SOVIET ATOMIC ENERGY VOLUME 19, NUMBER 6

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• Document Creation Date: December 23, 2016
• Document Release Date: March 15, 2013
• Sequence Number: 6
• Publication Date: December 1, 1965
• Content Type: REPORT

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Volume 19, Number 6;
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December, 1965
SOVIET
ATOMIC
ENERGY
ATOMHAFI 3HE'PrielF1
(ATOMN4YA INERG1YA)
TRAN/SLAtED FROM RUSSIAN
CONSULTANTS BUREAU
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4
,
? RESEARCH IN SURFACE FORCES
Academician B. V. Deryagin, Editor
Volume 1:
"This volume is a welcome addition as a work of ref eren ce
for research workers in the field of Surface chemistry"
?Journal of Scientific .Industrial Research
The 29 retior'ts in, this collection were presented,' at the
conference'on' surface forces held at the Institute of Phys-
ical Sciences of the Academy of Sciences of the USSR
Following an introductory paper, the remaining 28 pre-
sentations cover results of inVestigations (theory and prac-
tice) on surface forces iic various systems, their properties,
and 'methods of investigations carried out by Soviet sci-
entists. The editor, who has contributed to nearly half the.
I papers in this volume, is an academician of the Academy
-of Sciences of the USSR,and is also organizer and perma-
nent Director of the Laboratory of Surface Phenomena at
the Institute. A Special Research Report translated from
Ruisian.
CONTENTS: Introduction ?,Peneral problems in surface forces ?
Polymer adhesion ? Suhace forces in" thin liquid films ? Surface
effects in dispersed systems ? Surface forces in aerosols. ?
190 pages CB 196 k $27.50
- Volume 2i Three-Dimensional Aspects of
Surface Forces
I
Consists of ,38 of the papers read at the .Second Confer- -
ence on Surface -FOices (Institute of Physical Chemistry,
Academy of ScienceS, November 1962).? The selection of
papers, makes this a monograph on the three-dimensional ,
aspects of surface forces. Considefation is given to general
problems in surface forces and surface effects, as well as
to the effects of these forces on the processes occurring at
6olid?liquid interfaces, .at interfaces between these phases
and gases, and on the properties of thin films. The 'collec-
tion is.organized into five sections: Theoretical Problems
(5 papers); Electrical Surface Forces (7 papers); Experi-
mental Studies of the Properties of Thin Films (11 pa-
pers) ; Surface Phenomena in Dispersed and Porous Sys-
tems (6 papers); Surface Phenomena in Adhesion and
Friction (9 papers). A Special Research' Report translated
frem Russian. ,
Akipprex 290 pages CB 1966 ? $27.50
? t
CONSULTANTS BUREAU
22. West 17th Street, New York, New York 10011
? - ?
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ATOMNAYA hNERGIYA
EDITORIAL BOARD
A. I. Alikhanov
A. A. Bochvar
N. A. Dollezhal'
V. S. Fursov
I. N. Golovin
V. F. Kalinin
N. A. Kolokollsov-
(Asaistant Editor)
A. K. Krasin
A. I. Leipunskii
V. V. Matveev
M. G. Meshcheryakov
M. D. Millionshchikov
(Editor-in-Chief)
P. N. Palei
V. B. Shevchenko
D. L. Simonenko
V. I. Smirnov
A. P. Vinogradov
N. A. Vlasov
(Assistant Editor)
SOVIET ATOMIC
ENERGY
A translation of ATOMNAYA ENERGIYA,
a publication of the Academy of Sciences of the USSR
? 1966 CONSULTANTS BUREAU, A DIVISION OF PLENUM PUBLISHING
CORPORATION, 227 West 17th Street, New York, N. Y. 10011
Volume 19, Number 6
December, 1965
CONTENTS
RUSS.
THE DEVELOPMENT OF ACCELERATORS IN NOVOSIBIRSK PAGE PAGE
General Review of the Project -.G. I. Budker
Operational Status of the VEP-1 Electron Storage Rings?G. I. Budker, N. A. Kushnirenko,
A. . Naumov, A. P. Onuchin, S. G. Popov, V. A. Sidorov, A. N. Skrinskii,
and G. M. Tumaikin
Operational Status of the VEPP-2 Positron-Electron Storage Rings?V. L. Auslender,
G. A. Blinov, G. I. Budker, M. M. Karliner, A. V. Kiselev, A. A. Livshits,
S. I. Mishnev, A. A. Naumov, V. S. Panasyuk, Yu. N. Pestov, V. A. Sidorov,
G. I. Sil'vestrov, A. N. Skrinskii, A. G. Khabakhpashev, and I. A. Shekhtman
A High-Current Positron Source?G. I. Budker
Experiments on Charge-Exchange Injection of Protons into a Storage Ring
?G. I. Budker, G. I. Dimov, A. G. Popov, Yu. K. Sviridov, B. N. Sukhina ,
and L. Ya. Timoshin
Concerning the Possibility of a Self-Sustaining Thermonuclear Reaction in a Mirror
Machine?D. V. Sivukhin
Reduction in Radioactive Discharges to the Atmosphere and Study of Water Deaeration
Practice in the Primary Loop of the VVR-M Reactor?D. M. Kaminker,
K. A. Konoplev, Yu. P. Semenov, and V. D. Trenin .
Diffusion of Uranium in Molybdenum, Niobium, Zirconium, and Titanium
?L. V. Pavlinov, A. I. Nakonechnikov, and V. N. Bykov
Use of Concretes for High-Temperature Shielding of Nuclear Reactors?V. B. Dubrovskii,
N. V. Krasnoyarov, M. Ya. Kulakovskii, B. K. Pergamenshchik, M. S. Pinkhasik,
and V. I. Savitskii
NOTES ON ARTICLES RECEIVED
Calculating the Dipole Moment of a Cylindrical Slug?B. P. Kochurov
Reduction in the Thermal Neutron Flux Caused by a Hollow Channel in the Reflector
?A. S. Kochenov
Applicability of Various Approximations of the Method of Spherical Harmonics
for Calculating the Transmission of Neutrons Through Shields?N. A. Artem'eva,
K. K. Popkov, S. M. Rubanov, and L. S. Shkorbatova
Calorimetric Dosimetry of Gamma Radiation from Nuclear Reactors?V. M. Kolyada
and V. S. Karasev
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1467
498
1472
502
1476
505
1479
507
1482
510
1489
517
1495
521
1498
524
1504
530
1505
530
1507
531
1508
532
Annual Subscription: $95 Single Issue: $30
Single Article: $15
rAll rights reserved. No article contained herein may be reproduced for any purpose whatsoever
without permission of the publisher. Permission may be obtained from Consultants Bureau, A
Division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011, U.S.A.
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CONTENTS (continued)
Determination of the Surface Relief of Materials by Means of Reflected Gamma
RUSS.
PAGE PAGE
Radiation?P. L. Gruzin, V. N. Afanas'ev, and V.0. Gaiduchik
1509
533
Rules for Depositing Articles
1510
533
LETTERS TO THE EDITOR
On the Oscillation Decrements in Accelerators in the Presence of Arbitrary Energy Losses
?A. A. Kolomenskii
1511
534
Uniform Irradiation of the Surface of Specimens with Pulsed Electron Beams
?Yu. S. Ryabukhin, A. G. Vasil'ev, and A. N. Belyakov
1514
535
Optimum Control of Thermal Processes in Nuclear Reactors?I. M. Kurbatov,
M. P. Leonchuk, and A.S. Trofimov ? ? . ..
1518
537
Conditional Separation of Spatial and Angular Variables in Solving the Transport
Equation for Neutrons?V. V. Khromov and I. S. Slesarev
1523
540
Determination of Uranium (VI) in Carbonate Solutions by Absorption in the Short-Wave
? UV-Region?T. S. Dobrolyubskaya
1526
542
Statistical Characteristics of Functional Count-Rate Meters?V. M. Skatkin
1529
544
Corrosion Resistance of Structural MateriaVin Boron-Containing Solutions
?V. N. Belous, A. I. Gromova, E. T. Shapovalov, and V. V. Gerasimov
48
546
SCIENCE AND ENGINEERING NEWS
[XX International IUPAC Congress?L. T. Bugaenko
[IUPAC International Symposium on the Properties and Applications of Low-Temperature
Plasma?L. P. Kudrin
550]
553]
II All-Union Conference on Low Temperature Plasma Generators?L. P. Kudrin
1536
559
[Current Trends in Activation Analysis (College Station, Texas)?G. I. Kir'yanov
561]
NEWS AND COMMUNICATIONS
[Atoms for Peace (Budapest International Industrial Fair, May, 1965)
564]
[West German Nucleonic-Instruments Exhibit (Moscow, July, 1965)
566]
INDEX
Author Index, Vols. 18 and 19, 1965
1541
Tables of Contents, Vols. 18 and 19, 1965
1547
NOTE
The Table of Contents lists all material that appears in Atomnaya gnergiya. Items originally published
in English or generally available in the West are not included in the translation and are shown in
brackets. Whenever possible, the English-language source containing the omitted items is given.
The Russian press date (podpisano k pechati) of this issue was 12/6/1965.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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THE DEVELOPMENT OF ACCELERATORS IN NOVOSIBIRSK*
GENERAL REVIEW OF THE PROJECT
(UDC 621.384.60)
G. I. Budker
Translated from Atomnaya tnergiya, Vol. 19, No.
pp. 497-498, December, 1965
Original article submitted October 15, 1965
Part of the program of the Institute of Nuclear Physics, Siberian Division of the Academy of Sciences, USSR,
devoted to accelerators, consists in the development of plasma accelerators, iron-free pulsed accelerators, facilities
with colliding particle beams and special accelerator facilities for industry.
The Institute for Nuclear Physics has existed in Siberia since 1961, but operations were commenced several
years earlier in Moscow in the Laboratory for New Methods of Acceleration, I. V. Kurchatov Institute of Atomic
Energy, from which the Novosibirsk Institute was subsequently organized.
Operations on plasma accelerators are undertaken with facilities for investigating the so-called stabilized
electron beam. The basic idea of these operations consists in an attempt to utilize the powerful field of the self-
?
focussing closed relativistic electron beam for retaining the accelerated ions in orbit. These operations are proceed-
ing more slowly than would be desired. At present it can only be reported that we have produced a closed beam of
relativistic electrons at 130A, At the present time the assembly of the high-voltage internal injector on a spiral
ridge apparatus is completed and during next year we are hoping to increase several times the magnitude of the
circulating current. This makes it possible to proceed with a study of the phenomenon of constriction of the beam
into a narrow cord.
Operations on iron-free accelerators are being concentrated principally around single-turn accelerators with
shaping of the magnetic field by the form of the conducting surfaces, which should be accomplished by virtue of the
small thickness of the skin layer as a result of operating the accelerator on short pulses.
At the previous conference we spoke about certain accelerators being started-up in Novosibirsk. Moreover, a
number of models have been tested for planning electron accelerators, including accelerators with colliding pro-
ton beams.
As a result of these operations, confidence has built-up that for our type of laboratory the installation of high-
energy iron-free proton accelerators is certainly more reasonable than the installation of iron proton accelerators.
Certain experimental advantages of iron-cored accelerators .by no means compensate for the many-fold increase of
the cost in comparison with the cost of iron-free accelerators.
However, we have ceased development of a project for an iron-free proton accelerator of 500-1000 GeV with
a field of 200 kgauss and also an iron-free accelerator with colliding proton beams of 2 ? 12 GeV associated with
advances in the creation of superconductors. It may prove that during the time of construction of the high-energy
pulsed accelerator the technology and manufacture of superconducting materials will attain such a level that iron-
free pulsed accelerators might depreciate due to absolescence as they are constructed. In the solution of this pro-
blem we are standing at the crossroads.
Lately, we have obtained extremely satisfactory results in the development of accelerators for industrial pur-
poses. Recently, we have started up an electron accelerator of the high-voltage transformer type with a tube operat-
ing at the commercial frequency of 50-60 cps, with an electron energy of 1.5 MeV and a beam intensity of 25 kW
extracted in air. The efficiency of the accelerator exceeds 90%. The outside of the accelerator is a tank with a
diameter of 1.2 m and a height of 2.0 m without any external high-voltage or electronic equipment whatsoever. In
* Report read by G. I. Budker at the International Conference on High-Energy Accelerators (Frascati, Italy).
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the near future it is proposed to start up an accelerator of this same type with an energy of 3 MeV, and also a simi-
lar pulsed accelerator with considerably smaller dimensions. We are also proposing to utilize the accelerators as
electron and positron injectors in a synchrotron.
At the present time, two colliding beam devices are operating in the Institute. Experiments are being carried
out on the VP-1 electron-electron colliding beam apparatus concerned with the scattering of electrons by electrons
at large angles. Experiments have only just commenced on the VEPP-2 electron-positron colliding beam equip-
ment, with a maximum energy of 2 ? 700 MeV. An assembly is planned for light particles at high energies, and also
colliding proton beam equipment.
In all the devices we do not combine in any way the injection energy with the limiting energy of the storage
device. The energy of the injector is considerably lower. Acceleration up to the limiting energy is accomplished
in the storage device by raising the magnetic field after accumulation of the particles. This will be managed quite
inexpensively and it will complicate operation only trivially.
The experiments on colliding beams are being carried out under the direction of A. A. Naumov. and the
author of this paper.
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OPERATIONAL STATUS OF THE VEP-1 ELECTRON STORAGE RINGS
G. I. Budker, N. A. Kushnirenko, A. A. Naumov,
A. P. Onuchin, S. G. Popov, V. A. Sidorov,
A. N. Skrinskii, and G. M. Tumaikin
Translated from Atomnaya tnergiya, VoL 19, No. 6,
pp. 498-502, December, 1965
At the last accelerator conference in 1963, a report was given on the construction of the VEP-1 machine in-
tended for electron-electron scattering experiments at energies up to 2 ? 130 MeV [1]. By that time, the first ex-
periments on electron storage in a single magnetic track had been carried out with the machine. In the work which
has gone on during the past two years, it is possible to distinguish the following basic stages: simultaneous storage
of electrons in the two tracks, an investigation of some of the interaction effects of the two beams [2], and measure-
ments of the luminosity of the machine for electron-electron scattering in the angular range 45-90?.
The VEP-1 machine. A general sketch of the machine is shown in Fig. 1. Its basic elements are two paired,
high-vacuum, magnetic tracks, a special B-2S electron synchrotron, an electron-optical channel, and a system for
single-turn extraction of the beam from the accelerator and for injection into the storage rings [1, 3].
The radius of the storage ring magnetic tracks is 43 cm, and the aperture, 3 ? 4 cm. Opposite the point of
tangency of the orbits, slits have been made in the common portion of the magnet poles in order to extract the
electrons scattered at the point of intersection of the beams. The median plane of the storage rings is vertical.
The storage ring resonators operate at the second harmonic of the electron rotational frequency. In addition
to resonators and inflectors, each storage ring is equipped with several mechanical probes, a system for optical ob-
servation of the beam, plates for controlling the position and transverse dimensions of the beam, and apparatus for
varying and measuring the frequency of the betatron oscillations of the particles. The problems of electron beam
observation in a storage ring and of controlling the parameters of the beam are given in [4].
The energy at which the electrons are injected in the storage ring is 43 MeV. A special, iron-free, B-2S syn-
chrotron with spiral electron storage [3] is used as an injector. The current extracted from the synchrotron beam in
a pulse less than 5 nsec long is about 300 mA (more than 1010 particles). The energy spread does not exceed 0.2%.
The accelerator pulse repetition rate is once every 15 sec.
4 3
Fig. 1. General sketch of the VEP-1 machine: 1) compensating
magnets; 2) storage ring magnets; 3) resonators; 4) inflectors; 5)
titanium pump; 6) external vacuum chamber; 7) quadrupole len- ,
ses; 8) switching magnet; 9) correction coil; 10) bending magnet;
11) radiation and magnetic shield; 12) correction magnets; 13) in-
jector ? B-2S synchrotron.
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T, sec\
.100
200
100
x P.4x/.9-8mm Hg
uP=8x/0-8mm Hg
20 40 60 80 1, rriA
Fig. 2. Electron lifetime as a function of the
amount of beam current; energy, 43 MeV;
resonator voltage, 5 kV.
8
5
10 /1 30 40 50 I, mA
Fig. 4. Azimuthal dimension of a bunch as a func-
tion of the amount of beam current; energy, 43
MeV; resonator voltage, 5 kV.
10 20 30 40 I, mA
Fig. 3. Radial (ar) and axial (as) dimensions
of a bunch as a function of the amount of beam
current; energy 43 MeV, P = 8 ? 10-8 mm Hg.
Fig. 5. Diagram of counter locations for re-
cording electron-electron scattering at small
angles: 1) point of intersection; 2) scintil-
lation counters.
A great deal of the work with a beam in the storage rings was carried out at the injection energy. In that
situation, each injector pulse was used for the addition of electrons into one of the tracks of the storage rings. Work
at higher energies was broken down into cycles approximately 10 min long. Only half the cycle time was used for
measurement; the rest of the time was taken up by electron storage and by variation of the magnetic field intensity
in the tracks.
Electron storage. Despite the fact that one has managed to inject a current greater than 100 mA into the
storage rings in a single pulse, the average injection pulse does not exceed 10 mA. The stability of the injection
mode leaves room for improvement. The maximum current in either of the tracks of the storage rings has been
200 mA. A limitation is imposed by the instabilities which arise through interaction of the beam with the reasonator [5].
The dependence of electron lifetime in the storage rings on the amount of beam current is shown in Fig. 2
for an energy of 43 MeV.
A representation of the transverse dimensions of the beam at 43 MeV and their dependence on the amount of
stored current is shown in Fig. 3. The measurements were made by means of a photomultiplier and a high-speed
shutter, on which an image of the observed beam was projected, located in front of the photomultiplier. The results
are in agreement with estimates of the deterioration of the vacuum in the beam because of compensation of its
charge by ions of the residual gas.
The radial dimension of the beam is greater than the axial because of the contribution of radial phase oscil-
lations. Their amplitude also increases with increasing beam current as can be seen from Fig. 4 which shows the
dependence of azimuthal dimensions of a bunch on the amount of beam current. The measurements were made with
a resolution of about 1 cm by means of an electron-optical converter. It is of interest to note that an artificial in-
crease in transverse dimensions of the beam leads to a reduction of the phase dimensions of a bunch.
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?(_
15
10
1.5
10
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A
dr
-3
-2
a
2 6t, mm
-08 -06 -0.4 -02 0 02
04 0.6.AZ mm
-10 -8 -6 -4 -2 0 2 4 6 dy, cm
Fig. 6. Dependence of intersection efficiency on
beam thinning in the radial (a) and axial (b) di-
rections and on thinning out of bunches in phase
(c). The number of counts per millicoulamp is
plotted on the ordinate; measurements were made
for approximately 15 mA currents in each beam;
the solid lines are calculated curves; normaliza-
tion was done at the maximum count.
With an increase in electron energy, the transverse beam
dimensions are reduced. In our case, this leads to an increase
in the role of the ADA effect and to a sharp reduction in beam
lifetime. Artificial increase in the radial dimension of the
beam saves the situation.
Luminosity measurements. The final adjustment of the
machine, and check on the efficiency of the intersection
process, is performed by observing electron-electron scatter-
ing at small angles. The large cross section for this process
makes it possible to find the optimal operating conditions
without significant expenditure of time while varying the
numerous parameters of the machine.
The experimental geometry is shown in Fig. 5. Each
magnetic track of the storage rings had two scintillation
counters located at a quarter of a betatron oscillation from
the point of intersection on the beam path. The counters
were connected in pairs in two coincidence circuits with an
effective resolving time 2r = 4.5 nsec (the spacing between
two bunches in orbit).
The counter system recorded pairs of electrons which
were scattered at an angle of approximately 1.5?. The effec-
tive scattering cross section, integrated over the angle covered
by the two pairs of counters, was 200/y2 b, or 30 mb, 43 MeV
electrons. The work was done at a background level (random
coincidences) comparable to the magnitude of the signal. The
background was measured by parallel coincidence circuits
with a delay in one of the branches.
The number of counts in such a system, normalized to
the integral of the product of the two beam currents over the
time of measurement, can serve as a measure of the effici-
ency of the intersection process. A convenient unit of meas-
urement for this integral is the coulamp (short for coulomb-
ampere). In an hour of operation, the machine can produce
up to 3 coulamps. The average current in each of the tracks
is about 30 mA. Operation at higher currents is inefficient
because of the rapid intensification of "intersection effects" [2].
In Fig. 6 are shown the results of measurements of the
intersection efficiency as a function of beam displacements
in the radial and axial directions and of phase separation of
the bunches. The shape of the curves is in good agreement
with data on bunch dimensions. The absolute value of the
counts is several times less than expected. The discrepancy,
apparently, can be attributed to the inaccuracies of the geo-
metrical conditions of the experiment. A suggestion having
to do with coherent oscillations of a special kind which re-
duce intersection efficiency is in disagreement with data on
the effect of transverse beam dimensions on intersection effi-
ciency. Independently of the fact that an increase in trans-
verse dimensions might be produced by artificial excitation
of betatron oscillations or by intersection effects [2], the ob-
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lEsimraliziamv
?
2 2
Fig. 7. Diagram of the arrange-
ment of the detection system: 1)
vacuum chamber; 2) spark
chambers; 3) prisms; 4) scintil-
lation counters; 5) camera; 6)
magnet for upper track.
60 90
I20e, deg
Fig. 8. Angular distribution of elec-
tron-electron scattering. A calculated
curve for the Moeller cross section
is shown.
served reduction in counting rate is in good agreement with calcula-
tions performed for "purely incoherent" dimensions.
The value of the luminosity, defined as the quotient of the division of
the observed count rate by the effective cross section for the process, was, in
order of magnitude, 1022 cm-2? sec-1. It agreed with the initial results of
experiments on double bremsstrahlung observed in electron-electron scattering.
Initial electron-electron scattering experiments. In Fig. 7 is shown a
diagram of an experiment to measure the angular distribution for electron-
electron scattering in the range 45-90?. The detection system consisted of
four cylindrical spark chambers with a vertical axis which passed through the
point of intersection of the beams. A camera objective was located on the same axis; the prism system used had
axial symmetry. A second coordinate of the track was measured by means of tilted mirrors which were located
underneath the spark chambers.
Triggering of the spark chambers was accomplished by a coincidence circuit which was connected to two
groups containing five scintillation counters each.
The solid angle of the detection system was limited by the aperture of the slit in the body of the storage ring
magnet. The effective cross section of Moeller scattering, integrated over that solid angle, was 100/y mb.
In the first experiments, performed at an electron energy of 43 MeV, the spark chamber system was triggered
more than 300 times per coulamp; further, about 10 pictures corresponded to the detection of electron-electron
scattering, which did not disagree with our ideas about the value for the luminosity of the machine. Test measure-
ments with phase thinning of the electron bunches showed that the background did not exceed 10%. The result of
preliminary analysis of the pictures is shown in Fig. B. It is clear that the deviation from the calculated curve for
electron-electron Moeller scattering does not exceed the statistical error:
At the present time, experiments at an electron energy of 100 MeV are getting under way on the machine.
LITERATURE CITED
1. V. N. Baier et al., Proceedings of the International Conference on Accelerators (Dubna, 1963) [in Russian],
Moscow, Atomizdat (1964), p. 274.
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2. G. N. Kulipanov, Experimental data on the interaction of beams at intersection [in Russian], Report Presented
by the USSR at the International Conference on Accelerators, Frascati (1965).
3. E. A. Abramyan et al., see [1], p. 1065.
4. E. I. Zinin et al., System for control and monitoring parameters of the electron beams in the VEP-1 storage
rings [in Russian], Report Presented by the USSR at the International Conference on Accelerators, Frascati (1965).
5. V. L. Auslender et al., Report Presented by the USSR at the International Conference on Accelerators, Frascati
(1965).
141.1
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OPERATIONAL STATUS OF THE VEPP-2 POSITRON-ELECTRON
STORAGE RINGS
V. L. Auslender, G. A. Blinov, G. I. Budker,
M. M. Karliner, ?A. V. Kiselev, A. A. Livshits,
S. I. Mishnev, A. A. Naumov, V. S. Panasyuk,
Yu. N. Pestov, V. A. Sidorov, G. I. Sil'vestrov,
A. N. Skrinskii, A. G. Khabakhpashev, and I. A. Shekhtman
Translated from Atomnaya tnergiya, Vol. 19, No. 6,
pp. 502-505, December, 1965
The construction of the VEPP-2 machine planned for experiments with positron-electron interactions at ener-
gies up to 2 ? 700 MeV has been reported [1]. In the work that has gone on in the past two years, the following
fundamental stages can be pointed out: start-up of the synchrotron-injector; production of large electron currents
in the storage rings; investigation of the instabilities associated with the beam-resonator interaction [2], and posi-
tron storage. At the present time, work is going forward with the VEPP-2 machine on a study of the interactions of
the two beams and on measurement of the luminosity by positron-electron scattering at small angles.
VEPP-2 machine. An overall diagram of the machine is shown in Fig. 1. It consists of a B-3M synchrotron
with external injector, high-vacuum magnetic storage rings, a system for single-turn extraction of the beam from
the synchrotron and its injection into the storage rings, an electron-optical channel, and a converter for transform-
ing an electron beam into a positron beam. All these elements have been described in detail [1, 3].
The special B-3M synchrotron used as accelerator-injector is operating at the present time at a reduced level
with energies up to 200 MeV; the current extracted from the synchrotron beam in a pulse less than 20 nsec long
reaches 100 mA (more than 1010 particles); the energy spread does not exceed 0.2%; the repetition rate of the ac-
celeration pulses is ?3 Hz. Work on the start-up of the B-3M synchrotron is the subject of a report presented at the
conference on accelerators in 1963 [4].
The storage ring is a weak-focussing racetrack with four identical straight sections. The radius of the equi-
librium orbit is 150 cm, the length of the straight sections, 60 cm, and the chamber aperture is 8 ? 14 cm2. Two
straight sections are used for the injection of electrons
and positrons; a high-frequency resonator is located in
the third, and the straight section opposite the reso-
S nator is intended for experimental work.
?6Y63
View along A
The high-frequency system of the storage ring
operates at the first harmonic of the particle rotational
frequency, 25.1 MHz. The resonator is coaxial, half-
wave, and highly loaded by a two-disc condenser; Q
is about 4000. At the present time, a 20 kW high-
frequency generator is being used which delivers volt-
ages up to 35 kV to the resonator.
In each quadrant, the two internal windings of
the electromagnet coil are supplied individually, which
ensures displacement of the median plane in each
6 I A quadrant by ? 1 cm. The actual position of the orbit
is adjusted by shunting the appropriate quadrants. To
Fig. 1. General diagram of the VEPP-2 machine: 1) in- control the relative position of the electron and posi-
jectors; 2)B-3Msynchrotron; 3)quadrupole lenses; 5) para- tron orbits in the vertical, in quadrants not having in-
bolic lenses; 4)bending magnets; 6)converter; 7)storage ring. flector plates, "separating plates" have been installed
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T,
sec
0
Fig. 2. Vertical section of the
collision region and detection
system; 1) current windings; 2)
electrostatic quadrupole; 3) col-
liding beams; 4) internal vacu-
um chamber; 5) external vacu-
um chamber; 6) "window"; 7)
scintillation counter; 8) "thin"
spark chambers; 9) shower
chamber; 10) range chamber;
11) shield; 12) scintillation
counter.
/0-4 /0-3 /0 /0- I, A
Fig. 3. Electron lifetime as a function of the amount
of beam current: 1) 100 MeV; 2) 200 MeV.
1,
msec
10
1111.
11111
S.
/0 SO /00 I, mA
Fig. 4. Dependence of damping time on beam
current with (1) and without (2) ions present.
on which dc voltages up to 50 kV can be applied making it possible to control
the collision angle of the electron and positron beams at the point of intersec-
tion to 10-2 rad, and also to separate the beams for storage.
By means of eight current windings located in the straight section where
the beams collide (Fig. 2), it is possible to control the frequency of betatron
oscillations in the range Au'A.' 0.1, and also to produce a frequency dependence
on the radius (dp/dR) 0.03 (quadratic nonlinearity) and amplitude of the betatron oscillations [dp/d(a2)] 0.04
(cubic nonlinearity). In the same straight section, an electrostatic quadrupole has been installed making it possible
to separate the betatron oscillation frequencies of the electron and positron beams by Ay 0.05. (The numerical
data given refers to an electron energy of 100 MeV.) In the rest of the system, control and monitoring of beam
parameters is similar to that used for the VEP-1 machine [5].
The long lifetime of the beam makes it possible to decouple the operating energy of the storage ring from
the injection energy. The required operating energy is established by an increase in the magnetic field after storage.
Electron storage. The basic work in studying the process of injection into the storage ring was carried out at
100 MeV. This energy corresponds to a radiation damping time of about 1 sec for the betatron oscillations, which
also determines the selected repetition rate for the injection cycle, 0.5 Hz. The electron storage rate achieved on
the machine was approximately 30 mA per injection pulse.
An electron current of about 0.5 A (1011 particles) was obtained in the storage ring. Limitations arose because of the
instabilities that were reproduced by beam-resonator interactions [2]. Transverse beam instabilities were not observed.
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If the betatron oscillation frequencies are well removed from dangerous resonance values, the electron life-
times for the natural dimensions of the machine and for currents greater than 1 mA are determined mainly by the
ADA effect [6]. The dependence of electron lifetime on the amount of beam current is shown in Fig. 3. The life-
time is 450 sec for a current of 100 mA and an energy of 100 MeV. The curves were obtained at a vacuum of ap-
proximately 3 ? 10-8 torr, which was obtained without baking the chamber. After baking, the lifetime was more
than 3 h for small currents. Then the energy of the stored beam was increased to 550 MeV for a resonator voltage
of 20 kV. The increased beam energy caused intense outgassing from the walls of the storage ring vacuum chamber
which was reduced by extended treatment.
When working with intense electron beams in the VEPP-2 storage ring, an interesting phenomenon was ob-
served. When beam betatron oscillations occurred in a time which was much less than the natural radiation damp-
ing time. In Fig. 4, the dependence of damping time on the amount of stored current is shown with and without ions
present. A dependence of damping time on betatron oscillation frequencies far from dangerous resonances was not
observed within the limits of accuracy of the measurements. It is possible that this effect is associated with reso-
nance excitation of electromagnetic oscillations in vacuum chamber elements.
Positron storage. The electron beam is converted into a positron beam by a tungsten foil located in the focal
plane of two "parabolic" lenses; the foil thickness is about one radiation unit [1]. For a focal distance of 10 cm,
the beam diameter at the converter foil is riot greater than 1 mm. Inclusion of the lenses increases the injection
efficiency about 20 times.
Work is going on with 200 MeV electrons and 100 MeV positrons. The positron storage rate that has been
achieved is about 0.3 AA per injection pulse, corresponding to a conversion coefficient efficiency of 10-8. The
maximum positron current recorded in the storage ring was 0.4 mA (108 particles).
At the present time, work is being done on increasing the positron storage rate.
Experimental arrangements. In order to carry out experiments involving the investigation of positron-elec-
tron interactions, a system of spark chambers has been assembled which covers a solid angle of 2 ? 0.7 sr about the
vertical direction.
First along the path of escaping particles (see Fig. 2) are spark chambers with thin plates for the determination
of the flight angle of the particles and the coordinates of the interaction point. A magnetic field directed along the
line of the beam intersection permits one to determine the sign of the charge on the detected particles. It will be
possible to determine the type of particle by the nature of its interactions with the material in the plates of the
"shower" and "range" spark chambers. A rather complicated system of mirrors makes it possible to use a single camera.
Triggering of the entire spark chamber system is produced by four scintillation counters 40 ? 40 cm2 in size
connected in a coincidence circuit. An anticoincidence counter 120 ? 120 cm2 acts as a shield against cosmic radi-
ation. Between this counter and the chambers, there is a layer of lead 20 cm thick.
At an energy of 2 ? 300 MeV and storage ring currents of 1 ? 100 mA2, such a chamber system enables one to
detect several positron-electron elastic scattering events per hour. The same order-of-magnitude counting rate is
expected for It-meson pairs at the maximum of the cross section curve corresponding to the formation of the inter-
mediate p-meson.
For adjusting beam intersection in the storage ring, for measuring luminosity and controlling it afterward dur-
ing operation, a system has been set up to measure positron-electron scattering at small angles similar to the one
used with the VEP-1 machine [7]. The scintillation counters in this system, located in the injection straight section
of the storage ring, are planned for detection of positron-electron pairs which have undergone scattering at ap-
proximately 1.5?.
To reduce overloading by the intense electron beam, the positron counter is shielded by lead and separated
into two individual counters located 10 cm from one another along the beam path and connected in coincidence.
A preliminary study of background conditions indicates a satisfactory state of affairs.
LITERATURE CITED
1. V. L. Auslender et al., Proceedings of the International Conference on Accelerators (Dubna, 1963) [in Russian],
Moscow, Atomizdat (1964), p. 247.
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2. V. L. Auslender et al., Phase instability of an intense electron beam in a storage ring [in Russian], Report Pre-
sented at the International Conference on Accelerators, Frascati (1965).
3. G. I. Budker et al., Proceedings of the International Conference on Accelerators (Dubna, 1963) [in Russian],
Moscow, Atomizdat (1964), p. 1065.
4. G. I. Budker et al., Start-up of the B-3M synchrotron ? an injector for the positron-electron storage ring [in
Russian], Report Presented at the International Conference on Accelerators, Frascati (1965).
E. I. Zinin et al., System for control and monitoring electron beam parameters in the VEP-1 storage ring [in
Russian], Report Presented at the International Conference on Accelerators, Frascati (1965).
6. C. Bemardini et al., Phys. Rev. Letters, 10, 407 (1963).
I 7 G. I. Budker et al., Operational status of the VEP-1 electron storage rings [in Russian], Report Presented at the
International Conference on Accelerators, Frascati (1965).
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A HIGH-CURRENT POSITRON SOURCE
G. I. Budker
Translated from Atomnaya gnergiya, Vol. 19, No. 6,
pp. 505-507, December, 1965
The method used for obtaining positrons with the BEPP-2 machine and other accelerators has an important
defect ? the low coefficient for conversion of the initial electron beam into the narrow, almost monochromatic,
positron beam needed for injection into an accelerator or storage ring.
The method proposed below for obtaining almost monochromatic positrons in a narrow angular interval
this failing and is a practical solution for the problem of positron storage. In addition, it offers the possibility of
constructing positron accelerators or of converting existing accelerators into positron accelerators of the same intensity.
The essence of the method is that positrons, produced from a beam of electrons of relatively low energy (5-
10 MeV) in a broad range of angles and energies, are slowed down in a special target to thermal or epithermal ve-
locities, are extracted from the target by an electrical field, and are then accelerated to injection energy.
Special attention should be directed to positronium formation and the combination of gas molecules with posi-
trons leading to removal of positrons from the system. By choice of gas, it is possible to make the formation of posi-
tronium during slowing down sufficiently small,because positronium is not formed at positron energies below a cer-
tain value (9 eV for argon). In those cases where an electric field is applied, the magnitude must be chosen so that
the positron temperature is less than this threshold.
Even in noble gases, the positron enters into chemical combination with the gas, forming an ionized molecule.
However, this process begins at energies below 1.5 eV. By chance coincidence of the numerical parameters, the
time for slowing down from 9 to 1.5 eV because of elastic collisions of positrons with molecules is close to the anni-
hilation lifetime for positrons so that one can neglect this effect. The presence of an electric field produces heat-
ing of the positron gas to several electron-volts, and the effect of molecule formation is additionally diminished.
There are two possible methods for carrying out this idea as well as a combination of the two.
The first method ? a continuous one ?involves an electric field applied to the target (gaseous, as a rule) so
weak that the equilibrium positron energy will be below the threshold for positronium formation. This requirement
defines a maximum positron drift velocity in the electric field which is independent of pressure. Because of mobili-
ty, the weak electric field draws the slow positrons to the
edge of the target. In the case of gaseous targets, a sharp
boundary is formed by differential pumping or by chilling.
Since all the positrons approach the target boundary with
C-71.) practically zero energy, they form a parallel, mono-
chromatic beam by further acceleration in a uniform
electric field.
-
Fig. 1. Sketch of positron source: 1) accelerator; 2)
electron source (cathode) at a voltage of 3 ? 106 V; 3)
1 A electron beam emerging from accelerator and in-
cident upon apparatus for converting electrons into 6
MeV positrons; 4) 3 MeV tandem accelerator; 5) appara-
tus for converting electrons into positrons, maintained at
3. 106V; 6) positronbeam, accelerated to 3 MeV.
1476
The target length and the gas pressure within it are
determined by the fact that a positron must succeed in
escaping from the target during its lifetime while moving
in the gas with drift velocity. Since the positron drift
velocity is fixed, the time to escape from the target is in-
versely proportional to target length. The positron life-
time in the target is inversely proportional to the density.
By equating these times, it is possible to find the target
thickness (g/mm2) which is approximately equal to the
slowing down distance for positrons with an energy of
several hundred keV. By locating the target in a magnetic
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Fig. 2. Diagram of apparatus
for converting electron to posi-
trons; 1) solid converter; 2)
gaseous target of the first kind;
3) 6 MeV electron beam; 4)
magnetic field lines; 4a, 4b)
magnetic mirrors; 5) potentio-
meter for longitudinal, extrac-
tion electric field; 6) system
for producing a sharp pressure
drop by pumping or chilling; 7)
electrodes for accelerating slow
positrons to 10 keV; 8) rarefied
gaseous trap of the second kind;
9) electrostatic plugs for con-
fining slow positrons; 10) sys-
tern for rapid extraction and ac-
celeration of stored positrons;
11) a system of magnetic louvers
which close the magnetic field
for the ejection of positrons into
space; 12) positron beam.
trap which lengthens the path of fast neutrons, it is possible to slow down posi-
trons with energies up to 500 keV and more in the same thickness. With an ini-
tial electron energy of 6 MeV, it is therefore possible to slow down a large part
of the positrons emitted from the converter, The effective coefficient for the
conversion of electrons into a narrow beam of positrons in this case is of the or-
der of 3 ? 10-5. Its smallness is associated with the low initial electron energy
and the correspondingly small number of positrons emitted from the converter.
With increasing initial electron energy, the conversion coefficient rises sharply.
In the case of a solid target, it is impossible to use the effect of a magnetic trap;
however, the simplicity of a solid target as compared with a gaseous one is de-
serving of consideration. Unfortunately, in solids, the slowing down process, posi-
tron annihilation, and drift in an electric field are considerably less clear than
in gases.
In the second, pulsed method, the target is located beforehand in a mag-
netic and electrostatic trap which captures fast positrons and does not emit slow
ones. Initially, no extraction field of any kind is applied to the gaseous target.
Positrons in the target are stored for a time of the order of their lifetime. This
time is 1 msec at an argon pressure of 1 torr. Then the positrons are extracted
from the target by a short, pulsed, longitudinal electric field. This makes it
possible to increase the pulsed value of the positron current in the ratio of storage
time to injection time. This ratio is large for linear accelerators and especially
so for cyclic accelerators with one-turn injection.
, To increase the storage time, it is necessary to make the target sufficient-
ly rarefied. For practically reasonable values of length (1 m) and pressure which
correspond to a lifetime of 1 msec, positrons with an energy of several tens of
keV are slowed down in the target. Therefore, it is possible to consider a com-
bination of the first and second methods where positrons with energies of the or-
der of 500 keV are slowed down in a trap of the first kind with an extracting
electric field and, being accelerated to 10 keV, arrive in a trap of the second
kind where they are once again slowed down to thermal velocities and stored
for 1 msec.
To illustrate the proposed method, we present a scheme for the combined
method without discussing the problem of reasonable choices for the numerical
values of the parameters.
We have two 3 MeV electron accelerators with a current of 1 A in a pulse
1 msec long. It is required to obtain a narrow, monochromatic beam of positrons
with maximum intensity in a pulse 3 ? 10-8 sec long for single-turn injection into
a synchrotron. Just such a problem is presented by our machine with colliding
electron-positron beams, and the necessary equipment was set up. With the usual
method of conversion, it is possible to obtain a positron current of the order of 10-6A.
A diagram of the pertinent equipment is sketched in Fig. 1, and a diagram of the equipment for converting
electrons into positrons is shown in Fig. 2.
The length of each trap is ?1 m. Pressure in the first trap is 100 torr (argon or xenon), in the second, it is
less than 1 torr. The coefficient for the conversion of electrons in target 1 (see Fig. 2) into positrons with energies
that could be slowed down in the gas,including positron capture in the magnetic traps, is of the order of 3 ? 10-5.
Storage time in the second trap is of the order of 1 msec; the time required for injection into the synchrotron is
3 ? 10-8 sec; the ratio of the times is 3 ? 104, and the conversion coefficient is ?1. Therefore the apparatus con-
sidered above makes it possible to inject a 1 A current of 3 MeV positrons which exceeds the electron current in or-
dinary synchrotrons and which matches the maximum electron current in the B-3M accelerator at the Institute of
Nuclear Physics, Siberian Section, USSR Academy of Science.
For higher initial electron energies, the conversion coefficient rises sharply, and the positron current begins to
be limited by the Langmuir law or by plasma phenomena.
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We have developed a model of the electron-to-positron converter on which experiments will be begun in the
near future.
Note added in proof. After this report was presented at the conference in Frascati, we discovered that a simi-
lar method for the production of narrow, monochromatic positron beams by slowing down fast neutrons in a gas was
proposed by F. P. Denisov, P. A. Cherenkov, and A. M. Gromov at the end of 1964 (unpublished).
At the same time, we discovered that K. Robinson, in February 1965, put forward the idea of positron storage
in a high-vacuum magnetic trap using radiation damping (Preprint CEAL-1016).
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EXPERIMENTS ON CHARGE-EXCHANGE INJECTION OF PROTONS
INTO A STORAGE RING
G. I. Budker, G. I. Dimov, A. G. Popov,
Yu. K. Sviridov, B. N. Suhkina, and I. Ya. Timoshin
Translated from Atomnaya nergiya, Vol. 19, No. 6,
pp. 507-510, December, 1965
Charge-exchange injection of protons into a storage ring was achieved in August 1964 on an experimental
machine, a diagram of which is shown in Fig. 1.
The first experiments were carried out on a weak-focussing storage ring with an aperture 8 ? 4 cm and orbi-
tal radius of 42 cm. A hydrogen jet was used as an ionizing target which was directed along-a radius from the cen-
ter of the ring and which was switched on by means of an electrodynamic gate in a time of 300-to 600 ?sec. The
transverse dimension of the jet at the orbit was ?1 cm. The proton yield in the orbit rose with increasing jet den-
sity. Monitoring of the proton beam showed that it diverged after emerging from the ionizing target because of the
latter's finite thickness, expanded radially to 1.7 cm after a quarter wave length of the radial betatron oscillations,
and was focussed to the original transverse dimension in 3-4 mm more than a half wave length. The vertical trans-
verse dimension of the beam in the first revolution (3-4 mm) was practically unchanged, and there was no notice-
able loss of protons.
For charge-exchange injection into a storage ring without an accelerating field (quasi-betatron mode), the
protons moved in a tightening spiral because of energy loss in the jet. Proton storage in this mode was observed by
the luminous intensity of the hydrogen jet, which was detected by a photomultiplier, and also by broad-band induc-
tion electrodes and targets at the inner wall of the circular chamber. For 1 MeV protons and injection length of
20 ?sec (100 revolutions), Fig. 2 shows oscillograms of the negative ion current in front of the neutralizing target
(a), of the proton current from the ionizing target (b), of the luminous intensity of the jet (c), and of the proton
current at the internal target (d). From the oscillogram of jet luminosity and from the corresponding induction
electrode signals, it is clear that during the 100 revolutions when the beam was being introduced into the storage
ring, the orbital current increased linearly and then remained constant for ?150 revolutions. During that time,
the orbital radius was reduced (which was observed by means of vertical induction electrodes), but the beam had
not yet reached the internal target. Then the beam struck the internal target. The charge incident on the internal
target was 100 times greater than the charge in the proton beam during the first revolution. The signal amplitude
from the induction electrodes during storage was also 100 times greater than the signal with a baffle introduced at
the end of the first revolution. The accuracy of these measurements was ?10%. The photomultiplier signal,
which recorded the jet luminosity, increased only by 40-50 times during storage,which is apparently associated
with the difference in the transverse distribution of the stored pro-
ton current and of the current in the first revolution. Similar re-
lationships were obtained for injection up to 250 revolutions. Thus
the injection efficiency is close to 100% for charge-exchange in-
_
I I) I
Fig. 1. Diagram of the machine for charge-
exchange injection of protons into a storage
ring: 1) source of negative hydrogen ions; 2)
accelerator; 3) input gaseous target; 4) hy-
drogen jet in orbit; 5) storage ring.
jection in the quasi-betatron mode.
Change-exchange injection of protons in the resonance mode
was achieved for accelerating voltage amplitudes up to 6 kV and
for a.frequency multiplicity equal to one. In this mode, the accel-
eratinghf-field compensates for the proton ionization energy loss.
An oscillogram of the signal from the resonance induction elec-
trodes is shown in Fig. 3 for the injection of 1 MeV protons in the
resonance mode during 1500 revolutions (injection time, 300 ?sec);
the accelerating voltage was 1.5 kV. In Fig. 4, oscillograms are
shown which are typical for capture in the resonance mode (energy,
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Fig. 2. Current oscillograms for proton in-
jection into a storage ring in the quasi-
betatron mode: a) current pulse in front of
neutralizing target; b) proton current pulse
on emergence from ionizing target; c) pho-
tomultiplier signal; d) proton current pulse
from internal target. Horizontal scale,
10 ?sec/cm.
1 MeV, injection time, 20 ?sec). The first two oscillograms (see
Figs. 4a, b) are the signals from the broad-band induction electrodes
without accelerating voltage and with an hf accelerating field. A
comparison of signal magnitudes shows that the linear density of the
protons captured in the resonance mode, at the center of a bunch, is
1.5 times greater than the density of stored protons in the quasi-
betatron mode. The third oscillogram (see Fig. 4c) shows the signal
from the resonance induction electrodes, the fourth (see Fig. 4d)
shows the signal from the inner target during storage in the resonance
mode. A comparison of the latter oscillogram with the signal from
the inner target during injection in the quasi-betatron mode (see
Fig. 2) shows that an approximately constant particle loss occurs
with capture in the resonance mode in contrast to the quasi-betatron
mode. Further, the protons escape mainly in the inner portion of
the ring (the signal from the outer target is many times less). Par-
ticle loss for resonance mode injection was 20-25%. In Fig. 5, os-
cillograms are shown of signals from the resonance induction elec-
trode for proton storage in the resonance mode after 500 and 1000
revolutions (energy, 1 MeV). The storage current in the resonance
mode increases linearly with time.
In our experiments, a hydrogen jet ?1017 atom/cm' thick was
used, the total cross section for proton loss because of scattering in
hydrogen was 4.5 ? 10-22, cm2/atom, and the effective number of
injection revolutions allowing for the buildup in oscillations because
of ionization energy loss in the jet was ?5000. For injection up to
1500 revolutions, the particle loss ought not to be more than a few
percent, therefore we were unable to observe experimentally the in-
crease in losses during storage. The constant 20-25% particle loss
during injection in the resonance mode was in satisfactory agree-
ment with the reduction in the azimuthal dimension of the separa-
trix because of energy loss.
In the initial experiments, a high-frequency source of negative hydrogen ions was used which had a maximum
direct current of 21 ?A at 400 W. The ion extraction system was probeless; the extraction voltage was 12 kV. A
feature of such a source is the suppression of secondary electrons in the charge-exchange channel of the extracting
electrode by a voltage of 250-300 V. With this source, a beam of negative hydrogen ions with intensity to 12 ?A
was obtained from the Van de Graaf accelerator. The beam was fed into the storage ring in pulses 1-300 ?sec long
1480
Fig. 3. Oscillogram of signal from induction electrodes for resonance mode injection. Horizon-
tal scale, 500 ?sec/cm.
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..,Mfrarirr.
kiimami
1111111 Ill
IIIPJIMIIIIIIIJ
'IIIIIIIIIIIIIII
III I
PENNI
iii1111111111
I i
a 111
Ea III
1111r=51111
ME ,
Fig. 4. Oscillograms typical of reso- -
nance mode capture. Horizontal scale,
10 ?sec/cm.
)1!0114111!11111]illi
-A-
?
Fig. 5. Oscillograms typical of resonance
mode proton capture after 500(a) and 100
(b) revolutions. Horizontal scale 50
?sec/cm.
which were produced by means of a cutoff condenser installed in the
ion duct. After focussing, the beam was introduced into a gaseous
neutralization target 3-4 mm in cross section and having an angular
aperture of 2 ? 10-3, which was made up in the form of a flow tube
5 cm long and 1 cm in diameter with associated diaphragms and dif-
ferential pumping. The gas was delivered into the flow tube in sepa-
rate pulses 1 msec long by means of an electromagnetic valve. The
beam of atomic hydrogen from the target was introduced into orbit
with an accuracy of ?1 mm in position and 2 ? 10 inangle. Energy
stability was ? 0.2%.
To obtain maximum atomic beam yield, we measured mass-
spectroscopically the cross section for neutralization of negative hy-
drogen ions in a number of gases (H2, N2, C2H2, C3H8, CO2, SF6,
CC12F2) at energies of 1-1.5 MeV. It turned out that the maximum
atomic beam yield depended slightly on the type of gas or the ener-
gy, and was 50-55%. In the neutralizing target, hydrogen or carb9n
dioxide gas was used with optimal thicknesses of 2.5 ? 1016 and 3. 1015
molecule/cm2, respectively.
In order to store large currents, an arc source of negative hydrogen ions with currents to 1 mA and pulse length
of 1 msec was installed in the Van de Graaf accelerator. With this source, a beam of negative ions with an intensi-
ty of 800 ?A was obtained from the accelerator which made it possible to store 1012 protons (current, ?1 A) in the
orbit of our machine.
Unfortunately, accelerator failure (breakdown of the compressed gas in the accelerating tube) delayed the
performance of experiments on the storage of large proton currents although everything else had been made ready.
Nevertheless, results of the preliminary experiments leave no doubt but that currents will be stored in the near
future which will be limited by space charge.
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CONCERNING THE POSSIBILITY OF A SELF-SUSTAINING
THERMONUCLEAR REACTION IN A MIRROR MACHINE
(UDC 621.039.6: 533.9)
D. V. Sivukhin
Translated from Atomnaya Energiya., Vol. 19, No. 6,
pp. 510-517, December, 1965
Original article submitted February 20, 1965
An investigation is made of the energy balance in thermonuclear reactors of various types employing
magnetic mirror trapping. Only the energy loss due to the escape of Particles through the mirrors is
taken into account. It is very likely that a self-sustaining thermonuclear reaction cannot be produced
in such devices.
The experimental and theoretical investigations carried out to date do not yield a definite answer to the ques-
tion of whether it is possible to obtain a self-sustaining thermonuclear reaction in a mirror machine. The main dif-
ficulty is usually taken to be the production in a trap of this kind of a stable plasma with the required temperature '
and density. We shall assume that the stage has been reached when these problems have been successfully overcome.
We shall be investigating the matter within the following narrow formulation: is it poSsible'to obtain a self-sustain- .
ing thermonuclear reaction in a mirror machine despite the continuous escape of particles through the mirrors? It is
clear that such a one-sided approach to the problem can yield only the necessary, but by no means sufficient, con-
ditions for the production of a self-sustaining thermonuclear reaction.
With our formulation of the problem, the fundamental and most difficult question that must be answered con-
cerns the mean containment time of an ion in the trap. The first attempt to answer.this question was made by
Budker [1]. He employed the Landau kinetic equation, and after some simplifying assumptions he obtained a com-
paratively simple formula for the containment time rcont. Budker's formula was obtained by the present author in
[2] by a somewhat different method. The latter paper brings out more clearly the nature of the simplifying assump-
tions underlying the conclusions. They are as follows:
1. It is assumed that particles escape as a result of coulomb collisions only, which change the directions of
the particle velocity vectors. As soon as the direction of the velocity vector comes within the escape cone, the par-
ticle ceases to be contained by the magnetic field and escapes from the trap. Other escape mechanism are not
taken into account.
2. It is assumed that the plasma consists only of electrons and identical ions. Only ion-ion scattering is taken
into account. The scattering of ions by electrons is less by a factor of about il(mi/me) ? (Te/Ti), and so is not to be
taken into consideration.
3. The trap is assumed to be sufficiently long that the magnetic field may be taken to be uniform over the
whole length except at the ends, where its intensity rises sharply.
4. Nuclear reactions are assumed to have no effect on the particle escape rate, which is valid provided the
combustion rate is not too high. It will be shown below that this condition must be satisfied very well in our case.
5. Ion sources are available for injecting new ions into the trap to replace those that escape. The velocity
spectrum of the sources is arranged so that a steady state with a quasi-Maxwellian velocity distribution is always
maintained within the trap. By such a distribution we mean one characterized by the function C (A) exp
where C (0) depends only on the angle 0 between the direction of the magnetic field and the particle velocity vec-
tor. The function C ) reduces to zero within the escape cone and on its surface.
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6. The problem is solved in the diffusion approximation, in which the true diffusion coefficients in velocity
space and the coefficients of dynamic friction are approximated by their values for a Maxwell distribution. For the
diffusion approximation to be valid, the mirror ratio R must be large (ln R>> 1).
Of these simplifying assumptions the most important are No. 6 and the related No. 5. It is difficult, however,
to estimate what effect they have on the final results. One must consequently view Budker's formula in an orienta-
tive light, and not as an exact relationship. For our purposes this formula is conviently written in the form
1.81:r1X (R), (1)
cont
where Ti is the mean ion relaxation time,
3 1/3mi TI2
8ItnLel ?
(2)
Here mi is the ion mass, n is the plasma concentration, e is the electron charge. L is the coulomb logarithm, Ti is
the ion temperature (erg). The function X (R) depends on the method of injecting the ions into the trap. It is best
to inject perpendicular to the magnetic field, since the containment time is then a maximum. For this case Budker
states that the function X (R) may be approximated by X (R) = 1g10 R. Although this approximation was obtained for
large R it is approximately valid, in fact, for any R, since in the limiting case of R = 1 this approximation yields
the correct result: reont = 0. In the subsequent calculations we shall leave the function X (R) undefined until we
come to work out the final numerical results, when we shall utilize the approximation X = 1g10 R. Since ions escape
mainly as a result of ion-ion scattering, we would expect that a more precise theory would also yield a proportional
relationship between Teem and ri, i.e., we ought to get an expression of the form of Eq. (1), but with a more ac-
curate function X (R). In principle X (R) may depend not only on the mirror ratio R, but also on any other parameters
characterizing the departure of the ion velocity distribution from a quasi-Maxwellian distribution.
The containment time is given by the expression reent = niNesc, where Nese is the number of ions escaping
per second from unit volume of the trap. In the steady state and in the absence of nuclear reactions, Nese equals
the number of ions injected per second into unit volume of the trap. In this case we have
cont= Nesc ?
(3)
The latter expression will be employed even when nuclear reactions do occur. This is permissible firstly because
the systems we are considering have small combusion rates, and secondly because the fast ions formed in nuclear
reactions are not scattered much themselves, and have a negligible effect on the scattering of other ions.
The question of the containment time was also investigated theoretically by Judd, McDonald, and Rosenbluth
[3]. Their calculations were based on the Landau kinetic equation, but without the assumption of a quasi-Maxwel-
lian velocity distribution. A nonstationary problem without plasma sources was considered. The following expres-
sion for the containment time is given in [3]
3 nt2
T
cont 4 / 1 / 1 N
miLe4 f (R).
-v-2- /
(4)
Here "I" and / I N denote respectively the mean reciprocal ion velocity and the mean reciprocal ion ve-
locity squared; the function ,f(R) is approximated well by the expression f(R) = lgio R. Equation (4) suffers, however,
from the same fault as Budker's formula. Its derivation is based on the arbitrary neglect of certain terms in the ki-
netic equation in order that this equation may be solved by the separation of variables. In the case of quasi-Max-
wellian distribution, Eq. (4) reduces to Eq. (1) with X = 0.8 lgio R. For a monoenergetic particle spectrum, Eq. (1)
is also obtained with X 3.3 lgio R; in this case we must take Ti = (2/3) 6i, where 6i is the ion kinetic energy.
The following are the main reactions of interest in the design of thermonuclear reactions
D D He2+ n + 3.25 MeV; (5)
D D T p + 4 MeV; (6)
T + D --> He4 + n + 17.6 MeV; (7)
He3 + D --> He4 + p 18.3 MeV. (8)
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The rates of these reactions have been worked out often enough. The most complete information is given in the
paper by B. N. Kozlov [4]. The calculated values of (au) are given in that paper, where a is the reaction cross sec-
tion, u is the relative velocity of the reacting ions; the angular brackets denote an average over a Maxwellian Ve-
locity distribution. These quantities are functions of temperature alone. The results of the calculations were pre-
sented by B. N. Kozlov in the form of empirical formulas with suitable correction factots. Kozlov estimates the
error in his calculations to be 2.5% for Eqs. (5)-(7), and 15% for Eq. (8). Table 1 shows the appropriate data ob-
tained by the present author on the basis of Kozlov's empirical formulas. The indices 1, 2, 3 denote deuterium,
tritium, and Hes respectively. The quantities (a u)rip and (a u)/in refer respectively to the proton to the proton and
neutron branches of the D-D reaction as a whole.
Suppose the trap contains a mixture of deuterium, tritium, and Hes with absolute Concentrations
n1, n2,1-1.3 (ni + n2 + n3 = 11),
and relative concentrations ar, a2, a3 [ai = (ni/n), al + a2 + a3 = 1]. Let Nr be the number of particles Which react
in 1 cm3 per second. The ratio
N, _ N,
Nesc. n Tcont, (9)
=
is called the combusion factor of the fuel mixture. The following expression can readily be found for this quantity
(a2, (a) -4- 2a1a2 (au)12+ 2a5a3 (au)13)ntc0nts (10)
The combustion factor is an important characteristic of a thermonuclear reactor, and it is of interest to work it out
for various temperatures and for injected fuels of different percentage compositions. For this purpose it is useful to
tabulate the values of the parameter y = (WA. This parameter is a completely defined function of temperature,
density, and fuel composition, and depends on the density through the coulomb logarithm L( y L). It is thus suffi-
cient to work out Y for a single value of the density, say n = 1014 cm-3. We consider reactors of four types.
1. A reactor working on pure deuterium (a1 = 1; a2 = a3 = 0)..
2. A reactor working on a mixture of equal amounts of deuterium and tritium (ar = a2 = 1/2; a3 = 0).
3. A reactor in which the deuterium concentration is taken equal to al = 1/2, He' having an equilibrium con-
centration." The latter concentration is determined by the condition that the amount of He' formed in Eq. (5) must
equal the amount of He' used up in Eq. (8), i.e.,
TABLE 1. Thermonuclear Reaction Rates [Values of (au) TABLE 2. Values of Parameter y = (R)/99] at n =
1014 cm-3
are expressed in crn3 ? sec-1]
1,
keV
lip,
x1016
11,0
x1016
11,
x1016
12,
x1016
12-
>dole
20
0,024
0,0245
0,048
4,54
0,041
30
0,048
0,050
0,098
6,72
0,154
40
0,074
0,079
0,153
7,92
0,349
50
0,098
0,108
0,206
8,27
0,578
60
0,132
0,140
0,272
8,48
0,827
70
0,150
0,170
0,320
8,54
1,06
80
0,175
0,202
0,377
8,54
1,26
90
0,199
0,232
0,431
8,45
1,43
100
0,223
0,260
0,483
8,36
1,58
200
0,433
0,525
0,958
6,71
2,19
300
0,600
0,735
1,34
5,52
2,30
400
0,745
0,910
1,65
4,68
2,28
500
0,865
1,04
1,90
4,07
2,26
600
0,975
1,1/
2,14
3,59
2,12
700
1,06
1,27
2,33
3,25
2,04
800
1,15
1,35
2,50
2,94
1,97
900
1,23
1,43
2,66
2,71
1,90
1000
1,30
1,50
2,80
2,50
1,85
1484
Ti; keV
First
type
Second
type
Third
type
Fourth
type
20
6,2.104
1,17-103
1,64.103
5,0-104
30
1,7.104
4,4-102
5,2-102
1;12.104
40
7,2.103
2,4.102
2,7.102
4,3.103
50
3,8.103
1,7.102
1,8.102
2,3.103
60
2,2.103
1,25-102
1,35-102
1,3.103
70
1,5.103
100
1,05.102
8,9.102
80
1,05.103
81
87
6,2.102
90
7,8.102
69
74
4,6-102
100
6,0.102
60
64
3,5.102
200
1,1.102
26
28
70
300
43
16,5
18
30
400
23
12,5
13,5
18
500
14,5
9,8
10,5
12
600
9,8
8,0
8,7
9,2
700
7,3
6;8
7,4
7,3
800
5,6
5,9
6,4
6,1
900
4,4
5,1
5,6
5,2
1000
3,6
4,6
4,9
4,5
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=-
n3 al
a3 ? =_- ?
n 2 (au)13
The third constituent is tritium, with a concentration a2 = 1/2?a3.
4. A reactor operating on an equilibrium mixture of deuterium, tritium, and He3. In this case
.=-? I?a2 ? aa;
T*.
T*;
(1)
The investigation of the dynamic properties of the thermal simulator of a nuclear reactor as an element of a
control system is continued in the present article. As in [1], the effect of the other elements of the power plant (the
heat exchangers, the circulation pump, the power level control system, etc.) on the transient processes in the reactor
is neglected.
Two problems are posed in the present article. The first consists in determining, for the assigned linear de-
pendence g(r), the discharge G(r) which would secure under transient conditions the least deviation from a linear
dependence 0(T, 1) of the outlet temperature:
1 6
0* (T)=---
6,
i.e., the problem consists in determining the minimum of the functional
CO
[0 , 1)-0* (r)]2 dr.
(2)
This condition makes it possible to determine the optimum rate of changing the power level of the plant.
In the other problem, it is assumed that the variation of g(r) can be arbitrary. The regulating parameters
(the functions G(r) and (ter) are found from the condition for the minimum time of the transient process. Such a
formulation of the problem is perhaps the most comprehensive one for a check of the potential possibilities of the
reactor dynamics.
I. We shall assume that the thermal processes in the reactor channel are described by means of a system of
partial differential equations [2]:
ao 00
0