Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces
The numerical calculations of magnetic field of the l=2 torsatron magnetic system with non-circular poloidal cross-section of the torus is carried out in the work. It is shown that the value δi≈0.2 of maximal relative deviation of a non-circular poloidal cross-section from basic circular one results...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1221152017-06-28T03:02:40Z Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces Kotenko Магнитное удержание The numerical calculations of magnetic field of the l=2 torsatron magnetic system with non-circular poloidal cross-section of the torus is carried out in the work. It is shown that the value δi≈0.2 of maximal relative deviation of a non-circular poloidal cross-section from basic circular one results in a several-fold contraction of closed magnetic surface existence region. There is some increase in the values of rotational transform angle and the mirror ratio in the central closed magnetic surfaces. An enlarged clearance between the outer boundary of field line stochastic layer, i.e., the boundary of the plasma layer having transient plasma parameters (SOL plasma) and the surface of vacuum chamber can be obtained by the transition from the circular torus to the non-circular torus under consideration. Проведены численные расчеты модели магнитной системы l=2 торсатрона с некруговым полоидальным сечением тора. Показано, что максимальная величина относительного отклонения δi≈0,2 полоидального сечения некругового тора от базисного кругового сечения приводит к уменьшению области существования замкнутых магнитных поверхностей и некоторому увеличению величины угла вращательного преобразования и пробочного отношения на центральных магнитных поверхностях. Существенно увеличилось расстояние между слоем стохастических силовых линий, т.е. между плазмой переходных параметров (SOL-плазмы) и поверхностью вакуумной камеры. Проведені чисельні розрахунки моделі магнітної системи l=2 торсатрона з некруглим полоїдальним перерізом тора. Показано, що максимальна величина відносного відхилення δi≈0,2 полоїдального перерізу некруглого тора від базисного круглого перерізу призводить до зменшення області існування замкнутих магнітних поверхонь та до збільшення величини кута обертового перетворення і величини дзеркального відношення на центральних магнітних поверхнях. Суттєво збільшилася відстань між прошарком стохастичних силових ліній, тобто між плазмою перехідних параметрів (SOL-плазмою) і поверхнею вакуумної камери. 2017 Article Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces / V.G. Kotenko // Вопросы атомной науки и техники. — 2017. — № 1. — С. 18-20. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/122115 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 Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces Вопросы атомной науки и техники |
| description |
The numerical calculations of magnetic field of the l=2 torsatron magnetic system with non-circular poloidal cross-section of the torus is carried out in the work. It is shown that the value δi≈0.2 of maximal relative deviation of a non-circular poloidal cross-section from basic circular one results in a several-fold contraction of closed magnetic surface existence region. There is some increase in the values of rotational transform angle and the mirror ratio in the central closed magnetic surfaces. An enlarged clearance between the outer boundary of field line stochastic layer, i.e., the boundary of the plasma layer having transient plasma parameters (SOL plasma) and the surface of vacuum chamber can be obtained by the transition from the circular torus to the non-circular torus under consideration. |
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Article |
| author |
Kotenko |
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Kotenko |
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Kotenko |
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Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces |
| title_short |
Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces |
| title_full |
Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces |
| title_fullStr |
Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces |
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Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces |
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effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Магнитное удержание |
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Effect of a non-circular shape of the torus on the l=2 torsatron magnetic surfaces / V.G. Kotenko // Вопросы атомной науки и техники. — 2017. — № 1. — С. 18-20. — Бібліогр.: 10 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2017. №1(107)
18 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 18-20.
EFFECT OF A NON-CIRCULAR SHAPE OF THE TORUS ON THE l=2
TORSATRON MAGNETIC SURFACES
V.G. Kotenko
Institute of Plasma Physics of the NSC KIPT, Kharkov, Ukraine
The numerical calculations of magnetic field of the l=2 torsatron magnetic system with non-circular poloidal
cross-section of the torus is carried out in the work. It is shown that the value δi≈0.2 of maximal relative deviation of
a non-circular poloidal cross-section from basic circular one results in a several-fold contraction of closed magnetic
surface existence region. There is some increase in the values of rotational transform angle and the mirror ratio in the
central closed magnetic surfaces. An enlarged clearance between the outer boundary of field line stochastic layer,
i.e., the boundary of the plasma layer having transient plasma parameters (SOL plasma) and the surface of vacuum
chamber can be obtained by the transition from the circular torus to the non-circular torus under consideration.
PACS: 52.55.Hc
INTRODUCTION
As opposed to an ordinary circular torus poloidal
cross-section minor radius of which ac=const. in a
noncircular torus the poloidal cross-section minor radius
an≠const. In the field of fusion research an example of
noncircular torus implementation is, in particular, the
vacuum chamber of present-day tokamaks, which have a
D-shaped poloidal cross-section. For the first time, the
stellarator-type magnetic system with a noncircular torus
poloidal cross-section highly elongated along the
straight z-axis of the torus, has been discussed in [1, 2].
The authors reported that the influence of toroidal
effects on the plasma diffusion and thermal conductivity
can be significantly decreased in the systems. In paper
[3] were presented the numerical calculation results for
the ideal model of the l=2 torsatron magnetic system
with non-circular torus, which poloidal cross-section
shape differs to a lesser extent from the initial circle.
Each helical coil of the ideal model consisted of 1
filament-like conductor turn. The main goal of the
investigation was to discover the additional possibility
to enlarge the distance between the closed magnetic
surface existence region and helical coils, i.e., the first
wall-plasma spacing in the stellarator-type fusion reactor
[4, 5]. The present study takes into account the model of
the l=2 torsatron magnetic system with the non-circular
torus the helical coils of which have real size cross-
section.
INITIAL CALCULATION MODEL
As an initial calculation model with a circular torus,
we use an l=2 torsatron magnetic system. The main
geometrical characteristics of the model are similar to
heliotron Large Helical Devise magnetic system
characteristics [6]:
- toroidicity αс3=aс3/R0=0.25, R0 is the major radius of
the torus, aс3 is the average radius of helical coils (see
below);
- l=2 is the polarity;
- m=5 is the number of helical coil pitches along the
torus length.
Each helical coil comprises 35 filament-like
conductor turns. The turns of each helical coil are placed
in 5 layers in 7 turns at the layer. The layers are located
on the surfaces of 5 nested coaxial torus with minor radii
aci/R0=αci=0.2, 0.225, 0.25, 0.275, 0.3 (i=1-5,
Fig. 1,a). The base (central) turn of i-layer is marked on
i-torus according to the combined winding law [7]:
ci= 0-k( ei- 0). (1)
Here θci is the poloidal angle, 0=m is the cylindrical
winding law, ei=2arctg(((1+ ci)/(1- ci))
0.5
tg( 0/2)) is the
equi-inclined winding law, is the toroidal angle,
k=0.52. The last 6 conductor turns in i-layer are
arranged turn by turn along the base turn (packing by
method 2 [8]).
a b
Fig. 1. Poloidal cross-sections of the nested coaxial circular tori (a) and inscribed non-circular tori (b)
Helical coil conductor turn traces are marked by large black points
ISSN 1562-6016. ВАНТ. 2017. №1(107) 19
=0
o
=9
o
=18
o
Fig. 2. Poloidal cross-sections of the magnetic surfaces in the initial calculation model with circular torus.
Cross-sections of the vacuum chamber is pointed out by clarified line
Fig. 2 shows the calculated poloidal cross-sections
for the helical coils and the closed magnetic surface
configuration in the magnetic system model under
consideration. The cross-sections are spaced apart by the
toroidal angle φ within the limits of the magnetic field
half-period, φ=0º, 9º, 18º. As is seen from Fig. 2, the
chosen combined law for the helical coil winding
provides the mode for the closed magnetic surface
configuration with a centered planar magnetic axis [7].
In all three cross-sections, the magnetic axis traces are
disposed in the torus equatorial plane and its major
radius remains invariable, R0ax/R0=1. The mode can be
realized at compensating uniform magnetic field
Bz/B0=0.35, where B0 is the amplitude of the toroidal
component of the magnetic field generated by helical
coils on the circular axis of the torus. The average radius
of the last closed magnetic surface is rlc/R0=0.14. The
magnetic surface parameter values are presented below
(in brackets).
Fig. 2 also represents (dashed lines) the calculated
cross-sections of the surface of the outer boundary of the
field-line stochastic layer [9, 10], i.e., the boundary of
the plasma layer having transient plasma parameters
(SOL plasma).
CALCULATION MODEL WITH A NON-
CIRCULAR TORUS
Similar to magnetic system with circular torus each
helical coil of the magnetic system with non-circular
torus comprises 35 filament-like conductor turns. The
turns of each helical coil are placed in 5 layers in 7
turns at the layer. The layers are located on the surface
of 5 the nested coaxial non-circular torus. By analogy
with [3] the running radius of non-circular torus cross-
section was determined from the equation:
ni= ci(1-δi|cos( 0)|),
where δi=0.175, 0.178, 0.18, 0.182, 0.184 (i=1-5, see
Fig. 1, b). Consequently the base (central) turn of i-layer
is marked on non-circular i-torus according to the
combined winding law:
θ= 0-k (2arctg(((1+ ni)/(1- ni))
0.5
tg( 0/2))- 0),
where k=0.52.
Fig. 3 shows the poloidal cross-sections calculated
for the magnetic surface configuration generated by
helical currents, lying on the surfaces of non-circular
tori. It is seen from the Fig. 3, the combined law opted
for the helical coil windings for the system with non-
circular torus provides a mode for the closed magnetic
surface configuration with the centered planar magnetic
axis too. The mode is realized at a compensating
uniform magnetic field value Bz/B0 =0.361. The average
radius of the last closed magnetic surface is
rlc/R0=0.047. The rotational transformation angle (in 2π
units) is ιaxis→ιlc=0.98 (0.5)→1.14 (0.75) on the
magnetic surfaces, a zero-order magnetic well (hill)
U=-0.005 (0.002) takes place, and the value of mirror
ratio is γaxis→γlc=1.05(1.02)→1.31(1.55). The
appropriate parameter values for the initial magnetic
surface configuration are indicated in brackets.
Fig. 2 also represents (dashed lines) the calculated
cross-sections of the surface of the outer boundary of the
field-line stochastic layer.
=0
o
=9
o
=18
o
Fig. 3. Poloidal cross-sections of the magnetic surfaces in the calculation model with the non-circular torus
20 ISSN 1562-6016. ВАНТ. 2017. №1(107)
CONCLUSIONS
Numerical calculations of magnetic field in the l=2
torsatron magnetic system model with the non-circular
torus the helical coils of which have real size cross-
sections is carried out in the work. Similar to ideal
magnetic system model [3] the transition from the
circular torus to the non-circular one results in a several-
fold contraction of closed magnetic surface existence
region. A noticeable increase in the values of the
rotational transform angle and the mirror ratio is
observed in the central magnetic surfaces. A zero-order
magnetic well value takes place. An enlarged clearance
can be obtained between the outer boundary of field line
stochastic layer and the vacuum chamber surface. The
result received can promote the further development the
conception of stellarator-type fusion reactor with
enlarged the plasma-1
st
wall spacing.
REFERENCES
1. I.S. Danilkin, L.M. Kovrizhnykh. Magnetic trap for
current-free plasma with elliptic magnetic surfaces –
stellatron (finger-ring stellarator) // Pis’ma v Zhurnal
Ehksperimental’noj i Teoreticheskoj Fiziki 19 (4). 1974,
p. 193-197 (in Russian).
2. I.S. Danilkin, L.M. Kovrizhnykh. Stellatron-a
magnetic system for containment of current-free plasma
with improved toroidal equilibrium // Nuclear Fusion.
Supplement. 1975, p. 93-98.
3. V.G. Kotenko. Magnetic field of helical currents
flowing over the surface of a non-circular torus //
Problems of Atomic Science and Technology. Ser.
“Termoyaderny Sintez”, Moscow. 2013, v. 36, № 4,
p. 64-69 (in Russian).
4. V. Kotenko, E. Volkov, K. Yamazaki. The right
method of approach to the commercial fusion reactor
problem // 30th EPS Conf. on Contr. Fusion. and
Plasma. Phys. St. Petersburg, 7-11 July 2003, ECA.
v. 27A, P-3.1.
5. V. Kotenko, E. Volkov, K. Yamazaki. An eventual
approach to the commercial fusion reactor problem on
the base of the stellarator-type closed magnetic systems.
// Problems of Atomic Science and Technology. Ser.
“Termoyaderny Sintez”, Moscow. 2004, v. 3, p. 29-37
(in Russian).
6. O. Motojima. Status of LHD project and construction.
// 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. 41.
7. V. Kotenko, E. Volkov, K. Yamazaki. Field ripple
behavior in helical systems //Plasma Devices and
Operations. 2004, v. 12, № 2, p. 143-153.
8. V.G. Kotenko, D.V. Kurilo, Yu.F. Sergeev. The
influence of methods of conductor packing in the helical
coil poles on the magnetic configuration of l=2 torsatron
in the regime with a planar magnetic axis // Problems of
Atomic Science and Technology, Ser. “Termoyaderny
Sintez”, Moscow. 2005, v. 4, p. 42-52 (in Russian).
9. V.E. Bykov, Yu.K. Kuznetsov, A.V.Khodyachikh,
O.S. Pavlichenko, V.G. Peletminskaya. Magnetic
divertor in the l=3 torsatron // 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. p. 391.
10. V.G. Kotenko. Possible mechanism for onset of
vertical asymmetry of diverted plasma fluxes in a
torsatron // Fiz. Plazmy. 2007, v. 33, № 3, p. 280 (in
Russian), Plasma Phys. 2007, v. 33, № 3, 2007, p. 249
(Engl. Transl.).
Article received 22.12.2016
ВЛИЯНИЕ НЕКРУГОВОЙ ФОРМЫ ТОРА НА МАГНИТНЫЕ ПОВЕРХНОСТИ ДВУХЗАХОДНОГО
(l=2) ТОРСАТРОНА
В.Г. Котенко
Проведены численные расчеты модели магнитной системы l=2 торсатрона с некруговым полоидальным
сечением тора. Показано, что максимальная величина относительного отклонения δi≈0,2 полоидального
сечения некругового тора от базисного кругового сечения приводит к уменьшению области существования
замкнутых магнитных поверхностей и некоторому увеличению величины угла вращательного
преобразования и пробочного отношения на центральных магнитных поверхностях. Существенно
увеличилось расстояние между слоем стохастических силовых линий, т.е. между плазмой переходных
параметров (SOL-плазмы) и поверхностью вакуумной камеры.
ВПЛИВ НЕКРУГОВОЇ ФОРМИ ТОРУ НА МАГНІТНІ ПОВЕРХНІ ДВОЗАХОДНОГО (l=2)
ТОРСАТРОНУ
В.Г. Котенко
Проведені чисельні розрахунки моделі магнітної системи l=2 торсатрона з некруглим полоїдальним
перерізом тора. Показано, що максимальна величина відносного відхилення δi≈0,2 полоїдального перерізу
некруглого тора від базисного круглого перерізу призводить до зменшення області існування замкнутих
магнітних поверхонь та до збільшення величини кута обертового перетворення і величини дзеркального
відношення на центральних магнітних поверхнях. Суттєво збільшилася відстань між прошарком
стохастичних силових ліній, тобто між плазмою перехідних параметрів (SOL-плазмою) і поверхнею
вакуумної камери.
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