The influence of a transverse shift of torsatron magnetic surfaces on their parameters
The paper deals with the influence of the transverse shift (or axial shift along the axis of torus rotation) of magnetic surfaces on their parameters in a calculation model of the l=2 torsatron magnetic system. The shift can be realized by means of a special-purpose controlling coil of a helical typ...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Назва видання: | Вопросы атомной науки и техники |
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| Цитувати: | The influence of a transverse shift of torsatron magnetic surfaces on their parameters / V. G. Kotenko // Вопросы атомной науки и техники. — 2005. — № 1. — С. 36-38. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-784562015-03-19T03:02:22Z The influence of a transverse shift of torsatron magnetic surfaces on their parameters Kotenko, V. G. Magnetic confinement The paper deals with the influence of the transverse shift (or axial shift along the axis of torus rotation) of magnetic surfaces on their parameters in a calculation model of the l=2 torsatron magnetic system. The shift can be realized by means of a special-purpose controlling coil of a helical type. The coil action combined with the well-known action of common annular controlling coil is considered as an instrument for two-dimensional control of the plasma core position in stellarator-type plasma devices. В роботі з’ясовано вплив поперечного зміщення (або ж осьового зміщення вздовж осі обертання тора) магнітних поверхонь на їх параметри в моделі l=2 торсатрона. Зміщення здійснюється за допомогою спеціальної коректуючої обмотки гвинтового типу. Дія цієї обмотки в поєднанні з дією звичайної кільцеподібної коректуючої обмотки надає можливість 2-вимірного контролю за положенням плазмового шнура в плазмових пастках стелараторного типу. В работе выяснено влияние поперечного смещения (или осевого смещения вдоль оси вращения тора) магнитных поверхностей на их параметры в расчетной модели l=2 торсатрона. Смещение осуществляется с помощью специальной корректирующей обмотки винтового типа. Действие этой обмотки в сочетании с обычной кольцеобразной корректирующей обмоткой позволяет осуществить 2-мерный контроль положения плазменного шнура в плазменных ловушках стеллараторного типа. 2005 Article The influence of a transverse shift of torsatron magnetic surfaces on their parameters / V. G. Kotenko // Вопросы атомной науки и техники. — 2005. — № 1. — С. 36-38. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS:52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/78456 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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English |
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Magnetic confinement Magnetic confinement |
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Magnetic confinement Magnetic confinement Kotenko, V. G. The influence of a transverse shift of torsatron magnetic surfaces on their parameters Вопросы атомной науки и техники |
| description |
The paper deals with the influence of the transverse shift (or axial shift along the axis of torus rotation) of magnetic surfaces on their parameters in a calculation model of the l=2 torsatron magnetic system. The shift can be realized by means of a special-purpose controlling coil of a helical type. The coil action combined with the well-known action of common annular controlling coil is considered as an instrument for two-dimensional control of the plasma core position in stellarator-type plasma devices. |
| format |
Article |
| author |
Kotenko, V. G. |
| author_facet |
Kotenko, V. G. |
| author_sort |
Kotenko, V. G. |
| title |
The influence of a transverse shift of torsatron magnetic surfaces on their parameters |
| title_short |
The influence of a transverse shift of torsatron magnetic surfaces on their parameters |
| title_full |
The influence of a transverse shift of torsatron magnetic surfaces on their parameters |
| title_fullStr |
The influence of a transverse shift of torsatron magnetic surfaces on their parameters |
| title_full_unstemmed |
The influence of a transverse shift of torsatron magnetic surfaces on their parameters |
| title_sort |
influence of a transverse shift of torsatron magnetic surfaces on their parameters |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2005 |
| topic_facet |
Magnetic confinement |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/78456 |
| citation_txt |
The influence of a transverse shift of torsatron magnetic surfaces on their parameters / V. G. Kotenko // Вопросы атомной науки и техники. — 2005. — № 1. — С. 36-38. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT kotenkovg theinfluenceofatransverseshiftoftorsatronmagneticsurfacesontheirparameters AT kotenkovg influenceofatransverseshiftoftorsatronmagneticsurfacesontheirparameters |
| first_indexed |
2025-07-06T02:32:58Z |
| last_indexed |
2025-07-06T02:32:58Z |
| _version_ |
1836863118828896256 |
| fulltext |
THE INFLUENCE OF A TRANSVERSE SHIFT OF TORSATRON
MAGNETIC SURFACES ON THEIR PARAMETERS
V. G. Kotenko
Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and
Technology”, Kharkov 61108, Ukraine
The paper deals with the influence of the transverse shift (or axial shift along the axis of torus rotation) of magnetic
surfaces on their parameters in a calculation model of the l=2 torsatron magnetic system. The shift can be realized by
means of a special-purpose controlling coil of a helical type. The coil action combined with the well-known action of
common annular controlling coil is considered as an instrument for two-dimensional control of the plasma core position
in stellarator-type plasma devices.
PACS:52.55.Hc
INTRODUCTION
A special-purpose controlling coil (SPC) of the
torsatron has been a subject of discussion in paper [1,2].
With the SPC-generated magnetic field, the region of
closed magnetic surface existence in the torsatron
magnetic system can be shifted perpendicularly to the
equatorial plane of the torus (transverse shift or axial shift
along the axis of torus rotation). The SPC is an auxiliary
helical coil laid in a some special way on the surface of
the same torus where the main helical coil of the torsatron
resides. Each of l poles of the main helical coil is put into
correspondence to 1 pole of the auxiliary helical coil. Any
of the points of the auxiliary helical base line, along
which the auxiliary helical coil pole is laid, is at a
distance S=const from the main helical coil base line,
along which the main helical coil pole is laid. The
distance S=const. is reckoned along the torus parallel
drawn through this point. In Cartesian coordinates, where
the z-axis is coincident with the axis of torus rotation, the
equation for the auxiliary helical base line can be written
in a parametric form convenient for numerical
calculations:
x=(Ro+acosθ(ϕ))cos(ϕ±S/(Ro+acosθ(ϕ))),
y=(Ro+acosθ(ϕ))sin(ϕ±S/(Ro+acosθ(ϕ))),
z=asinθ(ϕ). (1)
Here Ro is the major radius of the torus, a is its minor radius,
θ is the poloidal angle, ϕ is the toroidal angle, θ(φ) is the
winding law of the main helical coil, the sign in the
argument expression depends on the direction of reckoning
the S distance. The method of construction an auxiliary
helical base line is similar to the method of construction a
conchoid of a plane line [3]. So eq. (1) can be considered as
an equation of conchoid of a spatial line, i.e., as an equation
of conchoid of helical line on the torus.
This papers deals with the influence of a transverse
shift of torsatron magnetic surfaces on their parameters.
CALCULATION MODEL
Calculation model of the torsatron magnetic system
had the following parameters: Ro=1, a=0.25, polarity l=2,
m=5 is the number of helical coil pitches along the length
of the torus. The electrical currents in the main filament-
like helical coil placed on the torus surface, give rise to a
longitudinal component of magnetic field bo on the torus
circular axis. Two SPC poles are displaced from the
corresponding poles of the main helical coil by S=0.35<2
π(Ro-a)/ml in the direction of toroidal angle ϕ increase.
The transverse magnetic field Bz was usually assumed
uniform in the calculations.
If the main helical coil is wounded by the cylindrical
winding law θ(ϕ)=5ϕ (straight line in Fig.1a), the SPC
winding law will have the appearance shown in Fig 1a
(curve2). Curve 2 in Fig.1b corresponds to the SPC
winding law when the main helical coil is laid by the
equal-inclined law θ(ϕ)=2arctg(1.291tg(2.5ϕ)), curve 1.
One can see here the significant nonlinear, difficult for
analytical description, difference between the “derivative”
(conchoid-type) winding law of the SPC and the
“original” winding law of the main helical coil.
0 20 40 60 80
0
100
200
300
, degree
, degree
1 2
0 20 40 60 80
0
100
200
300
, degree
, degree
1 2
Fig.1 The winding laws of the main 1a)- θ(ϕ)=5ϕ,
1b)- θ(ϕ)=2arctg(1.291tg(2.5ϕ)) and auxiliary 2a), 2b)
helical coils along the length of the helical pitch
36 Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 36-38
a
b
The paper presents the calculation results for the
torsatron model with a cylindrical winding law of the
main helical coil. Analogous results have been obtained
for the torsatron model with the equal-inclined winding
law of the main helical coil.
RESULTS OF CALCULATIONS
Fig.2a,b shows the calculated cross-sections of the
magnetic surface existence region and the equiconnect, as
the surface, on the outside of which the connection length
of the diverted field lines does not exceed the length of
the torus for two directions of integration [4,5].
Fig. 2a shows the calculated cross-sections for the SPC
turned out. The cross-sections are typical for the ordinary
torsatron in the regime Bz/bo=0.297 with minimal field ripple
value on the magnetic surfaces [6,7]. In this regime the
magnetic-axis major radius is Roax=0.9861, the magnetic-axis
minor radius is rax=0, i.e., the magnetic axis lies in the
equatorial plane (z=0) of the torus.
Fig.2b shows the cross-sections for the same regime
Bz/bo=0.297 but with the SPC turned on, when the SPC
current value is 0.031 of current value in the main helical
coil. It can be seen that all cross-sections are shifted
upward relative to the equatorial plane of the torus. The
shift value z=0.0203 (z/a<0.1) is estimated from the shift
of the magnetic-axis major radius. The value of the
magnetic-axis major radius remains the same,
Roax=0.9861, while the magnetic-axis minor radius
becomes different from zero, rax=0.0042, i.e., the plane
magnetic-axis transforms into a spatial magnetic axis.
Similarly to unshifted magnetic surfaces, the shifted
surfaces keep their shape, including the last closed
magnetic surface (LCMS) slightly decreased in volume.
The change in the equiconnect shape and equiconnect
position is more significant.
Fig.3 shows the magnetic surface parameters as
functions of the average magnetic surface radius. It is
seen from the figure that the magnetic surface shift is
accompanied by a decrease in both the LCMS average
radius and the rotational transform angle on the central
magnetic surfaces. The field ripple values and the
magnetic hill are increasing.
If the direction of SPC current changes, the cross
-sections shift downward relative to the equatorial plane
of the torus. Without a change in the current direction the
same effect can be attained by the use of the SPC, where
the distance S is reckoned in the opposite direction (in the
direction of decreasing ϕ).
ϕ=0o ϕ=9o ϕ=18o
Fig.2 Cross-sections of magnetic surfaces (dotted lines) and equiconnects (thin solid lines) within the half period of
magnetic field: a) the SРC is currentless, b) the SPC is turned on. Large solid points are the main helical base line
cross-sections, smaller solid points are the auxiliary helical base line cross-sections
a
b
0.00 0.04 0.08 0.12 0.16
0.00
0.50
1.00
1.50
2.00
2.50
10U,
r10U
i
i,
Fig.З. The field ripple γ, rotational transform angle ι (in
2π units), magnetic hill value U versus the average
magnetic surface radius r for shifted (solid lines) and
unshifted (dotted lines) magnetic surfaces
CONCLUSIONS
Magnetic-surface parameters in the l=2 torsatron
magnetic system model with the superimposed SPC
magnetic field have been investigated. The calculations
have shown that the superposition of the SPC magnetic field
exerts no critical effect. For the transverse shift z/a~0.1, the
relative changes of magnetic surface parameters are of the
same order. A marked change in the shape and position of
the equiconnect, i.e., the boundary of the stochastic layer of
magnetic field lines (SOL plasma), has been found. This
means the standard l=2 torsatron divertor configuration
transforms into an excessively localized divertor
configuration with a shortened connection length of diverted
magnetic field lines [8].
On the whole, it can be assumed that the above-
described changes mean the degradation of parameters of
the plasma confined on transversely shifted magnetic
surfaces. Thus, the SPC is to be considered, first of all, as
a tool for suppressing the magnetic-surface transverse
shift. An inaccuracy in both the manufacture and the
assembly of separate units of the real magnetic system
can provoke the transverse shift. Let us conceive that a
one-layer winding of the helical pole is laid along the
main helical base line on the same side, turn by turn with
a constant insulation spacing between them. Then the
helical line equation of the last turn in this layer is
supposed similar to equation (1) with the parameter S=(n-
1)d, where n is the number of turns in the layer, d is the
diameter of the conductor, including the insulation
thickness. As a result, the magnetic surface position can
disagree with the calculated value and equatorial
symmetry of different operating signals including the
plasma diagnostic signals can be violated. An interference
with other possible defects aggravates the problem. Partly
it can be settled through a symmetrical winding of the
conductor, i.e., turn-by-turn winding on both sides of the
main helical base line, or winding of each, taken
separately, turn by the winding law of the main helical
base line.
REFERENCES
1.V.G.Kotenko. Torsatron controlling coil of a special
purpose // Zhurn. Techn. Fiz. (74). 2004, No.9, p. 134-136
(in Russian).
2.Patent UA N 3094 IPC7 H05H1/16, 2004. / V.Kotenko,
D.V.Kurilo, Ju.F.Sergeev, V.G.Smirnov.
3.A.A.Savelov. Plane curves. M., 1960 (in Russian).
4.V.E.Bykov, Yu.K.Kuznetsov, A.V.Khodyachikh,
O.S.Pavlichenko, V.G. Peletminskaya. Magnetic divertor
in the l=3 U-3M system.//A Collection of Papers
Presented at the IAEA Technical Committee Meeting on
Stellarators and Other Helical Confinement Systems at
Garching, Germany 10-14 May 1993/ IAEA,Vienna,
Austria, 1993, p.391-396.
5.V.G.Kotenko, S.S.Romanov, N.T.Besedin. Stellarator-
type magnetic system for a research fusion reactor.//Ukr.
Fiz. Zhurn. (46). 2001, No.11, p.1127-1132 (in Ukraine).
6.V.Kotenko, E.Volkov, K.Yamazaki. Heliotron/torsatron
configuration with minimal field ripples.//Problems of
Atomic Science and Technology. Series: Plasma Physics
(9), 2003, No.1, p. 19-22.
7.V.Kotenko, E.Volkov, K.Yamazaki. Field ripple
behavior in helical systems.//Plasma Devices &
Operations (12). 2004, , No 2, p.143-152.
8.K.Nagasaki, K.Itoh, S.I.Itoh and A.Fukuyama. Analysis
of scrape-off layer in toroidal helical systems //
Proceedings of the First International Toki Conference
December 4-7, 1989/ NIFS-PROC-3, 1990, Nagoya,
Japan, p.65-68.
ВЛИЯНИЕ ПОПЕРЕЧНОГО СМЕЩЕНИЯ МАГНИТНЫХ ПОВЕРХНОСТЕЙ ТОРСАТРОНА НА ИХ
ПАРАМЕТРЫ
В. Г. Котенко
В работе выяснено влияние поперечного смещения (или осевого смещения вдоль оси вращения тора)
магнитных поверхностей на их параметры в расчетной модели l=2 торсатрона. Смещение осуществляется с
помощью специальной корректирующей обмотки винтового типа. Действие этой обмотки в сочетании с
обычной кольцеобразной корректирующей обмоткой позволяет осуществить 2-мерный контроль положения
плазменного шнура в плазменных ловушках стеллараторного типа.
ВПЛИВ ПОПЕРЕЧНОГО ЗМІЩЕННЯ МАГНІТНИХ ПОВЕРХОНЬ ТОРСАТРОНА НА ЇХ ПАРАМЕТРИ
В. Г. Котенко
В роботі з’ясовано вплив поперечного зміщення (або ж осьового зміщення вздовж осі обертання тора)
магнітних поверхонь на їх параметри в моделі l=2 торсатрона. Зміщення здійснюється за допомогою
спеціальної коректуючої обмотки гвинтового типу. Дія цієї обмотки в поєднанні з дією звичайної
кільцеподібної коректуючої обмотки надає можливість 2-вимірного контролю за положенням плазмового
шнура в плазмових пастках стелараторного типу.
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