Special correcting winding for l=2 torsatron with internal splitting of helical coils
special correcting winding for the l=2 torsatron toroidal magnetic system with non-standard internal split-type helical coils and with the coils of an additional toroidal magnetic field is considered. The numerical calculations have shown that the winding action upon the initial magnetic surface con...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Special correcting winding for l=2 torsatron with internal splitting of helical coil / V.G. Kotenko // Вопросы атомной науки и техники. — 2013. — № 1. — С. 24-26. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1092522016-11-22T03:03:12Z Special correcting winding for l=2 torsatron with internal splitting of helical coils Kotenko, V.G. Магнитное удержание special correcting winding for the l=2 torsatron toroidal magnetic system with non-standard internal split-type helical coils and with the coils of an additional toroidal magnetic field is considered. The numerical calculations have shown that the winding action upon the initial magnetic surface configuration leads mainly to a displacement of the magnetic surface configuration along the straight z axis of the torus. Рассмотрена специальная корректирующая обмотка для магнитной системы двухзаходного торсатрона с нестандартным (внутренним) расщеплением винтовых обмоток и с катушками дополнительного тороидального магнитного поля. Численные расчеты показали, что действие обмотки на исходную конфигурацию магнитных поверхностей приводит преимущественно к смещению конфигурации магнитных поверхностей вдоль прямой z оси тора. Розглянута спеціальна коригуюча обмотка для магнітної системи двозаходного торсатрону з нестандартним (внутрішнім) розщепленням гвинтових обмоток та з котушками додаткового тороїдального магнітного поля. Чисельні розрахунки показали, що дія обмотки на вихідну конфігурацію магнітних поверхонь зводиться переважно до зміщення конфігурації магнітних поверхонь уздовж прямої z осі тора. 2013 2013 Article Special correcting winding for l=2 torsatron with internal splitting of helical coil / V.G. Kotenko // Вопросы атомной науки и техники. — 2013. — № 1. — С. 24-26. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/109252 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Магнитное удержание Магнитное удержание |
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Магнитное удержание Магнитное удержание Kotenko, V.G. Special correcting winding for l=2 torsatron with internal splitting of helical coils Вопросы атомной науки и техники |
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special correcting winding for the l=2 torsatron toroidal magnetic system with non-standard internal split-type helical coils and with the coils of an additional toroidal magnetic field is considered. The numerical calculations have shown that the winding action upon the initial magnetic surface configuration leads mainly to a displacement of the magnetic surface configuration along the straight z axis of the torus. |
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Article |
| author |
Kotenko, V.G. |
| author_facet |
Kotenko, V.G. |
| author_sort |
Kotenko, V.G. |
| title |
Special correcting winding for l=2 torsatron with internal splitting of helical coils |
| title_short |
Special correcting winding for l=2 torsatron with internal splitting of helical coils |
| title_full |
Special correcting winding for l=2 torsatron with internal splitting of helical coils |
| title_fullStr |
Special correcting winding for l=2 torsatron with internal splitting of helical coils |
| title_full_unstemmed |
Special correcting winding for l=2 torsatron with internal splitting of helical coils |
| title_sort |
special correcting winding for l=2 torsatron with internal splitting of helical coils |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2013 |
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Магнитное удержание |
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http://dspace.nbuv.gov.ua/handle/123456789/109252 |
| citation_txt |
Special correcting winding for l=2 torsatron with internal splitting of helical coil / V.G. Kotenko // Вопросы атомной науки и техники. — 2013. — № 1. — С. 24-26. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT kotenkovg specialcorrectingwindingforl2torsatronwithinternalsplittingofhelicalcoils |
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2025-07-07T22:48:25Z |
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2025-07-07T22:48:25Z |
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1837030192982261760 |
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24 ISSN 1562-6016. ВАНТ. 2013. №1(83)
SPECIAL CORRECTING WINDING FOR l=2 TORSATRON WITH
INTERNAL SPLITTING OF HELICAL COILS
V.G. Kotenko
Institute of Plasma Physics NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
A special correcting winding for the l=2 torsatron toroidal magnetic system with non-standard internal split-type
helical coils and with the coils of an additional toroidal magnetic field is considered. The numerical calculations
have shown that the winding action upon the initial magnetic surface configuration leads mainly to a displacement
of the magnetic surface configuration along the straight z axis of the torus.
PACS: 52.55.Hc
INTRODUCTION
In this paper the l=2 torsatron magnetic system with
non-standard (internal) splitting of the helical coils into
two equal parts is discussed. In this magnetic system
unlike the system with standard (external) splitting of
the helical coils [1, 2], maximum helical coil splitting is
observed on the minor torus equator, and the helical coil
splitted parts have the points of contact on the major
torus equator [3]. To control the position of the closed
magnetic surface configuration in the direction
perpendicular to the equatorial plane of the torus [4] a
non-standard (internal) split-type special correcting
winding (ISCW) is suggested. An idea on ISCW
magnetic field structure is obtained by numerical
simulations on the effect of this field as a minority
magnetic field imposed on the magnetic field of a well-
known configuration.
1. CALCULATION MODEL
The general geometrical characteristics of the
computation model (Fig. 1,a) are close to the design
characteristic of the l=2 torsatron U-2M with the
additional toroidal magnetic field coils [5]: 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.
The calculation model consists of two single-layer
helical coils, each comprises 12 filament-like conductor
turns. The helical coil is splitted into two equal parts,
each comprises 5 conductor turns of the helical coil. The
currents in the helical coils are similar in direction and
strength, the total current in the coil is equal to Ih. The
rest of two innermost conductor turns (one in each of
the split parts) are the turns of the ISCW. The ISCW
scheme is shown separately in Fig. 1,b. The ISCW
splitting occurs along the base helical lines θ(ϕ)=mϕ
(dotted lines in Fig. 1,a,b) by the law
Δϕs=│sin(mϕ/2)│Δϕ, where θ is the poloidal angle, ϕ
is the toroidal angle, Δϕs is current value of the toroidal
angle of splitting, Δϕ=20o. It is seen that the ISCW
currents Is are equal in value but opposite in direction.
Below, it will be shown that ⎜Is⎜<<Ih.
In the present calculations, the transverse
compensating magnetic field Bz is considered as
uniform, the additional toroidal magnetic field is
assumed to be axisymmetric (Bϕ=BoRo/R, where Bo is
the value of the additional toroidal magnetic field on
the circular axis of the torus and R is the radius of the
point of observation counted off from the torus
rotation axis z). The magnetic surface configuration
in the torsatron with additional magnetic field coils is
affected by the parameter Kϕ=1/(1+Bo/bo) too (bo is
the amplitude of the longitudinal component of the
magnetic field generated by the helical coils on the
circular axis of the torus).
2. RESULTS OF CALCULATIONS
Fig. 2 a, b show the poloidal magnetic surface cross-
sections calculated for the initial magnetic surface
configuration (Is=0) and for the case with superposition
of the ISCW magnetic field (Is≠0). The cross-sections
are spaced round a toroidal angle ϕ (see fig. 1a) within
the limits of a magnetic field half-period, ϕ=0o, 22.5o
and 45o. In the figures, the inner circle is the cross-
section of a coaxial torus having the minor radius of
0.5a, and the outer circle is the cross-section of a torus
with traces of the conductor turns of the helical coils
(large black dots) and the ISCW turns (colour dots). All
the cross-sections of the last closed magnetic surface are
at the distance from the torus surface ~0.5a
(Bo/bo=1.56, Kϕ=0.39). For the model under
consideration Bz/bo=0.75.
a
=0
22.5
45 o
o
o
Ro a
I /2h
I /2h
Ro a
-I
I
s
s
b
Fig. 1. Top view of split-type helical coils of the computation model (a) with the ISCW indicated by colour lines (b),
Δϕ is the toroidal angle of splitting. The helical base lines are shown as dotted lines. The toroidal azimuths of
poloidal cross-sections are indicated. The additional toroidal magnetic field coils are not shown
ISSN 1562-6016. ВАНТ. 2013. №1(83) 25
As it is seen from Fig. 2 a, in all three cross-sections
the magnetic axis traces in the initial configuration are
disposed in the torus equatorial plane and the magnetic
axis major radius is invariable, Roax/Ro=0.945. Unlike
the system with standard splitting of the helical coils,
the magnetic surface configuration shifts inward the
torus as the angle of internal splitting of the helical coils
increases. The value of the average radius of the last
closed magnetic surface is rlc/a=0.27 (rlc/Ro=0.07), the
rotational transform angle on the magnetic surfaces
ι=0.44→0.5 (in 2π units), there is a small magnetic well
–U=0.023 in the configuration, and the mirror ratio
ranges within γ=1.004→1.21.
Fig. 2 b shows the magnetic surface cross-sections
for the case when the current ⎜Is⎜in the ISCW turns is
0.02Ih. It is seen that all the cross-sections, following the
magnetic axis displacement, are displaced down by
~0.1a relative to the equatorial plane. When the current
direction in ISCW turns changes to opposite one, the
magnetic surface configuration displaces up by the same
distance. 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 average value of the
last closed magnetic surface radius is rlc/a=0.26
(rlc/Ro=0.068), the formation of a magnetic island
structure is observed. The values of rotational transform
angle, i=0.46→0.57, the magnetic well depth, -U=0.02,
and the mirror ratio, γ=1.09→1.2, do not differ
substantially from the corresponding parameters of the
initial magnetic surface configuration.
3. MAGNETIC FIELD OF THE ISCW
Some idea on the ISCW magnetic field structure may
be obtained by numerical simulations on the effect of
this field as a minority magnetic field imposed on the
magnetic field of a well-known configuration. To study
the magnetic field of the ISCW (see Fig. 1,b) the
axisymmetric toroidal magnetic field configuration was
chosen. For this purpose it is sufficient to calculate the
model assuming Ih=0 without changing the value and
the direction of the additional magnetic field Bo and the
ISCW current ⎜Is⎜. The bos/Bo~0.002 ratio is taken to be
a measure of the contribution from the ISCW magnetic
field as a minority magnetic field. Here bos is the
magnetic field generated on the circular axis of the torus
by the ISCW turns with the current Is. The numerical
studies were carried out for the geometry of the initial
calculation model of the l=2, m=2 torsatron, taking
Δϕ =35о.
Fig. 2,c shows the positions of the traces (dotted
lines) calculated for five field lines of the resultant
magnetic field at the different poloidal cross-sections of
the torus. The starting points in the field line
calculations are at R~Ro+a in the poloidal cross-sections
ϕ=0o. The colour points at the torus cross-sections mark
the positions of the ISCW turn cross-sections. It is easy
to see from the figures that the field lines of the
resultant magnetic field look like spirals turning in the
direction of major radius R decrease. The geometric
singularities of spirals allow us to conclude about the
properties of the poloidal components BsR and Bsz of the
ISCW magnetic field.
Ro
0.5a
a
a
Ro
0.5a
a
b
a
Ro
c
ϕ=0o ϕ=22.5o ϕ=45o
Fig. 2. Characteristic poloidal cross-sections (see Fig. 1a) of the initial configuration of the magnetic surface in the
calculation model of l=2 torsatron (a) and in the case of the imposed ISCW magnetic field (b), traces of field lines
of the toroidal magnetic field in the poloidal cross-sections of the torus in the case of the minority magnetic field of
the ISCW superposition (c). The cross-sections ϕ=0o of the equiconnect [6] are shown by dashed lines
26 ISSN 1562-6016. ВАНТ. 2013. №1(83)
The spiral pitch is gradually decreases in the
direction of major radius R decrease. It means that the
values of the components BsR and Bsz are proportional to
the radius R (BsR, Bsz~R). Besides, the observed
constancy of the tilt angle of the spiral trace lines to the
torus equatorial plane points to the constancy of the
Bsz/BsR ratio value in these lines. As the trace line shape
of a single spiral remains unchangeable in every
poloidal cross-section, the observed ISCW magnetic
field properties are the same over the full length of the
torus.
In the torus equatorial plane the last spiral pitch is by
a factor of ~102 smaller than the starting pitch. Here, the
component Bsz is zero and the spiral is the plane curve.
The curve is well described by the equation:
R=Ro-a(1-2(tan(ϕ/8N))3/2),
where 0≤ϕ≤2πN, and N is the number of spiral
pitches (N=150). With the colliding beam fusion
reactor concept [7] in mind, an interesting possibility
arises in the case of practical realization of the spiral
magnetic field in the torus. The calculated large initial
pitch of the spiral gives a chance for the charged particle
injected from the starting point of field line calculation
to “miss” the injector and to hit it only after many
hundreds of rounds along the torus, being reflected from
the region of enhanced magnetic field. It is necessary to
make clear the peculiarity of charge particle trajectory
in the magnetic field.
CONCLUSIONS
The influence of the magnetic field of the new-
type special correcting winding on the centered
magnetic surface configuration with a plane magnetic
axis and increased clearance between the last closed
magnetic surface and the torus surface has been studied.
The configuration is realized in the model of the l=2,
m=2 torsatron with non-standard internal split-type
helical coils and with additional toroidal magnetic field
coils.
The calculations have shown that the ISCW action,
similar to the split-type SCW action [3], upon the initial
magnetic surface configuration leads mainly to a
displacement of the magnetic surface configuration
along the straight z axis of the torus. The displacements
of ~0.1a are not critical for the magnetic surface
parameters. In the torus equatorial plane the ISCW
magnetic field is directed, predominantly along the
major radius of the torus within torus volume.
REFERENCES
1. Nagato Yanagi, Kiyohiko Nishimura, Akio Sagara,
Osamu Motojima. Design studies on split-type helical
coils for FFHR-2S. // Proceedings of ITC/ISHW. 2007,
P1-095, p. 516-519.
2. Nagato Yanagi, Kiyohiko Nishimura, Gourab Bansal,
Akio Sagara and Osamu Motojima Proposals of Split
and Segmented-type Helical Coils for the Heliotron
Fusion Energy Reactor // Proceedings of ITC18. 2008,
P1-39, p. 273-276.
3. V.G. Kotenko, D.V. Kurilo, Yu.F. Sergeev,
E.L. Sorokovoy, Ye.D. Volkov. The Influence of a
Helical Coil Splitting on Magnetic Configuration of l=2
Torsatron with an Additional Toroidal Magnetic Field.
// Problems of Atomic Science and Technology. Seria
«Termoyaderny Sintez». 2009, v. 4, p. 30-36 (in
Russian).
4. V.G. Kotenko. A Special. Correcting Winding for the
l = 2 Torsatron with Split-type Helical Coils // Fusion
Engineering and Design (87). 2012, p. 118-123.
5. O.S. Pavlichenko. Status of “URAGAN-3M” and
“URAGAN-2M” Experiments. // A Collection of Papers
Presented at the IAEA Technical Committee Meeting on
Stellarators and Other Helical Confinement Systems.
Garching, Germany 10-14 May 1993, IAEA, Vienna,
Austria, 1993, p. 60.
6. V.G. Kotenko. Possible Mechanism for Onset of
Diverted Plasma Fluxes in a Torsatron // Fiz.Plazmy,
(33). 2007, № 3, p. 280 (in Russian), Plasma Phys. Rep.
(33). 2007, № 3, p. 249 (Engl.Transl.).
7. N. Rostoker, M.W. Binderbauer, H.J. Monkhorst.
Colliding beam fusion reactor // Science (278). 1997,
p. 1419-1422.
Article received 06.09.12
СПЕЦИАЛЬНАЯ КОРРЕКТИРУЮЩАЯ ОБМОТКА ДЛЯ l = 2 ТОРСАТРОНА С ВНУТРЕННИМ
РАСЩЕПЛЕНИЕМ ВИНТОВЫХ ОБМОТОК
В.Г. Котенко
Рассмотрена специальная корректирующая обмотка для магнитной системы двухзаходного торсатрона с
нестандартным (внутренним) расщеплением винтовых обмоток и с катушками дополнительного
тороидального магнитного поля. Численные расчеты показали, что действие обмотки на исходную
конфигурацию магнитных поверхностей приводит преимущественно к смещению конфигурации магнитных
поверхностей вдоль прямой z оси тора.
СПЕЦІАЛЬНА КОРИГУЮЧА ОБМОТКА ДЛЯ l = 2 ТОРСАТРОНА З ВНУТРІШНІМ
РОЗЩЕПЛЕННЯМ ГВИНТОВИХ ОБМОТОК
В.Г. Котенко
Розглянута спеціальна коригуюча обмотка для магнітної системи двозаходного торсатрону з
нестандартним (внутрішнім) розщепленням гвинтових обмоток та з котушками додаткового тороїдального
магнітного поля. Чисельні розрахунки показали, що дія обмотки на вихідну конфігурацію магнітних
поверхонь зводиться переважно до зміщення конфігурації магнітних поверхонь уздовж прямої z осі тора.
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