Magnetic surfaces of a combined magnetic system
The existence of closed magnetic surfaces in a model of the combined magnetic system is shown by numerical simulations. The numeric model contains a magnetic system of the l=2 torsatron with the coils of an additional toroidal magnetic field and the mirror-type magnetic system. The mirror-type magne...
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| Zitieren: | Magnetic surfaces of a combined magnetic system / V.G. Kotenko, V.E. Moiseenko, Yu.F. Sergeev, E.L. Sorokovoy, O. Ågren // Вопросы атомной науки и техники. — 2012. — № 6. — С. 22-24. — Бібліогр.: 3 назв. — англ. |
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irk-123456789-1090912016-11-21T03:02:30Z Magnetic surfaces of a combined magnetic system Kotenko, V.G. Moiseenko, V.E. Sergeev, Yu.F. Sorokovoy, E.L. Ågren, O. Магнитное удержание The existence of closed magnetic surfaces in a model of the combined magnetic system is shown by numerical simulations. The numeric model contains a magnetic system of the l=2 torsatron with the coils of an additional toroidal magnetic field and the mirror-type magnetic system. The mirror-type magnetic system is realized by switching off one of the coils of an additional toroidal magnetic field. Численными расчетами показано существование замкнутых магнитных поверхностей в модели комбинированной магнитной системы. В состав модели входит магнитная система двухзаходного торсатрона с катушками дополнительного тороидального магнитного поля и магнитная система типа пробкотрон. Последняя реализуется путем отключения одной из катушек дополнительного тороидального магнитного поля. Чисельними розрахунками показано існування замкнутих магнітних поверхонь у моделі комбінованої магнітної системи. До складу моделі входить магнітна система двозаходного торсатрона з котушками додаткового тороїдального магнітного поля та магнітна система типу пробкотрон. Остання реалізується шляхом відключення однієї з котушок додаткового тороїдального магнітного поля. 2012 Article Magnetic surfaces of a combined magnetic system / V.G. Kotenko, V.E. Moiseenko, Yu.F. Sergeev, E.L. Sorokovoy, O. Ågren // Вопросы атомной науки и техники. — 2012. — № 6. — С. 22-24. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/109091 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Магнитное удержание Магнитное удержание Kotenko, V.G. Moiseenko, V.E. Sergeev, Yu.F. Sorokovoy, E.L. Ågren, O. Magnetic surfaces of a combined magnetic system Вопросы атомной науки и техники |
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The existence of closed magnetic surfaces in a model of the combined magnetic system is shown by numerical simulations. The numeric model contains a magnetic system of the l=2 torsatron with the coils of an additional toroidal magnetic field and the mirror-type magnetic system. The mirror-type magnetic system is realized by switching off one of the coils of an additional toroidal magnetic field. |
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Article |
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Kotenko, V.G. Moiseenko, V.E. Sergeev, Yu.F. Sorokovoy, E.L. Ågren, O. |
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Kotenko, V.G. Moiseenko, V.E. Sergeev, Yu.F. Sorokovoy, E.L. Ågren, O. |
| author_sort |
Kotenko, V.G. |
| title |
Magnetic surfaces of a combined magnetic system |
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Magnetic surfaces of a combined magnetic system |
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Magnetic surfaces of a combined magnetic system |
| title_fullStr |
Magnetic surfaces of a combined magnetic system |
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Magnetic surfaces of a combined magnetic system |
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magnetic surfaces of a combined magnetic system |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2012 |
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Магнитное удержание |
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http://dspace.nbuv.gov.ua/handle/123456789/109091 |
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Magnetic surfaces of a combined magnetic system / V.G. Kotenko, V.E. Moiseenko, Yu.F. Sergeev, E.L. Sorokovoy, O. Ågren // Вопросы атомной науки и техники. — 2012. — № 6. — С. 22-24. — Бібліогр.: 3 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-07T22:33:27Z |
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| fulltext |
22 ISSN 1562-6016. ВАНТ. 2012. №6(82)
MAGNETIC SURFACES OF A COMBINED MAGNETIC SYSTEM
V.G. Kotenko 1, V.E. Moiseenko 1, Yu.F. Sergeev 1, E.L. Sorokovoy 1, O. Ågren 2
1Institute of Plasma Physics NSC “Kharkov Institute of Physics and Technology”,
Kharkov, Ukraine;
2Ångström Laboratory, Uppsala University, SE-75121 Uppsala, Sweden
The existence of closed magnetic surfaces in a model of the combined magnetic system is shown by numerical
simulations. The numeric model contains a magnetic system of the l=2 torsatron with the coils of an additional
toroidal magnetic field and the mirror-type magnetic system. The mirror-type magnetic system is realized by
switching off one of the coils of an additional toroidal magnetic field.
PACS: 52.55.Hc
INTRODUCTION
In paper [1] as a fusion neutron source for the sub-
critical fast hybrid reactor the combined magnetic
plasma trap has been proposed. The organic parts of the
combined magnetic system are a stellarator-type
magnetic system and a common mirror-type magnetic
system. In paper [2] the magnetic field in the ideal
model of the combined magnetic system has been
studied. The model comprises the magnetic system of
l=2 torsatron with additional axisymmetric toroidal
magnetic field and a single current-carrying turn as an
element of the mirror-type magnetic system.
In this paper the magnetic field of the combined
magnetic system in regard to width of the l=2 torsatron
helical coils and the coils forming the necessary value
of the additional toroidal magnetic field is studied. The
mirror-type magnetic system is realized under by
switching off one of the coils of the additional toroidal
magnetic field.
CALCULATION MODEL
The main geometrical characteristics of the
computational model are similar to the design
characteristics of the U-2M torsatron [3]. The model
comprises the 16 coils of the additional toroidal
magnetic field. The mirror-type magnetic system is
realized under by switching off the coil 14 (Fig. 1).
The following technical characteristics of the real
helical coils were counted in the calculation:
- toroidicity a/Ro=0.2618, a is the minor radius of
the torus (average radius of helical coils), Ro is the
major radius of the torus;
- l=2 is the polarity;
- m=2 is the number of helical coil pitches along the
length of the torus;
- there are 20 conductor turns in each helical coil;
- counted along the torus parallels the width of each
helical coil S/Ro=0.782;
- each helical coil is splitted into two equal parts,
each part comprises 10 conductor turns;
- the parts are separated by diagnostic gap having
the width ΔS/Ro=0.17 along the torus parallels;
- the central line of the diagnostic gap is the helical
base line marked on the torus according to the equi-
inclined winding law θ(ϕ)=2arctg(1.3074tgϕ), where ϕ
is the toroidal angle and θ is the poloidal angle. The
base line is the helical line, along which a supporting
structure of the helical coil is assembled;
- the conductor turns are packed turn by turn
symmetrically relative to the helical base line on the
both side of the diagnostic gap.
Fig. 1. Top view of the magnetic system
of the l=2 torsatron numeric model. The position of
dead coil 14 of the additional toroidal magnetic
field is indicated
The following technical characteristics of the real
coils of the additional toroidal magnetic field were
counted in the calculation:
- the average radius of the coils is ac/Ro=0.4 (the
radial thickness of coil winding 0.113Ro is not taken
into consideration);
- the coils have cylindrical form, the cylinder height
h/Ro =0.086;
- the calculation model of the coil comprises 3 turns
of the thin conductor. The plane of the central turn of
the coil model agrees with meridian (poloidal) plane of
the torus. The rest 2 turns of the coil lie in the end
planes of the coil. The end planes of the coil are parallel
the plane of the central turns of the coil.
ISSN 1562-6016. ВАНТ. 2012. №6(82) 23
a
a
av
Ro
b
a
av
Ro
ϕ=0 ϕ=π/8 ϕ=π/4 ϕ=π
Fig. 2. Characteristic poloidal cross-sections (see Fig. 1) of the initial configuration of magnetic surfaces
in the calculated model of l=2 torsatron (a) and by switching off the coil 14 (b)
In the present calculations, the transverse
compensating magnetic field Bz is considered as
uniform. The magnetic surface configuration in the
torsatron with an additional magnetic field coils is
affected by the parameter Kϕ=1/(1+Bo/bo) too (Bo is
the value of the additional toroidal magnetic field on
the circular axis of the torus, bo is the amplitude of
the longitudinal component of the magnetic field
generated by the helical coils on the circular axis of
the torus).
RESULTS OF CALCULATION
Fig. 2,a and b show the poloidal cross-sections of
the magnetic surfaces for the calculation model. The
cross-sections are spaced round a toroidal angle ϕ=0,
π/8, π/4 and π (see Fig. 1). In the figures, the dashed
circle is the cross-section of a torus a/Ro=0.2618 with
traces of the conductor turns of the helical coils (large
black dots). The inner circle shows the cross-section of
the vacuum chamber (the minor radius av/Ro=0.2) in the
U-2M torsatron.
Fig. 2,a shows the cross-sections of the initial
(undisturbed by switching off the coil 14) configuration
of the magnetic surfaces. It is seen from the figure the
initial magnetic surface configuration has the plane
magnetic axis (magnetic axis minor radius rax=0) and
the last closed magnetic surface transcending of the
torus volume. The mode is realized at the compensating
magnetic field value Bz/bо=0.507 and additional
toroidal magnetic field value Bo/bо=3.12 (Kϕ=0.24).
The magnetic axis has the shape of the circle with major
radius Rax/Ro=0.916 lying in the torus midplane. The
average radius of the last closed magnetic surface
rlc/a=0.7 (rlc/Ro=0.18). The shape of the magnetic
surfaces in the ϕ=π cross-section coincides with the
shape in ϕ=0 − cross-section. The rotational transform
angle is iax→ilc=0.1→0.33, and there is a small
magnetic hill (U=0.077) in the configuration. The
mirror ratio ranges within γax→γlc=1.013→1.72,
γ=Bmax/Bmin, where Bmax and Bmin are the maximum and
minimum magnetic field strengths on the magnetic
surfaces.
In the Fig. 2,b the cross-sections of the magnetic
surfaces by switching off the coil 14 are presented. It is
seen from the Figure that the switching off results in the
magnetic surface configuration decrease, so the cross-
section size of the last closed magnetic surface doesn’t
transcend the dimension of the vacuum chamber. The
destruction of the periphery layer of the magnetic
surfaces of the initial configuration arises from the
appearance of a great value of the resultant magnetic
field radial component (along the minor radius of the
torus) nearby the dead coil 14 locality. The parameter
Kϕ=0.24→0.25 increase due to coil 14 switching off
affects the dimension of the configuration to the lesser
extent [3].
It is seen that all the cross-sections, following the
magnetic axis displacement, are displaced by ~0.1a
relative to the equatorial plane. As the magnetic axis
displaces, it is gradually changing from a plane one to a
spatial one with the minor radius value of rax/a<<1. The
magnetic surface shape and the average value of the last
closed magnetic surface radius are changing from one
cross-section to another. The average value of the last
closed magnetic surface radius is rlc/a=0.38 (rlc/Ro=0.1)
in the ϕ=0 cross-section. The values of rotational
transform angle, iax→ilc=0.09→0.18, and the mirror
ratio, γax→γlc=1.56→2.06, differ substantially from the
corresponding parameters of the initial magnetic surface
configuration, and being in the initial configuration the
magnetic hill vanished, -U=0.001.
The magnetic axis displacement value and direction
depend on the position of the dead coil within the limits
of a magnetic field period. For example, the magnetic
24 ISSN 1562-6016. ВАНТ. 2012. №6(82)
surface configuration shifts upward by switching off the
coil 16. With that there is not distinct dependence of the
magnetic surface parameters on the dead coil position.
CONCLUSIONS
The numerical calculations have demonstrated the
possibility of the closed magnetic surface existence in
the combined magnetic system. The system contains a
magnetic system of the l=2 torsatron with the coils of
the additional toroidal magnetic field and the mirror-
type magnetic system. The mirror-type magnetic system
is realized by switching off one of the coils of an
additional toroidal magnetic field. Consequently, the
cross-section of the initial magnetic surface
configuration diminishes and brings to conformity with
the dimension of vacuum chamber, and there appear a
magnetic field ripple with acceptable value at the
context of the proposal [1] on the magnetic axis.
REFERENCES
1. V.E. Moiseenko, K. Noack, O. Ågren. Stellarator-
mirror based fusion driven fission reactor // J Fusion
Energy. 2010, v. 29, p. 65-69.
2. V.G. Kotenko, V.E. Moiseenko. Influence of the
value of a single magnetic field ripple on the torsatron
magnetic surfaces. // Problems of Atomic Science and
Technology. Ser. «Termoyaderny Sintez». Moscow,
2011, v. 3, p. 74-80 (in Russian).
3. V.E. Bykov, A.V. Georgievskij, Yu.K. Kuznetsov,
V.V. Nemov, V.G. Peletminskaya, A.V. Khodyachikh.
Calculations of the Uragan-2M torsatron magnetic
configuration. // Problems of Atomic Science and
Technology. Ser. «Termoyaderny Sintez». Moscow,
1988, v. 2, p. 17-21 (in Russian).
Article received 06.09.12
МАГНИТНЫЕ ПОВЕРХНОСТИ КОМБИНИРОВАННОЙ МАГНИТНОЙ СИСТЕМЫ
В.Г. Котенко, В.Е. Моисеенко, Ю.Ф. Сергеев, Э.Л. Сороковой, О.Агрен
Численными расчетами показано существование замкнутых магнитных поверхностей в модели
комбинированной магнитной системы. В состав модели входит магнитная система двухзаходного
торсатрона с катушками дополнительного тороидального магнитного поля и магнитная система типа
пробкотрон. Последняя реализуется путем отключения одной из катушек дополнительного тороидального
магнитного поля.
МАГНІТНІ ПОВЕРХНІ КОМБІНОВАНОЇ МАГНІТНОЇ СИСТЕМИ
В.Г. Котенко, В.Є. Моісеєнко, Ю.Ф. Сергеєв, Е.Л. Сороковой, О. Агрен
Чисельними розрахунками показано існування замкнутих магнітних поверхонь у моделі комбінованої
магнітної системи. До складу моделі входить магнітна система двозаходного торсатрона з котушками
додаткового тороїдального магнітного поля та магнітна система типу пробкотрон. Остання реалізується
шляхом відключення однієї з котушок додаткового тороїдального магнітного поля.
|