A modified lm=1 stellarator magnetic system
Numerical studies into the toroidal magnetic field structure of a new modification of the l=1 polarity stellarator with a single (m=1) helical coil pitch along the whole length of the torus have been undertaken. Depending on mutual toroidal and helical magnetic field directions, there may exist two...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-906142016-01-04T15:24:54Z A modified lm=1 stellarator magnetic system Kotenko, V.G. Магнитное удержание Numerical studies into the toroidal magnetic field structure of a new modification of the l=1 polarity stellarator with a single (m=1) helical coil pitch along the whole length of the torus have been undertaken. Depending on mutual toroidal and helical magnetic field directions, there may exist two centered magnetic surface/helical divertor configurations in the modified lm=1 stellarator. Similar helical divertor configurations have been realized in the tokamak [9, 10] in order to stabilize large-scale instabilities and to avoid current disruption. Проведено чисельні розрахунки тороїдального магнітного поля, створюваного модифікованою магнітною системою однозаходного (l=1) класичного стелларатора з одним кроком гвинтової обмотки (m=1) на довжині тора. В залежності від напрямку тороїдального магнітного поля відносно гвинтового магнітного поля в lm=1 стеллараторі можливе існування двох центрованих конфігурацій магнітних поверхонь та гвинтового дивертора. Аналогічні гвинтові диверторні конфігурації було реалізовано в токамаці з метою стабілізації крупномасштабних нестійкостей та придушення зривів плазмового омічного розряду. Проведено численное изучение структуры тороидального магнитного поля, создаваемого модифицированной магнитной системой однозаходного (l=1) классического стелларатора с одним шагом винтовой обмотки (m=1) на длине тора. В зависимости от направления тороидального магнитного поля относительно винтового магнитного поля в lm=1 стеллараторе возможно существование двух центрированных конфигураций магнитных поверхностей и винтового дивертора. Аналогичные винтовые диверторные конфигурации были реализованы в токaмаке с целью стабилизации крупномасштабных неустойчивостей и подавления больших срывов плазменного омического разряда. 2011 Article A modified lm=1 stellarator magnetic system / V.G. Kotenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 32-34. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/90614 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. A modified lm=1 stellarator magnetic system Вопросы атомной науки и техники |
| description |
Numerical studies into the toroidal magnetic field structure of a new modification of the l=1 polarity stellarator with a single (m=1) helical coil pitch along the whole length of the torus have been undertaken. Depending on mutual toroidal and helical magnetic field directions, there may exist two centered magnetic surface/helical divertor configurations in the modified lm=1 stellarator. Similar helical divertor configurations have been realized in the tokamak [9, 10] in order to stabilize large-scale instabilities and to avoid current disruption. |
| format |
Article |
| author |
Kotenko, V.G. |
| author_facet |
Kotenko, V.G. |
| author_sort |
Kotenko, V.G. |
| title |
A modified lm=1 stellarator magnetic system |
| title_short |
A modified lm=1 stellarator magnetic system |
| title_full |
A modified lm=1 stellarator magnetic system |
| title_fullStr |
A modified lm=1 stellarator magnetic system |
| title_full_unstemmed |
A modified lm=1 stellarator magnetic system |
| title_sort |
modified lm=1 stellarator magnetic system |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2011 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/90614 |
| citation_txt |
A modified lm=1 stellarator magnetic system / V.G. Kotenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 32-34. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T18:48:26Z |
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2025-07-06T18:48:26Z |
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1836924489491808256 |
| fulltext |
A MODIFIED lm=1 STELLARATOR MAGNETIC SYSTEM
V.G. Kotenko
Institute of Plasma Physics, NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
Numerical studies into the toroidal magnetic field structure of a new modification of the l=1 polarity stellarator with
a single (m=1) helical coil pitch along the whole length of the torus have been undertaken. Depending on mutual
toroidal and helical magnetic field directions, there may exist two centered magnetic surface/helical divertor
configurations in the modified lm=1 stellarator. Similar helical divertor configurations have been realized in the
tokamak [9, 10] in order to stabilize large-scale instabilities and to avoid current disruption.
PACS: 52.55.Hc
1. INTRODUCTION
From an engineering viewpoint the magnetic system
of the l=1 stellarator with a single (m=1) helical coil pitch
along the whole length of the torus is one of the simplest
stellarator-type magnetic systems. The stellarator contains
only one magnetic field period, lm=1. In comparison with
other helical coil systems (lm>1), the system under
discussion provides a better access to the working volume
and can minimize the helical coil materials consumption,
approaching in these characteristics to tokamak magnetic
systems that have an extensive magnetic divertor.
However, from the viewpoint of providing, for
example, a greater space between the magnetic surface
existence region, i.e., the plasma core, and the wall, the
classic scheme of the l=1 stellarator magnetic system
substantially ranks below more complicated l=2,3,4
polarity helical systems. This is connected with the
properties of both a spatial magnetic axis and a single
separatrix rib of the magnetic surface configuration in the
l=1 stellarator [1-3]. In the case of the lm=1 stellarator
with sizable toroidicity, the magnetic surface existence
region is localized close to the minor equator of the torus
[4]. For this reason, it may appear to be of little use for
the stellarator experiment.
This paper reports the results of numerical calculations
for the modified lm=1 stellarator magnetic system model
that permits one to avoid appreciably the above-
mentioned drawbacks.
2. THE ESSENCE OF MODIFICATION
The essence of modification consists in the fact that
one of the two helical coils of an ordinary lm=1 stellarator
(Fig. 1,a) is fully split into two equal parts [5]. The parts
have equivalent currents (-I) and are displaced [6]
symmetrically relative to the unsplit helical coil (current
2I) by a certain angle |Δϕ|<π in the toroidal direction
(see Fig. 1,b).
Ro a
-2I
2I
0
90
180 o
o
o
Ro a
-I
-I
2I
a b
Fig. 1. Top view of helical coils of a) ordinary lm=1stellarator and b) modified lm=1 stellarator.
The toroidal azimuths of poloidal cross-sections are shown (see Fig. 2)
3. CALCULATION MODEL
Numerical calculations of the modified lm=1
stellarator magnetic system were carried out for the
following ideal model:
32 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2011. № 1.
Series: Plasma Physics (17), p. 32-34.
- toroidicity α=a/R0=0.3 (a is the minor radius of the
torus, R0 is the major radius of the torus); - polarity l=1;
- number of helical coil pitches along the length of the
torus m=1;- the number of magnetic field periods lm=1;
- the number of filament-like helical conductor turns in
each of 3 helical coils is 1;
- the helical coils are laid on the torus according to the
cylindrical winding law θ(ϕ)=mϕ, where ϕ is the toroidal
angle and θ is the poloidal angle;
- the toroidal (poloidal) angle of relative displacement of
helical coils in the calculation model under consideration
is Δϕ=Δθ=30o.
The helical coil system is plunged into an
axisymmetric magnetic field Bφ=BBoRo/R generated by the
coils of the toroidal magnetic field (not shown in Fig. 1).
Here Bo is the toroidal magnetic field value on the circular
axis of the torus, R is the observation point radius counted
from the rotation z-axis of the torus. The transverse
magnetic field (perpendicular to the equatorial plane of
the torus) is assumed to be absent, BzB =0.
33
4. RESULTS OF CALCULATIONS
As the calculations have shown, the magnetic field
structure of the modified lm=1 stellarator depends to a
great extent not only on the value of the toroidal magnetic
field BBo, but also on its direction in relation to the value
and direction of the helical-coil magnetic field. The
calculations were performed for the both directions of the
toroidal magnetic field with the same absolute value of
the ratio BoB /bo=25 (BBo/bo=-25), bo being the amplitude of
circular-axis magnetic field generated by the helical
current 2I. Hereafter, the values of magnetic field
structure parameters for BoB /bo=-25 are presented in
brackets.
Fig. 2 shows the poloidal cross-sections of the
magnetic surface configuration calculated in the modified
ml=1 stellarator model. The cross-sections are spaced by
the toroidal angle ϕ within the limits of the magnetic field
half-period ϕ=0о, 90о, 180о (see Fig. 1,b). The dark and
light circles in Fig. 2 indicate the position of thin current-
carrying helical conductors with opposite current
directions, which form the helical coils of the calculation
model. They are found on the torus surface α =0.3 (thin
large circles).
Ro
a 2I
-I
-I
a
Ro
a 2I
-I
-I
b
ϕ=0о 90о 180о
Fig. 2. Cross-sections of magnetic surfaces (dotted lines) and equiconnect [7] (solid lines) in the modified lm=1
stellarator within the limits of the magnetic field half-period (see Fig. 1,b): a) Bo/bo=25, b) BBo/bo=-25
0.00 0.04 0.08 0.12 0.16 0.20
0.00
0.05
0.10
0.15
0.20
0.25
r/R
i
o
0.00 0.04 0.08 0.12 0.16 0.20
-0.10
0.00
0.10
0.20
U
r/Ro
0.00 0.04 0.08 0.12 0.16 0.20
1.00
1.20
1.40
1.60
r/Ro
Fig. 3. Rotational transform angle (i), magnetic well (hill) (U), field ripple (γ) as functions of the average magnetic
surface radius r/Ro in the modified lm=1 stellarator:Bo/bo=25 - solid lines, BBo/bo=-25 - dotted lines
From Fig. 2 it can be seen that the magnetic surface
configuration contains a spatial magnetic axis in the form
of m=1 helical line lying on the surface of the torus
rax/Roax=αax. The calculation gives the major radius of the
torus (magnetic-axis major radius) to be Roax/Ro=0.962
(0.962), and the minor radius (magnetic-axis minor
radius) to be rax/Ro=0.02 (0.013). Since (1-Roax/Ro)<<α
and αax<<α, the magnetic surface configuration appears
slightly shifted inward the torus. In the ordinary lm=1
stellarator model, the value of the shift is close to the
limiting value, (1-Roax/Ro)~α [4].
It is also seen from Fig. 2 that in all the three cross-
sections the form of the last closed magnetic surface
(average radius rlc/Ro=0.095 (0.2)) keeps well. This is an
evidence of a higher helical symmetry stability of the
modified lm=1 stellarator magnetic field relative to the
perturbation caused by bending of the straight magnetic
system into the toroidal one.
Fig. 2 illustrates the calculated cross-sections of the
equiconnect surface (solid lines) [7, 8], i.e., the surface of
the outer boundary of the stochastic layer of field lines. In
the vicinity of the layer the plasma of transient
34
parameters, the so-called SOL plasma, is confined. The
SOL plasma is a source of diverted plasma fluxes. It
follows from Fig. 2 that the considered modification of
the lm=1 stellarator can provide realization of two
different configurations of both the magnetic surfaces and
the helical divertor by switching the toroidal magnetic
field BBo direction.
The magnetic surface parameters as functions of their
average radii are shown in Fig. 3. It can be seen from the
figure that the rotational transform angle (in 2π units) is
rather small, i~4×10-2 (2×10-2) in the central part of the
magnetic surface configuration. In the outer region,
r/Ro > 0.05 (0.15), its value increases steeply up to
i~0.2 (0.14) on the last closed magnetic surface. A
moderate magnetic well (hill), U=0→-0.006 (0.07), and
the field ripple γ=1.1→1.37 (1.6) are observed on the
magnetic surfaces.
5. CONCLUSIONS
Consideration has been given to a new modification of
one of the simplest stellarator-type magnetic systems,
namely, the l=1 stellarator with a single (m=1) helical coil
pitch along the whole length of the torus, i.e., with a
single magnetic field period, lm=1.
The undertaken numerical studies have shown that the
proposed technique of converting the magnetic system of
the lm=1 stellarator into a modified version makes it
possible to form two different, sufficiently well centered
magnetic surface configurations. Their parameters meet
the requirements for the stellarator experiment. One of the
calculated magnetic surface configurations is
characterized by an enlarged distance between the last
closed magnetic surface and the surface of the support
torus.
The present numerical calculations have given an idea
of the position and form of the cross-sections for the
equiconnect being the surface of the outer boundary of the
layer of stochastic field lines. It has been demonstrated
that the helical coil system of the lm=1 stellarator
modification under consideration permits realization of
two different helical-divertor configurations. Similar
helical divertor configurations have been realized in the
tokamak [9, 10] in order to stabilize large-scale
instabilities and to avoid current disruption.
REFERENCES
1. А.I. Morozov, L.S. Solov’ev. Problems of Plasma
Theory. M.: “Gosatomizdat”, 1963, Is. 2 (In Russian).
2. V.G. Kotenko, S.S. Romanov. On the possibility of
control the ratio of a plasma radii and the first wall in
fusion devices. Kharkov: Preprint: KhFTI 83-8, 1983,
p. 1-12 (in Russian).
3. 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. 2000, v. 3, p. 541.
4. V.G. Kotenko. A modified magnetic system of the
lm=1 stellarator // International Conference-School on
Pl. Phys. and Contr. Fus Alushta, Ukraine, September
13-18, 2010, Book of Abstracts, p. 42.
5. V.G. Kotenko, D.V. Kurilo, Ju.F. Sergeyev,
E.D. Sorokovoy, Ye.D. Volkov. The influence of
helical coil splitting on the magnetic configuration of
l=2 torsatron with an additional toroidal magnetic
field // Voprosy Atomnoj Nauki i Tekhniki, RSC
“Kurchatov Institute”. Ser. “Termoyaderny sintez”.
2009, N. 4, p. 30-36 (in Russian).
6. V.M. Zalkind, V.G. Kotenko, S.S. Romanov. Magnetic
surface of the l=2 stellarator with displaced helical
windings. // Voprosy Atomnoj Nauki i Tekhniki RSC
“Kurchatov Institute”. Ser. “Termoyaderny sintez”.
2008, N. 4, p. 67-75 (in Russian).
7. V.E. Bykov, Yu.K. Kuznetsov, A.V. Khodyachikh,
O.S. Pavlichenko, V.G. Peletminskaya // 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. 391-396.
8. V.G. Kotenko. Possible mechanism for onset of
vertical asymmetry of diverted plasma fluxes in a
torsatron // Fiz. Plazmy. 2007, N 3, p. 280 (in
Russian). Plasma Phys. Rep. 2007, N 3, p. 249
(Engl. transl.).
Article received 01.10.10
МОДИФИЦИРОВАННАЯ МАГНИТНАЯ СИСТЕМА lm=1 СТЕЛЛАРАТОРА
В.Г. Котенко
Проведено численное изучение структуры тороидального магнитного поля, создаваемого
модифицированной магнитной системой однозаходного (l=1) классического стелларатора с одним шагом
винтовой обмотки (m=1) на длине тора. В зависимости от направления тороидального магнитного поля
относительно винтового магнитного поля в lm=1 стеллараторе возможно существование двух центрированных
конфигураций магнитных поверхностей и винтового дивертора. Аналогичные винтовые диверторные
конфигурации были реализованы в токaмаке с целью стабилизации крупномасштабных неустойчивостей и
подавления больших срывов плазменного омического разряда.
МОДИФІКОВАНА МАГНІТНА СИСТЕМА lm=1 СТЕЛЛАРАТОРА
В.Г. Котенко
Проведено чисельні розрахунки тороїдального магнітного поля, створюваного модифікованою магнітною
системою однозаходного (l=1) класичного стелларатора з одним кроком гвинтової обмотки (m=1) на довжині
тора. В залежності від напрямку тороїдального магнітного поля відносно гвинтового магнітного поля в lm=1
стеллараторі можливе існування двох центрованих конфігурацій магнітних поверхонь та гвинтового дивертора.
Аналогічні гвинтові диверторні конфігурації було реалізовано в токамаці з метою стабілізації
крупномасштабних нестійкостей та придушення зривів плазмового омічного розряду.
5. V.G. Kotenko, D.V. Kurilo, Ju.F. Sergeyev, E.D. Sorokovoy, Ye.D. Volkov. The influence of helical coil splitting on the magnetic configuration of l=2 torsatron with an additional toroidal magnetic field // Voprosy Atomnoj Nauki i Tekhniki, RSC “Kurchatov Institute”. Ser. “Termoyaderny sintez”. 2009, N. 4, p. 30-36 (in Russian).
6. V.M. Zalkind, V.G. Kotenko, S.S. Romanov. Magnetic surface of the l=2 stellarator with displaced helical windings. // Voprosy Atomnoj Nauki i Tekhniki RSC “Kurchatov Institute”. Ser. “Termoyaderny sintez”. 2008, N. 4, p. 67-75 (in Russian).
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