An l=2 torsatron with centered planar magnetic axis
The paper is concerned with properties of magnetic surface configurations that have the planar magnetic axis coincident with the circular geometrical axis of the torus. The calculations were performed for the model of an l=2 torsatron comprising additional toroidal magnetic field coils. The magnetic...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2008 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
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| Цитувати: | An l=2 torsatron with centered planar magnetic axis / V.G. Kotenko // Вопросы атомной науки и техники. — 2008. — № 6. — С. 37-39. — Бібліогр.: 6 назв. — англ. |
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Kotenko, V.G. 2017-01-06T13:08:33Z 2017-01-06T13:08:33Z 2008 An l=2 torsatron with centered planar magnetic axis / V.G. Kotenko // Вопросы атомной науки и техники. — 2008. — № 6. — С. 37-39. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS:52.55.Hc https://nasplib.isofts.kiev.ua/handle/123456789/110802 The paper is concerned with properties of magnetic surface configurations that have the planar magnetic axis coincident with the circular geometrical axis of the torus. The calculations were performed for the model of an l=2 torsatron comprising additional toroidal magnetic field coils. The magnetic surfaces with a negative shear and a high magnetic well can be realized in the system. Изучаются численным методом свойства конфигураций магнитных поверхностей, которые имеют плоскую магнитную ось, совмещенную с круговой геометрической осью тора. Расчеты проводились для модели двухзаходного торсатрона с катушками дополнительного тороидального магнитного поля. В системе могут быть реализованы магнитные поверхности с отрицательным широм и большой магнитной ямой. Вивчаються чисельним методом властивості конфігурацій магнітних поверхонь, які мають плоску магнітну вісь зуміщену з круговою геометричною віссю тора. Розрахунки проводились для моделі двозаходного торсатрону з катушками додаткового тороїдального магнітного поля. В системі можуть бути зреалізовані магнітні поверхні з від’ємним широм та великою магнітною ямою en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement An l=2 torsatron with centered planar magnetic axis Двозаходний торсатрон з центрованою плоскою магнітною віссю Двухзаходный торсатрон с центрированной плоской магнитной осью 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 |
An l=2 torsatron with centered planar magnetic axis |
| spellingShingle |
An l=2 torsatron with centered planar magnetic axis Kotenko, V.G. Magnetic confinement |
| title_short |
An l=2 torsatron with centered planar magnetic axis |
| title_full |
An l=2 torsatron with centered planar magnetic axis |
| title_fullStr |
An l=2 torsatron with centered planar magnetic axis |
| title_full_unstemmed |
An l=2 torsatron with centered planar magnetic axis |
| title_sort |
l=2 torsatron with centered planar magnetic axis |
| author |
Kotenko, V.G. |
| author_facet |
Kotenko, V.G. |
| topic |
Magnetic confinement |
| topic_facet |
Magnetic confinement |
| publishDate |
2008 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Двозаходний торсатрон з центрованою плоскою магнітною віссю Двухзаходный торсатрон с центрированной плоской магнитной осью |
| description |
The paper is concerned with properties of magnetic surface configurations that have the planar magnetic axis coincident with the circular geometrical axis of the torus. The calculations were performed for the model of an l=2 torsatron comprising additional toroidal magnetic field coils. The magnetic surfaces with a negative shear and a high magnetic well can be realized in the system.
Изучаются численным методом свойства конфигураций магнитных поверхностей, которые имеют плоскую магнитную ось, совмещенную с круговой геометрической осью тора. Расчеты проводились для модели двухзаходного торсатрона с катушками дополнительного тороидального магнитного поля. В системе могут быть реализованы магнитные поверхности с отрицательным широм и большой магнитной ямой.
Вивчаються чисельним методом властивості конфігурацій магнітних поверхонь, які мають плоску магнітну вісь зуміщену з круговою геометричною віссю тора. Розрахунки проводились для моделі двозаходного торсатрону з катушками додаткового тороїдального магнітного поля. В системі можуть бути зреалізовані магнітні поверхні з від’ємним широм та великою магнітною ямою
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110802 |
| citation_txt |
An l=2 torsatron with centered planar magnetic axis / V.G. Kotenko // Вопросы атомной науки и техники. — 2008. — № 6. — С. 37-39. — Бібліогр.: 6 назв. — англ. |
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| first_indexed |
2025-11-27T03:06:07Z |
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2025-11-27T03:06:07Z |
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1850793631814778880 |
| fulltext |
AN l=2 TORSATRON WITH CENTERED
PLANAR MAGNETIC AXIS
V.G. Kotenko
IPP, National Science Center “Kharkov Institute of Physics and Technology”,
61108 Kharkov, Ukraine
The paper is concerned with properties of magnetic surface configurations that have the planar magnetic axis
coincident with the circular geometrical axis of the torus. The calculations were performed for the model of an l=2
torsatron comprising additional toroidal magnetic field coils. The magnetic surfaces with a negative shear and a high
magnetic well can be realized in the system.
PACS:52.55.Hc
INTRODUCTION
It is known that transformation of a straight cylindrical
l=2 helical magnetic system into the toroidal l=2 helical
magnetic system is accompanied by transformation of the
straight magnetic axis which coincides with the cylinder
axis into a planar circular magnetic axis. The radius of the
circular magnetic axis Roax is less than the major radius of
the torus Ro, Roax/Ro<1 [1, 2]. This is one of the effects that
result from the helical symmetry violation of the straight
magnetic field, if the latter is bent into the toroidal field,
and lead to a change in the integral characteristics of the
magnetic surface configuration.
To date, two methods of changing the position of
the planar magnetic axis relative to the torus surface
are known [3, 4]. Both of them demand an essential
deformation of the helical current geometry. One method
implies the change in the helical base line winding law,
and the other involves the change in the conductor turn
packing in the helical coils.
The aim of the present work is to investigate
numerically magnetic surface configurations with a
centered (Roax/Ro=1) planar magnetic axis which were
formed as a result of combined application of the two
methods to the l=2 torsatron model with additional
toroidal magnetic field coils (ACs) as necessary elements
for creating a closed magnetic surface region.
THE CALCULATION MODEL
The calculation model of the l=2 torsatron magnetic
system with ACs is based on the design characteristics of
the U-2M torsatron [5].
The parameters of the calculation model are as
follows:
- toroidicity a/Ro=0.2618, a is the minor radius of the
torus (average radius of helical coils);
- l=2 is the polarity;
- m=2 is the number of helical winding pitches along the
length of the torus;
- the number of conductor turns in each single-layer
helical coil is 20 (40 in total).
Each of the helical coils consists of two equal parts
separated by a small diagnostic gap and comprising 10
conductor turns.
The helical base line, i.e., the helical line, along which
the load-carrying structure of the helical coil is
assembled, serves as the central diagnostic-gap line. The
helical base line winding law has the form [3]:
θ(ϕ)=θ1(ϕ)-k(θ2(ϕ)-θ1(ϕ)), (1)
where ϕ is the toroidal angle, θ is the poloidal angle, θ(ϕ)
1 and θ(ϕ)2 are the known cylindrical and equi-inclined
laws of helical line winding on the torus surface, k is the
numerical coefficient.
The compensating transverse magnetic field Bz is
assumed in the calculations to be a uniform field. The
planar magnetic axis regime is realized at a certain value
of the compensating magnetic field Bz=Bzm.
The ACs magnetic field Bϕ is axisymmetric (Bϕ
=B0R0/R, where B0 is the value of the additional toroidal
magnetic field on the circular axis of the torus, R is the
observation point radius counted from the main torus axis
(z-axis). The parameter K=1/(1+B0/b0) also exerts
influence on the magnetic surface configuration in the
torsatron with ACs. Here b0 is the amplitude of the
toroidal component of the magnetic field generated by
helical currents on the circular axis of the torus.
COMPUTATIONAL RESULTS
In accordance with ref. [4], the calculations were
carried out for two methods (1, 2) of conductor turn
packing in the helical coils along the base helical line.
Following method 1, each of 40 helical conductors is
wound round the torus by the same winding law (1). The
numerical calculations have shown that with this way of
packing, in order to bring the planar magnetic axis of the
magnetic surface configuration into coincidence with the
circular geometrical axis of the torus, one must put k=0.3
in Eq. (1).
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 37
Series: Plasma Physics (14), p. 37-39.
a
Ro
φ=0о φ=22.5о φ=45о
Fig.1. The cross-sections of magnetic surface configuration in l=2 torsatron calculation model (method 1 of conductor
turn packing, k=0.3). The parts of each helical coil are spaced by a small (diagnostic) gap
The scaled-down Fig. 1 shows the calculated poloidal
cross-sections of magnetic surface configurations for the
Bzm/b0=0.8 and K=0.285 (B0/b0=2.5) values. The cross-
sections are separated by the toroidal angle within the
limits of the magnetic field half-period ϕ=0°, 22.5°, 45°.
In the figure, the inner circle shows the cross-section of
the vacuum chamber in the U-2М torsatron. The
trapezoid-like patterns outline the conductor turn cross-
sections. The points inside the patterns mark the position
of thin current-carrying conductors of the calculation
model. They are located on the torus surface a/R0=0.2618
(dashed circles). On the same surface, in the middle of the
diagnostic gap, there is the base helical line of the
calculation model (no trace shown, de-energized). In all
three cross-sections the planar magnetic axis trace lies in
the equatorial plane of the torus; its major radius being
equal to R0ax1/R0=1.
The magnetic surface parameters are shown in Fig.2
as functions of the average magnetic-surface radius. It can
be seen from the Fig. 2(a) that the rotational transform
angle increases with radius within ι=0.29→0.35 (in 2π
units), there is a small magnetic well -U=0→0.055 in the
configuration, and the mirror ratio on the magnetic
surfaces ranges within γ=1.003→1.32.
Following method 2, each helical coil is formed by
using the turn-by-turn conductor packing on both sides of
the helical base line. The numerical calculations have
shown that with this method of packing, in order to make
the planar magnetic axis of the magnetic surface
configuration coincide with the circular geometrical axis
of the torus, in the law of helical base line winding (1)
one must put k=1.0 in Eq. (1).
Fig. 3 shows the calculated poloidal cross-sections of
the magnetic surface configuration. The cross-sections are
separated by the toroidal angle within the limits of the
magnetic field half-period ϕ=0°, 22.5°, 45°. There are
noticeable variations in the dimensions of poloidal cross-
sections of the helical coils. The regime with the centered
planar magnetic axis R0ax2/R0=1 occurs at Bzm/b0=0.98. In
certain poloidal cross-sections, if K=0.25, the last closed
magnetic surface size approximately equals the dimensions
of the vacuum chamber.
0.00 0.04 0.08 0.12
0.00
0.10
0.20
0.30
0.40 -U
r/R
i,
o 1.00
1.10
1.20
1.30
1.40
1.50
i
-U
a
0.00 0.04 0.08 0.12
0.00
0.04
0.08
0.12
0.16
0.20 -U
r/R
-U
i
i,
o 1.00
1.10
1.20
1.30
1.40
1.50
b
Fig.2. Rotational transform angle (i), magnetic well (-U),
mirror ratio (γ) as functions of the average magnetic
surface radius (r) for methods 1(a) and 2 (b) of conductor
turn packing
38
a
Ro
φ=0о φ=22.5о φ=45о
Fig.3. Cross-sections of magnetic surface configuration in l=2 torsatron calculation model (method 2 of conductor turn
packing, k=1.0)
The magnetic surface parameters are shown in Fig.2b
as functions of the average magnetic-surface radius. It can
be seen from the figure that the rotational transform angle
decreases with radius, ι=0.17→0.11 (in 2π units), there is
a great magnetic well -U=0→0.18, and the mirror ratio on
the magnetic surfaces makes γ=1.034→1.36.
SUMMARY
In the present work, numerical calculations have been
carried out to investigate the properties of magnetic
surface configurations with the centered planar magnetic
axis, which were formed in the model of the U-2M type
l=2 torsatron comprising additional toroidal magnetic
field coils. Two methods of conductor turn packing in the
helical coils along the base helical line have been
examined.
The calculations have demonstrated that with an
appropriate choice of the method of conductor turn
packing in the helical coils it is possible to realize the
magnetic surface configuration with a negative shear and
a high magnetic well. In some designs of fusion reactors
(tokamaks) a similar magnetic field mode is considered to
be the basic one [6].
REFERENCES
1. V.F. Aleksin. Magnetic field of helical currents lying
on the torus surface//Fizika plazmy i problemy UTS. Kiev:
“Izdat. AN Ukr. SSR”, 1963, N 3, p. 216 (in Russian).
2. A.I. Morozov, L. S.Solov’ev. Magnetic field geometry
//Voprosy Teorii Plazmy. Moscow: “Gosatomizdat”,
1963, v. 2, p.3-91 (in Russian).
3. V. Kotenko, E. Volkov, K. Yamazaki. Field ripple
behavior in helical systems // Plasma Devices and
Operations. June 2004, v. 12, N 9, p. 143-152.
4. V.G. Kotenko, D.V. Kurilo, Yu.F. Sergeev. The
influence of methods of conductor packing in the helical
coil poles on the magnetic configuration of l=2 torsatron
in the regime with a planar magnetic axis//VANT, Ser.
“Termoyaderny Sintez”. Moscow, 2005, v. 4, p.42-52 (in
Russian).
5. O.S. Pavlichenko. Status of “Uragan-3M” and
“Uragan-2M”//Collection of Papers Presented at the
IAEA Technical Committee Meeting on Stellarators and
Other Helical Confinement Systems, Garching, Germany
10-14 May, 1993. Vienna: IAEA, 1993, p. 60.
6. B.N. Kolbasov, A.A. Borisov, N.N. Vasiliev et al.
Concept of DEMO-S demonstration fusion power
reactor//VANT, Ser. “Termoyadernyi Sintez”. Moscow,
2007, v. 4, p.3-13 (in Russian).
Article received 22.08.08
Revised version 7.10.08
ДВУХЗАХОДНЫЙ ТОРСАТРОН С ЦЕНТРИРОВАННОЙ ПЛОСКОЙ МАГНИТНОЙ ОСЬЮ
В.Г. Котенко
Изучаются численным методом свойства конфигураций магнитных поверхностей, которые имеют плоскую
магнитную ось, совмещенную с круговой геометрической осью тора. Расчеты проводились для модели
двухзаходного торсатрона с катушками дополнительного тороидального магнитного поля. В системе могут
быть реализованы магнитные поверхности с отрицательным широм и большой магнитной ямой.
ДВОЗАХОДНИЙ ТОРСАТРОН З ЦЕНТРОВАНОЮ ПЛОСКОЮ МАГНІТНОЮ ВІССЮ
В.Г. Котенко
Вивчаються чисельним методом властивості конфігурацій магнітних поверхонь, які мають плоску магнітну
вісь зуміщену з круговою геометричною віссю тора. Розрахунки проводились для моделі двозаходного
торсатрону з катушками додаткового тороїдального магнітного поля. В системі можуть бути зреалізовані
магнітні поверхні з від’ємним широм та великою магнітною ямою.
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