electron beam or short wave electromagnetic radiation), where the conditions for
lasing can be realized directly in the medium during the action of the ionizing
source. Such a siruation has been treated in considerable detail for visible
band plasma lasers, however, for the shortwave band ~~las ~ 50 nm), only p~nping
has been disc ussed for which the energy input and the electron cooling are sub-
- stantially separated in time. This is explained by the lack of laboratory
sources of ionizing radiation with a flux adequate for pumping transitions in the
shortwave band. We shall estimate the requirements placed on the ionizing X-ray
radiation flux necessary to achieve lasing in the 1-2 mn range in this paper,
considering the "exotic" sources of [2].
We shall base our work on the well known scheme [3, 1] for the population in-
version of hydrogen-like levels of c= S, 4, 3. Ir.version occurs with the ni =
= 5.4 nf = 3 transition as a result of the fact that the lower levels nf go
through a radiation decay faster than the upp~er levels ni. We shal.l not consider
inversion relative to the nf = 2 level because of the reabsorption of the radi-
ation of the 2-~ 1 transit~.ons and the 1-~ 2 pumping by fast secondary electrons
(see [1) ,�.16) , The transitions ni = 5.4 nf = 3 have alas = 1- 2 rnn for a
nuclear charge of Z= 30. For example, for Z= 26 (iron), a43 = 2.77 nm and
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~53 = 1.9 nm; for Z= 29 (copper), a43 = 2.23 nm and ~53 = 1.52 nm; for Z= 30
(zinc), aq3 = 2.08 nm and. asg = 1.42 nm. The ionizaton potentials JZ = 13.6 Z2 eV
for the H-like ions of these elements are Jfe = 9.2 KeV, J~u = 11.4 KeV and
JZn = 12.2 KeV. It is necessary to steady-state pumping that the pimmping quantum
energy hwpump be greater than JZ. This corresponds to a pumping wavelength apump
of 0.1 nm and an effective source temperature of TS ~ 10 KeV.
In order that an inversion be realzed with the ni z 5,4 ng = 3, the plasma
electron concentration and temp~arature ~hould be comparatively low (see Figures
_ 5 and 3 in [1]): Ne (5-10~ � 1011 Z~ cm-3 = 1022 cm 3, Te (1-2) Z2 eV = 1-2 ReV.
If the medium is a solid in the initial state, for exampZe, a brass wire with a
radius of rp = 0.3 nm, then the dispersal of the electron concentration from Np~=
= Z� 1022 cm 3= 3� 1023 cm 3 to Ne = 1022 cm-3 with a velocity of vT =~~2Te/amP =
- Te~ = 0.5 � 10~ cm/sec (A = 2Z, mP = 1.6 � 10-24 g) occurs in a time of:
tdispersal ~r0~�T~~NeO~Ne) - 30 nsec.
The time that the hard pumping source acts tp~P should exceed the time for
dispersal to the requisite electron concentration: tp~p = tdis. We will note
that in the case of pump~ng due to thermal ionization and subsequent cooling [1],
the pumping time is not limited on the downside, but rather fram above (tp~p <
~ tdis~�
The threshold ionizing radiation intensity Ipump, given the condition that the
number of ionization and recombination events are equal, is related to the thresh-
old gain K,~ by the f ollowing f ormula:
K,~ = ~~`las~l6Aw) ~NZ-1~picIp~p/hwP~P) ,
where ~w is the effective line width; ~pi~ is the photoionization cross-section
_ of the Z- 1 ion; NZ_1 ~ NZ = Ne/Z = 3� 1020 cm-1,
Working fram a wire length of Z= lm, we set Kn = 10/Z = 0.1 cia 1. By taking the
. Stark line width, with a slight excess in the following form:
Am - il ~ n~-n? ~~P ~~3 5� 10168c ~ fira`4-�3'
m~ ~ i Z) ~0~~ c-1 AnA 5-?3,
We obtain the canditions; - f,, .
5� l Os ~--11p~tAt"~-+ 3(Z = 30) ,
1~~x ~ {3� 109 c-1 ~n~ 5-.3 (Z =30).
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For the case of QPi~ = 10-21 cm2, ~i~p = 10 KeV = 1.6 � 10-15 J, we have the
condition of Ipu~P1015 W/cm2 for the 3 transition and IPumPS � 101~ W/cm2 for
5+ 3(Z = 30). Such an intensitq at a distance of about one meter from the
pumping source corresponds to the liberation of 1014 J over 50 nsec, if more than
10 Y of the~~energy is contained in the hard radiation. The divergence of the
laser emission in tiis case should amount to vTtdis~Z = 10-3 rad.
The estimates presented here show that lasing can occur at a wavelength of
~las = 1.4 nm, something which was mentioned in paper [2], (the 5-~ 3 transition
in zinc is closest to the indicated wavelength, see above). However, the inform-
atd,on contained in paper [2] is completely inadequate both for assessing the
reliability of the experiment itself and for attempting to interpret it more
specifically. On the other hand, the consideration of the dynamics of forced
plasma dispersal with the action of high power electromagnetic radiation, similar
to that carried out in papers [4, 5], takes on additiona.l interest because of that
presented above.
BIBLIOGRAPHY
1. L.I. Gudzenko, S.I. Yakovlenko, "Plazmennyye lazery" ["Plasma Lasers"], Mosco~r,
Atomizdat Publishers, 1978.
2. C. Robinson, Jr., AVIATION WEEK SPACE TECHN., 114, No. 8, 25 (1981).
3. B.F. Gordiyets, L.I. Gudzenko, L.A. Shelepin, ZHURN. PRIKL. TEKH. I TEKHN. FIZ.
[JOURNAL OF APPLIED ENGINEERING AND TECHNICAL PHYSICS], 5, 115 (1966).
4. V.I. Derzhiyev, V.S. Marchenko, S.I. Yakovlenko, PIS'MA V ZhTF [LETTERS TO THE
JOURNAL OF TECHNICAL PHYSICS], 6, 605 (1980).
5. A.G. Zhidkov, V.S. Marchenko, "Preprint IAE-3389" ["Institute of Nuclear Energy
Preprint No. 3389"], Moscow, 1981.
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UDC 5 32
DYNAMICS OF HYDROELASTOPLASTIC SYSTEMS
Kiev DINAMIKA GIDROUPRUGOPLASTICHESKIKH SISTEM in Russian 1981 (signed to press
2 Feb 81) pp 2-10
[Annotation, editor's message, preface and table of contents from book "Dynamics
of Hydroelastoplastic Systems", by Sh. U. Galiyev, Institute of Streng*.h Problems,
UkSSR Academy of Sciences, Izdatel'stvo "Naukova dumka", 276 pages]
[Text] The book deals with mathematical formulation of the problem of nonlinear
interaction of solid deformable and liquid media, development of algorithms and
numerical investigation of the response of complex hydroelastoplastic systems to
explosion in water. A solution is given for a broad class of applied problems.
Major emghasis is on studying the influence that other than one-d.imensional cavi-
tation, as well as geometric and physical nonlinearities of shells have on un-
steady interaction of inedia; another topic etnphasized is calculation of the three-
dimEnsional stress-strain state of cylinders under the action of hydraulic impact.
The developed algorithms are shown to be workable, and the principles that govern
unsteady nonlinear processes arising in hydroelastoplastic systems are described.
For scientists, engine~rs and technicians dealing with problems of the mechanics
of continuous media, dynamic strength of structural components and high-strain
rate metalworking.
Figures 143, tables 17, references 199.
Editor's Message
A considerable number of works have dealt with the problem of unsteady interaction
of deformable solids with a liquid. Most have been based on assumptions permitting
linearization of the initial equations in whole or in part. Usually the simplest
structural components immersed in an infinite fZuid are considered, and analytical
methods are mainly used in the solution.
The present monograph outlines a theory of nonlinear interaction of deformable
bodies with a liquid. The author considers all major nonlinear effects that in-
fluence the dynamic strength of components interfacing with the liquid, and in
- this way considerably extends the range of problems covered by theory. The main
new feature of the developed approach is that of accounting for other than one-
dimensional cavitation in the liquid, which is principally what has determined
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the originality of the proposed research techniques and the results. In addition
to nonlinear factors that influence unsteady behavior of multiphase systems compris-
ing a solid deformable body and a liquid, consideration is taken in the solution
of the problems of boundednes~ of the lic~uid volume, the products of explosion
expanding in the liquid, and three-dimensionality of the stressed and strained
state of the obstacle.
The book gives a complete presentation of the specifics of the problem of hydro-
elastoplasticity and the place that it occupiesJ in the mechanics of continuous
media. Based on solution of specific prob].ems, the most significant factors are
~ revealed that influence unsteady processes in hydroelastoplastic systems, and their
interplay with ctzanges in parameters is demonstrated. The results enable prelimi-
nary evaluation of the influence that various nonlinear effects have on the strength
of a structural element, and provide a sound basis for disregarding secondary ef-
fects. The method of finite differences is used zn solving the problems.
The principal conclusions of the work and accuracy of results are confirmed by
- a large number of calculations done w~.th a variety of grids and computation algo-
rithms, as well as models of interacting m~dia~
The book is structured around original material obtained by the author personnaly,
_ makes an appreciable contribution to ttie mechanics of continuous media and dynamic
strength of structures, and will merit favor by scientists and specialists working
with problems in this field of inechanics.
Academician G. S. Pisarenko,
- UkSSR Academy of Sciences
Preface
Oscillations and movements of structural elements in a liquid are accompanied by
hydrodynamic loading that frequently is considerably dependent on the amount of
def ormation, which depends in turn on hydrodynamic pressure. Calculation of such
structures involves the necessity of simultaneous solution of equations that de-
scribe the motion of the liquid and solid deformable media. Therefore the theory
of interaction between structures and liquid as component parts contains both hydro-
dynamics and mechanics of a solid deformable body, and also the conditions on the
contact surface of the media. Problems of interaction are considered in a number
~ of previous works.
Of considerable interest are problems of unsteady interaction between deforma'~le
solids and liquid. The calculation of dynamic strength of thin-walled and thick-
walled structures in contact with a liquid (the hull of ships, pipelines, under-
water structures, boilers in electric power plants and so on), as well as the theo-
retical study of the shape alteration of bodies that are worked by liquid or located
in a flow of liquid, reduce to problems of this category. Unsteady processes give
rise to complex wave processes in the liquid and deformed body, often with accompa-
_ nying physically and geAmetrically nonlinear properties of the interacting media.
The pattern of interaction is non-one-d~.mensional, the contact surface of the media
is deformed, giving rise to difficulties in formulation of the conditions of join-
ing on this surface. Because of the complexity of accounting for these nonlinear
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- factors, until recently problems of interaction have been solved on the basis of
the following simplifying assumptions: 1) ideal liquid in motion without eddies;
acoustic approximat~on valid; 2) no cavitation in the liquid; 3) mat~rial of ob-
stacle conforms to Hooke law; 4) boundary conditions on the contact surface of
the media can be written without consideration of deformation of the surface. Of
all the possible nonlinearities, the geometric nonlinearity of the obstacle has
been taken into consideration in some cases. Many problems of interaction of an
underwater wave with obstacles that are important .for practice have been solved
in such a formulation. However, the results are valid in a limited range of vari-
ation of the load, geometry and material of the deformable body.
In the general case, the given assumptions may not be satisfied. The class of
problems that require consideration of the nonlinear properties of the interacting
media is constantly growing due both to the increase in requirements for strength
of present-day supporting members and structures, and to the increasing use of
high-energy unsteady technological processes. For this reason, recent years have �
Geen research in which interaction problems are solved with consideration of the
corresponding nonlinear phenomena in the contacting media.
Journal articles have used a variety of approaches to the problems and the methods
of solving them, which has been an impediment to familiarity with the problem of
ncnlinear interaction as a whole, and to analysis of the influence that different
nonlinear factors have on the behavior of a structural element. Inadequate atten-
tion is given to the influence that cavitation in a liquid has on the process of
interaction. This can be attributed to the fact that motion of a medium in cavi-
tation zones is not described by classical equat~.ons of hydrodynamics, as well
as to the fact that the boundaries of cavitation zones in the liquid are not known
at every instant. At the same time, even in i:he late forties it was noted that
it is important to account for cavitation as a factor that determines the destruc-
tive action of underwater explosions.
In addition to the given assu~ptions that allow use ~f mainly linear equations,
it is f urther assumed in calculations that obstacles can be treated as plates or
shells. Such an approach needs ref inement for thick-walled bodies in the case
of short pu].ses close to regions of rapid shape change or points of attachment
of the body. This explains the interest that has arisen in the interaction of
underwater waves with three-dimensional bodies.
= A previous work has made an attempt at systematic presentation of the nonlinear
- theory of interaction of a liquid with deformable bodies. In addition, the same
work analyzes the influence of various nonlinear factors on interaction of under-
water waves with obstacles, and presents the results of numerical calculations
for thin-walled and thick-walled bodies. Despite isolated inadequacies, this paper,
published in 1977 [Ref. 32J aroused the interest of specialists [Ref. 25] and was
published in English translation in the United States in 1980 (Ref. 175].
Our book is a further development of the monograph of Ref. 32. It presents a non-
linear theory of interaction of deformable bodies with a liquid, accounting for
all major nonlinear phenomena in unsteady interaction between a liquid and obsta-
cles. Component parts of the theory are new models of a cavitating liquid with
regard to the fact that a real liquid does not work well on tension. The f irst
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model is based on the assumption that zones of destruction (cavitation) in rare-
faction waves can be approximately modeled by some continuous medium in which pres-
sure is constant. In the second model the speed of sound in a mixture of liquid
and gas bubbles filling a region of destruction in the liquid is taken as a constant
quantity much less than the speed of sound in the intact liquid or gaseous medium.
T:~e problem of calculating the interaction of pressure waves with obstacles with
regard to cavitation in the general three-dimensions~l model is formulated as a
new class of problems of mathematical physics.
Most of the book deals with solving topical problems. Equations that describe
the motion of liquid and deformable obstacles are numerically integrated by a fi-
nite-difference method. The behavior of thin-walled and thick-walled structural
elements in an underwater explosion is studied as well as the arisal and development
of cavitation accompanying wave processes in a liquid. It is shown that different
kinds of nonlinearities have different kinds of influence on thin-walled obstacles.
The geometric nonlinearity of an obstacle shows up only during flexures that exceed
its thickness. Nonlinear terms in tt~e conditions on the interface between media
have less influence on interaction. Accounting for plastic properties enables
,determination of the residual change in shape of an obstacle.
An expanded description is given of algorithms used in the calculations for solving
the unsteady three-dimensional problem of hydroelasticity for thick-walled atruc-
tural elements of cylindrical shape. Emphasis is placed on analysis of the strength
of structures, and on inver,tigation of the c~iffraction of elastic waves at corner
points, stiffener ribs and joinings between components.
In constructing the theory, the author has used relatively "simple" models of the
~ interacting media: the liquid is taken as inviscid both inside and outside of
cavitation zones, plastic properties of the body are accounted for by the theory
of flow with isotropic strengthening. On the one hand, this is due.to the fact
that the exactness of the models used for the media is not the same. Obviously
it does not make sense to improve the accuracy of equations defining the plastic
flow of material when the accuracy of theories used for the cavitating liquid has
not been fully determined. On the other hand, the use of complicated models (plas-
tic behavior of the obstacle material, gas-liquid mixture in cavitation zones,
and so on) is difficult in many cases bec;ause af a lack of experimentally def inable
parameters. Finally, the author has aimed at simplicity in formulating the problem,
feeling that simple models (where they are successful) often contain the germ of
what is typical of the physics of the problem. Indeed, it is the "simplicity"
of the models used that has enabled solution of a broad range of heretofore un-
formulated problems of interaction of the given complex media. Let us note that
the behavior of each of them in high-speed processes has only recently come under
investigation.
The problem of interaction is considered .~s a problem of investigation of the beha-
vior of systems with parameters whose time and space distribution is unknown and
is to be found during solution. The inadequate coverage of this class of problems
has made it necessary to develop nonstandard solution algorithms that enable calcu-
lation of the motion of cavitation zones in a liquid, plastic zones in a solid
and on the interface between media in space.
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Considerable attention is given to investigation of accuracy of the resuits. In
some cases, an approach is used that is based on reducing (fractionating) the spac-
ing of a grid. However, for complicat~d problems *his approach is limited by the
capabilities of the computer. Besides, it answers the question of th~ accuracy
of solution of the formulated problem, but not the question of carrespondence of
the results to actual processes, and because of the novelty qf the given problems,
- this correspondence is very important. Theref ore, in verifying the results, more
extensive use is made of calculations in accordance with different models of cavi-
tating ar.d ideal liquids, the solid deformable body, and the process of interaction.
We assume that agreement of results found by different approximate theories (in
the solution of particular problems they get progressively more complicated) is
the most weighty proof of their objectivity. Theoretacal results are compared
with data of experiments. It is shown that the proposed approximate models of
a cavitat_ing liquid are completely satisfactory from ~he standpoint of probleffis
of unsteady interaction of deformable bodies with a liquid. At the same time,
- differences between some results is an indication of the need for improving the
theory and the direction of future research.
The book examines a complex of problems that arise in calculations of the strength
and stiffness of structural elements to the action of under~aater pressure wa.ves.
The algorithms developed are general to some extent. They may be of use both in
the solution of problems of hydrodynamics and solid-state mechanics, and in the
application of other numerical methods, such as the finite element method, to the
calculation of hydroelastoplastic systems. The results can provide sounder prelimi-
nary estimates of the influence that various nonlir~ear~.ties have on the interaction
process, and can also serve as a basis for a variety of simpli�ying assumptions
in formulati.on of problems. The list of references cites papers that have had
an influence on the writing of this book.
The author thanks Academician V. V. Novozhilov of the USSR Academy of Sciences,
professors A. K. Pertsev, V. V. Matveyev, L. I. Slepyan, R. I. Nigmatullin,
R. F. Ganiyev and U. K. Nigul for constructive comments or.. the manuscript. Th~
author is especially grateful to Academician G. S. Pisare:nko of the UkSSR Academy
of Sciences for interest in the work, and for assistance in def ining the aim and
nature of the research.
Contents page
Editor's Message 6
Preface ~
PART ONE: Nonlinear Interaction of Deformable Bodies With Liquid
Chapter l.: Theory of Nonlinear Interaction of a Solid Deformable and a Liquid
Medium 12
1. Equations of hydrodynamics of ideally elastic fluid 12
2. Cavitating liquid model based on constancy of pressure 18
3. Cavitating liquid model based on constancy of the speed of sound 23
4. Equations of motion of deformable body 2~
5. Boundary conditions on contact surface of def ormable body and liquid 33
6. Deformable coordinates in liquid 38
7. Principal equations of the theory 45
8. Liquid model with cons~deration of cavitation 47
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Chapter 2: Some Approaches to Solving Problems of Nonlinear Interaction of
Deformable BodieS With Liquid ~ SO
1. One-Dimensional interaction of a wave in a liquid with a deformable body 50
2. Equations of theory of shallow shells 58
3. Finite-difference approximation of boundary conditions on an interrace 64
4. Problems of high-strain rate working of inetals by liquids 67
Conclusion ~1
PART TWO: Influence of Cavitation and Other Nonlinear L.ffects on Uns~eady
Processes in Deformable Systems That Contain Liquid
Chapter 3: Cavitation in Liquid Arising Upon Interaction of Underwater Wave
With Elastic Structural Elements 74
1. Dynamics of linear interaction of plates with liquid 74
_ 2. Influence that cavitation on plate surface has on deformation 82
3. Influence of non-one-dimensional cavitation in a pipe on bottom strain 89
4. Influence of non-one-dimensional cavitation on deformation of cylindrical
shell 110
S. Influence that cavitation on panel surface has on deformation 119
Chapter 4: Nonlinear Interaction of Liquid With Elastic Obstacles 123
1. Formulation of problem of interaction of hydraulic impact with pipe bottom 123
2. Finite-difference equations and algorithms for solving the problem of pipe
~:.t~~^: strain by t~ydraulic impact 12g
3. Numerical study of process of interaction of hydraulic impact with pipe
bottom 135
4. Investigation of accuracy of results found for pipe bottom 147
5. Comparison of accuracy of two mathematical models of cavitating liquid 155
- 6. Region of applicability of equations of acoustics in solving problems of
unsteady interaction of def ormable bodies with liquid 157
7. Finite cylindrical shell under pulsed internal loading 162
Chapter 5: Plastic Deformation of Obstacles by Liquid 173
1. Deforznation of tank bottom under h}-draulic impact 173
2. Hydroelastoplastic processes in exFlosive forming presses 181
3. Pulse expansion of cylindrical sheils by liquid 187
4. Hydroelastoplastic processes upon hydraulic impact in a pipeline, and
when a cylindrical vessel hits an obstacle 197
5. Sizing and ~oining pipes by hydraulic impact 201
6. Calcula*_ion of complex hydroelastoplastic system 204
_ Conclusion 207
PART THREE: Pulse Loading Response of Composite Circular Cylinders Submerged
in an Acoustic Medium
Chapter 6: Equations of Unsteady Hydroelasticity and Some Results of
Calculations 212
1. Method of studying interaction of cylinder with underwater wave 214
2. Finite-difference approximation of boundary conditions on cnntact surfaces
of composite cylinder elements 221
3. Algorithms for calculation of displacements of corner points 223
4. Interaction of infinite cylinder with underwater wave 226
S. Tnfl;~ence of interaction model on results of calculations 232
Chapter 7: Results of Calculations of Reinforced Isotropic Finite and
Infinite Cylinders 235
1. Finite smooth cylinder 235
2. Finite smooth cylinder reinforced in the middle 241
3. Periodically reinforced infinite cylinder 24g
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Chapter 8: Results of Calculation of Multilayered Composite Cylinders of
Finite Length 253
1. Multilayered cylinder 253
2. Cylinder comprised of butt-joined components 258
3. Ribbed composite cylinder 262
Conclusion 266
Keferences 26$
COPYRIGHT: Izdatel'stvo "Naukovo dumka", 1981
6610
CSO: 1862/262
. .
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UDC 537.53
CALCULATING ENERGY CHARACTERIST ICS OF ELECTRON-BEAM CONTROLLED CO PROCESS LASER
WITH TURBOCOMPRESSOR COOLING
Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 259, No 5, 1981 (manuscript re-
ceived 21 Apr 81) pp 1094-1098
[Articl.e by Academician N. G. Basov, Ye. P. Glotov, V. A. Danilychev, A. M. Soroka, ;
- L. M. Urin and V. T.. Yugov, Physics Institute imeni P. N. Lebedev, USSR Academy of
Sciences, Moscow]
- [Text] Electron-beam controlled (EBC) C02 lasers are currently in wide use in
technological applications [Ref. 1]. Ref. 2 demonstrated the feasibility of a
considerable increase in the specific power output and efficiency of EBC-C02
laser emission by cooling the lasing mixture to temperatures of T~ 170-200 K, and
proposed an arrangement of turbacompressor cooling in which a gas refrigeration
engine is realized on the work ing laser mixture. Of even more promise is the use
of this arrangement in EBC las~rs using carbon monoxide; these lasers, in contrast
to C0~ lasers, can in principle operate effectively only with cooling of the gas ,
mixture to cryogenic temperatures of ~100 K[Ref. 3].
At the present time, a lasing efficiency rt~~60% has been experimentally attained
on an EBC-CO laser [Ref. 4]. At the same time, cooling of the laser mixture to
cryogenic temperatures requires lar~e energy expenditures, which can appreciably
reduce the technical efficiency rlT, the major characteristic of process lasers.
Ho~aever, the active medium of the CO laser is fundamentally different from that
of the COZ laser in that during the lasing process the vibrational energy remaining ~
_ in the working med.ium as a consequence of the difference of n from unity is not
nearly instantaneously converted to heat, but remains stored ~or some time on vibra-
tional levels. This peculiarity together with considerably greater quantum ef -
ficiency (~95% instead of ~47%) leads to a situation where the fraction of pumping
energy that is converted to heat during excitation is extermely low (~10%) in the
working temperature range as compared with the analogous quantity for the C02 laser
medium (~80-90%). As a result, the effective specific heat of the CO laser mixture
cef = cP/dT is nearly an order of magnitude greater than that of the C02 laser (cP
is the specific heat at constant pressure, dT is the fraction of pumping energ;~
expended on heating the gas). Another important peculiarity of the working med ium
of CO lasers at low temperatures (T S 200 K) is that the energy stored on vibra-
tional levels is dissipated due to spontaneous emission rather than due to colli-
sional relaxation. As a consequence, it is possible to attain high technical ef -
ficiency of the CO laser desp ite the need of intense cooling of the laser mixture.
108
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In this paper, the authors calculate the energy characteristics of an EBC CO laser
with turbocompressor cooling.
1. The equations that describe changes in gasdynamic and optical characteristiics
- of the laser medium in a rectangular active volume take the form
s
Pu = Pouo, Pudx + dx p p P7' d[PLC~pT + 2), = S7Q,
dx ~uw) _ ~etQ- Q.-Qcs~
where p, u, y, u, p are the density, velocity, adiabatic exponent, molecular weight
and pressure of the laser mixture; Q is the specif ic pumping power, the "zero" sub-
script refers to the input to the active volume. ~Let us note that the quantity
dT in optimum mixtures does not exceed 10-15%. This is due to the fact that the
pi~mping efficiency nef (the fraction of energy expended on vibrational excitation
of C0, N2) reaches 90-95%, while the energy expended on heating due to anharmonicity
' of the molecules in V-V exhcanges, as well as due to V-T relaxation at T S 200 K is
extremely small. Q~B is the specific energy of radiation, w is the vibrational
energy of a unit of volume, Q* is specific power of relaxation losses--power lost
due to spontaneous emission and V-T relaxation.
The dependence Q*(~~, T) is determined by the dynamics of the change in populations
of vlbrational levels of CO and the characteristics of the cavity. To determine
this dependence, numerical solutions were found for rate equations with consider-
ation of the populations of 30 levels of the CO molecule [Ref. 5]. Fig. la shows
. the calculated dependences of specif ic lasing power on time at different tempera-
tures for a mixture of C02:N2:He = 1:2:3 at density po= 1/3 amagat unit and specific
Q~n, W/cm2 a w*, J/Z�amagat b Q~, W/cm3�amagat
140
-
~
~ ' S00 S00
I %
!60 ~ l
I I �
r2 L3 300 300
1 ~ ' o
BO I l ~
I ~
~ ~ 100 > Z 100
I j
: ~ ~
0 SO T, u s 0 100 Z00 300 T, A
Fig. l. a--calculated time dependences of specific lasing power
at different temperatures (T = 60 (1), 100 (2) and 200 K(3)) for
density of a].aser mixture of C02: N2:He=1:2:3 of po=1/3 amagat
unit, specific pumping power Q= 300 W/cm3 and threshold gain of
k= 5�10-4 cm 1; b--threshold pumping energy w~ (1) and steady-
state power of relaxation losses Q* (2) as functions of laser mix-
ture temperature. Points show the results of experiments from
Ref . 3
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pumping power of Qo = 300 W/cm3 (threshold gain k= 5� 10-4 cm 1) . The density and
temperature of the mixture were held constant over the extent of the entire calcu-
laticn, giving the universal curves shown in Fig. lb for threshold pumping energy
w* and steady-state power of relaxation losses Q~ corresponding to the flat sections
of curves 1, 2, 3 on Fig. la as functions of laser mixture temperature. Threshold
pumping energy is a linear function of density of the mixture, which is in good
agreement with experiment [Ref. 3]. Fig. lb also shows experimental points for
the dependence of w*/p (normalized to normal gas density) on temperature of the
laser mixture [Ref. 3]. The experimental points lie somewhat higher than the calcu-
lated curve. This is due to heating of the gas before the instant of lasing onset,
so that the observed threshold pumping energy corresponds to a temperature higher
than the initial temperature.
An important distinguishing feature of the CO laser is that even at normal gas
density, V-T relaxation becomes the d~cisive pro~ess of losses only at tempera-
tures higher than room level. At T~ 200 K the loss power is determined by the
rate of spontaneous decay of vibrational levels [Ref. 5]. Consequently at rela-
tively low temperatures the power of relaxation losses is proportional to p.
In an electroionization discharge at constant beam current density, the specific
pumping power increases with increasing gas density more strongly than linearly:
Q~ pf (p) (f (p) - 1 in the sticking mode and f(p) = fp in the recombination mode) .
Therefore in the CO EBC laser it is advisable to increase the pressure of the mix-
ture, enabling not only a reduction in overall dimensions of the facility, but
also more efficient use af the advantages of the electroionization discharge. On
the other hand in the case of. a continuous-wave C02 laser the Q* is determined
by V-T processes, and increases with increasing gas density more strongly than
- the pumping power (Q* ~ p2) [Ref . 2] .
Integrating the systems of equations of gas dynamics and the balance of vibrational
energy with accuracy *0 0(M2) (in present-day EBC lasers M2 ~ 0.1), we can get an
expression for the physical efficiency of an EBC CO laser
~7 - 1) ToH'.~TK) / 1 i t
n~ � n~ r-~T T - S7 ~ 7~cD pouo( TK - To)J f Q.~x)dx.
'Y~ x - To)Po y - \ o
where nef is the pumping efficiency averaged over the entire volume of the active
medium, w*(TK) is the threshold pumping energy corresponding to the final~tempera-
ture, TK is the vibrational energy of a unit of volume carried out of the active
volume; Z is the length of the active region along the flow corresponding to heat--
ing of the mixture to TK. In the sticking mode the value of Z is determined from
the relation
(3) 1 = uoPo ln Tx ~
7- ~ arQo To
where Qo is the specific pumping power at the input to the electroionization die-
char~e.
In tliis paper calculations of the energy characteristics of EBC CO lasers were
done for three pumping powers: Qo= 100, 300, 1000 W/(cm3�amagat).
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In connection with tlie fact that gas density in the heating process falls off
, (p = const, pK = ppTp/TK), the working voltages should decrease as the energy input
increases to prevent breakdown. This leads to a reduction of pumping power at
predetermined beam current density and, what is more significant, to a reduction
in the efficiency of pumping of vibrational levels. However, in the mixture under
consideration with a change of E/p by 2-2.5 times the quantity nef remains practi-
cally constant and fairly high, nef ' 0.9 [Ref. 5]. Therefore conditions were calcu-
lated under which the gas is superheated by no more than a factor of 2.5.
~o mas ' fii mas
Q 6
.
Q6 3
- 4B ~
~~~~i~~
~ _ ` `
06
i~-�~.~ p �,~J 4y ~ Z �
.
/ ~ ~
j I i~ ~
44 ' ~
I X ` \
42 ~ ~
4Z ~ J /
i ~ ~
i ~ ~ ~
i' i
60 100 140 /B0 Z20 T,K ~ 60 !00 !y0 oJK
Fig. 2. a--dependence of efficiency r1~ on the final temperature
of the laser mixture at initial temperatures T= 60 (I, II, III)
and 100 K(1, 2, 3). The fraction of energy input going to heat
dT = 0.1; b--To-maximum physical efficiency rt~ Max (solid curves)
- and technical efficiency nT Max (broken curves) as functions of
= initial temperature in the case of turbocompressor cooling. The
temperature of the mixture at the output from the heat exchanger
TX = 320 K; ~K = E,.I. = 1
Fig. 2a shuws curves for the physical efficiency as a function of energy input
(d.~.= 0.1 = const) at different pumping powers and initial temperatures T= 60 K
(I, II, III) and 100 K(1, 2, 3). The initial rise in n~ is due to excess of the
energy input over the threshold (see second term in (2)), while the drop with a
further increase in energy input is due to the abrupt increase in the power of
rel~ucation losses Q~ as temperature increases (see Fig. lb). It can be seen that
as the pumping power Qo increases, the maximum value of n~ rises and corresponds
to large energy inputs. For example at initial temperature T= 100 K, Qo= 1 kW/
(cm3�amagat), the maximum value of n~ corresponds to heating of the laser plasma
by 4T = 93 K.
The solid curves on Fig. 2b show the maximum value of n~ a~ a function of the ini-
tial temperature of the mixture at different values of Qo. As the specific pumping
power increases, tlie value of To at which lasing stops increases; however, even
at Qo = 300 W/(cm3�amagat) this temperature is only 160 K.
2. The problem comes up of getting low temperatures at the input to the active
medium of the EBC CO laser by a method with maximum technological feasibility and
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minimum possible energy expenditures. The most optimum method of handling this
job is to use an arrangement of turbocompressor cooling of the laser mixture
[Ref. 2] in which the mixture after the discharge chamber enters a compressor
where it is compressed by a factor of IIK (the degree of compression), and then
a heat exchanger where due to the high density and difference of temperatures with
_ the cooling agent it is effectively cooled to a temperature TX higher than room
- level, and firially it enters a turbine where, in doing work it is adiabatically
= cooled to the required temperature To. Realization of the refrigeration cycle
within the laser facility, i. e. cooiing the gas to a temperature lower than the
coolant, requires additional energy expenditures, leading to a reduction in tech-
nical efficiency. Additional energy expenditures on c~oling are associated only
with the part of the energy input that goes to heating of the gas. Therefore it
is extremely important to select mixtures, temperatures and pumping conditions
such that the quantity dT will be minimum. As noted above, in the EBC CO laser
_ at T~ 200 K relaxation losses are due to spontaneous de-excitation, and consequent-
ly do not lead to vol.umetric gas heating. Besides, the threshold pumping energy
w* that remains in vibrational degrees of freedom is also dissipated mainly due
to de-excitation rather than V-T processes, and consequenr_ly does not heat the
mixture.
The expression for technical efficiency of the EBC CO laser with turbocompressor
- cooling takes the form
(4) nT = n~/I1 + bt~T" - 1\TK~t" - T�tTl,
~ To ~ TK - To ~
where TX is the temperature of the mixture at the output from the heat exchanger;
~x, ~T are the degrees of adiabaticity of the compressor and turbine. In existing
aircraft engines ~K, and especially ~T are close to unity [Ref. 6]. In the case
of an ideal compressor and turbine ~~K =~.j, = l~ , relation (4) takes the form
~S) ~lr - 1 +S7~T~To _ I~ .
- It can be seen that for completely adiabattc compressor and turbine, and predeter-
- mined To, the optimum value of TK from the standpoint of nT is the same as for n~,
since they differ only by a constant factor. On the other hand, in the case of
tl, the electron concentration is determined from the following equation:
dt = S - Rne ~ ~3)
- where S= kZN2 [~f ( r~, t) dvJ 2; ki = 3.5 � 10-15 exp 1 T~~ [Ref . 6J is the constant
v2
of associative ionization, N is the concentration of N2 molecules; ~ is the recombi-
nation coefficient; vm = min{v**;(12novt)~}.Using expressions (1) and (3), let us
determine the time of increase (tm) in the rate of electron production due to as-
sociative ionization to its maximum, assuming that in this time v** ~(12novt)~,
4vi2
tm 3nov ' ~4)
From (3) we can find the electron concentration after time tm, assuming that
_ tm~ 1 /l3n~ :
ne 8 vn~ k
S' (5)
z
Let us make estimates for N=2�1019 cm 3, no= 0.03, vi = 32, S= 10-~ cm3 s-1, which
corresponds to the experiment of Ref. 4. In this case, ne= 2�1011 cm 3, i. e.
the shielding of the applied voltage by layers near the electrode is small, and
within tm = 300 us atter disconnection of the external source, current will flow
once more, which agrees satisfactorily with the experiment of Ref. 4. Let us note
that flow of the current to be registered requires that the pwnping level no must
be sufficient for producing an electron concentration such that shielding by elec-
trode layers is not complete. In addition, the pumping level must ensure the
127
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condition v**~ vi. Since ki is an exponential function of T, ne and tm are also
shargly dependent on the temperature of the mediimm; ~herefore the given effect
may be absent at low temperatures.
We can see from (4) and (2) that t~~t~, i. e. we can assume quasi-steady pumping
- of vibrational levels of *_he molecules of the medium by current that arises due
to associative ionization processes. Therefore after a certain transient process
the electron concentration will be described by the following equations [Ref. 7]:
n** 2
dt - kZN2 f v+ 1 dv -~ne . (6)
~v� ~
Z
As implied by Ref. 7, in this case associative ionizational instability should
develop, which leads to breakdown of the gas-discharge gap.
Thus for the case of pulsed pumping we have described a mechanism of development
of considerable electron concentration and breakdown in times that are longer by
a considerable factor than the characteristic recombination time. The case where
establishment of the distribution function of molecules with respect to vibrational
levels is commensurate with the duration of external pumping, while instability
develops on the decomposing phase, was considered in Ref. 9 with consideration
of processes of step-by-step ionization, vibrational kinetics and Joule heating.
In addition, let us note that the process of plasma decomposition is determined
not only by the recombination time, but also by the time of decomposition of layers
near the electrode. The redistribution of electric fields in the gap may have
a considerable effect on the electrical density of the medium [Ref. 10]. However,
numerical analysis is needed to explain the dynamics of independent ionization
in the plasma on the decomposition stage. We will be giving the results of such
numerical calculations in a later paper.
REFERENCES
1. Vel_ikhov, Ye. P., Pis'mennyy, V. D., Rakhimov, A. T., USPEKHI FIZICHESKIKH
NAUK, Vol 122, No 3, 1977, p 419.
2. Bychkov, Yu. I., Genkin, S. A., Korolev, Yu. D., Kreyndel', Yu. Ye., Mesyats,
G. A., Filonov, A. G., ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 66,
No 2, 1974, p 622.
3. Kostylev, A. A., Londer, Ya. I., Terent'yev, A. P., U1'yanov, K. N., Fedorov,
V. A., T1:PLOFI7.IKA VYSOKIKH TEMPERATUR, Vol 17, No 6, 1979: p 1167.
4. Gurevich, D. B., Kanatenko, M. A., Podmoshenskiy, I. V., FIZIKA FLAZMY, Vol 5,
No 6, 1979, p 1359.
5. Aleksandrov, N. L., Konchakov, A. M., Son E. Ye., FIZIKA PLAZMY, Vol 4, No 1,
1978, p 169.
6. Polak, L. S., Sergeyev, I. A., Slovetskiy, D. I., TEPLOFIZIKA VYSOKIKH TEMPERATUR,
Vol 15 No 1, 1977, p 15.
128
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7. Zhdanok, S. A., Napartovich, A. P., Starostin, A. N., PIS'MA V ZHURNAL TEKH-
- NICHESKOY FIZIKI, Vol S, No 3, 1979, p 155.
8. Zhdanok, S. A., Napartovich, A. P., Starostin, A. N., ZHURNAL EKSPERII~~TTAL'~
NOY I TEORETICHESKOY FIZIKI, Vol 76, No 1, 1979, p 130.
9. Baiadze, K. V., Vetsko, V. M., Zhdanok, S. A., Napartovich, A. P., Starostin,
A. N., DOKLADY AKADEMII NAUK SSSR, Vol 249, No 4, 1979, p 832.
10. Feoktistov, V. A., ZHURNAL PRIKLADNOY MEKHANIKI I TEKHNICHESKOY FIZIKI, Vol 5,
1977, p 41.
COPYRIGHT: Izdatel'stvo "Nauka", "Pis'ma v Zhurnal tekhnicheskoy fiziki", 1981
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�
PARTICULARS OF OPTICAL DISCHARGE SLOW BURNING INITIATION IN AIR ON OPTICAL BREAK-
DOWN INOCULATION PLASMA
Leningrad PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI in Russian Vol 7, No 15, 12 Aug 81
(signed to press2l Jul 81, manuscript received 6 May 81) pp 897-900
[Article by I. A. Bufetov, A. M. Prokhorov, V. B. F~dorov and V,. K. Fomin, Physics
Institute imeni P. N. Lebedev, USSR Academy of Sciences, Moscow]
[Text] In Ref. 1, 2 on investigation of optical discharge in the slow-burning
mode, the authors observed formation and prolonged existence (~1 ms) of a break
in the plasma column at the po;nt of discharge initiation when laser breakdown
of air was used to produce the inoculating plasma. It is shown in the~present
paper that formation of the break is due to onset of a cool gas flow directed per-
pendicular to the laser beam that maintains the optical discharge.
Since the observed velocities of the slow burning front are of the order of 10 m/s,
the motion of gas at the same or higher velocity in the discharge region may have
a considerable effect on the conditions of propagation. Therefore we did experi-�
ments to detect and study the motion of air upon relaxation of the cloud of heated
gas that is formed as a result of laser breakdown. Air breakdown was achieved
by focusing (f= 22 cm) the emission pulse (E = 1 J, t= 40 ns) of a Q-switched neo-
dymium laser. Morion of the heated gas was registered by the Tapler schlieren
technique. It was found that by time t~ 30 us after the breakdown, a cool air
jet is formed that moves al.ong the axis of the heated zone toward the laser with
initial vel.ocjty ot 150-200 m/s. Jet diameter is about 1.5 mm. The ~et arises
as a resul.t of asyrmnetric compression of the hot gas after expansion is completed.
Upon passage of the jet through the entire heated zone with dimension of ~1 cm,
its velocity~ at t= 80 us decreases sharply to ~10 m/s, and then damps out within
a time of about 1 ms; the cool gas flow expands on the beam axis to a diameter
of 0.5 cm. At the same time, the hot gas region acquires the shape of a vortex
ring whose axis coincides with that of the laser beam. The rate of increase in
the outer radius of the ring decreases from 20 m/s at t= 100 us to 2 m/s at t= 1 ms.
An investigation was made of the influence of the observed gas motion in the re-
gion of the laser spark that initiates the discharge on development of slow optical
combustion. A Q-switched laser with the above-mentioned parameters was used to
produce an inoculating plasma in a weakly focused beam of a millisecond pulsed
neodymium laser with power of up to 2 MW maintaining the discharge. The laser
beams are mutually perpendicular in the region of intersection [see Ref. 3]. If
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~ �
a ~ C _
[5c~r [5ar
6
b d
[5cM ~4cM
0 0.2 0.4 0.6 t, ms 0 O.Z '0.4 0.6 t, ms
Fig. 1. Continuous slit scan of optical discharge plasma lumi-
nescence in the mode of slow combustion. The direction of ob-
servation is perpendicular to the initiating and maintaining
laser beams. The camera slit i.s located along the axis o; the
millisecond laser, with beam directed from the top down on the
figure; a) ignition on the axis of beam with diameter d= 4 mm;
b) ignition on axis of beam with d= 4 mm, unilateral pickup;
c) ignition at 3 mm from axis of beam with d= 4 mm; d) ignition
on axis of beam with d= 10 mm, the arrow denoting the instant
of an abrupt change in velocity.
the point of. focusing of the igniting radiation was situated on the axis of a main-
taining beam with diameter of 4 mm, formation of a break in the plasma column at
the point of discharge initiation was observed just as in Ref. 1, 2(F3g. la).
Formation and reclosure of this break is complezely explained by the arisal and
subsequent damping of a flow of cool air directed along the axis of the maintaining
beam. As it has high velocity, this flow carries plasma out of the beam in the
vicinity of initiation and prevents propagation of the discharge into this region.
In analogous geometry of the experiment it was also possible to observe "unilateral
pickup" of slow burning (Fig. lb): on one side of the cold air stream the inocu-
lating plasma is completely carried out of the beam as a consequence of some asym-
metry of the hydrodynamic motion, and on the other side there is pickup of the
discharge. But because of the presence of tne cool gas flow, the discharge does
not cross the ignition point fdr a time of the order of 1 ms. In a subsequent
experiment with displacement of the ignition point 3 mm to the side from the beam
of the millisecond laser, the most intense part of the gas flow is on t~e ~utside
of the maintaining beam; a nonluminescent region does not form (Fig. lc). Finally,
with focusing of init iating radiation on the axis of a large-diameter maintaining
beam (beam diameter of the order of the dimensions of the inoculating plasma), the
nonluminescent region occupies only part o� the beam diameter. No break in the
plasma column is observed when photographed from the side (Fig. ld). On the other
hand, observation along the direction counter to the beam maintaining the discharge
- in an analogous experiment shows (Fig. 2) that a luminescent ring is formed upon
pickup of the inoculating plasma. The central part of the ring corresponds to
the region of cool air flow. The symmetry of the ring is lost when its diameter
goAs beyond that of the beam of the maintaining plasma. The shape of the plasma
column thereafter begins to approach a cylinder (Fig. 2, frame 3) [photo~not re-
produced]. At the same time, there is an abrupt reduction in the velocity of
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plasma propagatio~i: from 80 m/s, the rate of increase in the outer radius of the
plasma ring, to 40 m/s, the rate of propagation of the planar front (Fig. ld).
The time coincidence of these two values (the change in discharge syunnetry and
the abrupt reduction in its propagation velocity) is evidence of the change in
- the gasdynamic mode of propagation of the combustion front as the cambustion wave
goes out to the lateral surface of the laser beam that maintains the discharge.
The results may serve as a basis for optimizing conditions of f orced initiation
of slow combustion of optical discharges by optical breakdown. Let us note also
, that the particulars of laser ignition considered in this paper explain the failure
of the attempt in Ref. 4 to initiate a discharge by gas breakdown with a giant
pulse, and the requirement for minimizing the energy of the initiating pulse to
ensure discharge ignition in Ref. S. The fact is that under the conditions of
sharp focusing of the maintaining beam typical of Ref. 4 and 5, the inoculating
plasma may simply be completely carried off by the cool gas flow from the region
with high intensity of ttie radiation that maintains the discharge.
REFERENCES
1. Bufetov, I. A., Prokhorov, A. M., Fedorov, V. B., Fomiri, V. K., PIS'MA V
ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 32, 1980, p 281.
2. Bufetov, I. A., Proktiorov, A. M., Fedorov, V. B., Fomin, V. K., KVANTOVAYA
EI,~KTRONIKA, Vol 8, 1981, p 751.
_ 3. Bufetov, I. A., Fedorov, V. B., Fomin, V. K., KRATKIYE SOOBSHCHENIYA PO FIZIKE,
FIAN, No 10, 1980, p 21.
4. Mul'chenko, B. F., Rayzer, Yu. P., Epshteyn, V. A., ZHiTR1VAL EKSPERIMENTAL'-
NOY I TEORETICHESKOY FIZIKI, Vol 59, 1970, p 1975.
5. Franzen, D. F., J. APPL. PHYS., Vol 44, 1973, p 1727.
COPYRIGHT: Izdatel'stvo "Nauka", "Pis'ma v Zhurnal tekhnicheskoy fiziki", 1981
6610
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UDC 533.951
INTERACTION OF STRONG ELECTROMAGNETIC WAVES WITH COLLISIONLESS PLASMA
Gor'kiy VZAIMODEYSTVIYE SIL'NYKH ELEKTROMAGNITNYKH VOLN S BESSTOLKNOVITEL'NOY PLAZ-
MOY in Russian 1980 (signed to press 7 Jul 80) pp 2-5, 212-214
[Annotation, editor's message and abstracts from book "Interaction of Strong Elec-
tromagnetic Waves With Plasma", edited by Doctor of Physical and Mathematical Sci-
- ences A. G. Litvak, Institute of Applied Physics, USSR Academy of Sciences, 500
_ copies, 214 pages]
[Text] The collection contains survey articles dealing with one of the urgent
problems of plasma physics: theoretical and experimental investigation of strong
Langmuir turbulence excited in a dense collisionless plasma by intense radiation.
An investigation is made of problems of the theory of modulation instability of
Langmuir oscillations, the dynamics of strong Langmuir turbulence, and self-stress
of radiation in a homogeneous plasma, deformatiun of the density profile and reso-
nant absorption of strong electromagnetic waves in an inhomogeneous plasma. The
results of theoretical research are supplemented by a survey of model microwave
experiments on the action of electromagnetic waves on an isotropic plasma.
The materials of the collection may be of interest to an extensive class of spe-
cialists dealing with the interaction of electromagnetic radiation with matter,
as wel.l as nonlinear effects in the laboratory and in cosmic plasma.
L:clitor's Mes~a~;e
The probl.em of interaction of strong electromagnetic waves with plasma is among
the problems of plasma physics being most actively researched. The interest in
this problem is dictated primarily by the varied applications associated with rf
and laser heating of. plasma, with research on laser-driven inertial fusion reactions.
Of no less importance is the fundamental significance of this problem, since inter-
action of iiitense radiation with plasma is accompanied by arisal of some fundamental
nonlinear phenomena such as parametric plasma instabilities, deformation of the
plasma density profile under the actiun of pondermotive force, formation of self-
cunsistent distributions of plasma and field--cavitons--excitation of strong plasma
turbulence, generation of flows of fast particles and quasisteady magnetic fields
- and so on. These effects must be studied for many other divisians of plasma physics
as well.
Z33
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This collection is devoted to one of the key questions of the problem of interaction
of intense electromagnetic waves with plasma: investigation of processes of resonant
excitation of Langmuir oscillations by electromagnetic radiation, resulting in
strong Langmuir turbulence and collisionless a~sorption of powerful radiation.
Most of the content of the collection is made up of solicited survey articles on
the theory of resonant interaction of radiation with plasma. These articles can
_ be conditionally divided into two groups. The f irst includes two surveys dealing
with the theory of modulation instability of Langmuir oscillations and strong Lang-
muir turbulence in a homogeneous plasma. The results of these works are valid
for describing processes in a smoothly inhomogeneous plasma in the field of an
S-polarized electromagnetic wave as well.
The second group includes three works in which an examination is made of the in-
fluence of nonlinear effects on excitation of Langmuir oscillations by the f ield
_ of a~-po].arized electromagnetic wave obliquely incident on an inhomogeneous plasma
layer. The first of the articles considers steady-state nonlinear models of inter-
action, the second examines the dynamics of interactiun in an external quasistatic
- r-f field, and the third investigates the dynamics of resonant interaction of an
electromagnetic wave with an extended plasma layer.
The specifics of the investigated problem are associated with the fact that in
most cases of practical interest it is impossible to use the well developed ap-
paratus of the theory of weak plasma turbulence since nonlinearity leads to con-
siderable distortion of the dispersion characteristics of plasma oscillations.
Besides, as the plasma interacts with coherent radiation, nonlinear processes fre-
quently have a dynamic nature so that it is necessary to deal with investigation
of dynamic partial differential equations. All the theoretical papers presented
are based on a unified physical approach that turns away from investigation of
a system of equations of a collisionless plasma toward examination of comparatively
simple physical models described by equations of the field and quasihydrodynamics
of the plasma averaged with respect to the period of r-f oscillations. The com-
plexity of the problem is apparently the reason for the fact that despite a common
approach in some the articles of the collection in the examination of certain physi-
cal models, assumptions are made that are contradictory to some extent, and also
the evaluation of rigor. and substantiation of fundamentally important statements
is sometimes sub,jective. Considering that more complicated models have to be used
to get closer in viewpoints, and especially to determine the conditions of applica-
bility of specific results, the editorial staff has decided not to try to reach
full "reconciliation" of factions, and has even welcomed the argumentative trend
of some papers. We hope that this will enable the reader to get a more complete
idea not only of the advances that have been made in studying the problem, but
also of the existing difficulties and contradictions.
Although a rather large number of surveys and even monographs have been published
heretofore dealing with the description of experiments on interaction of electro-
magnetic waves with plasma, we have also deemed it advisable to supplement the
theoretical articles in a special way with an attempt to formulate the results
of model microwave experiments of the greatest importance for construction of a
general physical picture of interaction.
~ A. G. Litvak
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UDC 533.951
STRONG LANGNNIR TURBULENCE AND ITS MACROSCOPIC CONSEQUENCES
[Abstract of article bv Galeyev, A. A., Sagdeyev, R. Z., Shapiro, V. D. and SheV~
chenko, V. I.]
[Text] An examination is made of the thecry of strong turbulence based on the
concept of collapse of Langmuir waves as a mechanism of pumping short-wave oscil-
lations. A theory of quasi-steady turbulence is developed, assuming that the energy
of Langmuir waves excited by an external source is transferred to the region of
strong Landau damping as a consequence of collapse. T.he turbulence spectrum is
determined, and the effective collision frequency is calculated that characterizes
the rate of absorption of energy of the external source. The authors discuss the
macroscopic consequences of the collapse of Langmuir waves upon ab sorption of an
electromagnetic wave in the vicinity of plasma resonance aiid in application to
relaxation of electron beams. Figures 9, references 43.
UDC 533..951
MODULATION INSTABILITY OF LANGMUIR OSCILLATIONS IN THE FIELD OF AN ELECTROMAGNETIC
WAVE
[Abstract of article by Litvak, A. G. and Frayman, G. M.~
[Text] The survey presents existing notions on strong Langmuir t urbulence excited
in a homogeneous plasma by a monochromatic electromagnetic wave. A systematic
examination is made of substantiation of model equations~that des cribe Langmuir
oscillations in an external field, one-dimensional models of the nonlinear stage
of modulation instabil~ty, collapse of inhomog�aneous Langmuir cavitons, macro-
scopic characteristics of strong turbulence, and self-stress of the electromagnetic
wave. Figures 5, references 41.
i7DC 533.951
DENSITY .NMP OF PLASMA ~N FIELD OF A STRONG ELECTROMAGNETIC WAVE, AND ITS INFLUENCE
ON THE EFFICIENCY OF RESONANT ABSORPTION .
[Abstract of article by Gil'denburg, V. B.]
[Text] A systematic exposition is given of the theory of steady-state nonlinear
deformation of the resonant region of an inhomogeneous plasma in the field of a
strong electromagnetic wave. On the basis of quasi-static model s, the author de-
termines the conditions of onset, parameters and structure of a stepwise self-
consistent transition of field and density through the plasma resonance surface.
An investigation is made of the influence that such a transition has on the ef-
ficiency of processes of collisional absorption and wave transformation in an in-
homogeneous plasma. The paper gives the results of numerical calculation of flat-
layered plasma-field~ structures fornted by a strong p-polarized wave. Figures 8,
references 41.
135
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UDC 533.951 �
DYNAMICS OF INTERACTION OF R-F FIELD WITH INHOMOGENEOUS PLASMA AND ACCELERATION
, OF' PARTICLES IN PLASMA RESONANCE REGION
[Abstract of article by Kovrizhnykh, L. M. and Sakharov, A. S.]
[Text~ It is shown within the framework of the homogeneous pumping field model
that under conditions where the r-f pressure of a self-consistent field plays an
appreciable part in the resonance region, the solution goes out to the state o�
quasiperiodic generation of p eaks of Langmuir oscillations and ion density cavities
(cavitons). On the initial stage of development of the process, the electrons
are accelerated chiefly in the direction of reduction of plasma density, and then
upon formation of cavitons there are two-sided overswings of the accelerated elec-
trons. Estimates are found f or the energy of accelerated ion~ in a strong pumping
field, where an appreciable part is played by effects associated with electronic
nonlinearity. Figures 12, ref erences 47.
UDC 533.951
DYNAMICS OF PARAMETRIC PLASMA TURBULENCE
[Abstract of article by Andreyev, N. Ye., Silin, V. P. and Stenchikov, G. L.J
[Text] A numerical study is done on the dynamics of nonlinear interaction of a
p-polarized wave with an inhomogeneous plasma. The initial self-consistent homo-
geneous system of equations takes consideration of the inf~uence of pondermotive
force on hydrodynamic plasma flow ar,d quasilinear relaxation of the electron velo-
city distribution function. The authors explain the dynamics of the change in
plasma density and absorption of electromagnetic field energy by the plasma and
~ the nature of the velocity d istribution of electrons. An examination is made of
the generation of the second harmonic of radiation. It is found that there are
~ two qualitatively different modes of interaction that depend on the plasma flow
velociry gradient in the vic inity of the critical density. Figures ll, references
- 32.
- UUC 533.951
EXPERIMENTAL INVESTIGATION OF RESONANT INTERACTION OF INTENSE ELECTROMAGNETIC WAVES
WITH ISOTROPIC PLASMA
[Abstract of article by Brodskiy, Yu. Ya., Gol'tsman, V. L., Litvak, A. G. and
Nechuyev, S. I.]
[Text] The paper gives a br ief overview of existing model experiments for the
purpose of formulating conclu sions of importance to construction of a theory of
interaction of strong electromagnetic waves with isotropic plasma. In the first
part an analysis is made of the results of known quasistatic experiments on inves-
ti~ation of the structure and dynamics of an elementary cell of interaction--the
caviton. The second part gives information on nonlinear processes that has been
13b
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obtained on the basis of the authors' measurements of the integral characteristics
of transmitted and reflected electromagnetic waves and plasma oscillations, and
energy functions of electron distribution. Figures 16, references 29.
COPYRIGHT: Institut prikladnoy fiziki AN SSS~t, 1980
6610
CSO: 1862/269
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UDC 621.378.325
INFLUENCE OF LASER EMISSION WAVELENGTH ON PLASMA FORMATION THRESHOLD WITH
IRRADIATION OF OPAQUE MATERIALS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 7(109), Jul 81 (manuscript
received 11 Nov 80) pp 1582-1584
[Paper by Ye. A. Berchenko, A.V. Koshkin, A.P. Sobolev and B.T. Fedyushin]
[Text] A large number of experimental results for plasma formation
thresholds is analyzed for the case where opaque materials are ir-
radiated with laser radiation. An empirical equation is derived
which makes it possible to predict the moment of plasma f ormation ~
for a wide range of irradiation conditions. Questions of the impact
of. laser emission wavelength on the "flare" process and the preci-
- sion of predictions of rhe moment of plasma formation are discussed.
An attempt is made in this paper to analyze literature devoted to the theoretical
~ and experimental study of the process of plasma formation with the irradiation of
an opaque barrier by a laser. In the modern theoretical "flare" model of laser
radiation absorption [1], the following physical factors are taken into account:
the reflection of radiation from the barrier; heat sinking into the barrier; the
change in the optical and thermodynamic characteristics of the irr~ldiated material
as a function of temperature; fusion and vaporization of the material of the
barrier; gas dynamic processes upon dispersal of vapor and ambient atmosphere;
temperature nonuniformity within the vapors (the possibility of a break b etween
the electron temperature and the heavy particle temperatur~; ionization kinetics;
the actual laser emission power density as a function of time.
However, it is known that~~~model [1] does not provide for satisfactory agreement
with experimental results, because of which, the opinion was advanced concer.ning
- the possible influence on the "flare" process of some effects [2-4] which were
not taken into account [1], such as electron emission from the barrier, anomalous
heating of surface defects, amplification of the wave field close to defects as
well as when reflected frcm~ the barrier and effects related to overheating of the
melt of the barrier material (dielectrification of the metal and explosive dis-
- i.ntegration of the metastable liquid).
Moreover, the reflective and thermodynamic properties of matter at high temper-
atures are IlOt suff.icnelty well known, something which in turn leads to marked
errors in theoretical predictions. One way or another, an adequate "f lare" absorp-
tion model should include an accounting for the considerable number of physical
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~ t' [~N~1
~ ~microseconds]
Figure 1. Plasma formation delay as a function
~o ~o of the rate of rise in the laser
? emission power density for the first
� Q~e ~ (squares) , second (trinagles) and
��'~�~o third (circles) groups of experi-
~ ments (see the text).
e~ o
~oo~~~e Key: 1. Log(q) [MW/(cm2 . usec) ] .
-2
- -4 -2 ~ ~1)~94~MBm/(cMt�,aucl~
P
v,4
d=1MnM
0,2 1 um
Figure 2. Histograms af the probability density of
~ Q a the quantity e*/~ with the irradia-
tion of a metal barrier.
_ P
~4 ~=JO~BMMN
10.6 um
4?
~ p .~~!!"l~~nr''""c'~)
~b) ~ ,JI~~m2�us~)
effects and be extraordinarily voluminous (to the extent necessary). Because of
this, we have undertaken an attempt to establish the laws governing the plasma
formation process based on an analysis of experimental data.
For practical purposes, the question of the time of absorption "flare" develop-
ment, t*, for various irradiation conditions is of special interest. All of the
experiments considered by us were broken down into three groups: 1) A metal target
(as a rule, aluminum), a= 10.6 um; 2) Metal target, a= 1 um; 3) A target made
- of a dielectric (glass fiber reinforced plastic), a~ 1 um. Such differences in
the formulation of the experiment as the pressure and kind of ambient gas, the
dimater of the irradiation spot, etc., were not t~iken into account within the
scope of each group of experiments. The permissibility of this simplification
follows, for example, the results~~of [SJ. Subsequent analysis also demonstrated
that the influence of these factors does not exceed the scatter in the experimental
data, related primarily to the space-time inhomogeneity of the irradiation, the
natural difference in the properties of the samples being irradiated, the multi-
plicity of experimental techniques as well as a certain ambiguity in the concept of
"pl.asma formation" itself.
To simplif.y the procedure for taking into account the actual timewise form of a
" laser pulse, only those experiments were selected in which the absorption "flare"
occurred at the leading edge of the pulse for close to its maximum. In this case,
the form of the pul.se can be described by a single parameter - the characteristic
rate of rise of the emission flux density c~ = qm/'r, where qm is the maximum value
of the emission flux density; T is the rise time of the laser pulse. Thus, the
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plasma formation delay tiine, other conditions being equal, will depend only on the
ratE of rise in the emission flux density: p* = t*(q). Experimental values [2,
5- 19] of t* are shown in Figure 1 as a~~function of q for all three groups of
- experiments. These data are satisfactorily described by the empirical formula:
t* = 7q-2/3~ ~1)
where t* is in microseconds while q is in MW/(cm2 � usec). The curve of (1) is
shown in Figure 1 with t~e dashed line.
This formula can be qualitatively interpreted as the time for heating the surface
of the target up to a certain fixed temperature as a function of q, assuming that
the emission flux density rises linearly [20].
Having this interpretation in mind, as well as the approximate relationship
between the energy densit}~ at the target, the temperature of the surface and the
point in time, which follows from heat conductivity theory, formula (1) can be
generalized for the case of an arbitrary laser pulse shape:
e*/~ = s= 10 J/cm2 � usec1~2 (2)
r~
where e'=(9(t)dt is the emission energy density at the target at the moment
S
_ of ~lasma formation. Expression (2) is to be treated as an equation for the
quantity t*,
The aggregate of experiments considered here was subjected to statistical process-
ing to estimate the precision of (2) as well as to determine the plasma formation
threshold as a function of the wavelength of the acting radiation. Histograms of
the distribution function (probability density) o� the quantity for laser emission
wavelength oE a= 1 and 10.6 um (alwninian as the barrier material) are shown in
rigure 2. It follows fram these graphs that for both wavelengths, the maximum
value of the distribution function corresponds to a value of S= 7.5. For a wave-
len~th of a= 1 um, the mathematical mean value is S= 9.9, while the dispersion
(meln square deviation) is cr = 6.6. For the radiation of a C02 laser, these
quantities are R= 9.6 and Q= 6 respectively.
7'hus, the analysis of the experimental data performed here does not allow us to
talk of a marked difference in the plasma formation threshold for wavelengths
of a= 1 and 10.6 um.
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BIBLIOGRAPHY
1. I.E. Markovich, A.P. Golub', I.V. Nemchinov, A.I. Petrukhin, Yu.Ye. Pleshanov,
"Deponir. VINITI" ["Manuscript Deposited in the All-Union Institute of Scien-
tif ic and Technical Information"J, No. 33U0-79 (1979)e '
2. C.T. Walters, R.N. Barnes, R.E. Beverly III, J. APPL. PHYS., 47, 2937 (1978).
3. V.A. Batanov, F.V. Bunkin, A.M. Prokhorov, V.B. Fedorov, ZhETF [JOURNL~L OF
EXPERIMENTAL AND THEORETICAL PHYSICS], 63, 586 (1972).,
4. B.M. Kozlov, A.A. Samokhin, A.B. Uspenskiy, KVANTOVAYA ELEKTRONIKA, 4, 524,
(1977) .
~ 5. N.N. Kozlova, "Kand. Diss. MFTI" ["Candidate Dissertation, Moscow Engineering
Physics Institute"], Moscow, 1975.
6. P.D. Thomas, AIAA J., 13, 1279 (1975).
_ 7. A.N. Pirri, AIAA J., 15, 83 (1977).
8. W.E. Maher, R.B. Hall, J. APPL. PHYS., 46, 761 (1975).
9. V.A. Boyko, V.A. Danilychev, V.D. Zvorykin, N.V. Kholin, L.Yu. Chugunov,
KVANTOVAYA ELEKTRONIKA, 3, 1,955 (1976).
~ 10. V.P. Ageyev, A.I. Barchukov, F.V. Bunkin, V.I. Konov, S.B. Puzhayev, A.S.
Silenok, N.I. Chapliyev, KVANTOVAYA ELEKTRONIKA�, 6, 78 (1979),
11. V.P. Ageyev, A.I. Barchukov, F.V. Bunkin, V.I. Konov, S.M. Metev, A.S. Silenok,
N.I. Chapliyev, IZVESTIYA W~OV SSSR, SER:.FI7.IKA [PROCEEDINGS OF THE USSR
HICHER EDUCATIONAL INSTITUTES, PHYSICS SERIES), No. 11, 34 (1977).
12. V.A. Boyko, V.A. Danilychev, V.V. Vladimirov, B.N. Duvanov, V.D. Zvorykin,
I.V. Kholin, PIS'MA V ZhTF [LETTERS TO THE JOURNAL OF TECHNICAL PHYSICS],
4, 1,373 (1978).
13. A.V. Bessarab, V.M. Romanov, V.A. Samylin, A.I. Funtikov, ZhTF [JOURNAL OF
TECHNICAL PHYSICS], 48, 1,751 (1978).
14. A.V. Bessarab, V.N. Novikov, D.V. Pavlov, A.I. Funtikov, ZhTF, 50, 886 (1980).
15. N.N. Kozlova, A.I. Petrukhin, V.A. Sulyayev, KVANTOVAYA ELEKTRONIKA, 2, 1,390,
(1975) .
16. Ye.A. Berchenko, A.P. Sobolev, B.T. Fedyushin, KVANTOVAYA ELEKTRONIKA, 6, 1,546,
(1979).
17. A.I. Korotchenko, A.A. Samokhin, A.B. Uspenskiy, KVANTOVAYA ELEKTRONIKA, 6,
210 (1979).
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18. A.A. Bakeyev, B.A. Barikhin, V.V. Borovkov, L.A. Vasil'yev, L.I. Nikolashina,
A.I. Pavlovskiy, N.V. Prokopenko, L.V. Sukhanov, A.I. Fedosimov, V.I. Yakovlev,
KVANTOVAYA ELEKTRONIKA, 7, 349 (1980).
19. I.E. Markovich, A.I. Petrukhin, Yu.Ye. Pleshanov, V.A. Rybakov, "Tezisy dokl.
IV Vsesoyuz. soveshchaniya po nerezonansnomu vzaimodeystviyu opticheskogo
izlucheniya s veshchestvom" ["Abstracts of Reports of the Fourth All-Union
Conference on Nonresonant Interaction of Optical Radiation with Matter"],
Leningrad, 1978, p 276.
20. J. Radi, "Deystviye moshchnogo lazernogo izlucheniya" ["The Action of High
Rower Laser Radiation"], Moscow, Mir Publishers, 1974.
COPYRIGHT: Izdatel'stvo "Radio i svyaz"', "Kvantovaya elektronika", 1981
8225
CSO: 1862/252
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_ UDC 621.373.826
THEORY OF STEADY OPTICAL GAS BREAKDOWN CLOSE TO METAL SURFACE
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 7(109), Jul 81 (manuscr3pt
received 1 Nov 80) pp 1485-1490
(Paper by A.A. Vedenov, G.G. Gladush and A.N. Yavokhin, Institute of Nuclear
Power imeni I.V. Kurchatov, Moscow]
[Text] The causes of the formatxon of a plasma f lare close to
the surface of inetals are studied theoretically in this paper
for light power densities on the order of 1 MW/cm2 (low threshold
breakdown). It is demonstrated that the physical nature of this
phenom~enon can be similar to the ignition of chemical combustion
reactions by a hot surface. The breakdown takes place because of
thermal ionization of the metal vapors, although the vaporization
of the matQ~ial is insignificant in this case. 2'he effect of
diffusion and overheating of the electrons on the amount of the
tt~reshold power density is analyzed.
1. It is well known that the laser radiation power density at which a plasma
appears above a target surface can be several orders of"Tnagnitude less than the
breakdown threshold of the pure gases, in the atmosphere of which the laser inter-
acti.on takes place [1 - 4]. The presence of a plasma can b ecome the decisive
factor in the interaction of the radiation and the matter, since it can both
strongly 'shield the surface [2] and promote the radiation heating of the material
[5]. The phenomenon of low threshold breakdown has not yet been uniquely
theoretically explained. Thermal breakdown is studied in this paper as one of
_ the possible reasons for the formation of a plasma at the surface of a solid.
In the case of a low incident radiation power density q, the ambient gas of the
medium is heated by virtue of the thermal conductivity from the surface of the
absorbing target.. The essence of thermal breakdown consists in the fact that at
a radiation density which exceeds a certain critical value, qn [qp], the gas is
heated up to such a high temperature that its further hPating then becomes
possible because of the intense thermal ionization, with subsequent direct
absorption of the laser beam energy. Such a breakdown mechanism was used in paper
[6~ to analyze the interaction of a radiation pulse with a metal, where vaporiza-
tion is significant, while the heating of the vapors took place with the
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formation ~f an intense shock wave. For large values of q, this approach yielded
good agreement with experimental data on the surface shielding time. In the quasi-
~ steady-state case, where the pressure in the gas volume has time to equalize~
deperlding on the power density and the external pressure~ two interaction variante
are possible. The vapors of the material can either slowiy diffuse from the focal
spot into the ambient gas, or can displace it~ forming a steady-state jet. A
theoretical analysis of optical breakdown in these cases was reported in [7]. The
results of analytical and numerical study of the first of the indicated variants
ar e presented below.
2. Although the occurrence of a plasma flare is a nonsteady-state process, we shall
initially treat steady-state problems, since the breakdown phenomenon can be
treated mathematically as the transition from one steady-state to another.
We shall assume that the laser beam is focused on the aurface of the material in
a spot of radius R. In the absence of a well developed vaporiaation mode~ the
en ergy carried away by the material vapors is small~ and for this reason, the
temperature in the spot is governed by the thermal conductivitq of the target:
Tp = aqR/Km where Km and a are the thermal conductivity and absorption coeffic-
ients of the target material. At a distance remote from the spot, the gas temper-
ature falls off, as with increasing distance from a point source: proportional to
r-l. It will be seen from the following that breakdown occurs at a distance from
the target which is considerably less than the rAdius of the focal spot R. For
- this reason~ one can disregard side losses and limit oneself to the spherically
symmetrical or plane case.
To ascertain the main laws gbverning the phenomenon~ we shall initially consider the
simplest case of an equilibrium isotemperature medium. In the steady-state case~
the temperature of this medium is determined by the energy balance equation:
_ a xrz ~~(2 - a) K(T, N) qR1;
41Le~u~apa 2JLm 3/~ ~/2 I/4 ~
K tT ~ N~ " cmc~= (-14~) PN (kT eXp 2kT
N=N,~To)~ T ~R)~To; T (00)=0, ' (1)
~ah ere NS is the equilibrium vapor density; p is the pressure of the ambient
medium; I is the gas ionization potential; w is the laser radiation frequency;
o~a, ve, m and e are the scattering cross-section~ the thermal velocifiy, mass
and charge of an electron; K is the heat conductivity coefficient of the gas
medium. The ~act that the light absorption coefficient K is due to electron
scattering at neutral particles (for a C02 laser) is taken into account in (1).
'1'l~e dcnsity of the metal. vzpors which diffuse from the target and the temperature
f;all c,f~ at a char~lcteristic distance on the order of R. The absorption factor
K, in v~iew oi' the ~h~rp dependence on T, falls off over a significantly shorter
distr.ince, and for tliis reason, the vapor concentration N can be taken as constant.
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We shall assume for simplicity that K does not depend on temperature; then, by
introducin~; the dimensionless variables 9=(T/Tp - 1)I/2Tp, r/R and expanding
the exponent close to Tp [9], we derive the following from (1):
~ 2 ae a~ D
b a~ + a~~ _ - ee;
9(1)=~~ 9(00)= -!/27'0;
p = 9R'K (To) ~ (2 - a). ~ 2~
xTa 2To
Equation (2) is not integrated, but considering the fact that breakdown occurs
close to the surface (at a distance of D-1/2 � 1), one can shift over to a
plane geometry. In this case, the problem reduces to a problem of as3+s~metrical
ignition or ignition by a hot surface [9]. Zel'dovich's condition for ignition
- has the form:
D>'/e(li2To)Y. ~3~
In making the transition to dimensionless variables, we obtain the condition
for the quantity q at which breakdown occurs:
~ (~,-~-1) xN In-1 32~Q~Rs
9n = 2 aR x/ ~
r _ ~:[e'a,,Q,.~, r?~m ~5~ ~ pNQ/2 ~k7�~ - I /4 (4)
cmw= l �
where a is the heat of vaparization; Np is the co~fficient in the expression
NS = Np � exp(-a/kT), which depends on th2 material; q* = 1 MW/cm2.
It can be seen from (4) that the breakdown flux density basically depends on
the properties of the target material: the thermal conductivity, the absorption
factor, the vaporization energy and the ionization potential of the vapor atoms.
- The properties of the surrounding gas and its pressure havE a weak influence on
the breakdown thresl~old. The influence of the light frequency should be manif est
in the absorption factor. Estimates based on formula (4) for difficultly
Eusible metals, for. example, for tungsten, yield qP = 1 MW/cm2, which is close
to tl~at observed in experiments [4]. However, the surface temperature T~ [TP]
~ at whicli breakdown occurs is more importa~nt in this approach. It is essential
that the pressure of the saturated vapors of the material, which depends ~harply
on tl~e temperature of~~the surface, does not exceed the ambient gas pressure.
Ot{ierwise, as was stated in section 1, a hydrodynamic outflow of the vapor will
appear and the governing laws will be different. According to estimates, the
transition temperature is T~p` = 5,000 to 6,000 �K, and for this reason, even for
difficultly fusible materials, Tp is close to the boiling point Tk (for W,
Tk = 5,800 �K). Consequently, it is necessary to calculate TP more precisely.
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Because of this, equation (1) was solved with variable coefficients. The metal
vapor density was cal.culated by means of the diffusion equation:
z
~Z ar Dr d~ - ~
(5)
N(R)=N�(To); N(oo)=0,
where D is the diffusion coefficient, whi~h depends on temperature.
System (1) and (5) was solved by a plotting technique. Various distribution
profiles of the tem perature T and the metal vapor density were established as
a function af the power density q, Curves f or T as a function of the radius
are shown in Figure 1 for nitrogen at p= 3 atm and for tungsten. The ~hermal
physical constants expressed as a funetion of temperature were taken from [10],
a= 5 percent. Initially, the curve T(r) is close to r-1. At a certain value, ~
q= q, the temperatiire profile ceases to be monotonically declining, the value of
aT/8rpat~the surface of the metal increases with time and becomes positive, while
a temperature maximum appears close to the surface at~d the temperature subsequently
rises rapidly. Thus, a thermal breakdown of the gas occurs in the laser beam at
- q= q~. The curves for qP and TP are plotted in Figure 2 as a function of the
ambient nitrogen gas pressure. The curve for the boiling point is also plotted ~n
the same graph as a function of pressiiz�e [10]. It can b e seen that the curve
for TP for a pressure above atmospheric runs below the boiling point curve. Thus,
for tungsten-nitrogen vapor, an equilibrium thermal breakdown in the target vapors
is possible. Since the thermal-physical coefficients of nitrogen and air are
close, these results can also apply to air. As follows from [11], the burning of
tungsten in air takes a course through a surface oxidation reaction. The heat of
the reaction is liberated at the solid surface. Since the ionization potential
of tungsten oxide, W03 (11.7 eV), is higher than the ionization potential of
tungsten vapors (8 eV), then the breakdown temperature TP, taking the combustion
reaction into ac~.ount, apparently does not decrease. The threshold light power
density is reduced in this case by virtue of the combu~tion power, which is
difficult to estimate under the conditions because of the lack of data on the
reaction rates at high temperatures. In principle, an equilibrium thermal break-
down can also occur for other difficultly fusible materials, for example, molyb-
- denum, titanium and tantalum.
S111CC the ionization potential of the metal atoms is markedly less than the
i.onization potential of the ambient gas, despite the fact that the density of
c>f the metal vapors is usually substantially lower than the ambient gas density,
tt~ermal ionization of just the vapors governs the conductivity of the medium and
consequently, the absorption factor. The contribution of the ambient gas is small.
Estimates based on formula (4) for air assuming that the latter consists of the
easily ionized compound NO (overstated conductivity) yfeld a value for the break-
down temperature which exceeds the boiling point of tungsten. A numerical solution
oE equation (1) for an air pressure of 1- 3 atm, taking into account the radiation
ahsorption factor by air where the radiation is at a wavelength of 10.6 um [2],
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t/r, Figure 1. Gas temperature distribution as a function
6 of the radius, Tp = 5,400 �K.
1 s
Key: 1. Initial distribution;
Zs 2. Steady-state distribution at .
o q < qp~
~ T~ 3-6. The distribution of T(r) for
3 q > qp ; t/T = 0 .1 (3) , 0.2 (4) ,
03 0.3 (5) and 0.301 (6); T= 54 msec
o~ _ and qp = 0.9 MW/cm2.
1 J 3 r/R
Figure 2. The breakdown power density qp
and the surface temperature
4.�~a"~' T.,,u~Y Tp as a funct~on of the external
qp, MW/ ~ ~ T pressure.
7 3 I S,d ~ .
~ Key: 1. Nitrogen;
o i ~6 2. The functions specified by
~ formula (4);
I
- ~ ~ ~ 3. The boiling point of
' a9 I dt tungsten as a function of
4
o ~ , ~ pressure;
0,8s 4. Nitrogen, taking into
~ 48 account Te > T, points
O,B i ~ A and B were calculated
4 4'6 taking plasma diffusion
o~f , ~ , into account .
0 1 1 3 4 70 40 60 dOQsnr~
yielded a breakdown temperature of 12,000 �K, something which is knowingly higher
than the boiling point of any material. This indicates the unreal nature of the
presuppositions of [13] and the erroneous conclusions of paper [14], where it is
proposed that a low threshold laser breakdown be explained by the thermal breakdown
of pure air.
3. It was assumed above that the plasma is in a state of local thermodynamic
equilibrium, where the temperature of the electrons Te is equal to the gas temper-
ature., Since the radi.ation energy is absorbed by the electrons, and the latter
give up hc~at to the gas as a consequence of elastic and inelastic collisions, then
it is possible, generally speaking, for the electron gas to overheat. The latter
is extremely important, since the plasma density depends strongly on the tempera-
ture of the electrons. These effects can be taken into account by means of thermal
balance equations for the electrons and hea.vy particles:
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s
-~Z a~ Xerz arP = R Kq- 3M8 n,k (Te -T~ Ve ~NEQy-}- RcQK~~ (6a)
~ i Jr ~r, d~ - MS nak ~T r- T~ Ue ~NT6y -I- ILaQK~;
� n'~ -1 2ntcz V N exp I-- "2kT~,' N N~- N ~6b)
~ z - cp ,
\
where Qk is the coulomb cross-section; d is the inelastic loss coefficient; Ke =
= venf/3 (NEcry + nSak) is the coefficient of electron heat conductivity. Adding
(6a) and (6b), and considering the fact that for the given conditions Ke < K, we
obtain equation (1), in which, however, the absorption factor depends on the
electron temperature Te. The size of the latter is determined by equation (6a).
In the absence of el.ectron thermal conductivity, Te will be maximal:
4neaMR' ~
T e -T + 3kcrn~w~di~ q'
It can be seen from (7) that f or molecular gases, f or example nitrogen, the
electron temperature exceeds the gas temperature by the small amount of' = 3U0 �K
(for q= 1 MW/cm2, r= R, d= 15 [15]). By substituting (7) in (1), one can, as
is done for example, in MHD generators with a nonequilibrium plasma [51J, take
tlie impact of electron heating on the plasma conductivity into account, and conse-
quently, its impact on the breakdown threshold. Curve 4 in Figure 2 was plotted
taking this effect into account. It can be seen that the influence of nonequi-
librium is small for molecular gases. In reality, the heating will be even less
for molecular gases, since in prebreakdown modes, the frequeney of coulamb col-
lisions is on the order of the elastic collisions and much greater than the
- inverse energy time 3m~Svy/M. This leads to more efficient energy transfer fram
the electrons to the vibrational molecular degrees of freedom and the gas temper-
ature.
In atomic gases, the break in the temperature of the electrons can prove to be
substantial. For example, for Ar, in accordance with (7), Te - T= 6,000 �K.
However, the electron thermal conductivity will be significant at atmospheric
pressure. Dor this reason, it is necessary to solve (6a) and (6b) simultaneously
to find Te and T. At high pressures (p > 20 atm), the electron thermal conduc-
tivity becom.es small, and for this reason, the inf luence of electron heating can
be taken into account just as for the case of a molecular gas. Calculations
based on (1) and (7) yield a breakdown temperature in Argon at a tungsten surface
_ si?bstantially lower than for nitrogen: Tp = 3,800 �K. Such a low value of the
temperature also makes it.possible ta use this approach for less difficultly
fiisible materials. For. example, Tp = 3,050 �K for steel at p= 15 atm. Thus,
tlie. hreakdown power density depends on the properties of both the target material
and the ambient gas.
4. Tt was stated at the outset of this paper that the thermal breakdown was
analyzed for the simplest case: the case of an Pquilibrium plasma, where the
electron concentration is determined by Saha's formula. Because of the large
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_ spatial gr,ldients for some parameters of the problem, the plasma ~ losses due to
diffusion fr