JPRS ID: 9656 USSR REPORT PHYSICS AND MATHEMATICS

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- JPRS L/9656 -
10 April 1981
- USSR Re ort _
_ p
PHYSICS AND MATHEMATICS
(FOUO 3/81)
FBIS FOREIGN BROADCAST INFORMATION SERVICE _
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~7?RS r~/9656 `
. .
_ ~ 10 Apri1 1981
USSR REPORT =
~ PHYSICS AND MATHEMATICS
(FUUO 3%81)
.
`CONTENTS
CRYSTALS AND SEMICONDUCTORS '
_ Electron-Ho1e Liquid in SemiconducCors in Strong Magnetic Fields 1
~ LASERS ~ND PIASERS
~
Estimating the Degree of Hazard to Human Eyes From Directional
, ~ Laser Beams S
Light Amplification in Halogen Atom Recombination Reaction,s 15
Effect of Gas Density Disturbances on the Li~miting Characteristics
of Repetitively Pulsed Ultraviolet Preionization Lasers 27 -
,
Study of ttie Quasi-Steady Interaction of C02-Laser Radiation With a -
Graphite 'iarget in the Air ..................ez. 33
Experimental Study of Internal Losses in Iodine La.sers Pumped by Open.
~j High-Cu.rrent Discharge Ultraviolet Radiation 40
~ Stin?ula~ed Light Scattering in a ThermQdynamically Nonequilibrium
~ Medium [dith E:tcitation of Collective Motio~s as a Result of
` Light-Initiated Chemical Reaction 53 l
_ CO2 Gas Dynamic Laser Using the Combustion Products c>f C2H2-CO-N20-N2
Mixtures 62
Kinetic Pracesses in Gases, and the Molecular Laser ~ 67
= MOLECULAR PHYSICS ~ _
; Probabilities of Optical Transitions of Diatomic Molecules 72 -
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NUCLEAR PHYSICS
_ Approximate Compression Theory and Dimensior~less Relations for
- Thin-Shell Targets 76 _
Calculating the Compression of D~-Gas Class ~he?,1.,,Targets Considering
,
� C02-Laser Radiation Refraction arid~~Resonance Absorption 102
Singular Self-Similar Conditions of Laser Compression of Matter to
Superhigh Densities 1_09
l.! ~ -
_ ~
Problem of Laser-Initiated Thermonuclear Fusion 114
Effect of Drift Instability and Its Stabiliaat ion on Plasm~ Transfer
in a Toroidal Stellarator ::131
THERMODYNAMICS ` ^ ~
Heat and Charge Transfer on the Surface of Metals in Chemically
Active Flows 135
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CRYSTALS A.ND SEMTCONDUCTORS
' ~r` UDG 537.311.33
~LECTRON-HOI~E LIQUID IN SII~IICONDliCTORS IN�STRONG MAG?~TETIC FIELDS
Nioscow TRUDY ORDENf~ LENINA FIZICHESKOGO INSTITUTR IMENI P. N. LEBEDEVA: ELEKTRON-
Id0-DYROCHNAYA ZHIDKOST' V POLUPROVODNIKAKH V SIL'NYKH MAGNITNYKH POLYAIQi in Russian
Vol 123, 198~ (signed ~o press 23 May 80) pp 2, 118-119
11
[Annotat3on and abstracts from book "Works of the Order of Lenin Physics Institute
imeni P. N. Lebedev: Electron-Hole liquid in Semiconductors in Strong Magnetic
Fields", edited by i~T, G. Bas~v, izdatel'stvo "Nauka", 1450 copies, 119 pages]
- [Text] The book is dedicated to theoretical and experimental studies of the be-
havior of an electron-hole liquid in strong magnetic fields. L. V. Keldysh et al.
_ analyze the change in bonding energy and other para.meters of electron-hole drops
in indirect semiconductors in quantizing magnetic fields a.nd predict some new phe-
_ ~ nomena, in particular the magnetic oscillations of carrier density in electron-
hole drops. In other papers these effects are experimentally investigated by
studying the spectral form and intensity of germanium photoluminescence ir. the -
fundamental absorption region, and also by methods of long-wave infrared spectros-
copy. Oscil?ations in the intensity of plasma absorption have been observed in
+.he resonant absorption spectra of an electron-hole liquid in the far infrared in
~ a ma.gnetic field with a period corresponding to sequential passage ,~f Landau levels
through the Fermi level of electrons wi~h minimum effective mass. Investigation of
the kinetics of photoluminescence in pure germanium has revealed nscillations of
- the caxrier lifetime in an electron-hole liquid, which gives unambiguous eonfirma-
- tion of the effect of oscillations of density and other parameters of the electron-
hole liquid in a magnetic field. It has been shown that exciton-impurity camplexes
, play an important part in processes of magnetic oscillations in doped n-germanium.
The collection is intended for physici~ts a.nd engineers involved in soZid-state
research. ~
~ - UDC 537.311.33
- ELECTRON-HOLE LIQUID IN SF~IICONDUCTORS IN A MAGNETIC FIELD
' [Abstract of paper by L. V. Keldysh and A. P. Silin]
- [Text] Known results for the energy of an electron-hole liquid in semiconduc+_.ars
without a magnetic field are used to get esti.nates of the additional oscillating
_ component in the energy and equilibrium density of an electron-hole liquid in a
i
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ma,gnetic field. It is shown that these additions may explain th'e fluctuations of
integrated intensity of recombination radiation of an electron-hole ~.iquid in ger-
manium in a magnetic field. References 13�
- UDC 537�311~33
ELEGTRON-HOLE LIQUID IN A SUPERSTRONG MAGNETIC FIELD
[Abstract of paper by T. A. Onishchenko]
[Text] A method is presented for calculating the energy of interaction of electroi
liquids with maximally strong anisotropy thai: leads to a coIImmon law of E~orr~n"'-n~
and two consequences are considered for strongl.y anisotropic electron-hole systems:
thermodynamics of the gas-liquid transition tfor quasi-unidimensional systems), and
the semimetal-dieiects~ic transition. Spec:ific calculations are done for systems,
in a superstrong magnetic field. Figures 2, references 11. ,
UDC 537 � 317. . 33
QUANTUM OSCILLATIONS GF INTENSITY OF PLASMA ABSORPTION IN~`AN ELECTRON-HOI~E DROP IN
GERMANIUM `
[Abstract of paper by V. A. Zayats,. V. L. Kononenko a.nd V. N. Murzin]
[Text] The authors stiudy the intensity dependences of absorption in the plasma
resonance re~ion in an elect~on-hole drop in germanium at 1.5 K in mr~gnetic fields
with intensity of up to 40 k0e for all three principal field orientations:
HII[100], [110], [111]. It is shown that periodic changes of intensity observed in
fields of 5-25 k0e are due to quantum oscillations oF the ~her~odynamic character-
istics of the electron-iioie drop, prima.rily the equilibrium densities of particles
in the electron-hole liquid. It is estaolished that the direct cause of change in
the intensity of resonant absorption in the electron-hole drop in a magnetic field
is to be found in the cha.nges in overall number of carriers in the condensed phase _
that are due to fluctuations of carrier lifetime in the electron-hole drop as a
result of coxresponding antiphase changes of equilibrium density. T',z~ monotonic
fall-of'f of intensity of absorption in fields stronger than 17-25 k0e is also clue -
to a reduction of..carrier lifetime in the electron-hole drop as a consequence of
self-compressibility of the ?lectron-hole liquad in the magnetic field. Figures 4, _
- references 12.. , ~ ~ ~
' UDC 537.311.3
r~IAGPdETIC OSCILLATIONS OF~LUMINESC~NCE OF ELECTRON-HOLE DROPS IN PURE GII~MANIUM
[Abstract of paper by K. Bettsler, B. G. Zhurkin and A. L. Karuzskiy]
[Text] It is shown that charge carrier density n oscillates in an electron-hole
drop when a magneti,c field is applied. These density oscillations lead to oscil-
lations of lluninescence intensity and lifetime of the line of the electron-hole
drop (LA - 709 meV).. Zhe properties of the electron-hole drop that depend on densi-
ty n Were studied by investigating these magnetic oscillt3,tio~is. It was found that
2
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quantum efficiency in the electron-hole drop is only 25q in contrast to previously
made estimates of this quantity. The principal non-radiative'process in the
electronWhole drop is Auger recombination, which is intensified by e- e-, e- h- and
_ h-h-co�rrPlations. A proof is derived from the differences in oscillatory behavior -
- of TA- and LA-lines tnat the radiative transiti~n in the electron-hole drop with -
_ emission of a TA-phonon is forbidden in the first order. Figures 6, references 21.
' UDC 537�311.33 -
- SPECTRAL DEFENDEPICE OF MAGNETIC OSCILLATIONS Or LUMIIITESC~NCE INTENSITY OF AN
ELECTRON-HO~E DROP IN PURE GERMANIUM -
[Abstrsct of paper by K. Bettsler, P. S. Gladkov, B. G. Zhurkin and A. L. Karuz-
skiy ]
[Text] An investigation is ma.de of oscillations of intensity at different points
of the luminescence line (I~A- 709 meV) of electron-hole condensa.te in pure Ge.
At short delay times (t < 10 us) the relative amplitude of oscillations in the
= center of the line is minimum and increases toward the edges. The resultant spec-
tral pattern of the oscillations is explained within ~he framework of tlie drop
model. From the oscillations of inten~ity at three points of the line, the ~
authors calculste the ma,gnetic oscillations of spectral width of the line and the
characteristic energies of the electron-~iole condensate (oscillations of the chemi-
cal potential, and of the kineti~c, exchange and correlational energies per particle
~ pair in the electron--hole condensate) . Figures 2, references 11.
UDC 537�311.33
MAGNETIC OSCILLATIONS OF THE HAL~F'-WIDTH OF mgF r,rIMINESCENCE LINE OF ELECTRON-HOLE
~ DROPS IN PURE GERMANIUI~~
[Abstract of paper by B. PQ. Balter, K. Bettsler, B. G. Zhurkin and A. L. Karuzslsiy]
[Text] Magnetic oscillations of the half-width of the radiative recombination
~.ine of electron-hole drops in germanium (line LA - 709 meV) were experimentally
~ observed. It is shown that the observed oscillations can be explained by Fermi
energy oscillations of cha.rge carriers with density p~ in the drops. 'I`he ratio -
between dEF/EF and dp~/p~ is int,roduced and used as the basis for calculating the.
- ma.gnetic field d~pendence of the half-width ~E of ~;he line with consideration of
oscillations of p~. The theoretical curve agrees we 11 with experimental data.
Figure 1, references 8.
UDC 537.311.33
MAGNETIC OSCILLATIONS OF LUMII~TESCENCE OF ELECTRON-HOLE DROPS IN ARSENIC-DOPED
_ GER~~ANIUM -
[Abstract of paper by V. P. Aksenov, K. Bettsler, B. G. Zhurkin and A. L. Karuz-
- s~:iy ] ~
[Text] I~lagnetic oscillations of intensities of phononless (NP) and LA-phoi,on lumi-
nescence lines of electron hole drops (EfID) are ob served in Ge:As, as well as
3
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oscillations of the intensity ratio (NP/LA)E~. The relative a.mplitude of oscil- -
lations for EHD of the LA-linechangeslinearly with an increase in delay time tdel
after the stimulating pulse, whereas the relative amplitude of oscillations of EHD
- of the NP-line is independent of tdel� Figures 2, references 6. _
UDC 537�311.33 -
MAGNETOPLASMA RESONANCE IN ELECTRON-HOLE DROPS IN GEI~MANIUM
[Abstract of paper by V. I. Gavrilenko, V. L. Kononenko and V. N. Murzin] -
[Text] A detailed examination is made of the problems of the theo.ry of magneto- _
plasma resonance (MPR) in electron-hole drops (EHD) that are small in size com-
pared with a wavelength of `electroma.gnetic radiation, considering both the electro-
and ma.gnetodipole mecha.nisms of absorption. An analysis is made of the principles
governing MPR in EHD with man5 kinds of carriers, and a relation is established
between the position of the resonant f~equencies of MPR in EHD a.nd~the parameters
that charact~rize the carriers in the condensed phase. An in-depth comparison is _
ma.de between the theory and'+he overall experimental pattern of MPR in EHD, and it
is shown that a quantitative description of experimental data is possible. This
compaxison is used as a basis for defining a.nd analyzing some important paxameters
and relations that characterize the electron-hole liquid in an EHD: effective
. ma.sses of the carriers in drops, variation in density of the EHD in a magnetic
field, frequency,dependerice of da.mping of plasma fluctuations, and the mechanisms
of such damping.. Z'he pap,er points out new possibilities and prospects for further
investiga~ion of MPR in EHD. Figures 24, tables 2, references 57.
UDC 537�311.33
SHAPE OF ELECTRON-HOLE DROPS IN A NIAGNETIC FIELD '
[Ab stract of paper by V. L. Kononenlto ]
[Text] An examination is made of the shape a,~d capillary oscillations of electron-
hole drops in a.magnetic field with consideration of ma.jor influencing factors
surface tension, interaction with the natural phonon wind, recombination magnetism,
and also dia- and paramagnetism of carriers in the drop. It is shown that in an
undeformed cubic crystal, fairly sma.l.l electron-hol.e drops axe always stretched out
_ along the field, and as dimensions increase, the drops are either flattened out _
- along the field (in the case of predominant influence of recombination magnetism),
or continue to be stretched out (in the case of phonon wind predominating). The
author considers the problem of the critical size of the electron-hole drop in
these two cases. Numerical calculations are done on the shape and frequency of
capillary oscillations of drops depending on their volume and the magnetic field
intens~~~y. ~he results agree well with experimental data relating to the shape of
- the electron-h.ole" drop in a magnetic,fiel.d. Figures 4, table l,'references 26.
;
COPYRIGHT: Izdatel'stvo "iVauka",,1980~ ,
[38-6610] . ~ ~
66io
cso: 1862 - ~
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LASERS AND MASERS
~
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UDC 614.89:621:373.826
ESTIMATING TIiE DEGREE OF HAZARD TO HUMAN EYES FROM DIRECTIONAL LASER BF~1MS
Mos~ow KVANTOVAYA ~LEKTRONIKA in Russian Vol 7, No 12, Dec 1980 pp 2523-2530
[Article by V. T. Kibovskiy, V. I. Kukhtevich, L. A. Novitskiy, All Union Scientific
Research Institute of Opticophysical Measurements, rloscow]
[Text] A study is ma.de of the problems of the quantitative evaluation
of the degree of hazard from directional laser beams by the model of
, interactian of gaussian radiation beams of different divergence with
the optical system of the eye. Expressions are obtained for determin-
ing the dimensions of the illumination spot on the retina under the
~ conditions of the worst acco~nmodation. Formulas are presented f or
estimating the degree of hazard as a function of the diameter of the
laser beam in the plane of the pupil.
~ Directional laser beams in the spectral region of (1.5-1.4 microns are highly dan~erous
to human eyes, inasmuch as when such a beam hits thepupil, the radiation is focused
~ on the retina in a small spot with high radiation intensity in the vicinity of the
- spot, which can lead to damage to the retina with comparatively low intensity of the
radiation on the cornea [1]. Here and hereafter, by radiation intensity we mean
; the surf ace density of the power (watts/cm2) for continuous ra3iation or the sur-
- face density of the energy (joules/cm2) for pulse radiation. THe laser safety
j norms existing at the present time [2, 3] establish the maximum admissible levels
; (MAL) of radiation intensity on the cornea with uniform illumination of the entire
area of the pupil by a parallel beam of rays for directional beams. Under such
irradiation conditions, the degree of hazard of the ?aser beam for the human eye
estimated by its effect on the retina is determined by the ratio of the intensity
of the radiation incident on the pupil WPupil to the corresponding value of the MAL
i on the pupil WP~'1. I-Iowever, under actual conditions the radiation beam incident
' on the pupil can be essentially nonuniform, converging or diverging, can have a
diameter ttiat is less than the pupil diameter for such irradiation conditions
encountered in practice, it is necessary to more precisely define the criterion for
quantitative evaluation of the degree of hazard of the radiation inasmuch as the
~ estimate by the criterion of Wpupil~~il for the investigated case turns 'out to
be insufficiently reliable. ;
Let u~ introduce the hazard coefficient of a directional laser beam for the human
~ ~~L
! ~ eye R= W~aX/W where W~X is the maximum intensity of the radiation at the
' illumination spot on the retina when a real beam hits the sye; W~ - is the maximum
, 5
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' admissible value of the intensity on the retina when illuminating tha pupil by a.
parallel uniForm beam having intensity WP
Pi~ in the plane of the pupil. At the -
present time the radiation intensity on the retina is basically considered by the
formulas of references j4, 5]. However, the model for converting the laser beam by
the optica'1 system of the eye adopted ~n these papers does not take into account
the�neculiarities of focusing of a nonuniform beam and it does not consider the -
condit;ons of the worst accomodation in the calculaCion.
Let us express in~aX in terms of the energy and spatial parameters o� the incident
c
beam for which we consider the system for irradiating the eye (Figure 1) by a gaussian
beam, directed along the viewin~ axis.The beam with gaussian intensit~ . distribu-
tion obviously must be considered to be the most dangerous of the ones actually
encountered in practice inasmuch as it creates a greater local intensity on the
retina at the distribution maximum by co~parison with the beam having~the same power, "
divergence and diameter, but more uniform intensity distributiori. The gaussian
e'
~ ~ I _
ZB Fn F N f.~ frn ~v
-f
_ frn f, r
-Z Z~=f~n
-~ak
B A
_ Figure l. Diagram of irradiation of the -
eye by a directional laser beam..
I:ey: 1. principal
_ radiation beam is characterized by angu~ar divergence 6 with respect to the level
- 1/e2, the confocal parameter Re = 2a/~r8 , and it has constriction w~ = A/~r8 [6],
which in the general ~ case can be located at any arbitrary distance z from the plane -
of the pupil. Here the constriction can be located inside the radia.~or (a laser with-
out a shaping optical system) , at the exit surface of th~ radiator (a laser with
_ collimating optical system) or at a great distance, to several liundreds of ineters,
from the exit sur..face of the radiator (laser with focusing optical system). In the
investigated model of irradiation the pri.mary spatial paramF ter influencing W~ax
will be the distance z; here the distance from the eye to t:ze exit plane of the
radiator has no basic significance. In accordance with tr~e si~n rule adopted in
the optical system, the distance z is reckoned from the plane of the pupil, and
we shall consider it negative iF the constriction ~5 to the left of the pupil (the
eye is irradiated by a diverging beam), and positjve if the constriction is located
to the right (the eye is irradiated by a converging beam) .
The simplified optical system of the eye (see Figt~re 1) is a positive lens (the
- crystalline lens) behind which a substance is locata~. with index of refraction n' _ `
J~1.336 (the vitreous body). Let us consider that tt~e front and rear principal, planes
-s ~ of the eye are matched with the plane of the pup~l AA' . The distance from the
_ principal plane of the eye to the retina is equal to the rear focal length of the
- g
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c;
- eye with accommodation at rest (accommodation at infinity) fPrin - 22�3E5 mm. On
ar_cc~mmodation oF the eye to some plane BB' l.ocated at a distance ~.a~ from the pupil,
the rear focal point f' of the eye is in front of the retina a distance f' fron the
AA' plane. The nu;nerical values of f' and n' are taken from the data for a
prin
_ schema.tic normal eye according to Gulstrand [7]~
The radiation intensity distribution function at the illumination spot on the retina
W~(p) can be found knowing the field amplitude distribution E~(p) on the retina.
Inasmuch as the illumination spot dimensions are small, the surface of the retina
will be considered flat within the limits of the spot. By the irradiation diagram
_ (see Figure 1) we assume that the eye is irradiated by radiation from a coherent
source located at the center of the constriction of the incident beam and having
dimensions less than the minimum dimension resolvable by the eye at the distance z.
Inasmuch as the optical systein of the normal eye is isoplanar (the eye aberrations
do not influence tlie structural symmetry of a beam incident on the retina), the
space-frequency spectrum of the amplitude distribution E~ (K) is the amplitude trans-
fer function of the optical system of the eye lcprin~K~ ~8~ � Let us represent the
function k.prin~K~ in the form of the product of the functions 1cD(r,) kab(K), where
kD(K) is the amplitude transf er function of the aberrationless system describ ing
the diffraction field distrib ution on the retina which occuxs both as a result of
limited dimensions of the input gaussian beam and as a result of beam diffraction
_ at the pupil; kab(K) is the amplitude transfei function of the optical system de-
scribing the f ield distribution caused only by eye aberrations without considering
diffraction.
_ On diffraction of a gaussian beam of radiation on a circular iris (the pupil), the
~ield distribution in the beam after the iris depends on the parameter a= rPupil~
~`~pupi 1~ 6], where ri~upil is the radius of the pupil of the eye; wpupil is
the radius of the incident gaussian beam in the plane o= the pupil. From [6] it
follows that for ct > 2.2 the field distribution after the iris coincides with the
gaussian curve, and the beam can be considered as unlimited, wh.ereas for oc < 0.2
thc incident beam car~ be considered uniform, and the field dist~ribution after the
iris can be described by the known Airy formula [8]. For simplification let us
replace the Airy distribution by gaussian distribution having the same amplitude
at the maximum as the Airy distribution. This substitution does not lead to an
error in estimating the degree of danger inasmuch as the intensities at the maxi-
mum distributions are equal. For intermediate values of 0.2 < a< 2.7 the field
distribution function after the iris is described analytically by a quite complex
- expression [6]; therefore we sha11 also replace this function by the gasussian dis-
trib~ition liaving the same maximum amplitude as the actual distribution. Thus, for
any a the Eield distribution on the retina without considering aberrations will be
described by L-he gaussian curve with the radius w~, with respect to the level of de-
2
- cr~ase in amplitudc by e times; then ~ K = e~~Kwa~ . In order to find the form
~ of tl~e ftinction k.a~ ) let us use the~ata from reference [9 ] in which graplis of
the intensity distr.ibution on the retina are presented for irradiation of the eye
- by lhe ligh~ of an incoherent source with dimensions less than the minimum dimen-
sion resolvable by the eye at the given distance. For large pupil diameter (more
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than 5 mm), the~e curves, when descrihing both the diffraction and aberration blur
of ttie illumination spot can be completely approximated by gaussian curves with a
radius w~ with respect to the level of decrease of inte~s ty by e2 times. Here the
spectrum or the intensity distribution function e~~KWE~2~2 is the transfer f unction
of the optical system of the eye for incoherent light. Let us represent the trans-
fer function in the form of the product of the function 1~(K)hab(r.), where hD(K)
_ and hab(r) are the corresponding transfer functions of the aberrationless and purely
~ aberration system f or incoherent radiation. Approxi.mating the actual intensity dis- .
_ tribution in the diffraction pattern of the aberrationless system by a gaussian
curve with radius wD, we obtain =
-~:sxtnaG)'�
hao = e �
where c~ab = w~ - wD. The function hab(K) is the Fourier transform of the
function kab 2
I (p)I ; consequently,
k~~ ~P) e--p2;~�~6 and k~6 ~x) = e-inx~e6)'.
. Knowing kD(k) and kab(K`, we find the normalized spectrum of2the amplitude distribu-
_ tion of the field on t2e ~etina E~(K) = k rin~K~ e(~Kwc where w~ = Wa wab' `
P�
from which E~(p) = e-p ~W~. The radiation intensity is equal to the square of the
f ield amplitude; therefore the intensity distribution on the retina is described by _
the expression
l~~ (P)= W~ exexp (-2p=/a~~). -
~1)
For determination of the function w(z) let us find the dependence of w and w on ~
c oc ab
z. Let us first consider the re~ion z for which a> 2.2. In this region, a gaus-
sian beam is formed aFter the crystalline lens which is characterized by the confor-
mal parameter Re and has a new constriction of radius wo located at some distance
z' from the plane of the pupil. Applying the well-known formula [6] for determining _
Re, considering the index of refraction n', we obtain
, G~U ~n L\ n,R3 12 / zn, ~ 2_,~_
_ 2f 1 +l r ~ c2>
Afrer conversions considering the expressions for c~~ and Re, we obtain
y wu - 0~64 n~2in aa> (3)
er~bg
~ r~p ~ n ~2 zz~-~/` ; ~4)
(7~/~zrc)z za
- ~ ~ _ - [(~/~2n)" -f- (z -f- i'ln')=] ' ~S~ -
jrn
~a~
Key: a. prin b. pupil ~
8
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- Ubvi~usly the worst conditioiis of irradiation of the eye wi11 be thuse foz which ~
_ the illunination spot size on the retina is minimal. Tn the case where the con-
striction of the beam incident on tre pupil is to the left of the front focal point
_ of the eye FP~~n, the least spot size corresponds to the size of the new constric-
\
= tion, that is, we consider that For ot > 2.2 wa = w~. The new constriction is
- on the retina at a distance Q which will be called the worst accomodation distance.
The local leagtii f' for the worstaccommodation will be found irom the known exDres-
sion for z' [ 6], which, considering n' , assumes the form:
Z~ r 1- n'z/f~ ~ l c
- f (n'R3/2f')' -I- (n'2/i' -~-1)' J ~ ~6)
Inasmuch as the ne~,r constriction is located on the r.etina, let us consider z' = fpriri
Then equation (6) reduces to the form
~E,--i)+.r ~p2+~92-2~~-(92+p2)=o, ~ -
where x= L' /f' ; q= n'R /2I' ; p= n' z/f' Solving equation (7) for any
prin e prin prin'
given distances z, it is possible to define the values of f' , S and 2, = f x/
ac prin ~
~X - 1~ .
- For a, < 2.2, the illumination spot begins to "blur" as a result of diFfraction, and
for a< 0.2 its size is completely determined by the diffraction on the pupil. Let -
_ us assume that foz~ ~.2 < cx < Z, 2 the spot size w varies in accordance with the -
linear law ~a = 0.25 [3.4 +~aJ~f ~rin~n~2r u il obtained from the condition that
P P P
: 2. 2, w~ = w~, and for a= 0. 2, wa = 0. 9~f ~ prin~n ~ Zrpupil ~ the last expression is
nbtained from the condi*_ion of equality of the total powers in the Airy distribution
and in the gaussian d~stribution equivalent to it).
Tn orcler to find u; we use the values of the St~`e].1 coeffi~ient ~ for different
pupil diauieters. `~bUnder the approximation conditions assumed previously, the _
- Strell coe~f icient is equal ~o the ratio of the maximum intensity in the system with -
~ aberral�ions to th~ maximum gaussian distribution of rhe intensity which would occur
at tt~e retina in tl?~ absciice of aberrations. From the conditionlof eq~a~ity oF the
t~~tal. powei�s in botl~ distrlbutions we obtain ~ab ~'~~fprin � 1) ~/n'2rpupi'1' -
Substituting the e~cpressions obtain ~d above i.n the equation far w2, for rhe case
c
where the constriction is t~ the left of FP~,in we obtain:
- ~z~ _ ~f~:~ ( Y2 ~z) -I- 0,81 [5-' (z)-� Ij~'�`=, (8) .
n'2r3p =
- wl~er. e '
0,64a~ for a _ 2
,2; ,
Y~z) _ ~~2~ (3,4 ~-a~) for 0,2~a ~ 2~2~
~'9 for a50,2.
_ 9
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The graphs o~ the function l~ (z) are ptesented in Figure 2 for a pupil of diametFr
, dpupil 8~� ~the worst case of "night" vision). For the calculations the
coefficient y was determined by the data from reference [9], where for a> 1 a -
value of 2wpupil was taken as th? pupil diameter. From Figure 2 we see that with in-
. creasing distance of the constriction from the front focal point F the illumination
_ prin
spot size unde~+. tile ccnditions of ~orst accomodation decreases from a value of -
6f' /n' to a minimum value of w~ln, after which it begins to i.ncrease as a result
prin c
of diffraction and aberration broad~ning and reaches a value which in practice is F
completely determined by the aberrations of the eye. At greater distance from the
constriction, this value i~emains constant .
= In Figure 2 graphs are also presente.d for the distance of the worst accom~odation
1L as ~ funcfiion oF z. ror each value of 6 there is a least value of Rm R which
ac ac -
decr.eases with an increase in 0. However, R, cannot be less than the distance to
- ac
the near point of the eye (~125 mm) [7]. This explains the horizontal sebment of
the graph for 6= S mrad. To the left of the point z~ln corresponding to Qa~n, the _
- function 2 (z) sharply approaches infinity, and to the right of this point it
approachesaz.
As a result of the investigation above of the process of shaping the illumination
spot on the retina of an eye irradiated by a diverging gaussian beam, a result is
obtained which is important to estimating the degree of hazard of the radiation:
on the beam axis there is a p oint at a distance from ~ens of centimeters 'to several
meters (depending on 8) from the initial constriction at which under the conditions
of worst accommodation of the eye it is posGible to obtain an illumination spot on
the retina of minimum size (about 5 microns) which is appreciably less than the _
illumination spot size obtained on the retina on removal of the eye to inf inity _
(about 20 microns). �
For the case where thF beam: constriction is to the right of the point Fpr.in the
worst accommodatioii condilions will be accommodation at infinity (f' = fprin~' here,
tor u> 2. 2 a minimum spot will be formed on the retina with radius wi = Ofprin~n~ '
The general function w~(z) in the case where the constriction is to the right of
- F includir~g f or the cases where the eye is irradiated by a converging beam (z > 0) ,
_ prin
will be described by the formula (8) , where
20rep/n. f or a> 2, 2;
, y (z) (0,28ra~,i,l) (5a -1) - - 0,45 (a - 2,2j for 0,2 < a < 2,2;
- . , U~~ �for a 5, which requires activation energy [9]. The same
~ thing occurs for the B-state of the IC1 molecule; in this case the levels v' > 2 _
predissociate easily and are populated on recombination [18]. Under t~he conditions -
of an inert matrix the radiationless transition ot the states of the lI-multiplet
to the ground state is not observed, and the 3II-states decay only in the radiation
' times where the molecules on the lowest level v' = 0 radiate [19, 20]. For Sr2,
~ under the matrix conditions, only the B state was observed; the other states could
not be detected. For ICl, the states A and B were observed, and their decay took
, place independently. In the bas phase during the Br-Br, I-C1 recombination, primar-
ily ttie A state is populated [7, 8, llJ. Thus, for this series of halogen molecules
_ ttie electron conversion has little significance.
Classification of Various Cases of the Population of Excited States
, What has been discussed above permits the following diagram of the population and
excited state relaxation processes of the C12 molecules during recombination to be
adopted:
' CI-{-CI-~-M=CIz(3I7)-{-M; (1)
CI~(3IIi)-f-M_Clz(3II~)-f-M; ~2~ '
17 ~
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Cl2(3II, v')-1-M=CIz('II, v'-}-Du')~-M; (3)
~lz(3II)-I-M->CI,(~Ee )-FM; ~4~
Cl Z('II;)->Cl2(lEg f~ cu. (,5)
Here (1) is recombination to the bound states of the 3II-multiplet and the i.nverse
process of dissociation from these states; (2) is the conversion between the multi-
plet components; (3) is the vibrational re~axation in the excited states; (4) is
the conversion to the ground state; (5) are the radiat'on transitions. The recombi-
nation constant to the 3II~u state is known [10]: kl(~II~+u) = 5�10-34 cmb/sec.
Under rapid conversion conditions (the corresponding estimate was presented above),
it is necessary to define the complete recombination constant to the 3II-multiplet
- kl. Considering that recombination takes place to all of the bound states except
3II~u without a change in tlie electron state, we obtain the'estimate kl > 6k1(3II~+u).
The vibrational relaxation rate constant k3 can be estimated from the fact that at
- a pressure of 1-3 mm Hg a re~ shifr of the chemiluminescence spectrum is still
- observed [9, 10], that is, the vibrational relaxation rate is omparable to the
radiation loss rate. As a result, we find k3 =(1-3)�10-13 cm~/sec, T= 300 I:. The
calculation of k3 by the empirical formulas of [22] (see also [23]) leads to a
value of 4�10-13-cmj/sec, that is, for T= 300 K the vibrational relaxation rate
does not exceed the quenching rate by much. With an increase in T, the inequality
- k3 > k4 will become stronger. Thus, for T= 450 K the estimate by formulas [22]
gives k3 = 10-12 cm3/sec, that is, for pressures exceeding several milli.meters of .
mercury, it will be possible to establish the vibrational equilibrium in the excited
states. ~
fMl
71
B ~
i
i
~)e 3 I A
C , ~
4
L ~
Tp T
It is important to compare the role of the individual processes (1)-(S) as a func-
tion of the experimental conditions: density [M], composition [X]/[M] and tempera-
fture T([X] is the concentration of X atoms). For this purpose the set of parameters
-l~~], [X]/[M], T is broken down into recions in each of which one process of deactiva-
tion of the electron-excited states or another predominates. The convenience of the
breakdown into the limiting regions consists in the following. Simple expressions
for the populations of the excited states are obtained in each of the regions which
permit analysis of their concentration and temperature functions. It is possible to
isolate the regions of greatest interest in laser respects. This subdivision per-
mits estimation of the populations of the states in the individual regions in the
absence of complete information about the deactivation processes.
18
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Let us begi.iiwith tlie case oL tiigh dilution: [X]/[M] � 1. The figure illustrates the
breakdown of the plane of significant pazameters [M], T into the regions A, B, C i.n
which the inverse process (1) and processes (4), (5), respectively predominate. The ~
processes of internal conversion are considered to be the fastest. Curve 1 is de-
fined by the condition [MJ =(EkSi~Ki~~~~k1'i~ICi), where summation is carried out
with respect to the electron states, between which effective exchange takes place.
Ki are the chemical equilibrium constants of these states with the dissociated
states. The line 2 is found from the condition Ek4i~Ki ~kl'i~Ki, line 3, from
~~1~ ~~kSi~Ki~ ~ ~~k4i~~`i~ ' curve 4 ~Ml = ~ K~k ~ K~' bounds the region of
t a ~
parameters below, in which vibration equilibrium can be established in the excited
states. In region A the recombination and dissociation processes (1) predominate, -
there�ore ttie population of each of the states can be calculated using the equi-
liqrium constants:
~(XY]i=[X 1 [Yl/K~ ~6)
(for generality the atom coricentrations [X] and [Y] are introduced). In region B
the recombitiation (1) and quenching (4) processes predominate, population and radia-
tion have an apparent two-particle nature:
~[XYI~=(Ekl;/K;Ek,j/Kf)[XIfYI.
In region C the recombination (1) and radiative emission (5) processes are the most =
important, population and radiation are of a three-particle nature:
- (XY 1;=(~kl~/K~~kS f/KJ) [X ~ [Yl [M1. ~g~
- From (6)-(8) it follows that for the investigated case of a highly dilute mixture
with f ixed [X], [Y], the highest concentrations of excited particles are realized
in the region of parameters B.
Using the lcinetic ~arameters of the reactions (1~-(5) discussed above and the equi-
librium constants of the electron states of thE 1I-multiplet of C12, it is easy to
calculate curves 1-3 of the figure. Here let us present only the characteristic
values [M]3 = 1.3�1017 cm 3, T2 = 450 K. F~rmulas (6)-(8) are used below to cal-
culate the light amplification.
Abov e, we discussed the processes oF quenchl.ng in a molecular or inert gas. With
an increase in the halogen atom concetitration, a violet shif t of the radiation spec-
tra and a decrease in the glow [7, 8], which was interpz~eted as strong quenching of
the radiation lu~,i.i.nescence dn the atoms, were detected. ~~ukE~.ver, as is obvious from
[7], this quenching depends on the type of dilvent. It is also known rhat additives
oF the mol.ecules, for example, HC1 (the ground state 1L'~) also lead to the violet
shift and quenching of the radiation. Considering this fact and the above discussed
argumer.ts about conversion of electron states in halogens, it is possible to present
, another explanation For the observed eff ects: an increase in the atom concentration
leads to acceleration of the vibrational relaxation inside the multiplet 3]I in the =
19
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~ '
atomic states Cl(2P3~2), to variation of the distribution function with respect to
~ vibrational levels, which causes a violet shif t of the spectra; part of the mole-
cules are converted to the lower and less glowing levels, (The vibrational relaxa-
tion rate on the atoms is discussed, for example, in [24],)
If the quenching in the atoms differs significantly from quenching in the molecules,
then it is necessary to make the following substitution in the above-discussed re-
sults: k4 } k4M~ + k4X~[X]/[M]. This leads to expansion of the region B in which
- the quenching is significant, and to constriction of the regions A and C(see the
dotted line on the curve). We shall assume that the quenching constant in the atoms
k41 = 10-11 cm3/sec [7, 8]. Th~n for [X]/[M] = 0.1, it turns out that [M]3 =~p16
cm 3, T2 = 600 K. ~Cn the absence of a diluent, the subdivision of the plane of the
parameters requires only the two regions A and B. The temnerature at which
the change in nature of tlie population takes place is T2 = 800 I:.
Inasmuch as for the Br2, IC1 and I2 molecules the conversion between states of the
mu~tiplet is appreciably weaker, for the corresponding reactions the system (1)-(5)
i:s simplified: the process (2) can be omitted, and each of the states must be con-
sidered independently. In the above-presented formulas it is necessary to consider
only one term in the sums. Applying these formulas, for example, for the state
A3~luBr2, we find [ri]3 = 1017 cm 3, T2 = 400 K. The calculation of k3 by the for-~.
mulas [22] shows that under these conditions, vibrational equilibrium can be estab-
i lished in state A of the Br2 molecule , I the case o the absence of dilution
with quenching constant on the atams k4~Br~ = 10-11 cm~/sec, we find the tempera-
- ture boundirg the region A and B, TZ = 600 K. Analogous estimates have also been
obtained for other halogens.
Criteria for Obtaining Inverse Population and Amplif ication Coefficients
Let us discuss the inversion radiation criteria and the magnitude. of the amplif ica-
tion in halogen recombination reactions. The amplification (absorption) coefficient
is conveniently represented in the form oc = a+ - a, where a+ corresponds to the
radiation of quanta, a corresponds to absorption. The amplification condition a>
0 assumes the simplest form if the following two conditions are satisf ied: equili-
brium exists between the bound states of the electron-excited molecule and the
dissociated states, and equilibrium can be established in the vibrational subsystem
of the electron ground state: The complete equilibrium, of course, must be absent.
Ttie region of parameters where the first condition is satisfied has already been dis-
~ cussed above (region A). For the grourd state in a number of cases vibratianal
relaxation times are known. Thus,,for C12 at T= 500 K, according to [22J, p~v = 10-6
sec-atm; for Br2 - pT~ = 3�10-~ sec-atm. For [X]/[M] ~ 0.1., [M] ~ 1019 cm 3 these
values are an order less than the characteristic recombination times. Let us note
that in the presence of atoms the vibrational relaxation is accelerated [24]. Thus,
_ ior '1'-~ 5001: Ciie equ~il:ibrium :in the vibrational subsystem of the ground state must be
_ able to~6e established. On satisfaction of the~two above-indicated conditions the
inversion criterion assumes the form [1, 25]
20
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IX1[YI~K(T)e~w/kT [XY1~ ~9)
where K(T) is the equilibrium constant of the entire process X+ Y= XY, w is the
phototransition frequency.
If the condition of equilibrium with dissociatea states is not satisfied, but equi-
librium exists in the vibrational subsystems of the ground and excited states (re- _
gions B and C), then the inversion criterion can be written in the form
(XY),>(Z;/Zo)[XY]oe-~~tt� ~~~~kT,~~E~o=E~n-1--EoD�1�, (lU) -
where Zi and Z~ are the statistical sums of the excited (i) and ground (0) states; .
Eiv'1G'' ~Ov"Q" are the energies of the vibrational-rotational levels of the electron -
states i and 0. .
The criteria (9), (10) make it possible to find the operating temperature
ranges of the recomb ination laser. For concreteness, let us consider the region A.
_ As is obvious, the criterion (9) for fixed w essentially depends on T and depends
slightly on.the concentrations. For the estimates it is convenient to set [X] _
[Y] _[XY] and def ine the "limiting" temperature T~im [26J, below which (T ~ Tlim~
condition (1) is satisfied. For C12, setting [C1] = 1018 cm 3 -
, we f ind the f ollow-
ing: for a= 1170 nm, ~'lim - 1070 K; for a= 738 nm, T1~ = 600 K. For Br2, set-
_ ting [Br] = 1018 cm 3, at 1200 nm we find Tlim 800 K; for a= 1400 n:.i, Tl~ _ ~
950 K. Analogous estimates are also obtained for other pairs of recomUining atoms.
If the criteria (9j, (10) are satisf ied with reserve, then for calculating the
light amplif ication coefficient it is sufficient to calculate ec+. For the transi-
tions between the iv'Q', Ov"Q" levels of the XY molecule, a~" is def ined by the -
, ,
amplification cross section o~v�Q� and the population of the state iv'R' -[XY]i~~R~:
+ iv Q
' a-~Ov"Q" ~~~iv' Q'' For the amplification cross section at the maximum of the
, doppler-broadened 1 ine, the Following expression is valid =
" ; c~' 4n2 I R`p I2 qv,
QOv^("'-' - ~11~
3j (2nkT/mxY)~~= ~21~ ~ 1)
where R~ is the electron matrix element; y,~, � and SQ,Q� are th~ rranck-Condon and -
v
Hanle-London factors; m~, is the mass of the XY molecule. If equilibrium is
realized in the sub system of vibrational-rotational levels of the state i(the re-
gions A, B and C), then instead of (7; it is convenient to use the cross section
in tlie calculation for the complete population of the state i[XY],: 1
1
- , a(-h) _ Qi ~X Y~i~ 6t = QOv"!" ~21 1) 2--Eiv'!'~kT~Zj ~7'~ ~12` ~
_ /
For the Fixed band in the radiation spectrum v' v" the maximum of a~+~ corresponds
to transitions with zotational levels with !C' ~ Qm =?kT/2B~ � Bv, is the rotational
= 21 ~
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constant of ttie state i, v'. The generalization of (11) to the case of impact
. ~r.oaclening is realized using the knoam Voigt formula. However, the impact broaden-
I.ng cross scctions, as a rule, are not known; therefore here we shall present the
formula for calcul.ating cx~' suitahle for such large pressures where the rotational _
structure disappears in the radiatiori spectrum:
a+~~'~�~ 6 X 1']; ~
a~ ~a~ _ R~3IRoI2q~,o,B~,hc~~', f B~.(~,-7l
v`~ ~ I ex 1� ~ )
31~ (kT)2 B~~ - B=,� I p I ~Bu~ - BU,, ~,~,v.kT ~ 13 _
Here aV,v� is the wavelength of the light for the transition iv' v". Expression
(13) gives the spectral distribution of the value of a'(h)~in the given radiation
band iv'-Ov". For arbitrar.y pressures, it is possible to use (13) as the estimate
for the lower bound of the interval of variation of a+. _
- Light amplification coefficient
- _ -
- I TYPe of bx. T .
x+a+n+ transition I t0-�a cM~ I ~ K I ~ I �~-0~
1 2250 740 3-9
I I I
. Cl Cl M 3TI~+u ~ Eg 2 I 3400 I 1060 I 0-16
~ 2 I 3400 1170 0-18
- ~ (0,08) f I
' i ,3 1200 0-18
(0,06) 3150 ]240 U-,-19
Br -r Br M 3i7~u ~ Eg 1280 0-20
~~9 I 3150 I 1430 I 0-23
Br Cl M I 3I7o+ ~ E~' ~ 4 I 1800 I 8~ I 0-12'
J-}- Cl M I 3IIo+ ~ E~" I 40 I 0 ( 720-755 ( 0-9 ito. ll
J-}- Cl M I~ I71 ' E+ I 5 5300 I 200 0- ] 3 -
I I I
J T J-I- M I 317~+u i Eg I 7 I 4400 I 1220-1920 I o-22 ta.38
.1 -I J_f M `I 3R~u ~~g~ I 1 I 2100 1300-1500 0-18 to 20
I I
~
The "broadened" values are presented.
_ Let us proceed to the calculation of the amplification for specifi systems. For _
_ the C12 molecule iL is necessary to consider that the transition B~II~+u ~lEg has ~
the same structure as the transition lEg lEg for the b-type Hund bond [27]: the
22 _
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I' and R branches are :in~~n~e, and the Q-branch is absent. The nuclear spin of the
= 34C1 and 37C1 isotopes is 3/2; therefore transitions from the even rotational levels -
- of tt~e upper state predominate. The spectroscopic parameters of C12 were taken from
_ [28] , the matrix element from [14] , tize factors q~~ � fr~m [29] . Let us present
1~ v
the results for the transition from the level v' = 0. Inasmuch as for the transi-
tions 0-} 17, 0-> 18, 0-} 19 the values of q~,v� are clase and approximately equal
to 0.1, we Find csi = 8.3�10-19�(1000 K/T)2 cm2 for them at the transitions from the
rotaCional levels 2' ~ Q for both P and R-branches. The oscillatory statistical
m
sum was calculated at the classical limit, 6~� = 3� 10-20 (1000 K/T) 2 cm2; v" = 17 ,
:18, 19, -
An analogous calculation was made for the more forbidden transitions: A3IIlu X~'~~:
-21 2
csi = 5'10 (1000 K/T) cmZ, ~1 in the vicinity of 1200 nm; 3II2u X1Eg: c~i = 8�10-~2
2 2
(1000 K/'T) cm ~ in the vicinity of 1300 nm.
In region A(see the figure) the value of a+ is reprQSented in the following form by
using the above-presented cross section for the B-~ X transition and the expression
for the population o~; the ~-srate (6)
a+~~`~ r~=a~~~T) [X l[Y l~ a~~,~=bx~lO00I(/T)s,:2eT~/T. -
(14) -
�
The parameters of formula (14) for Cl2 with doppler broadening are presented 9.n the
table for ~~i series oF transitions. TFie parameters are presented there for the value
of a(a, T)''calculated using (1~) for the case of high pressure, for a= av~~,,,
T > 800 k. _
In region I3 for C12 the value oF a+ does not have such simple form (see formula
The values of o;~' wi11 be presenCed only �or a few cases. In the absence of dilution
- at T= 450 K we find c~+ = 7� 10-41 cm5 x[81] 2_3or a= 1060-1200 nm. At the same
temperature [Cl] /[ri] 0.1 and [Cl] = 101 cm , impact broadening is felt in tne
value of a+; therefore we shall present the upper and lower bounds of the interval ~
of variation of a+: 5� 1U-40 cm5 X[ Cl a+ > 2� 10-4~' cm5 x[ Cl ] 2, the last value
_ was Cound using the "broadened'~cross section (13). For [C1]/[M] = 0.01 and T= 450K,
whicl~ cor. responds to the boundary of the regions A and B, we shall present only the
locaer bound for cx+: 4�1U-40 em5 x jCl]2. It is obvious that in order to obtain the -
aniplitication coefi:icient- 10-4 to 10-3 cm 1 it is necessary to create [Cl] ~?~.1018
cni 3 . .
- Pur ~i~e Br2 niolecu.le the A31?lu state has the tqpe of boad close to case C. I'or the
transitiuns t131I -Y1~;+, the sclection rules and the structure of the transitions ar.e
g
valid just as Lor ~I[lu-lz:~ for the a-type bond [30]. 'Phe spectroscopic paramerers
are ~~resented in [23] . Tl~e r?~~rix element R~ for the A-> X transition can be calcu- -
lated by tlie split,tiug of the 3;T-multiplet and using the matrix element R' of the
- transition 11I - l~
~ 2p
lu ~ ~(see also the survey [31] According to [32] for the
K'
.
23
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-
equilibrium posi.tion of the bromine nuclei in the A-sCate, Fc~ = 0.26 nm, IR~~2 =
- 0.17 ~R' ~2. The values of qv,V� for the A-X system are pre~anted in [33J. The
calculation for the amplification cross sections at the transitions 0-~ 18-20 gave:
_ 6i = 1.3-10-18 (10~0 K/T)~~cm2, the broadened value of 6~v� is 2�1--20 (1000 K/T)2 _
cm2. ror the parameters for which the type A population is realized (see the fig-
ure), the values determining the amplification by formula (14) are presented,in the
table. The broadened value of a(a, T) is presen there also. In the region B for
T= 400 K in the absence of a diluent, we find a~~~ = 5�10-40 cm5 x[Br]2, a= 1200-
_ 1300 nm. For dilution of [Br]/[M] = 0.1, let us present the bounds of the region
uf variation of a~+~:3�10-39 cm5 x[Br]2 > a~+~ > 5�10-41 cm5 x[Br]2. For the di-
= lution [Br ]/[M] = 0. Ol (the boundary ef the regions A and B) , we find the lower ~
_ bound et~+~:2.5�10-40 cm5 x[Br]2. In order to obtain amplification in the range of
10-4 to 10 j cm l, the following concentrations are necessary: [Br] = 10~'$ cm-3.
_ The results of calculating a(~) for other recombination reactions of the group VII
_ atoms are presented in the table f or the case where the population of the bound
states is in equilihrium with the dissociated states (region A).
Let us briefly repeat the basic conclusions obtained above. Using experimental
- data, the radiation channel of the recombination reactions, the role of various
electron states, and the processes of vibrational relaxation are discussed. It is
demonstrated l.hat there are various types of populations of excited electron states.
~ The regions of the parameters are estimated: density, temperature, dilution, for .
which one type of population or another is realized. Various methods of creating
an invers e population in a reacting gas will correspond to various types of popu-
. lation. Thus, on initiation of the recombination reactions by a shock wave, during
photolysis of a slightly diluted gas, case A must be realized. During photolysis
of a highly di.luted gas in the heating-cooling method case~ B will be realized, and
so on. An esti.:nate was presented of the conditions under which population inversion
occurred.The light amplif ication cross sections were calculated for various electron
transitions. The light ampl~ification coefficient was calculated for the regions
of. parameters with different L-ypes of po ulation, It is obvious that for concentra-
- tions oL the recombining atoms (1-5)�101~ cm 3 and temperatures not exceeding 600-
800 K, for l.he l~alo~en atom recombination reactions, light amplification on the
order oL- 10-3 cni 1 can be realized in the near infrared range. The indicated con-
ditions are realized in the hearing--cooling method (see, for example, [l, 34]) and
for excitation of radiation recomtiin~ation during photolysis [35] .
BIBLIOGRAPHY
1. A. S. Bast?kin, V. I. Igashin, A. N. Nikitin, A. N. Orayevskiy, �I:HIMICHESKIY~
= I;AZERY (Chemical Lasers) , rioscow, VINITI, 1975. ~
2. V. A. Kochelan, Yu. A. l~ukibnyy, S. I. Yekar, KVANTOVAYA ELEKTRONIICA (Quantum
J Electronics), No 1, 1974, p 279.
_ 3. B.Fon ten,S.Forest'ye,KVANTOVAYA ELEKTRONIKA, No 3, 1976, p 897.
4. l.. A. Izmaylov, V. A. ICochelap, Yu. A. Kukibnyy, UKR* FIZ. ZtiURNAL (Ukrainian
Phys ics Journal), No 21, 1976, p 508.
24
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- 5. A. S. Bashkin, A. N. Orayevskiy, KVANTOVAYA EL~kTRONIKA, No 3, 1976, p 29.
6. B. A. Thrush, R. Golde, REP. PROGR. P1iYS., No 36, 1973, p 1285. ~
M. A. A. Cline, D. H. Steclman, TRANS. FARADAY SOC., No 64, 1968, p 1816.
8. R.`J. Browne, E. A. Qoryslo, J. CHEM. PHYS., No 52, 1970, p 5774.
,
M. A. A. Cline, J. A. C~oxun, A. R. Woon-Fat, TRANS. FARADAY SOC., No 67, 1971,
p 3155. -
10. M. A. A. Cline, D. J. Smith, J. CHEM. SOC. FARAD. TR., part II, No 75, 1979,
- P 67. -
11. i~i. A. A. Cline, J. A. Coxon, PROC. ROY. SOC. LONDON, ~10 298A, 1967, p 430.
_ 12. B. Genri, M. Kasha, UFN (Progress in the Physical Sciences), No 108, 1972, p 113.
13. R. E. Huie, N. J. T. Long, CHEM. PHYS. LETTS, No 44, 1976, p 608. ,
_ 14. M. A. A. Cline, J. S. McDermid, J. CHEM~ SOC. FARAD. TR., part II, No 74, 1978,
p 1935, ' ,
15. M. A. A. Cline, J. S. McDermid, J. CHEM. SOC. FARAD. TR., part II, iJo 75, 1979,
_p 1313.
16. V. E. Bondyhey, C. Fletcher, J, CHEM. PHYS., No 61, 1975, p 3615.
- 17. G. Capelle, K. Sakurai, H. P. Broida, J. CHEM. PHYS., No 54, 1971, p 1728.
18. R. D. Gordon, K. K. Innes, J. C'tiEM. PHYS., No 71, 1979, p 2824. _
19. V. E. Bondybey, S. S. Barder, C. Fletcher, J. CHEM. PHYS., No 64, 1976, p 5242. -
_ 20. V. E. Bondybey, L. L. Brus, J. CHEi4. PHYS., No 64, 1976, p 3248.
21. R. S. Nlulliken, PHYS. REV., No 36, 1930, p 1140; No 46, 1934, p 529; No 57, 1940,
- p 500.
; 22� R. C. Millik a1, D. R. White, J. CHEM. PHYS., No 39, 1963, p 3209.
~ 23. B. F. Myers, E. R. Bartle, J. CHEM. PHYS., No 48, 1968, p 3935.
' 24. Ye. Ye. Nikitin, GAZODINAriICHESKIYE LAZERY I LAZERNAYA FOTOKFiIMIYA (Gas Dynamic
' Lasers and Laser Photochemistry), Moscow, MGU, 1978, p 126.
25. S. I. Pekar, V. A. Kochelan, DAN SSSR (Reports of the USSR Academy of Sciences),
- No 196, 1971, p 808.
26. V. L. Tal'roze, Ye. B. Gordon, Yu. L. Moskvin, A.. P. Kharitonov, DAN SSSR, No
� 214, 1974, p 864.
27. M. A. A. Cline, J. A. Coxon, J. MOL. SPECTROSC., No 33, 1970, p 381.
~
25
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. 28. TERMODINAMICIiESKIYE SVOYSTVA INDIVIDUAL~NYKH VESHCHESTV (Thermodynamic Proper-
ties of Individual Substances), Edited by V. P. Glushko, Moscow, Izd-vo AN
SSSR, Vol l, 1962. ~
29. J. A. Coxon, J. QUANTUM SPECTROSC. RAD. TRANSFER, No 11, 1971, p 443.
- 30. J. A. Coxon, J. MOL. SPECTR. vo 33, 1971, p 443.
31. J. A. Coxon, MOL. SPECTR., No 1, 1973, p 177.
32. R. J. LeRoy, R. G. MacDonald, G. Burns, J. CHEM. PHYS., No 65, 1976, p 1485. -
33. J. A. Coxon, J. MOL. SPECTROSC. No 41, 1972, p 566. ~
34. V. 9. Kochelap, Yu. A. Kukibnyy, KVANTOVAYA ELEICTRONIKA, No 2, 1975, p 1471.
- 35. I. A. Izmaylov, V. A. Kochelap, KVANTOVAYA EL~KTRONIKA, No 6, 1979, p 2349.
Report r~ceived 4 April 1980
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~ � '
f ~
r,
i .
I -
,
~
i
i
; UDC 621.373.826.038.826
i
EFFECT OF GAS DENSITY DISTURBANCES ON THE LIMITING CHARACTERISTICS OF
- REPETITIVELY PULSED ULTRAVIOLET PREIONIZATION LASERS
~ Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 7, No 12, Dec'80 received
20 May 80 pp 2589-2593 '
; [Article by V. Yu. BaranoV, D. D. Malyuta, V. S. Mezhevov, A. P. Napartovich,
Nuclear Power Institute imeni I. V. Kurchatov, Moscaw]
'
; [Text] ~xperimental results are presented from a study of the effect
of smal7. (~1%) gas density disturb~nces on the average power
of a repetitively pulsed laser with the application of an
electrode system with ultraviolet preioniza~ion.
~
- ~ 1. Introdu ction
; Iahen building efficient periodically pulsed.lasers (PPL) researchers have
- encountered the phenomenon of decreasing maximum energy contribution in an
~ individual current pulse with an increase in the pulse repetition frequency f. _
. The energy contribution in the discharge decreas es noticeably for frequencies
appreciably less than the gas exchange frequency in the interelectrode gap
~ fp=v/b~ (v is the gas flow velocity in the interelectrode region; bp is the
~ electrode width). The restriction of the energy contribution per pulse is
_i connected with pinching of the discharge. The basic known causes of pinching
; for f106'~sec-1 (here ~kp~~~5�104 cm 1,
v-2.5�104 cm/sec for gases usually used as buffer gases C02, SF6, and so on),
at the same time as the probabilities..of recombinations of the iodine atoms and
the radicals .~l'1 [I l o, ~`/'1 [R Jo, ~'Z IR ~ o under standard conditions are appreciably
less than 106 c.m 1. The probability of induced transitions Q_ to~ the inte~nsi-
. ties ~WO~o^'10 watts/cm2 is also appreciably less than S2~ (vy~5�10-19 cm [10]). _
Under these conditions the expressions for jR], [I] obtained from the system of
equations (12) are simplified significantly, and the heat release (3) can be _
~ represented in the form
" Q = Qo + I- ~q~ )0 Qv~o~ exp (iSZt - iqr) ~ 2Qo u exp (i52t - iqr) -I- _
1
complex con~ugate}, (13)
where Qo= 9Y ~'i ~ I l o~ R ~ o-I- qz ~z ~R ~ 01 is the uniform heat release in the
~ absence of a scattered field.
' Substituting T1 in (7) in the form of T1=T� (T exp{i (SZ t-qr)} complex -
conjugate), where T~ is the deviation of the temperature from the equilibrium
, value of T~ in the absence of the scattered field= and substituting (11), (13) in
(8) , we discover that in the investigated case 2 Qp/p c�~ (y-1) and the
second term in (13) can be neglected. In addition, assuming that the relative -
~ variation of the amglitudes is small at distances�o~ the order of the w~ve
length, in (9) we keep only the first spatial derivative of the amplitude, and in
(7), (8) we in general neglect the derivatives of the amplitudes inasmuch as the
: absorption of the ultrasonic and the temperature waves a and aT is ~reater than
their amplification in the process of stimulated'scattering. 'Abstracting from trie
~ process oF ampli.fication of electromagnetic waves and the active medium of the -
laser, we assume that ~ED(r)I2~const.
Considering the assumptions made, we obtain exponential growth of the scattered
radiation in the region of nonlinear interaction:
IE~(s`) 12= IE~(~=~) IZ exp {g(S2)~I, ~14~
where ~ is the coordinate in the direction kl, and g(S2) is the steady-~state
amplification coefficient: _
g�~ - I 4nn p Re Az ~ Eo ~2 ~
(15)
nz~ _ 9i ~ Rlo o ~
Q 2hwa S2 � ~
A1 P~v~a ~S2 -F" YXQZ - 4 iY~ -
A - S~Z - Q1 - iS~ zI'- `Qz (Y- ~ ~
- ~ P~T q P~T ~iS2 YX~Ia) ' -
57
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. For scattering on an ultrasonic wave ~2 ~~MS � q2~P~~� ~x9~)2�
. � F
Neglecti~g the~~small terlns in (~5), we~ find~ the expression for the ~amplification
. coefficient:
!SZ kl ~Y=n~ts~~ aszMB E z I ki I Yv c9i~'i IRloaveo ~
g l 32an= (SZ -~~a16~s +~8S2Mb~z ~ o 8npcp 2?~wo x ~
~ B~Mg = I k~ I Ya c9~~`~'i [R)oQY~o xY
X 61M6 -~M6~z +~a~MS~z I E~ I~ 8npcp 2ri.(~p vs X ~1.6~
' ~ ~ x ~-QMS . ~rr�p. C
_ ~~oz,~,. _
oQnA4uw noeepxHOtmr
/ ~ ~ Kpu?nu~eecKOtl ~ 2 ~
~ ~vrarnHOCmu _
~ ~
no~noK menna ~ 3) 4
- - nomoK eeccSecntea 5
no~epnoe us~yyonue ~
Figure 1. Laser heating system. The laser emission is absorbed in -
a plasma corona in the region of densities close to critical. The -
heat fluxes that arise, reaching the ablation surface, cause
evaporation of the substance, creating a recoil pulse compressing
the target.
Key:
1. Ablation surface , ~
2. Critical density surface
3. Heat flux
4. Flaw of substance
5. Laser radiation
_
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~ ~ ,
" _
~.o _ ~ _
_ i
~~�j_._-_
� ' k:
~`arsy:^n i .
_ . -4~:..
~.0 - _ ~Y:-' s~~" ~ _ .
' " n-~~ � ~~-z
>~~"':~c .
S.0 vc,_
- - ~ ~_s=~a~~
~ y ='i::-__i:~: _
. - C~=4.- - _ =
1.0 a - - - ii-
='-"='3-
- t"_ .-.:a �
. _ , -i=z r` .
"'i.
~ . 7.0 : ~=~~:i;'r.;='--� .
~ _ .
. ~ ` 3, ~ ~
: _ -
J.0 _ - l=.~-_. : - .
' 1 0 ~ . ' - _ ~
` 0.0
0.0 I.0 7.0 7.0 1.0 S.0 ~.0 i.0 '
T "`'-T ~ T"
.~t�l.l
/ ~
7.0
i
~.0
_ _ ~~~~i%^ ,~ti=_' . .
f.a ~/,~i.�, 'i~
L-~.o ~ -';i.'
- ~
~ ~
~.o
,
t.o
' . ` _
1 ~.e - ~1
o -
_ = ,
o ,.o ~.o ..o ,.o ,.o ,.o
Figure 2. Results of machine simulation of interaction of a ~
powerful electromagnetic wave with plasma E2z8~rnT near the
reflection point (taken from [24]). A plane electromagnetic
wave is incident from the left. T~ao successivP times are -
depicted: a-- the high-~amplitude standing wave is obvious, the
plasma profile is modulated under the effect of the ponderoiuotive
forces; in the density region greater than critical, the electro-
magnetic wave damps; b-- the development of wave instability
- can be seen.
COPYRIGHT: Institut avtomatiki i elektrometrii, SO AN SSSR,
Novosibirsk, 1979
[ 814i+/0581-I~-10845 ]
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EFFECT OF DRIFT INSTABILITY AND ITS STABILIZATION ON PLASMA TRANSFER IN A TOROIDAL
S TE LLARAT OR
~Kiev VLIYANIYE DREYFOVOY NEUSTOYCHIVOSTI I YEYE STABILIZATSII NA PROTSESSY PERENOSA
PLAZMY V TOROIDAL'NOM STELLARATORE in Russian 1979 (signed to press'17 Apr 79)
pp 3-5, 37-38 _
[Introduction and conclusion from book "Effect of Instability and Its Stabilization
on Plasma Transfer in a Toroidal Stellarator", by Aleksandr Yur'yevich Voloshko,
Institut yadernykh issledovaniy, 180 copies, 40 pages]
[Text] Introduction
Drift instabilities of plasma have become during the past decade an object of
close at tention of investigators involved in the problem of conL-rolled thermo- _
nu~~lear fusion. This was determined by the fact that in practically all experi-
- ments on toroidal confi..^.ement of plasma, abnormal heat and particle losses were
observed [1-7] which significantly exceed the neoclassical values, in some cases -
by an order or more.
'Drift fluctuations may make an appr~ciable contiributa.on to energy losses from the
plasma even if their relative level is very low [2, 4, 8-9].
Thermal conductivity at relatively low values of plasma density in tokamaks is in
good agreement with the pseudo-~classical formula proposed by L. A. Artsimovich to
describe the experimental results obtained in the T-3 tokamak [11]:
.7C1 ~.se ~a l'AC Jc�fF, _
Here C2 is a constant value approximately equal to 10, pee is the Larmor radius of
the electron in a poloidal magnetic field, veff is the effective frequency of
electron collisions determined from measurements of the electric conductivity of
the plasma: veff ~ wpe~4~Q'
It was subsequently shown that the pseudo-classical law of losses is valid not only
for tokamaks but in some cases for stellarators with current [2-7] and during con-
- finement of a currentless plasma [10~. ,
~ 131 ~
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It follows directly from the pseudo-classicalformula that heat losses through the
electron channel decrease as Te increases (as approximately Te3~2) in the case of
Coulomb conductivity of the plasma. In the general case the heat losses of the
plasma in toroidal configuration are determined by the total effect due to th~Ymal
conductivity perpendicular to the magnetic field and due to particle diffusion [12],
~ which increases with an increase of electron temoerature (the "plateau" reyion).
- The observed increased energy losses through the electron channel may be related
to breakdown of magnetic surfaces (due to current flow in the plasma), to drift in-
~ stabilities, to instabilities on trapped electrons and so on [13-17]. However,
there is as yet no experimental proof of a direct relationship of abnormal electron
thermal conductivity with the presence of one or another instabilities in the
plasma.
With regard to charged particle confinement, measurement of the diffusion coeffi- -
cient was also usually ak~normal, although to a lesser degree in the extent of ab-
- normality than for the coe�ficients of electron thermal conductivity. Detailed
experimental invest igations on stellarators (Uragan-1 Uragan-2 [18], Kleo [5],
- W=PB (3l, Heliotro n-D [19] and so on) showed that turbulent diffusion is similar to
neoclassical diffusion for. the "plateau" by the nature of. the dependence on plasma
- parameters, while it may differ from it by approximately an or_der in ahsolute value,:
_ as a function of the ratio of the thermal electron velocity and the rate of current
drift (see, for example (5, 20, 43]). These experimental results are in qualita-
: tive agreement with the results of [21] on the effect of drift instability in a
plasma with current on particle diffusion.
As indicated by numerous theoretical [22-25] and experimental [survey 26] investi-
gations, the negative effect of. drift instabilities may be reduced considerahly if
the magnetic configuration has sufficient crossing of lines of force or a"mag-
- .netic well." Alan g with this, suppression of drift fluctuations can be achieved
by increasing the ion viscasity due to inereasing the collision frequency of ions
with ions or of ions with neutral .3~.a"re's [26] . Variation of the effective frequency
- of_ ion collisions durinq hinh-f.rec{uency heating of a plasma has a similar effect on
the am~litude of dr ift instabilities [27-28, ~7], due to which the use of ion vis-
cosity to staUilize drift fluctuations may be promising in confinement of thermo- _
nuclear plasmas.
A decrpase in the 1PVe1 of fluctuatzons can also be achieved by using feedback [29~
or. dynar~ic stabilization (29-30J .
A knowledge of the tvpe of fluctuations, their ~vave s~ructure, mechanisms of oscil-
lation and amplitud e restriction is necessary for effective use of one or another ~
method. of stabilization. -
Thi~ paPer is a survey of. com~lex experimental investigatios of low-frequency
drift f.luctuati~ns of an SFiF discharge plasma confined in the high-shear Saturn
1=3 toroidal stellarator.
- The.method of creat ing the plasma, the diagnosis used and the plasm~ parameters are
descrihed in the f_irst part of the paper.
_ 132 -
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The second part contains data of ineasuring the spatial and time characteristics of
_ the low-frequency oscillations, their dependence on plasma parameters and the con-
_ fining magnetic field. The measurements made it possible to determine the type of
observed fluctuations and to indicate the mechanisms of their excitation.
- The third part is devoted to experimental investigation of the mechanism of stabil-
~ ization of drift-dissipative instability by shear and by the effect of the ion
mass. It is specifically shown that the amplitude restriction of drift fluctua-
tions is determined My Landau attenuation on ions with the presence of sufficiently
high shear in the system.
~~art~4 contains a qualitative theoretical consideration of the effect of electrons
traoped in the potential w eIl of the drift wave (resonance electrons [13, 28, 31, 32]
and expressions of the coefficients of electron thermal conductivity are .presented
for the "plateau" region (on the plasma diffusion curve) and data of ineasuring the
_ heat losses through the electron channel are also given. It is concluded from
analpsis of the functions that the observed pseudo-classical behavior of thermal
conductivity is the consequence of a linear relationship between the values of
k~ ~vtE and veff realized in the experiment.
Part S is devoted to study of the confinement of charged plasma particles as a
function of plasma parameters and the parameters of the magnetic configuration:
- the particle losses correspond in both value and by functional dependence to neo-
classical theory at high shear values.
Conclusions
- Analysis of the experimental results presented in the given paper on investigation
of currentless plasma confi.nement in the Saturn 1=3 to ro idal stellarator permits
the following conclusions:
1. There are significant losses of charged particles perpendicular to the confin-
ing magnetic �ield (I'~oC ~2) in an SHF discharge plasma, caused by drift-dissipative
instability which develops due to the density gradient and curvature of the lines
of force.
2. The level of the drift fluctuations and consequently of the turbulent plasma
flows caused by them (rSoz6 -1�5, r ae'3) can be reduced by increasing the shear.
_ The stabilizing role of shear is manifested in a decrease of the dimensions of the
localization region of drift fluctuations and by suppression of longitudinal modes
_ with large numbers and phase velocities close to Vti. Stabilization of these modes
is determined by Landau attenuation on the ions.
3. The threshold value of shear (6kr ~ 0.05) dependent on r4i was found, beginning
with which strong sun.pr~ssion of the observed fluctuations is observed. The level
of drift fluctuations is less, the higher the ion mass'in the entire range of
shear variation.
4. Energy losses through the electron channel are determined completely by drift-
dissipative instability and are the result of interaction of resonance electrons
with these fluctuations in the region of intermediate collision frequencies. The
133
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obs~rv~d pseudo-classical depPndence of thermal conductivity is the result of the
relationship between the values of ve and kllvte realized in the experiment. `
5. Turbulent plasmas in the case of small values of shear (6 < 0.05) completely
determine the charged particle losses from the confining space (otn oC ~-2), Th~
effect of drift instability on plasma losses decreases as shear increases and con- -
finement is determined by neoclassical diffusion perpendicular to the confining
magnetic field at shear values of A~ 0.1.
_ COPYRIGHT: Institut yadernykh issledovaniy AN USSR, 1979
[58-6521]
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CSO: 1862
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THERMODYNAMICS
HEAT AND CHARGE TRANSFER ON THE SURFACE OF METAIS IN CHEMICALLY ACTIVE FLOWS
Riga PEP,ENOS TEPLA I ZARYADA NA POVERKHNOSTI METALLOV V KHIMICHESKI AKTIVNYKH
POTOKAKH in Russian 1980 (signed to press 31 Jan 80) pp 4-7, 245-246
~ [Annotation, foreword and table of contents from book "Heat and Charge Transfer on
the Surface of Metals in Chemical].y Active Flaws", by Viktor Konstantinovi_ch
Mel�nikov, Mayya Vilkhelmovna Zake and Viktor Nikolayevich Kovalev, Izdatel'stvo
"Zinatne", 1000 copies, 247 pages]
~ , .
[Text] The results of theoretical and experimental investigations of the processes
of heat and electric cliarge transfer on the surface of titanium and zirconium dur-
ing transient heating by high-temperature flows of chemically active gases are
- outlined in the monograph. The chemical kinetics oE high-temperature oxidation and
nitriding of inetals in flows of an argon and oxygen and nitrogen mixture was inves-
~ tigated experimentally. Data are presented on the integral radiating capacity of
metals for transient heating and chemical reaction modes. Electric charge transfer
_ on the surface of chemically reacting metals was investigated and data were found
on the effect of the electric field on transfer processes. A system of initial
- equations was analyzed, generalized dimensionless numbers for different kinetic
laws were found and the main fc,rmulas for calculating a number of characteristics
of heating modes of inetals were derived. The experimental installation and method
. of ineasurements for complex investigation of the processes of heat and electric
charge transfer on the surface of inetals are described.
Forev~ord
= Simultaneous heat and charge transfer on the surface of inetals in chemically active
gas:flows is of impc~rtant scientific an3 practical interest since transient proces-
ses with phase and chemical transformations of inetals play a specific role in modern
devices of high-temperature equipment and techno3ogy.
Similaz processes occur in roc~Cet technology [72, 141], during spontaneous combus-
tion of inetal particles [142, 162], during the use of briefly operating MHD gener-
ators [51] and in plasma-chemical technology of synthesizing inorganic compounds
[112, 138~. In the latter case interaction of the particles is related to processes
of charging and recharging by plasma ions and electrons [197]. Therefore, investi-
_ gations of processes of heat and charge transfer during transient heating of inetals
in cl-iemically active flows are an extremely timely problem for engineering practice.
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Study of the processes o~ transfer on the surface of inetals in chemically active
- flows has begi~n only during the past decade in our country and abroad. Investiga-
' tions of Soviet thern~ophysicists, who are pioneers in this field of science, have
a~quired especially important significance. A large number of theoretical and
experimen~al papers have now been published on the problem under consideration.
In this regard study of transfer processes on the surface of inetals in high-temper-
ature chemically active media has assumed an independent direction.
Due to the importance of the problem, it has become necessary to systematically
outline the theoretical and experimental investigations of the transfer processes
and methods of diagnosing them.
Investigations of mass and enegy transfer in inert and chemically active flows of
a low-temperature plasma with metal particles have been conducted for many years
under the supervisian of Academician Yu. A. Mikhaylov at the Institute of Physics
_ oi the Latvian SSR Academy of Sciences. One of the trends of this vast field of
science is brought to the reader's attention in the proposed monograph. It is de-
_ voted to investigation of heat and charqe transfer on the surface of inetals during
transient heating by chemically active flows of a low-temperature plasma. Th~ given
investigation is far from complete. Hc~wever, the }~resented theoretical and exper-
imental material. will help further development of the theory of transient mass and
~nergy transfer on the surface of inetals in a low-temperature plasma. This should
naturally precede investiqations of the mechanisms of transfer since simultaneous
mass and energy transfer may significantly affect individual components of the
process.
The more widespread metals--titanium and zirconium--were taken as the object of
investigations and oxygen and nitrogen were taken as the chemically active plasma.
- Th~ given paper is devoted to study of inetals in flows of a weakly ionized plasma,
i.e., a plasma with electron concentration of ni = 1010-1012.
- Concepts of the main processes--chemical kinetics, thermal radiation and charge
transfer--are given in the monograph. The chemical kinetics of oxidation and ni
triding of inetals in low-temperature plasma flows was investigated ex.perimentally.
Moreoverr data are presented in the paper on the integral radiation capacities of
metals during heating and chemical reaction. The system of initial equations was
analyzed and generalized criteria for different kinetic laws and also the main
formulas were found to calculate a number of heat transfer characteristics. Data
- of investigations on charge transfer on the surface of a chemically reacting metal
in the transient heatinq mode and also data on the ef�ect of the electric field on
~he main processes are presented. Methods of diagnosis and ex~erimental installa-
- tions are described. The devices and installations developed by che authors per-
_ mit one to expand the capabilities of experimental investigations of many transient
thermal process~s.
It should be no ted that the list of the literature given at the end of the book
cloes not claim to be complete. It contains sources, the data of which are pre-
sent;ed by the authors in the monograph and also papers which contain a detailed
bibiiography.
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- The results of investigations carried out directly by the authors of the book and
, published during the past five years are outlined in greatest detail.
The authors hope that the results of investigations of heat and charge transfer on
. ~he surface of inetals in chemically active plasma flows, presented in the mono-
c~.raph, will contribute to further development of the theory and practice of using
a low-temperature plasma in various sectors of the national economy.
. The authors would like to thank comrades A. G. Blokh and Ye. S. Ozerov for useful
comments in discussion of the manuscript.
Contents Page
Foreword 5 -
~ Li~t of Main Notations 8 -
Chapter 1. P9ain Concepts and Definitions g
1.1. Chemical kinetics 9
- 1.2. Thermal radiation 16
' 1.3. Charge transfer 23
- 1.4. Equations of heat and electric charge transfer 34
Chapter 2, Chemical Kinetics of Oxidation and Nitriding of Metals 40
2.1. Main physical and chemical properties of titanium, zirc:~nium
and compounds of them ' 40
_ 2.2. Methods of investigating chemical kinetics 4~
2.3. Chemical kinetics during oxidation 53
2.4. Chemical kinetics during nitriding ~1
Chapter 3. The Radiation Capacity of Meials 74
_ 3.1. The radiation capacity of inetals in an argon medium 74
3.2. The radiati~n capacity of inetals in an oxidizing medium 78
3.3. The radiation capacity of inetals during nitriding 100
Chapter 4. Heating Modes of Metals During Chemical Reactions 105
- 4.1. Initial equations 105
4.2. Generalized criteria 111 -
- 4.3. Main characteristics 119
- 4.4. Critical heating modes of titanium and zirconium plates 129
Chapter 5. Processes of Charge Transfer on the Surface of Metals ~n
a Plasma Flow . 136
' S.1. Electrical properties o� a plasma flow 136
5.2. Charge transfer during heating of inetals in an inert gas 142
5.3. Charge transfer during oxidation of inetals 155 ~
5.4. Charge transfer during nitriding of inetals 168
5.5. Effect of electric field on transfer processes 174
_ Chapter 6. Experimental Installations and Method of Measurements 182 `
6.1. Experimental installation 182
6.2. Arc gas heater 193
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6.3. Ra.diometers for measuring directional radiation 196
= 6.4. Models of an absolute black body 203
~ 6.5. Enthalpic probes 21'Z
Conclusions 22b
Bibliography , 233
Subject Index 243 -
COPYRIGHT: Izdatel'stvo "Zinatne", 1980
[60-6521]
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