Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems)
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| Date: | 2000 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Cite this: | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) / V.G. Kotenko, G.G. Lesnyakov, S.S. Romanov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 44-46. — Бібліогр.: 4 назв. — англ. |
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| author | Kotenko, V.G. Lesnyakov, G.G. Romanov, S.S. |
| author_facet | Kotenko, V.G. Lesnyakov, G.G. Romanov, S.S. |
| citation_txt | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) / V.G. Kotenko, G.G. Lesnyakov, S.S. Romanov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 44-46. — Бібліогр.: 4 назв. — англ. |
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UDC 533.9
44 Problems of Atomic Science and Technology. 2000. № 6. Series: Plasma Physics (6). p. 44-46
STELLARATOR FIELDS WITH 2-WIRE LINES WOUND ROUND THE
TORUS (L=3,4 SYSTEMS)
V. G. Kotenko, G. G. Lesnyakov, S. S. Romanov
Institute of Plasma Physics, National Science Center
"Kharkov Institute of Physics and Technology", 310108, Kharkov, Ukraine
1. Introduction
In this paper calculations are extended to the models
of new stellarator-type magnetic systems [1, 2],
subsequently referred to as YAMATOR [3, 4], where
the poloidal magnetic field components are formed with
the help of 2-wire lines wound round the torus.The
winding is made in such a manner that the wires of the
lines lie on the nested tori of the same major radius Ro
and different minor radii a1 and a2=a1+h, h being the
distance between the wires of the line. The number of 2-
wire lines forming the YAMATOR magnetic system
determines its polarity l. Here we outline some the
results concerning the l=3,4 YAMATOR systems.
2. Calculation model
Numerical calculations of toroidal systems were
carried out for the following basic model [2]: 2-wire
lines were wound on the torus along the helical line θ
=mϕ , θ is the poloidal angle, ϕ is the toroidal angle,
m=3 is the number of helical pitches along the torus,
h/Ro=0.15 is the distance between the wires of the line,
a1/Ro=0.3, a2/Ro=0.45 are the aspect ratios of nested
tori. The system is plunged into an axisymmetric
toroidal magnetic field Bϕ =BoRo/R, Bo is the toroidal
magnetic field value on the circular axis of the system,
R is the radial position of the observation point,
reckoned from the straight axis z. At operating basic
conditions the controlling transverse magnetic field is
Bz=0. The model allows a simple transition to the
torsatron system if Bo and the inner (or outer) helical
current I are put to zero. This circumstance has been
used to test the magnetic well value. The present results
are in good agreement with the known literature data.
3. The l=3 system
This system consists of three 2-wire lines wound
round the torus displaced from the other one by angle θ
=2π/3 in the poloidal direction. Fig.1 presents 3 poloidal
magnetic surface cross-sections within one magnetic
field period T=2π/ml ((a) ϕ =0, (b) ϕ =T/4, (c) ϕ =T/2).
Calculations were performed for Bz=0, Bo/bo=3.33,
with bo being the amplitude of the circular-axis
magnetic field generated by the helical current I
traversing the torus of the minor radius a1. It is seen
from the figures that, similarly to l=1,2 systems, there
are inner and outer closed magnetic-surface domains.
As in l=1,2 systems, the shape and position of the outer-
domain magnetic surfaces are almost independent of the
toroidal angle ϕ . The properties peculiar to these
surfaces are a very small rotational transform angle, i∼
10-2 (from here and on i is given in unit of 2π) and the
magnetic hill (+U) increasing as the average magnetic-
surface radius increases. So, the main parameters of the
outer-domain magnetic surfaces are not adequate for the
stellarator experiment. The parameters of the inner-
domain magnetic surfaces meet the requirements for
stellarator experiment. The magnetic surface parameters
of inner domain as functions of average magnetic-
surface radius r/Ro are shown in Fig.2. It is seen that in
the l=3 system, the magnetic well depth (-U)=38%,
i=0.25 can be attained.
4. The l=4 system
This system consists of four 2-wire lines wound
round the torus displaced from the other one by angle θ
=π/2 in the poloidal direction. Fig.3 presents 3 poloidal
magnetic surface cross-sections within one magnetic
field period in this system for Bz=0, Bo/bo=3.75. As in
the l=1,2,3 systems, two domains of closed magnetic
surfaces exist, and the main parameters of the outer-
domain magnetic surfaces are not adequate for the
stellarator experiment. In the inner domain (see Fig. 2)
the l=4 system provides (-U)=45% and i increases
from 0.25 to 0.4 at the last closed magnetic surface
(LCMS).
5. Effect of the parameter h
In the YAMATOR systems there is a parameter h,
defining the spacing between the wires of the 2-wire
line, which has no analogy in conventional stellarator
magnetic systems. Its value determines the ratio of one
helical coil minor radius to another a2/a1, and thus
governs the YAMATOR magnetic system design. Fig. 4
presents the LCMS parameters as functions of the ratio
a2/a1 (a1=const.) for l=3,4 systems at Bz=0,
Bo/bo=3.33, 3.75, respectively. As the parameter h
decreases, the magnetic well appreciably increases and
the LCMS rotational transform angle ι lc decreases; this
is accompanied by an increase in the magnetic axis
radius Rax/Ro (ϕ =0 cross-section), the rotation of field
lines slows down mainly at the inner parts of the
magnetic surfaces. From Fig.4 it also follows that in the
YAMATOR system the magnetic well growth is not
accompanied, as it takes place in conventional
stellarator systems, by an essential loss of the LCMS
volume. If (-U) increases (h decreases), the average
LCMS radius rlc/Ro varies only slightly in these
systems. If the transverse controlling magnetic field is
45
applied (Bz≠0), the behavior of the average LCMS
radius relative to the magnetic well value is similar.
6. Modular YAMATOR system
It has been indicated earlier [2] that a simple
realization of a module version of the YAMATOR
system consists in joining the 2-wire line segments 1 on
the module ends by means of radial current-carrying
jumpers 2 of length h (see Fig 5). The jumper currents at
the adjacent ends of modules arrainged in series are
equal and opposite. So, the magnetic field perturbations
caused by these radial currents seem to be compensated
very well, at least, for the case of filament-like
conductors considered here. Indeed, numerical
calculations of a six-module version of the l=3
YAMATOR system [1] at basic operating conditions
with the intermodule angular distance ∆ϕ =4o have not
shown any appreciable disturbances of the magnetic
surface configuration or magnetic surface parameters.
0.5 1.0 1.5 2.0 2.5 3.0
R / Ro
-1.0
-0.5
0.0
0.5
1.0
Z
/ R
o
(a)
0.5 1.0 1.5 2.0 2.5 3.0
R / Ro
-1.0
-0.5
0.0
0.5
1.0
Z
/ R
o
(b)
0.5 1.0 1.5 2.0 2.5 3.0
R / Ro
-1.0
-0.5
0.0
0.5
1.0
Z
/ R
o
(c)
Fig.1.
0.0 0.1 0.2 0.3
r / Ro
0
10
20
30
40
-U
, %
0.1
0.2
0.3
0.4
ι
1. l=3, m=3
2. l=4, m=3
1
2
Fig.2.The rotational transform angle ι and the magnetic
well (-U) versus the average magnetic-surface radius
r/Ro in the l=3, 4 YAMATOR systems
0.5 1.0 1.5 2.0 2.5
R / Ro
-1.0
-0.5
0.0
0.5
1.0
Z
/ R
o
(a)
0.5 1.0 1.5 2.0 2.5
R / Ro
-1.0
-0.5
0.0
0.5
1.0
Z
/ R
o
(b)
0.5 1.0 1.5 2.0 2.5
R / Ro
-1.0
-0.5
0.0
0.5
1.0
Z
/ R
o
(c)
Fig.3.
46
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
a / a
0.2
0.3
r
/
R
o
0.0
0.1
0.2
0.3
0.4
0.5
0.6
ι
12
lc
lc
1.1
1.2
1.3
R
a
xi
s
/ R
o
30
40
50
-U
,%
l=3
l=4
Fig.4 Radius Rax/Ro of the magnetic axis at ϕ =0,
LCMS rotational transform angle ι lc, magnetic well
(-U) and LCMS average radius rlc/Ro versus the nested
tori minor radii ratio a2/a1, where a1=const
1
2
3
Fig.5 Top view of the six-module version of the l=3,
m=3 YAMATOR (third part): the 2-wire line segment,
1; the radial current-carrying jumper, 2; toroidal field
coil, 3
7. Summary
The main special feature of the new magnetic
systems is the possibility to form on their base a toroidal
magnetic field with a large magnetic well (-U∼ a1/Ro).
The latter grows as the polarity l increases, and for a
given l it can still be increased if the parameter h<<a1.
In a real YAMATOR these methods to adjust the
magnetic well value will have a natural limitation due to
the finite size of current-currying conductors, this being
aggravated by an increasing toroidicity of the
configuration. There is another limitation caused by the
rotational transform angle value acceptable for
stellarator experiment, since this angle always decreases
as the magnetic well grows. The other characteristic
feature of the YAMATOR systems is a great volume of
the magnetic surfaces, especially in l>1 systems with a
low h value. Both the features seem to be very attractive
for the commercial fusion reactor on condition that the
first wall problem is finally solved. However, to support
this suggestion, comprehensive theoretical,
experimental and engineering investigations must be
done. The nearest step includes the study of the
influence of finite-size conductors on the magnetic
configuration in the real YAMATOR, elucidation of the
possibility to construct an effective divertor in it, and
the neoclassical transport loss estimation.
Acknowledgments
The authors are grateful to Prof. E. D. Volkov, Prof.
K. S. Stepanov, Dr. S. V. Kasilov, Dr. A. N. Dakhov for
every kind of assistance.
References
1. V. G. Kotenko. Report, 2nd Ukrainian Conf. on
Controlled Nuclear Fusion and Plasma Physics,
Kharkov, December 20-23, 1993 (Proceedings
unpublished).
2. V. G. Kotenko, G. G. Lesnyakov, S. S. Romanov.
Voprosy Atomnoj Nauki i Tekhniki (NNTs "KhFTI",
Kharkov, 1999). Problems of Atomic Science and
Technology, Series: Plasma Physics, Issues 1 (1), 2
(2), p.49 (NSC "KhIPT", Kharkov, 1999) (in
English).
3. V. G. Kotenko, G. G. Lesnyakov, S. S. Romanov. 7th
Ukrainian Conf. on Controlled Nuclear Fusion and
Plasma Physics, Kiev, September 20-21, 1999.
Book of abstracts, p. 48 (in Ukraine).
4. V. G. Kotenko, G. G. Lesnyakov, S. S. Romanov.
10th Intern. Toki Conf. on Plasma Physics and
Controlled Nuclear Fusion (ITC-10), January 18-21,
2000. Abstracts, PI-8, p. 60.
Acknowledgments
References
|
| id | nasplib_isofts_kiev_ua-123456789-78489 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:31:31Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kotenko, V.G. Lesnyakov, G.G. Romanov, S.S. 2015-03-18T15:40:27Z 2015-03-18T15:40:27Z 2000 Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) / V.G. Kotenko, G.G. Lesnyakov, S.S. Romanov // Вопросы атомной науки и техники. — 2000. — № 6. — С. 44-46. — Бібліогр.: 4 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/78489 533.9 The authors are grateful to Prof. E. D. Volkov, Prof. K. S. Stepanov, Dr. S. V. Kasilov, Dr. A. N. Dakhov for every kind of assistance. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) Article published earlier |
| spellingShingle | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) Kotenko, V.G. Lesnyakov, G.G. Romanov, S.S. Magnetic confinement |
| title | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) |
| title_full | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) |
| title_fullStr | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) |
| title_full_unstemmed | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) |
| title_short | Stellarator fields with 2-wire lines wound round the torus (L=3,4 systems) |
| title_sort | stellarator fields with 2-wire lines wound round the torus (l=3,4 systems) |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78489 |
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