Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field
By numerical solving of the particle motion equations the separation of carbon isotopes 12C and 13C in varies magnetic field configuration is considered. It is shown, that isotope separation can be improved considerably sampling of distribution of a magnetic field Чисельним рiшенням рiвнянь руху р...
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| Zitieren: | Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field / A.G. Belikov, V.G. Papkovich // Вопросы атомной науки и техники. — 2009. — № 5. — С. 57-59. — Бібліогр.: 3 назв. — англ. |
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Belikov, A.G. Papkovich, V.G. 2016-03-16T21:35:28Z 2016-03-16T21:35:28Z 2009 Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field / A.G. Belikov, V.G. Papkovich // Вопросы атомной науки и техники. — 2009. — № 5. — С. 57-59. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 28.60.+s https://nasplib.isofts.kiev.ua/handle/123456789/96467 By numerical solving of the particle motion equations the separation of carbon isotopes 12C and 13C in varies magnetic field configuration is considered. It is shown, that isotope separation can be improved considerably sampling of distribution of a magnetic field Чисельним рiшенням рiвнянь руху розглянуто подiл iзотопiв вуглецю 12C i 13C у двох рiзних конфiгурацiях магнiтного поля. Показано, що подiл iзотопiв можна значно полiпшити вибором розподiлу магнiтного поля. Численным решением уравнений движения рассмотрено разделение изотопов углерода 12C и 13C в двух различных конфигурациях магнитного поля. Показано, что разделение изотопов можно значительно улучшить выбором распределения магнитного поля. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ядернo-физические методы и обработка данных Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field Вплив розподiлу магнiтного поля на подiл iзотопiв у системi з гострокутною геометрiєю поля Влияние распределения магнитного поля на разделение изотопов в системе с остроугольной геометрией поля Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field |
| spellingShingle |
Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field Belikov, A.G. Papkovich, V.G. Ядернo-физические методы и обработка данных |
| title_short |
Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field |
| title_full |
Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field |
| title_fullStr |
Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field |
| title_full_unstemmed |
Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field |
| title_sort |
effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field |
| author |
Belikov, A.G. Papkovich, V.G. |
| author_facet |
Belikov, A.G. Papkovich, V.G. |
| topic |
Ядернo-физические методы и обработка данных |
| topic_facet |
Ядернo-физические методы и обработка данных |
| publishDate |
2009 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Вплив розподiлу магнiтного поля на подiл iзотопiв у системi з гострокутною геометрiєю поля Влияние распределения магнитного поля на разделение изотопов в системе с остроугольной геометрией поля |
| description |
By numerical solving of the particle motion equations the separation of carbon isotopes 12C and 13C in varies magnetic
field configuration is considered. It is shown, that isotope separation can be improved considerably sampling of
distribution of a magnetic field
Чисельним рiшенням рiвнянь руху розглянуто подiл iзотопiв вуглецю 12C i
13C у двох рiзних конфiгурацiях магнiтного поля. Показано, що подiл iзотопiв можна значно полiпшити вибором розподiлу
магнiтного поля.
Численным решением уравнений движения рассмотрено разделение изотопов углерода 12C и
13C
в двух различных конфигурациях магнитного поля. Показано, что разделение изотопов можно значительно улучшить выбором распределения магнитного поля.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/96467 |
| citation_txt |
Effect of magnetic field distribution on isotopes separation in system with acute-angle geometry of magnetic field / A.G. Belikov, V.G. Papkovich // Вопросы атомной науки и техники. — 2009. — № 5. — С. 57-59. — Бібліогр.: 3 назв. — англ. |
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| first_indexed |
2025-11-24T16:01:09Z |
| last_indexed |
2025-11-24T16:01:09Z |
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| fulltext |
EFFECT OF MAGNETIC FIELD DISTRIBUTION ON
ISOTOPES SEPARATION IN SYSTEM WITH ACUTE-ANGLE
GEOMETRY OF MAGNETIC FIELD
A.G. Belikov, V.G. Papkovich∗
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received July 7, 2009)
By numerical solving of the particle motion equations the separation of carbon isotopes 12C and 13C in varies magnetic
field configuration is considered. It is shown, that isotope separation can be improved considerably sampling of
distribution of a magnetic field
PACS: 28.60.+s
Theoretical analyses of isotopes separation in
cusp and some experiment confirmation of the pre-
dictions of the theory were conducted in [1]. Typ-
ical configuration magnetic lines of force in system
is shown in Fig.1. Because of nonadiabatic mo-
tion of a charged particle passing near the zero
field region (a magnetic field component along z-
axis is varying from its maximum magnitude at the
ends of the system to zero at its center) the tra-
jectories of particles experience appreciable changes.
r
z
0 1 2-1
zero magnetic �eld plane
left cusp
boundary
right cusp
boundary
Fig.1. Cusp magnetic field configuration
The particles, located at radius r0 relative to sym-
metry axis in the left cusp boundary, start in axial
direction with velocity v0. After crossing the plane
of zero magnetic field the particles having the same
initial conditions but small mass difference begin to
move on noticeably different trajectories. On the
left part of the system these particles are moving
performing small radial oscillations and they encircle
the axis in the right part of the system. In this re-
gion the most of their directed velocity converted to
transverse velocity. After passing of the system the
particles continue to move in homogeneous or near
homogeneous magnetic field. The subsequent calcu-
lation allowed to evaluate the permissible values for
the initial transverse velocities, exceeding of which
leads to deterioration of isotopes separation, and di-
mension of the region of injection. It was shown that
such system allows the separation both heavy and
light isotopes. More complete description of these
results is given in [2].
Although the trajectories of particles have been
calculated in different configurations of magnetic
field, as a rule, the isotopes of different elements were
considered. And this imposes some difficulties for es-
timation the advantage of one magnetic field distri-
bution in comparison to another one.
The trajectory of particle motion is characterized
by two nondimensional parameters: kr0 is a posi-
tion of a particle initial location, where k = π/2L,
2L is a distance between the planes where the max-
imum magnitude of magnetic field is reached; and
η = r0/rl, where rl = Mcv0/eH0 is Larmor radius,
which involves the initial particle velocity v0 along z-
axis, and a magnetic field strength H0 at the position
of particle location. If the magnetic field distribution
was given a condition for optimal isotope separation
can be found by changing of these parameters.
The purpose of this work is to compare the sep-
aration of isotopes of one and the same element in
different magnetic field configurations. The carbon
isotopes 12C and 13C were selected for that. In nat-
ural conditions carbon represents a mixture of two
isotopes . And in this mixture it is the order of 1.1%
isotope 13C contained. But it has many applications
in science and technologies.
∗Corresponding author E-mail address: papkovich@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2009, N5.
Series: Nuclear Physics Investigations (52), p.57-59.
57
As it is known [3] the solution for the magnetic
field component Hz and Hr in such system can be ex-
pressed in cylindrical coordinates by the sum of har-
monics. Each of these three harmonics is a product
of trigonometric and Bessel’s functions of imaginary
argument and zero or first order. The coefficients at
each harmonic can be found from boundary condi-
tions at the ends of system. In early works, when the
trajectories of particle motion were calculated, usu-
ally, the magnetic field distribution as a first term of
a series had been taken, and it can be written in the
following form:
Hz = −H0 sin(kz), Hr =
H0r
2
cos(kz) .
It is assumed that condition kr ¿ 1 was satisfied.
As a result of calculation it was found that there is
some critical meaning of parameter η (ηcr = 0.72).
When η exceeds ηcr the particle does not pass the
system because of reflection. In subsequent calcula-
tions it was found that quantity of ηcr can be much
closer to 1 when the magnetic field distribution as a
sum of several harmonics is taken. If we assume that
at the ends of system radial uniformity of the mag-
netic field at a distance at least bounded by trajec-
tory of a particle is fulfilled. Then for the magnetic
field of three harmonics the following expression can
be written
lHz =− 1, 17I0(kr) sin(kz)− 0, 13I0(3kr) sin(3kz)−
− 0, 01I0(5kr) sin(5kz),
Hr =1, 17 I1(kr) cos(kz) + 0, 13 I1(3kr) cos(3kz)+
+ 0, 01 I1(5kr) cos(5kz).
Fig.2. Distribution of carbon isotopes 12C and 13C
over the cross section at kz = 1.54 after passing the
magnetic field of the first harmonic, general solution
The calculation of the trajectories of particles
moving in a magnetic field distribution of the three
or four harmonics shows that the ranges of varia-
tion of the dimensionless parameters for the particles
passing through system can be notably expended. It
should be noted, that there are different ways for
selection of separated isotopes after they pass the
cusp. In some fixed plane kz = const near the exit
the particles of different masses will occupy differ-
ent regions of azimuthal angles over the cross section
in this plane. In axial direction the intervals where
these isotopes fall are shifted along z-direction.
In Fig.2 the distribution of carbon isotopes over
the cross section at kz = 1.54, after passing the mag-
netic field of the first harmonic, was shown. The
dimensions of the region of azimuthal angles occu-
pied by different isotopes are determined by initial
radial component of velocity and radial dimensions
of the region of injection. Parameters kr0 and η
in this calculation were of such that for particles
with initial radial velocity scattered in the range
0.02v0 > ṙ0 > −0.02v0 and radial dimension of in-
jection region 4r = 0.002 there were full isotope
separation.
In Fig.3 the regions of azimuthal angles for the
same isotopes, which they occupy after passing the
system with magnetic field distribution of three har-
monics, were shown. One can see that regions oc-
cupied by each isotope shifted on more than π/2.
The heavier isotope 13C is finishing its first turn
while a lighter one is traveling on the second turn.
In this case the interval of initial radial velocity is
two times greater than that in the case of the mag-
netic field of the first harmonic and the radial dimen-
sion of injection region is four times greater amount-
ing to 4r = 0.008. Radial intervals where isotopes
fall after they pass the system also are different.
For example in the plane kz = 2 the heavier iso-
tope 13C is within the radii 4r = 0.81 . . . 0.94, and
lighter one is within the radii of 4r = 0.5 . . . 0.85.
Fig.3. Distribution of carbon isotopes 12C and 13C
at kz = 2 after passing the magnetic field of three
harmonics
As it is possible to see from Fig.4 after some
shifting along kz (kz = 2.2) the intervals of ra-
58
dial positions, where separated isotopes locate, are
not overlapped. For 12C this interval is 4r =
0.5 . . . 0.7, and for 13C it is 4r = 0.9 . . . 1.0.
Fig.4. Distribution 12C and 13C isotopes at
kz = 2.2 after passing the magnetic field of three
harmonics
The displacement of the starting position of a
particle for some angle in azimuthal direction does
not change the regions of isotopes disposition over
cross section relative the one to another because of
the symmetry of the system. The whole picture in
the cross section of this plane is turning at the proper
angle. The appreciable improvement of the separa-
tion of isotopes with heavy atomic weights in the
magnetic field distribution of three harmonics is ob-
served too.
References
1. B.S. Akshanov, N.A. Khizhnyak. A new efficient
method isotope separation // Letters in ZhTF.
1991, v.17(6), p.13-16 (in Russian).
2. A.G. Belikov, V.G. Papkovich. On possibilities
of isotope separation in cusp magnetic field //
Problems of Atomic Science and Technology.
Ser. ”Plasma electronics and new methods of ac-
celeration”. 2004, N4, p.58-63 (in Russian).
3. K.D. Sinelnikov, N.A. Khizhnyak, N.S. Repalov,
et al. The investigation of charge particle mo-
tion in a magnetic trap of acute-angle geometry
// Fizika plasmu i problemu upravlayemogo ter-
mojadernogo synteza. 1965, N4, Kyiv: ”Naukova
Dymka”, p.383-402 (in Russian).
ВЛИЯНИЕ РАСПРЕДЕЛЕНИЯ МАГНИТНОГО ПОЛЯ НА РАЗДЕЛЕНИЕ
ИЗОТОПОВ В СИСТЕМЕ С ОСТРОУГОЛЬНОЙ ГЕОМЕТРИЕЙ ПОЛЯ
А.Г. Беликов, В.Г. Папкович
Численным решением уравнений движения рассмотрено разделение изотопов углерода 12C и 13C
в двух различных конфигурациях магнитного поля. Показано, что разделение изотопов можно значи-
тельно улучшить выбором распределения магнитного поля.
ВПЛИВ РОЗПОДIЛУ МАГНIТНОГО ПОЛЯ НА ПОДIЛ IЗОТОПIВ У СИСТЕМI З
ГОСТРОКУТНОЮ ГЕОМЕТРIЄЮ ПОЛЯ
А.Г. Бєлiков, В.Г. Папкович
Чисельним рiшенням рiвнянь руху розглянуто подiл iзотопiв вуглецю 12C i 13C у двох рiзних кон-
фiгурацiях магнiтного поля. Показано, що подiл iзотопiв можна значно полiпшити вибором розподiлу
магнiтного поля.
59
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