SCIENTIFIC ABSTRACT TERNOV, I.M. - TERNOVENKO, N.M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001755420005-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 16, 2001
• Sequence Number: 5
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

S 07/56 - 2 A -:z - xe '7 1
On the Problem of the Covariant Determination of the Spin-pseudovector
It further holzls that
. k F7-87V Cos 6'P k Y 1-0, ' sin 6,
1 0 ~2 - 0
~
~3 - ks, ~4 - ikal several special cases are investigated.
There are 7 references, 6 of which are Soviet.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (Moscow state
University)
SUBMITTED: October 27, 1958
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TMOV, I.M.; TLTIIANDV. V.S.
Effect of vacuum fluctuations on the polarization of electrons
moving in a magnetic field. Zhur.el-spA teor.fiz. 37 no.4--
1137-1139 0 159. OIRA 13 -.5
1. Moskovskly gosudarstvewiyy universitet.
(Electrons) (Magnetic fields)

9(3),24(4)
AUTHORS: Ternov, I. M,, Tumanov, V. S. SOV/20-124-5-21/62
TITLE-. On the Radiation of a Polarized Electron (Ob izluchenii poly-
arizovannogo avetyashchegosya elektrona)
PERIODICAL: Doklady Akademii nauk SSSR, 1959, Vol 124, Nr 5, pp 1038-1041
('USSR)
ABSTRACT: The authors investigated the radiation of a polarized rela-
tivistic electron in a constant and homogeneous magnetic field.
In this connection it is useful to demand that the wave
function of the electron moving in the magnetic field
A
- 0 be a solution of the
= -(1/2)yH, A
= (1/2)xH, A
x
z
Y
Dirac equation and, besides, an eigenfunction of the operator
of the spin Iro ction on the kinetic momentum:

CC + -'P- A)~ It is useful to make such a
P)+ - 6(-V
C
selection of the wave function because the orientation of the
spin of the electron with respect to the direction of its
motion in a magnetic field remains conserved. The steady
solution of the Dirac equation in the system of coordinates
Card 1/3 r, 1, z is explicitly written down. An expression for the

On the Radiation of a Polarized Electron SOV/20-124-r-21/62
polarized radiation of the electron at its spontaneous tran-
sition from the initial to another state in written down. The
matrix elements of the Dirac matrices are proportional to
certain Laguerre-functions. The authors above all estimate the
intensity of radiation at transitions with approximation of the
polarization of spin, The intensity of the radiation which is
connected with depolarization is much lower than the corre-
sponding value for transitions with conservation of polariza-
tion. For the investigation of the angular distribution of
radiation intensity the usual approximation of matrix elements
must be carried out, and the above-mentioned expression for
the intensity of the polarized radiation of the electron must
be summated with respect to all harmonics and radial transi-
tions. Next, rather long expressions are derived also for
the integral intensity of radiation. The p6larization of the
electron manifests itself already in the terms of the order
of magnitude -P , although the radiation with the re-orienta-
tion of spin is of the order *-2. The authors thank 11rofessor
A. A. Sokolov and Professor D.' D. Ivanenko for discuosing the
problem and its results. There are 7 Soviet references.
Card 2/3

On the Radiation of a Polarized Electron SOV/20-1124-5-21/62
ASSOCIATION: Moskovskiy gosudarstvennyy universitet im. M. V. Lomonosova
(Moacow State University imeni h. V. Lomonosov)
PRESENTED: October 31, 1958s by N. 11. Bogolyubov, Academician
SUBMITTED: October 24, 1958
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69-45 3
S/139/6o/ooo/ol/027/041
$13 0 E032/E4 III
AUTHORS% Ternov, I.M. and Tumanov, V,,S.
TITLE *. '_0_n__th-e-1Td1-t-u~f Polarized Electrons in a Magnetic Fielak
PERIODICAL: Izvestiya vysshikh uchebnvkh zavedeniy, Fizika,
1960, Nr 1, PP 155-163 (USSR)
ABSTRACT-. It is well known that the effect of electromagneti,~l
fields on the motion of a polarized electron beam , an,
in the general case, be reduced to a change rn-the
momentum and the direction of the spin vector. In the
case of a purely magnetic field, this change takes place
in such a way that the component of' the spin vector in
the direction of motion is conserve(L The situation is
however complicated by the interaction of the electron
with the electromagnetic vacuum, This leads to an
additional energy which should be included in the
generalized Dirac equation. A consideration of the
effect of the vacuum inter-action energy shows that in
the non-relatiViStLC Aj)j)r0XtMati0n, the electron has a
vacuum magnetic moment (in addition to the Bohr magnoton)
Card 1/3 so that the Hamiltonian in the generalLzed Dirac 1-f

4r,4-- A
I I -
S/139/60/000/01/027/o4i
E032/Elii4
On the Motion of Polarized Electrons in a Magnetic Field
equation for an electron in the magnetic field is of
the form given by Eq (3), The presence of the additional
vacuum moment leads to the fact that the change in the
momentum vector and in the spin direction, when the
electron moves in a magnetic field, is such that the spin
component in the direction of motion is no longer an
integral of motion, since the operator (uP) no longer
commutes with the Hamiltonian of' the generalized Dirac
equation. In this way, the original polarization of the
electron beam gradually changes with time, The vacuum
intelraction plays the major part in the change in the
polarization since the kinematic (non-vacuum) part of the
magnetic moment is automatically taken into account by
the Hamiltonian given by Eq (2) and has no effect on the
polarization, The vacuum corrQctiott to the Dirac
equation (Eq (3) ) in the form of an additional field
moment is only significant in the non-relativistic
approximation, The relativistic problem must he
Card 2/3 considered separately and this is done in 50MC detail in

69i~ ~' 3
S/139/60/000/01/027/041
E032/E414
On the Motion of Polarized Electrons in a Magnetic Field
the present paper. The treatment given holds up to
ultra-relativistic electron velocities, The derivation
is given of radiational corrections to the Dirac
equation, and the effective energy of interaction of an
electron with vacuum is computed, An estimate is also
given of the change in the orient-ation of the electron
spin vector which is due to the vacuum interaction,,
The discussion is concluded with an example in which the
electron moves in a direction perpendicular to the
magnetic field. Acknowledgement is made to Professor
A.A,Sokolov for disc-iision of the results obtained.
There are 10 referen,_*,-r, 0 of which are Soviet and
4 English,
ASSOCIATIONtMoskovskiygosuniver.4i.tet imeni M.V.Lomono1jova
(Moscow State University imeni M,V,Lomonosov
SUBMITTEDs July 234 1959
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S/139/0/000/0i/o/jo/oli 1
F
AUTHORS, Voroblyev. A.A., and Ternov, JL'Q -391
TITLE- lilt ernati_9nal Confnr ince on Hi-i-h-ener-gy Partic-le AcceloriAtors
and on.- 1X_UUU'11La"o11
A
PERIODICAL: Izvestiya vysshikh uctiebny1ch zaveder?iv, Fizi1ra.
1960, Nr 1, pp 2~6 - 2111 (USSR)
ABSTRACT: The conference was opened by the Chairman of CERIN,
Dr. Rnker,
At the first session four papers were read on the necessity
of building new high-energy accelerators. Ono of these
papers was read by Professor Panovskiv, who argued that
large accelerators give no information i-rhich could not be
obtained from cosmic rays,, The evening session on
September 14 and two sessions on September 15 were
occupied by twenty-one papers on extension of the
accelerator energies towards higher values. During these
sessions papers -ere prezented by Kolomenskiy, V~P.
Dmitriyevskly (descriptxon of a 12 MeV cyclotron i-n Dubno,
which uses spatial variation of the magnetic f.Leld) and
Cardl/4 ~X

S/139/6o/ooo/oi/oWo4i
International Conference on tiigii-L-iiergyF-'P"Da'r~'L2~o' Accelerators and
on Nuclear-physics Instrumentation
V.I. Zamolodchtkov (description of a 1.5 m cyclotron
with azimuthal variation of the magnetic field), The
morning sess-ion on September 15 included 7 papers on
acceleration of charge5 in plasmas,.IL-I
among the3e were pApers by Rodionov, Academician
I.F. Kvartskhava (experimental LtivestigatiOnS Of f)I-OdUCtI.On
and acceleration of plarnas), Academician
(coherent shock acceleration of ring plasmas),
A.N. Lebedev and A.A, Kolomenskiv (theory of stochastic
acceleration and accumulation): A.A. Vorob~vpv dreur the
attention of the conforence T.0 tile Absence Of PIT)erS On
inj ec t ion.
The morning session on September 16 was devoted to
fundamental limitations of accelerator4j. 7
Among the papers presented at this session there were
communications from D.G. Koshkarev (theory of non-linear
problems of betatron oscillations and particles losses
in resonances); V.V- Vladimi-rskiv (space-charge limitations),
Card2/4 Lebedev, Finkel,shteyn and Veksler~

6'4~,A 0-
S/139/60/000/01/0110/0"1
International Conference on Accelerators and
on Nuclear-physics Instrumentation
Another group of papers dealt with departure from cyclic
acceleration of electrons due to radiat-i.on and quantum
of f (3c. 1, t3 (A.N. 1.0)4~dov and D.G. Komhkarov
in this group).
At the evening session on September 16, twelve papers
were presented which described technical details of high-
energy accelerators.
The 7 BeV proton synchrotron in Moscow and % planned
50 BeV synchrophasotron i.n Serpukhov were descri.bed by
V.V, Vladimir6kly.
Engineer_Zinov~y*v -described -)0, 90 and 200 'MeV linear
electron accelerators, constructed at UFT1.
A.A. Voroblyev- read a paper on "The Theory of Cyclic
Waveguide, El.ectrcn Ar~celerator,3", based on his own work
and that of A.N. Didenko, Ye.S, Kovalenko and 13,N.Morozov,
At the morning sessicn on September 17, devoted LC
Card3/4
ztt,
M
1~ !W-
MITI

S/139/60/ooo/01/040/041
International Conference an H_igh-energEY2%1dR21a Accelerators and
on Nuclear--physics Instrumentation
production, extraction and
high-energy machines, papers
(formation of a meson beam
Dubno synchrophasotron) and
kmicrowave separation of
separation of particles in
were read by S.V. Chuvilo
of 7 BeV/c momentum in the
by Professor Panovskiy
particles).
ASSOCIATIONS: Moskovskiy gosuniversitet irieni M.V. Lomonosova
(Moscow StatE University imeni M. V. Lomonosov)
Toms kx;7~o_f -it ek-lin L c lies ki y institut imeni S.2,L Kirova
(Tomsk Polytechnical. Institute imeni S.1M. Kir
SUBMITTED- December 11, 1959
Card 4/4

ACCESSION NR: AP4041444 s/0188/64/000/003/0101/0103
AUTHOR: Sokolov, A. A.; Te=ov. I. X.; Loskutov, YU. X.
TITLE: The problem of radiation damping of betatronic oicillations
SOURCE: Moscow. Universitet. Vestnik. SeriYa 3. Fizika, astronomiya, no- 3, 1964,
ICI-103
TOPIC TAGS: betatron, betatronic oscillation, cyclic accelerator, radiation damp-
ing, quantum theory, cyclic electron accelerator, electron accelerator, electron
radiation, electron oscillation, electron motion, parabolization
ABSTRACT: After the demonstration of the influence of quantum fluctuations of
radiation on the movement of electrons In a cyclic accelerator, the development of
the quantum theory of electron movement acquired theoretical and practical signi-
ficance. Recently, in a paper by S. A. Kheyfets and Yu. F. orlov (ZhETF, 45, 1225,
1963), an attempt was made to obtain not only fluctuation activation of betatronic
oszillations, but also classical damping using a nonrelativistic approximation in
addition to the quantum method. These authors feel that one cannot obtain radia-
tion damping In elthor the classical.case or the quantum case because quadratic
terms in rand dr are neglected in the equations of movement, i.e. "paraboliza-
,Card_, 1/3 d-t

ACCESSION NR: Ap4o41444
tion" of the potential energy describing the betatronic oscillations is carried
out. The present authors then point out that."parabolizatioWl of the potential
energy actually takes place In both the classical and quantum calculations. Never-
theless, in spite of the assertions of S. A. Kheyfets and Yu. F. Orlov, with the
help of the classical theory the authors at once found an expression fo5 radiation
damping:
x+ 0~x_ q
x+j
i-They then review'their previous work on the application of quantum theory to the
excitation of betatronic oscillations, and show that the criticism of Kheyfets and
Orlov concerning the origin of classical damping cannot be applied to the ultra-
'stic case of "free!' betateonic oscillations. Atte tion is'-drawn, in this
relativi n
connection, to the work of Gutbrod (Zs. f. Phys., 168, )77, 1962). Taking into
account all the terms of the analysis, one can obtain the following expression for
the change in.the quantum number s;
dl 48 -/_3 Rla%0 (I - q)y- (2)
where WkI Is the classical 'expression for the energy'being radiated In a unit of
Cwd 2/3

ACCESSION NR: AP4041444
time. In conclusion, the authors remark that the quantum fluctuations of the
radius have great practical significance. in this regard, If the first quantum
term in the right hand side of equation (2), corresponding to the quantum fluctu-
ations, Is neglected, then the square of the amplitude of the radial fluctuAtions
rapidly vanishes in the presence of relatively large energies. Acutally- however,
the amplitude.of the vertical or axial oscillations tends toward a sm4II positive
limit. It also follows that the effect of classical damping begins to decrease at'
energies on the order of 400-600 Mev. The article is followad by a brief rebuttal
by S. A.,-Kheyfets. Orig. art. has: 9 formulas.
ASSOCIATION: Kafedra tooratichaskoy fiziki Moskoviskogo universiteta (Department,
I of Theoretical Physics, Moscow University)
SUBMITTED: 07Dec63 ENCL: 00
SUB CODE: NP NO REF SOV: 007 OTHER: 003
Crd 3/3

--431MM
T 17 1 T IT. ~T~ ~T
ACCESSION NR: AP4043800 S/0188/G4/000/004/OOGZ/0070
AUTHOR: Ternov 1. At., Bagrov, V. G., Rzayev, R. A.
TITLE: Influence of synchrotron radiation of electrons on their spin orientation
SOURCE: Aloscow, Universitet. Vestnik. Seriya 3. Mika, astronornlya, no. 4, 1964,
62-70
TOPIC TAGS: electron, magnetic field, synchrotron radiation, electron spin, electron
spin polarization, electron spin orientation
ABSTRACT: The influence of an electromagnetic field on the movement of a polarized
beam of electrons generally leads to a change in both the momentum vector of the
particles and their spin orientation. In the case of a magnetic field which Is uniform in
space and consLant in time this change occurs in such a way that the state of polarization
of the electron spin, determined relative to the direction of motion of the electron and
relative to the direction of the external magnetic field, doesnotchango with time. During
motion in a magnetic field an electron becomes a source of extremely strong clectromag-
netic radiation which can lead to a change in the orientation of electron spin. In this
article the author considers the problein of the behavior of electron spin during synchrot-
rorvgdiation. Two states of polarization are investigated: relative to the directioa of
Cord

ACCESSION NR: AP4043800
motion (longitudinal) and relative to the direction of the magnetic field (for practical
purposes transverse). Expressions are derived for the wave functions, followed by an
analysis of the probability of spontaneous transitions. In his exposition of the formulas
characterizing spectral distribution, the author cites
dy F.
AC 'R 0 + U?
where F is dependent on the state of polarization of thb electron spin. The state of
longitudinal polarization is
F- - (2 (1 + ~Iylj (x) dx, (2)
(3)
F" ~10'2K% (y) - X~,, (x) dx)
where arrows indicate transitions corresponding to spin flipping and without change
,,in spin orientation (4). These formulas show that transition probability is gonerall
4 E1/2 /
(that Is,
independent of the inItial state of polarization. In the case E, whenUi).
Cord 2/5

ACCESSION NR: AP4043800
spin flipping is expressed in terms proportional to the square of the Planck constant 112.
The state of polarization along a magnetic field Is
(4)
T". 2 (1 + ZY) (x)) dx + VyW% (y) - C. (2 + jV)
(5)
Y'(I(,/.(Y) t;K%(tM-
where the arrows indicate retention of polarization and change of polarization
(spin flipping). The results differ appreciably from the preceding case: dependence on
initial spin state enters into both expressions. Limiting the problem to the region of
energies E