Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing
Numerical studies were undertaken to elucidate the influence of the helical-coil finite angular size on l=4 stellarator magnetic surface characteristics. The calculations are applied to the closed magnetic surface configuration removed from the torus surface. The magnetic surface characteristics d...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2009
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| Цитувати: | Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing / V.G. Kotenko // Вопросы атомной науки и техники. — 2009. — № 1. — С. 19-21. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-881672015-11-09T03:02:09Z Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing Kotenko, V.G. Магнитное удержание Numerical studies were undertaken to elucidate the influence of the helical-coil finite angular size on l=4 stellarator magnetic surface characteristics. The calculations are applied to the closed magnetic surface configuration removed from the torus surface. The magnetic surface characteristics did not change significantly in comparison with ideal model of the l=4 stellarator magnetic system. Виконано чисельне дослідження впливу скінченної кутової ширини гвинтових обмоток на властивості магнітних поверхонь в 4-заходному стелараторі. Розрахунки торкаються конфігурації замкнутих магнітних поверхонь, віддалених від поверхні тора. Властивості магнітних поверхонь в порівнянні з ідеальною моделлю 4- заходного стеларатора суттєвих змін не зазнали. Проведено численное изучение влияния конечной угловой ширины винтовых обмоток на свойства магнитных поверхностей в 4-заходном стеллараторе. Расчеты относятся к конфигурации замкнутых магнитных поверхностей, удаленных от поверхности тора. Свойства магнитных поверхностей по сравнению с идеальной моделью 4-заходного стелларатора существенно не изменились. 2009 Article Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing / V.G. Kotenko // Вопросы атомной науки и техники. — 2009. — № 1. — С. 19-21. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/88167 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Магнитное удержание Магнитное удержание |
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Магнитное удержание Магнитное удержание Kotenko, V.G. Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing Вопросы атомной науки и техники |
| description |
Numerical studies were undertaken to elucidate the influence of the helical-coil finite angular size on l=4 stellarator
magnetic surface characteristics. The calculations are applied to the closed magnetic surface configuration removed
from the torus surface. The magnetic surface characteristics did not change significantly in comparison with ideal model
of the l=4 stellarator magnetic system. |
| format |
Article |
| author |
Kotenko, V.G. |
| author_facet |
Kotenko, V.G. |
| author_sort |
Kotenko, V.G. |
| title |
Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing |
| title_short |
Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing |
| title_full |
Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing |
| title_fullStr |
Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing |
| title_full_unstemmed |
Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing |
| title_sort |
magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2009 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/88167 |
| citation_txt |
Magnetic surfaces of an l=4 stellarator in regard to helical coil angular size and method of conductor turn packing / V.G. Kotenko // Вопросы атомной науки и техники. — 2009. — № 1. — С. 19-21. — Бібліогр.: 6 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT kotenkovg magneticsurfacesofanl4stellaratorinregardtohelicalcoilangularsizeandmethodofconductorturnpacking |
| first_indexed |
2025-07-06T15:52:05Z |
| last_indexed |
2025-07-06T15:52:05Z |
| _version_ |
1836913394567872512 |
| fulltext |
MAGNETIC SURFACES OF AN l=4 STELLARATOR
IN REGARD TO HELICAL COIL ANGULAR SIZE
AND METHOD OF CONDUCTOR TURN PACKING
V.G. Kotenko
Institute of Plasma Physics, NSC “Kharkov Institute of Physics and Technology”,
Kharkov, Ukraine
Numerical studies were undertaken to elucidate the influence of the helical-coil finite angular size on l=4 stellarator
magnetic surface characteristics. The calculations are applied to the closed magnetic surface configuration removed
from the torus surface. The magnetic surface characteristics did not change significantly in comparison with ideal model
of the l=4 stellarator magnetic system.
PACS: 52.55.Hc
1. INTRODUCTION
The l=4 stellarator is generally referred to the class of
helical magnetic systems applicable for plasma
confinement [1, 2]. An analytical estimation [1] and
numerical simulations [2] of an ideal model of the l=4
stellarator comprising filamentary helical coils have been
carried out. They show a possibility to realize a magnetic
surface configuration with a steeply growing angle of
rotational transform near the configuration edge and a
negligibly small value of the rotational transform angle in
the central part of the configuration. Therefore, two
comparable-in-volume regions with different plasma
confinement can be formed in a magnetic plasma trap
based on the l=4 stellarator magnetic system.
One of two regions (the inner one) is, in fact, a region
of plasma confinement in a simple axisymmetric toroidal
magnetic field.
In another (outer) region plasma confinement takes
place in a toroidal magnetic field with rotational
transformation of field lines.
It is not improbable [3] that a significant difference in
the transport coefficients in these regions can lead to
formation of a zone with decreased values of transport
coefficients (transport barrier) and transition to high
plasma confinement mode (H-mode).
Moreover, similar to the magnetic systems of l=2 and
l=3 stellarators the magnetic system of the l=4 stellarator
can provide a controllable and deep detachment of the
closed magnetic surface configuration from the torus
surface, i.e., plasma column-wall spacing [4].
Probably, the practical realization of the l=4 stellarator
will create a need to determine the influence of a real
finite size of helical coils on the basic characteristics of
magnetic surfaces. In this paper magnetic surface
characteristics are numerically studied for the l=4
stellarator with regard to the angular size of a single-layer
helical coil and one of possible methods of conductor turn
packing in the layer [5].
The main purpose of the study is to get a general idea
about the tendencies in variations of l=4 stellarator
magnetic surface characteristics when passing from the
ideal magnetic system closer to the real one.
2. CALCULATION MODEL
The calculation model has the following parameters:
- toroidicity α=a/R0=0.25 (a and R0 are the minor and
major radii of the torus, respectively);
- l=4 is the polarity;
- m=2 is the number of helical winding pitches along
the torus length;
- the number of conductor turns in each of 8 single-
layer helical coils is 7 (56 in total).
Each helical coil comprises the base conductor turn
lying along the base helical line. The last 6 conductor
turns are wrapped beginning with the base line on the
both sides symmetrically of it (in the ideal model the
helical coils comprise the base conductor turn only).
The base helical line is marked up on the torus
according to the cylindrical winding law:
θ(ϕ)=mϕ, (1)
where ϕ is the toroidal and θ is the poloidal angle.
0o
11.25
22.5o
o
Ro a
Fig.1. Top view of the helical coils (shaded) of the l=4
stellarator calculation model. The toroidal azimuths of
poloidal cross-sections are indicated (see Fig. 2)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2009. № 1. 19
Series: Plasma Physics (15), p. 19-21.
The angular size of helical coil measured along the
minor torus equator is close to the maximum possible
value, Δϕ ~π/lm.
With the described method of packing, the points of
the helical line of the nth conductor turn shift relative to
the points of the helical base line with regular intervals
counted along the torus parallels. So, the linear size of
each helical coil measured along one of the torus parallels
is the constant value, ΔЅ=R0(1-α)Δϕ (see Fig. 1).
The helical coil system is plunged into toroidal
axisymmetric magnetic field Bφ=B0R0/R, where B0
determines the value of the toroidal magnetic field on the
circular axis of the torus, R is the observation point radius
counted from the major axis (z-axis) of the torus.
The transverse magnetic field is assumed to be absent,
Bz=0.
3. COMPUTATIONAL RESULTS
Fig. 2 shows poloidal cross-sections of the magnetic
surface configuration calculated in the l=4 stellarator
model with taking into account the single-layer helical
coil angular size and the described method of conductor
turn packing in the layer. The cross-sections are spaced
by the toroidal angle ϕ within the limits of the magnetic
field half-period ϕ=0о, 11.25о, 22.5о (see Fig. 1). The
results of simulation concern the magnetic surface
configurations moved away from the torus surface,
rlc/a~0.4 (rlc is the average radius of the last closed
magnetic surface). For the given value of the toroidal
magnetic field Bo this can be reached by variation of the
helical coil current.
The points and circles in Fig.2 mark the position of
thin current-carrying conductors with alternate current
directions forming the helical coils of the calculation
model. They are located on the torus surface a/R0=0.25
(thin circles).
It is seen from Fig. 2 that in all three cross-sections the
closed toroidal magnetic surfaces (dotted lines) are rather
well centered and have a square contour in the edge
region of the configuration. This is an evidence of a
higher helical symmetry stability of the l=4 stellarator
magnetic field relative to the perturbation caused by
bending of the straight magnetic system into the toroidal
one.
Fig. 2 also shows the calculated cross-sections of the
equiconnect surface [6] (solid curves). The equiconnect
surface is a surface of the outer boundary of the stochastic
layer of field lines, i.e. the outer boundary of the plasma
layer with transient plasma parameters, the so-called
scrape-off layer (SOL) plasma. The positioning of the
equiconnect cross-sections may by useful to prevent
direct interaction of the SOL plasma with the vacuum
chamber wall, the radiofrequency units used for plasma
generation and heating and with diagnostic tools.
The magnetic surface parameters as functions of their
average radii are shown in Fig. 3 by solid lines.
It can be seen from Fig. 3a that the rotational
transform angle is negligibly small, i<10-2-10-3 (in 2π
units), in the central part of the magnetic surface
configuration, r/rlc<0.5 (inner region). In the outer region,
r/rlc>0.5, its value is steeply growing to i~0.47 (0.5) on
the last closed magnetic surface, rlc/R0=0.112 (0.103).
Here, the shear value is several times higher than standard
one in the l=2 or l=3 helical magnetic systems. In the
outer region a moderate value of the magnetic well,
-U=0→0.026 (0.018), is observed (Fig. 3b and c) the field
ripple γ=1.1→1.33 (1.3). The characteristics of the ideal
model of the l=4 stellarator are presented in brackets.
Ro
a
φ=0о φ=11.25о φ=22.5о
Fig.2. Cross-sections of magnetic (dotted lines) and equiconnect surfaces (the surface of the outer boundary of
stochastic layer of field lines, i.e. the outer boundary of a plasma layer with transient plasma parameter, the so-called
scrape-off layer (SOL) plasma, solid lines) in the l=4 stellarator calculation model within the limits of the magnetic
field half-period (see Fig.1)
20
0.00 0.05 0.10
0.00
0.10
0.20
0.30
0.40
0.50
r/R
i
o
0.00 0.05 0.10
0.00
0.01
0.02
0.03
r/R
-U
o
0.00 0.05 0.10
1.00
1.10
1.20
1.30
1.40
r/Ro
a b c
Fig.3. Rotational transform angle (a), magnetic well (b), field ripple (c) as functions of the average magnetic surface
radius for the “real” (solid lines) and ideal (dashed lines) model of the l=4 stellarator
4. SUMMARY
The numerical calculations having been performed
demonstrate that in the l=4 stellarator model with helical
coils of finite angular size the magnetic surface
characteristics such as the rotational transform angle,
maximum field ripple value and the average radius of the
last closed magnetic surface differ less than ~10% of the
value inherent in the ideal model of the l=4 stellarator
comprising filamentary helical coils. Also, the magnetic
surface position and shape and form of the rotational
transform angle radial dependence do not have a
noticeable change. One can only observe a magnetic well
increase by a factor of 1.5. Owing to the form of the
equiconnect, the SOL plasma-wall interaction is supposed
to be reduced in a plasma trap based on the l=4 stellarator
magnetic system.
REFERENCES
1. L.S. Solovyov, V.D. Shafranov. Closed magnetic
configuration for plasma confinement // Voprosy Teorii
Plasmy / M.: ”Atomizdat”,1967,v.5, p. 3 (in Russian).
2. C. Gourdon, D. Marty, E. Mashke, J. Dumont.
Configurations du type stellarator avec puits moyen et
cissaillement des lignes magnetiques//Proc. 3rd Intern.
Conf., Novosibirsk, 1968/ Vienna, 1969, v. 1, p.8 47-861
(in French).
3. B.A. Carreras, D.E. Newman, V.E. Lynch,
P.H. Diamond. Self-organized criticality as transport
process paradigm in plasma confined in magnetic field//
Fizika Plazmy. 1996, v.22, N 9, p. 819-833 (in Russian).
4. V.G. Kotenko, V.I. Lapshin, G.G. Lesnyakov,
S.S. Romanov, E.D. Volkov. A Version of Advancement
Towards a Commercial Fusion Reactor//Plasma Fusion
Res. Series. 2000, v. 3, p.541-544.
5. V.М. Zalkind, V.G. Kotenko, S.S. Romanov. The l=2
stallarator with displaced helical windings//Voprosy
Atomnoj Nauki I Tekhniki. Ser. “Termoyaderny sintez”.
2008, iss. 4, p. 67-75 (in Russian).
6. V.G. Kotenko. Possible mechanism for onset of
diverted plasma fluxes in a torsatron // Fiz. Plazmy. 2007,
v. 33, N 3, p. 280 (in Russian) // Plasma Phys. Rep. 2007,
v. 33, N 3 p. 249 (Engl. Transl.).
Article received 22.09.08
Revised version 7.10.08
МАГНИТНЫЕ ПОВЕРХНОСТИ 4-ЗАХОДНОГО СТЕЛЛАРАТОРА С УЧЕТОМ УГЛОВОЙ ШИРИНЫ
ВИНТОВЫХ ОБМОТОК И СПОСОБА УКЛАДКИ ПРОВОДНИКОВ
В.Г. Котенко
Проведено численное изучение влияния конечной угловой ширины винтовых обмоток на свойства магнитных
поверхностей в 4-заходном стеллараторе. Расчеты относятся к конфигурации замкнутых магнитных
поверхностей, удаленных от поверхности тора. Свойства магнитных поверхностей по сравнению с идеальной
моделью 4-заходного стелларатора существенно не изменились.
МАГНІТНІ ПОВЕРХНІ 4-ЗАХОДНОГО СТЕЛАРАТОРА З УРАХУВАННЯМ КУТОВОЇ ШИРИНИ
ГВИНТОВИХ ОБМОТОК ТА СПОСОБУ УКЛАДКИ ПРОВІДНИКІВ
В.Г. Котенко
Виконано чисельне дослідження впливу скінченної кутової ширини гвинтових обмоток на властивості
магнітних поверхонь в 4-заходному стелараторі. Розрахунки торкаються конфігурації замкнутих магнітних
поверхонь, віддалених від поверхні тора. Властивості магнітних поверхонь в порівнянні з ідеальною моделлю 4-
заходного стеларатора суттєвих змін не зазнали.
21
5. V.М. Zalkind, V.G. Kotenko, S.S. Romanov. The l=2 stallarator with displaced helical windings//Voprosy Atomnoj Nauki I Tekhniki. Ser. “Termoyaderny sintez”. 2008, iss. 4, p. 67-75 (in Russian).
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