The divertor region formation in the stellarator system “Yamator”
By imposing a certain optimum vertical magnetic field and using the equi-inclination law of helical conductors winding, regularizations have been carried out for the region of the edge closed magnetic surfaces and the divertor region in the configurations of the l = 1, m = 3 and m = 5 Yamators. Magn...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1221162017-06-28T03:02:43Z The divertor region formation in the stellarator system “Yamator” Lesnyakov, G.G. Магнитное удержание By imposing a certain optimum vertical magnetic field and using the equi-inclination law of helical conductors winding, regularizations have been carried out for the region of the edge closed magnetic surfaces and the divertor region in the configurations of the l = 1, m = 3 and m = 5 Yamators. Magnetic configuration modes have been found, at which the narrowest regions with stochastic behavior of magnetic field lines are formed close to the conditional separatrices. С помощью наложения определённого оптимального вертикального магнитного поля и применения равнонаклонного закона намотки винтовых проводников осуществлены регуляризации областей краевых замкнутых магнитных поверхностей и дивертора в конфигурациях l = 1, m = 3 и m = 5 Яматоров. Найдены режимы магнитных конфигураций, в которых, вблизи условных сепаратрис, сформированы наиболее узкие области со стохастическим поведением силовых линий поля. За допомогою накладання визначеного оптимального вертикального магнітного поля і застосування рівнонахиленного закону намотки гвинтових провідників виконані регулярізації областей крайових замкнених магнітних поверхонь та дивертора в конфігураціях l = 1, m = 3 и m = 5 Яматорів. Знайдені режими магнітних конфігурацій, в яких, поблизу умовных сепаратрис, сформовані найбільш вузьки області зі стохастичною поведінкою силових ліній поля. 2017 Article The divertor region formation in the stellarator system “Yamator” / G.G. Lesnyakov // Вопросы атомной науки и техники. — 2017. — № 1. — С. 21-24. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.55.-s; 52.55.Hc; 52.55.Rk; 52.70.Ds; 52.55.Dy http://dspace.nbuv.gov.ua/handle/123456789/122116 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 Lesnyakov, G.G. The divertor region formation in the stellarator system “Yamator” Вопросы атомной науки и техники |
| description |
By imposing a certain optimum vertical magnetic field and using the equi-inclination law of helical conductors winding, regularizations have been carried out for the region of the edge closed magnetic surfaces and the divertor region in the configurations of the l = 1, m = 3 and m = 5 Yamators. Magnetic configuration modes have been found, at which the narrowest regions with stochastic behavior of magnetic field lines are formed close to the conditional separatrices. |
| format |
Article |
| author |
Lesnyakov, G.G. |
| author_facet |
Lesnyakov, G.G. |
| author_sort |
Lesnyakov, G.G. |
| title |
The divertor region formation in the stellarator system “Yamator” |
| title_short |
The divertor region formation in the stellarator system “Yamator” |
| title_full |
The divertor region formation in the stellarator system “Yamator” |
| title_fullStr |
The divertor region formation in the stellarator system “Yamator” |
| title_full_unstemmed |
The divertor region formation in the stellarator system “Yamator” |
| title_sort |
divertor region formation in the stellarator system “yamator” |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2017 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/122116 |
| citation_txt |
The divertor region formation in the stellarator system “Yamator” / G.G. Lesnyakov // Вопросы атомной науки и техники. — 2017. — № 1. — С. 21-24. — Бібліогр.: 5 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-08T21:09:13Z |
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2025-07-08T21:09:13Z |
| _version_ |
1837114542461550592 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2017. №1(107)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 21-24. 21
THE DIVERTOR REGION FORMATION IN THE STELLARATOR
SYSTEM “YAMATOR”
G.G. Lesnyakov
Institute of Plasma Physics of the NSC KIPT, Kharkov, Ukraine
E-mail: lesn@kipt.kharkov.ua
By imposing a certain optimum vertical magnetic field and using the equi-inclination law of helical conductors
winding, regularizations have been carried out for the region of the edge closed magnetic surfaces and the divertor
region in the configurations of the l = 1, m = 3 and m = 5 Yamators. Magnetic configuration modes have been found,
at which the narrowest regions with stochastic behavior of magnetic field lines are formed close to the conditional
separatrices.
PACS: 52.55.-s; 52.55.Hc; 52.55.Rk; 52.70.Ds; 52.55.Dy
INTRODUCTION
The present work is a continuation of our earlier
investigation on the l = 1 Yamator having a low aspect
ratio Ah1 = R0/ah1 = 3.333 (R0 being the major radius of
the torus, ah1 /R0 = 0.3 the minor radius of the internal
helical conductor), and a helical magnetic axis [1-4].
Ah2 = R0/ah2 = 2.222 (ah2 /R0 = 0.45 the minor radius
of the outside helical conductor), ah2 = ah1 + h,
h/R0 = 0.15 - being the line conductor spacing. Apart
from the rotational transformation angle, i(а) 0.6, (i is
given in units of 2 , а is the radius of the last closed
surface) and a significant magnetic well, (-U) > 8 %, the
l = 1 Yamator is noteworthy for its unique feature,
namely, two fins on the separatrices (two X-points).
Two X-divertors are formed at intersections of two
characteristic separatrices of the l = 1 Yamator, Fig. 1.
The separatrix fins of the l = 1 Yamator lie on both sides
of the two-wire helical winding, being symmetrical
relative to its azimuth. It is known that in most magnetic
systems, the magnetic field toroidicity disturbs the
separatrices. Consequently, their locations are called the
conditional separatrices. The regions being in the
neighborhood of the separatrices turn into the layers of
magnetic field lines with stochastic behavior.
Bo
Fig. 1. Magnetic surfaces of the linear l = 1 Yamator.
Solenoids of the longitudinal magnetic field are not
shown. Two intersecting circles represent the
separatrices. One of them (the greater) is the separatrix
with a cylindrical magnetic surface, the part of which
lies between the helical conductors. The rotational
transformation on the separatrices is equal to i = m l,
where m is the number of magnetic field periods
The purpose of the research has been to analyze
numerically the possibilities, which may appear helpful
in regularizing the edge region of the plasma
confinement volume, and/or the layer of magnetic field
lines adjacent from the outside to the stochastic layer of
the separatrix region. The outside layer of magnetic
surfaces in the neighborhood of the separatrices was
regularized in the l = 1, m = 3 and m = 5 Yamators
either by matching the corresponding vertical field, or
by applying the equi-inclination law of helical
conductors winding instead of the common cylindrical
law.
RESEARCH RESULTS
The main changes on regularization of both the
structure of closed magnetic surfaces and the behavior
of the field lines in the edge region are shown in Figs. 2
to 6. The edge region also includes the closed magnetic
surfaces, which embrace the region of conditional
separatrices.
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
Fig. 2. Closed magnetic surfaces and magnetic field
lines of the separatrix region, in the l = 1, m = 3
Yamator with helical conductors wound in accordance
with the cylindrical law, = m ( and are the
poloidal and toroidal angles, respectively), without
imposition of the external vertical magnetic field,
Вz
ext
= 0. The poloidal cross-section of the torus is
= 0 . The magnetic field of the stellarator toroidal
solenoids, В0, is described by the ratio В0/b0 = 2.0,
where b0 is the toroidal magnetic field of the helical
conductor with the minor radius ah1
mailto:lesn@kipt.kharkov.ua
22 ISSN 1562-6016. ВАНТ. 2017. №1(107)
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
a
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
b
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
c
Fig. 3. Closed magnetic surfaces of the confinement
volume and closed magnetic surfaces embracing the
separatrix region of the l = 1, m = 3 Yamator with the
cylindrical law of helical conductor winding, = m ,
and the imposed vertical magnetic field
Вz
ext
/B0 = 0.014167 (В0/b0 = 2.0): а – poloidal cross-
section of the torus = 0 ; b = 30 ; с = 60
(magnetic field half-period)
The crescent-shaped region (see Fig. 2), representing
the remains of the separatrices and their neighborhood,
is transformed into the layer of closed magnetic surfaces
by imposing a certain optimum external vertical
uniform magnetic field Bz
ext
on the configurations under
study for both m = 3 (see Fig. 3) and m = 5 (see Fig. 5)
cases. The resulting layer encompasses the regions of
two conditional separatrices. It should be noted that in
the configuration with the imposed optimum vertical
magnetic field, the magnetic axis is shifted towards the
increasing major radius of the torus, while the mean
radius of the closed magnetic surfaces is appreciably
reduced. In the closed magnetic surface layer of the
l = 1, m = 3 configuration, which embraces the
conditional separatrices, the rotational transformation
angle varies from i+S ≈ 0.356 (the surface with i+S lies
closer to the conditional separatrix) to iend ≈ 0.1154, and
for the l = 1, m = 5 configuration it ranges from
i+S ≈ 0.604 to iend ≈ 0.48.
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
a
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
b
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
c
Fig. 4. Closed magnetic surface structure of the l = 1,
m = 3 Yamator with the equi-inclination law of helical
conductor winding, without imposition of the vertical
magnetic field, Вz
ext
= 0 (В0/b0 = 2.0): a – poloidal
cross-section of the torus = 0 ; b = 30 ;
с = 60 (magnetic field half-period). The region of
conditional separatrices is well seen in the figures
ISSN 1562-6016. ВАНТ. 2017. №1(107) 23
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
a
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
b
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
с
Fig. 5. Magnetic surfaces of the confinement volume
and closed magnetic surfaces near the separatrix region
of the l = 1, m = 5 Yamator with the cylindrical law of
helical conductors winding, = m , and the imposed
vertical magnetic field Вz
ext
/B0 = 0.0146 (В0/b0 = 1.0):
а – poloidal cross-section of the torus = 0 ;
b = 30 ; с = 60 (magnetic field half-period)
The equi-inclination law of helical conductors
winding, as applied to the configurations, leads to the
recovery of the layer of closed magnetic surfaces
outside the conditional separatrices, and makes it more
stable even at Вz
ext
= 0 (see Figs. 4 and 6). For plasma
confinement, it is particularly important that with the
use of the equi-inclination law of helical conductors
winding the maximum size of closed magnetic surfaces
is created in the configuration. The magnetic axis lies
closer to the geometrical axis of the torus, and the shear
of magnetic field lines increases. The displacement of
the external layer of closed magnetic surfaces to the
separatrix location, and the increase of its transverse
size can be also characterized by the value of rotational
transformation angle on the magnetic surface nearest to
the conditional separatrices, i+S 0.6.
0.5 1.0 1.5
R / Ro
-0.5
0.0
0.5
Z
/
R
o
Fig. 6. Magnetic surface structure of the l = 1, m = 5
Yamator configuration with the equi-inclination law of
helical conductor winding, without imposition of the
vertical magnetic field, Вz
ext
= 0, В0/b0 = 1.2. Poloidal
cross-section of the torus at = 0
CONCLUSIONS
The present studies have demonstrated that the best
regularization of the peripheral (edge) region and the
divertor region of Yamators is attained in cases when
for creating the magnetic configuration the equi-
inclination law of helical conductors winding is applied.
The modes of magnetic configurations for l = 1, m = 3
and m = 5 Yamators have been found, at which the
narrowest region with stochastic behavior of magnetic
field lines is formed in the neighbourhood of the
conditional separatrices (see Figs. 4 and 6). The result is
that this region with stochastic behaviour of magnetic
field lines in the vicinity of the conditional separatrices
of the Yamator appears to be embraced from the outside
by closed magnetic surfaces. Moreover, these magnetic
surfaces also form a closed spatial divertor region of
quite great sizes in both longitudinal (azimuthal) and
transverse directions. This is particularly significant for
distribution and utilization of the heat of plasma that is
diverted from the magnetic trap. One may reason much
upon new functions and the mode of operation of the
proposed divertor. But it is possible that the divertor
structure of this sort and its updated development would
meet the idea [5] that the advanced divertor solutions
will set the innovative magnetic geometries.
24 ISSN 1562-6016. ВАНТ. 2017. №1(107)
REFERENCES
1. V.G. Kotenko, G.G. Lesnyakov, S.S. Romanov.
Stellarator fields with 2-wire lines wound round the
torus // Problems of Atomic Science and Technology.
Series “Plasma Physics”. 1999, issues 1(1), 2(2), p. 49-
51.
2. V.G. Kotenko, G.G. Lesnyakov, S.S. Romanov.
Yamator: high magnetic-well value stellarator // J.
Plasma Fusion Res. SERIES, 2000, Issue 3, p. 154-157.
3. G.G. Lesnyakov, V.G. Kotenko, E.D. Volkov.
Mapping of magnetic field lines at the edge of the l=1
helical-axis Yamator // International Conf. and School
on Plasma Physics and Controlled Fusion. September
16-21, 2002, Alushta (Crimea), Ukraine. Book of
Abstracts, organiz. NSC KPTI, Kharkiv, Ukraine. 2002,
p. 56.
4. G.G. Lesnyakov, V.G. Kotenko, E.D. Volkov.
Mapping of magnetic field lines at the edge of the l=1
helical-axis Yamator // Problems of Atomic Science and
Technology. Series “Plasma Physics” 2002, № 4 (7),
p. 67-69.
5. M. Kotschenreuther, S. Mahajan, P.M. Valanju, et al.
Taming the heat flux problem: advanced divertors
towards fusion power // J. Fusion Energy. 2016, v. 35,
p. 27-30.
Article received 25.11.2016
ФОРМИРОВАНИЕ ОБЛАСТИ ДИВЕРТОРА В СТЕЛЛАРАТОРНОЙ СИСТЕМЕ ЯМАТОРА
Г.Г. Лесняков
С помощью наложения определённого оптимального вертикального магнитного поля и применения
равнонаклонного закона намотки винтовых проводников осуществлены регуляризации областей краевых
замкнутых магнитных поверхностей и дивертора в конфигурациях l = 1, m = 3 и m = 5 Яматоров. Найдены
режимы магнитных конфигураций, в которых, вблизи условных сепаратрис, сформированы наиболее узкие
области со стохастическим поведением силовых линий поля.
ФОРМУВАННЯ ОБЛАСТІ ДИВЕРТОРА В СТЕЛАРАТОРНІЙ СИСТЕМІ ЯМАТОРА
Г.Г. Лесняков
За допомогою накладання визначеного оптимального вертикального магнітного поля і застосування
рівнонахиленного закону намотки гвинтових провідників виконані регулярізації областей крайових
замкнених магнітних поверхонь та дивертора в конфігураціях l = 1, m = 3 и m = 5 Яматорів. Знайдені
режими магнітних конфігурацій, в яких, поблизу умовных сепаратрис, сформовані найбільш вузьки області
зі стохастичною поведінкою силових ліній поля.
|