The influence of the helical-coil angular size on the Yamator magnetic surface characteristics
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| Дата: | 2002 |
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| Мова: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Назва видання: | Вопросы атомной науки и техники |
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| Цитувати: | The influence of the helical-coil angular size on the Yamator magnetic surface characteristics / V.G. Kotenko, E.D. Volkov // Вопросы атомной науки и техники. — 2002. — № 4. — С. 65-66. — Бібліогр.: 3 назв. — англ. |
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irk-123456789-802512015-04-15T03:01:58Z The influence of the helical-coil angular size on the Yamator magnetic surface characteristics Kotenko, V.G. Volkov, E.D. Magnetic confinement 2002 Article The influence of the helical-coil angular size on the Yamator magnetic surface characteristics / V.G. Kotenko, E.D. Volkov // Вопросы атомной науки и техники. — 2002. — № 4. — С. 65-66. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/80251 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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Magnetic confinement Magnetic confinement |
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Magnetic confinement Magnetic confinement Kotenko, V.G. Volkov, E.D. The influence of the helical-coil angular size on the Yamator magnetic surface characteristics Вопросы атомной науки и техники |
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Article |
| author |
Kotenko, V.G. Volkov, E.D. |
| author_facet |
Kotenko, V.G. Volkov, E.D. |
| author_sort |
Kotenko, V.G. |
| title |
The influence of the helical-coil angular size on the Yamator magnetic surface characteristics |
| title_short |
The influence of the helical-coil angular size on the Yamator magnetic surface characteristics |
| title_full |
The influence of the helical-coil angular size on the Yamator magnetic surface characteristics |
| title_fullStr |
The influence of the helical-coil angular size on the Yamator magnetic surface characteristics |
| title_full_unstemmed |
The influence of the helical-coil angular size on the Yamator magnetic surface characteristics |
| title_sort |
influence of the helical-coil angular size on the yamator magnetic surface characteristics |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2002 |
| topic_facet |
Magnetic confinement |
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http://dspace.nbuv.gov.ua/handle/123456789/80251 |
| citation_txt |
The influence of the helical-coil angular size on the Yamator magnetic surface characteristics / V.G. Kotenko, E.D. Volkov // Вопросы атомной науки и техники. — 2002. — № 4. — С. 65-66. — Бібліогр.: 3 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T04:13:09Z |
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2025-07-06T04:13:09Z |
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1836869421804552192 |
| fulltext |
THE INFLUENCE OF THE HELICAL-COIL ANGULAR SIZE ON THE
YAMATOR MAGNETIC SURFACE CHARACTERISTICS
V.G.Kotenko, E.D.Volkov
Institute of Plasma Physics, NSC KIPT, 61108 Kharkov, Ukraine
PACS: 52.55.Hc
INTRODUCTION
New stellarator-type magnetic systems, called as
Yamator, have been considered in papers [1-3].
Numerical calculations were carried out there for the ideal
toroidal models of Yamator magnetic systems with
filament-like (i.e., vanishing transverse dimensions)
helical conductors. The calculations have demonstrated
that the closed magnetic surface region with a high
magnetic well value -U~0.1-0.5 can exist. The practical
realization of those magnetic systems will evidently meet
the necessity to determine the influence of real finite size
of helical conductors/coils on the basic characteristics of
the magnetic surfaces, first of all, on the magnetic well
value. In this paper the magnetic surface characteristics
are numerically studied for the Yamator with helical coils
in the form of finite-angular-size thin strip. The main task
of the study has been to get a general idea about the
tendencies in variations of Yamator magnetic surface
characteristics when passing from ideal magnetic systems
closer to the real ones.
CALCULATION MODEL
As an initial ideal model, the l=2, m=3 Yamator
magnetic system [1] was chosen for calculations. This
system consists of two (l=2) 2-wire lines with equal-in-
magnitude and opposite-in-direction wire currents. The 2-
wire lines are wound round the torus along the helical
lines θ=mϕ and θ=mϕ+π, θ is the poloidal angle, ϕ is the
toroidal angle, m=3 is the number of helical line pitches
on the length of the torus. The wires (helical
conductors/coils) of each 2- wire line lie on the coaxial
tori of the same major radius Ro and different minor radii
a1=0.3 and a2=0.45, a2-a1=0.15 being the distance
between the wires of the 2-wire line. Here and in what
follows the lengths are given in Ro units. The amplitude of
the circular-axis magnetic field generated by the helical
current traversing the torus of the minor radius a1 is bo. In
the ideal model the magnetic surface configuration forms
if the superimposed toroidal circular-axis magnetic field
strength is Bo/bo=2.5. The magnetic surface characteristics
are presented in Table 1 (System 1, see below).
Fig.1 shows the scheme of the l=2 m=3 Yamator
magnetic system with helical coils in the form of thin
strips. The strip angular sizes are ∆θh=45o (poloidal angle)
and ∆ϕh=15o (toroidal angle). The strip was approximated
by 11 filament-like conductors with a toroidal angular
distance of δϕ=1.5o between them. Each of 11 filament-
like conductors obeys the winding law θ=mϕ (cylindrical
law).
For comparison to the ideal model, the regime of the
magnetic axis geometry similarity was taken. The
Yamator magnetic system belongs to the type of helical
magnetic systems, where the undistorted magnetic axis is
Ro
a1
a2
Fig.1. A scheme of l=2, m=3 Yamator (top view) with
real-angular-size helical coils: there are 11 filamentary
helical conductors spaced 1.5о apart along the toroidal
angle in each helical coil. The longitudinal magnetic field
coils are not shown.
a helical line, wound round the imaginary torus almost of
a circular cross-section and closed on itself after one go-
round along the torus. At the upper right of Fig.2a the
major radius of this torus is designated as Roax (magnetic
axis major radius), the minor radius–as rax (magnetic axis
minor radius, index 1 concerns the ideal magnetic system,
index 11- the one with a strip).The magnetic axis
geometry similarity means fixing the value of the
magnetic-axis major radius, (Roax)1=(Roax)11=Roax=const.
For the ideal Yamator magnetic system under
consideration, (Roax)1=1.1372 for (Bo/bo)1=2.5. For the
system with a helical strip the calculations give
(Roax)11=1.1372 provided that (Bo/bo)11=1.986. The
(Bo/bo)1/(Bo/bo)11 ratio for a given magnetic field Bo
strength points to the necessity of raising the helical
current by a factor of ~1.26 to form the similar (in above-
given sense) magnetic surface configuration in the
Yamator with a helical strip.
RESULTS
Fig.2 shows three poloidal magnetic-surface cross-
sections within ½ magnetic field period (a) ϕ=0, b) ϕ=15o,
c) ϕ=30o ) for the Yamator magnetic system with a helical
strip (dotted lines) and the cross-section of the last closed
magnetic surface (LCMS) for the ideal Yamator model
(thin solid line). It is seen from the figures that the
magnetic surface existence region has appreciably
decreased as compared to that in the ideal model. The
LCMSs are not equidistant, i.e., in each cross-section
there exists the θ azimuth region, where LCMS contours
Problems of Atomic Science and Technology. 2002. № 4. Series: Plasma Physics (7). P. 65-66 65
coincide. At the upper right of Fig. 2a the toroidal
projection of the magnetic axis trajectory on an enlarged
scale is shown. It can be seen that the magnetic axis
minor radius increases, (rax)11>(rax)1, as the helical-coil
angular size increases.
0.60 1.00 1.400.80 1.20
Roax
(r )ax 1
(r )ax 11
R
a)
0.60 1.00 1.400.80 1.20 R
b)
0.60 1.00 1.400.80 1.20 R
c)
Fig.2. The magnetic surface poloidal cross-sections for
Yamator magnetic system with helical strip (dotted lines)
and the LCMS for ideal Yamator magnetic system (thin
solid line). The poloidal cross-sections of the coaxial tori
and the helical strips are shown, the longitudinal
magnetic field coils are not shown.
The geometrical parameters of magnetic systems and
magnetic axes under comparison, and the magnetic
surface characteristics are summarized in Table 1. Here, –
Ulc is the magnetic well value on the LCMS, iax, ilc are the
rotational transform angles (in units of 2π) near the
magnetic axis and on the LCMS, γax, γlc are the magnetic
field ripples on the magnetic axis and on the LCMS,
respectively; rlc is the average LCMS radius.
Table 1
System 1 11
l 2 2
m 3 3
a1 0.3 0.3
a2 0.45 0.45
θ mϕ mϕ
θh 0o 45o
ϕh 0o 15o
Bo/bo 2.5 1.986
rk 0.27 0.24
-Ulc 0.25 0.184
iax 0.26 0.33
ilc 0.29 0.33
γax 1.15 1.17
γlc 2.28 2.08
Bz/bo 0.0 0.0
From the analysis of Table 1 it becomes clear that in
the Yamators with a thin helical strip of the poloidal
angular size ∆θh≤45o the magnetic well is reduced by ≤
20%, the LCMS average radius is cut down by ≤ 11%, the
magnetic field ripple value on the LCMS falls off by ≤
11%. The magnetic surface configuration still remains
shearless, the rotational transform angle increases by ≤
20%. The calculations were performed for the controlling
transverse magnetic field Bz/bo=0, z is the principal
(straight) axis of the system
SUMMARY
The calculations performed have demonstrated the
possibility of existence of the inner closed magnetic
surface region in the Yamator with helical coils in the
form of the finite angular size thin strip. In the l=2, m=3
Yamator with ∆θh=45o angular size helical coils, the
magnetic surface characteristics, including the magnetic
well value, differ by no more than ~10-25% from the
ideal level.
A new method of comparison between the magnetic
surface characteristics in ideal and real helical magnetic
systems is suggested. It is based on searching for the
magnetic-axis geometry similarity regime, i.e., equal
values of magnetic-axis major radii.
REFERENCES
1. V.G.Kotenko, G.G.Lesnyakov, S.S.Romanov, Probl. of
Atomic .Science and Techn. Ser. Plasma Phys.
NSC”KIPT”, Kharkov, 1999, Iss. 1(1), 2(2), p.49-51.
2. V.G.Kotenko, G.G.Lesnyakov, S.S.Romanov. 7th
Ukraine Conf. on Contr. Fus. and Plasma Phys., Kiev,
September 20-21, 1999, Book of Abstracts, p.48 (in
Ukrainian.).
3. V.G.Kotenko, G.G.Lesnyakov, S.S.Romanov. Plasma
Fus. Res. SERIES: Vol 3(2000), p.154-157.
V.G.Kotenko, E.D.Volkov
Institute of Plasma Physics, NSC KIPT, 61108 Kharkov, Ukraine
PACS: 52.55.Hc
Introduction
Calculation model
Fig.1. A scheme of l=2, m=3 Yamator (top view) with real-angular-size helical coils: there are 11 filamentary helical conductors spaced 1.5о apart along the toroidal angle in each helical coil. The longitudinal magnetic field coils are not shown.
Results
System
Summary
References
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