Investigation of divertor field lines in the NCSX stellarator
Divertor field lines calculations for NCSX stellarator are presented. The recommendations are given for the correction of the vacuum vessel and FW shape in order to perform an optimum arrangement of divertor system components. Представлені розрахунки диверторних силових ліній для стеларатора NCSX. З...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2003 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Cite this: | Investigation of divertor field lines in the NCSX stellarator / V.A. Rudakov, A.V. Georgiyevskiy, W. Reiersen // Вопросы атомной науки и техники. — 2003. — № 1. — С. 7-12. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860238515971817472 |
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| author | Rudakov, V.A. Georgiyevskiy, A.V. Reiersen, W. |
| author_facet | Rudakov, V.A. Georgiyevskiy, A.V. Reiersen, W. |
| citation_txt | Investigation of divertor field lines in the NCSX stellarator / V.A. Rudakov, A.V. Georgiyevskiy, W. Reiersen // Вопросы атомной науки и техники. — 2003. — № 1. — С. 7-12. — англ. |
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| description | Divertor field lines calculations for NCSX stellarator are presented. The recommendations are given for the correction of the vacuum vessel and FW shape in order to perform an optimum arrangement of divertor system components.
Представлені розрахунки диверторних силових ліній для стеларатора NCSX. Зроблені пропозиції щодо корекції вакуумної камери з метою оптимального розташування диверторних пристроїв.
Представлены расчеты диверторных силовых линий для стелларатора NCSX. Сделаны рекомендации по коррекции вакуумной камеры с целью оптимального расположения диверторных устройств.
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| first_indexed | 2025-12-07T18:27:06Z |
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INVESTIGATION OF DIVERTOR FIELD LINES IN THE NCSX
STELLARATOR
V.A.Rudakov 1, A.V.Georgiyevskiy 2, W.Reiersen 2
1 Kharkov Insitute of Physics and Technology; 2 Princeton Plasma Physics Laboratory (USA)
Divertor field lines calculations for NCSX stellarator are presented. The recommendations are given for the correction
of the vacuum vessel and FW shape in order to perform an optimum arrangement of divertor system components.
PACS: 52.55.Hc
The paper is aimed to studying the divertor magnetic
fluxes in the NCSX stellarator for the purpose to establish
the optimum places for arrangement of divertor system
components. The vacuum vessel and the first wall (FW)
of the NCSX stellarator have a complicated spatial
configuration that makes as a nontrivial problem of
determining the regions where the divertor magnetic
fluxes cross the first wall.
The vacuum configuration studied for NCSX was
based on the LI383 magnetic system with a major radius
of Ro=1.7 m and with M45 coils. The last closed
magnetic surface (LCMS) is shown in Fig.1 at the V=0.5
cross-section. The location of the LCMS was determined
by starting field lines on the midplane on the inboard and
outboard sides of the v=0.5 cross-section for Rst=1.21-
1.25m and Rst= 2.20 - 2.29m. In searching for the LCMS
we usually used 200 field periods. The central iota was
calculated to be 0.66. Iota drops below 0.6 and returns to
0.6 at the LCMS. There are the 3/5 islands inside of
LCMS.
Fig.1. V=0.5,(Vst=0.5,U=0, Rst=2290 mm),
Divertor line , L=±11.1, (Vf=3.517, Uf= 0.388)
Fig.2. Divertor field line length dependence versus
start radius, Vst=1.5
Connection lengths have been calculated as a function
of starting point as shown in Figures 2 and 3. For starting
points on the open field lines between the LCMS and the
3/5 islands outboard the plasma, the connection lengths
are still long, more then 100m. For starting points outside
the 3/5 islands, the connection lengths quickly become
small, dropping from more than 750m (200 field periods)
to less than 15m in only a few mm. The same steep drop
may be seen for starting points inboard of the plasma
where island structures are not apparent.
Fig.3. Divertor field line length dependence versus
start radius, Vst=1.5 (positive and negative directions)
An alternative method for following field lines is to
actually start them on the first wall. This is practically
true for non-vacuum configurations (with finite beta and
plasma current), in which it is difficult to determine the
precise location and geometry of the LCMS. By starting
the field line on the first wall, we reduce the number of
dimensions to scan from 3 to 2 and preclude following
any field lines that do not intercept the first wall. We can
also quickly determine where the longest field lines will
intercept the first wall.
In Figs. 4 and 5 is seen that all of the long (>5m) field
lines start and finish on points that connect the tips of the
bean (u=0.3, 0.7) in the v=0 cross-section, and the nose
with corners (u=0.4, 0.6) in the bullet-shaped (v=0.5)
cross-section. The largest bubbles, which correspond to
the longest field line lengths, are clearly clustered near the
nose and corners of the bullet cross-section (Figs.6, 7).
Away from these points, the field line lengths are quite
small. These regions correspond to the places where the
value of the poloidal field normal to the first wall surface
is at a relative maximum, as shown in Figure 8. Minimum
of field line lengths is observed in the regions where the
poloidal field normal to the first wall surface is zero.
The longer field lines spend most of their transit time
close to the LCMS. Only near the end of their transits
they do depart from the close proximity to the LCMS and
intercept the first wall away from the helical stripes (see
Fig.9, 10). The field line starts in the upper tip of the
bullet-shape cross-section (v=0.5, 1.5, ...) The field line
proceeds along the thin line and is inside the all
Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 13-15 13
-0,4
-0,3
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0
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-0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6
R, m
Z,
m
0.5
1.5
2.5
3.5
S
0.1
0.20.3
0.5
0.8
0.9
0.7
F
1
10
100
1000
1,21 1,215 1,22 1,225 1,23 1,235 1,24 1,245 1,25
Rst, m
L,
m
Series1
Series2
Series3
-1000
-800
-600
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0
200
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1000
2,19 2,2 2,21 2,22 2,23 2,24 2,25 2,26 2,27 2,28 2,29
L,
m
Series1
Series2
Rst, m
intermediate cross-sections (0,0.25, 0.5, 0.75, 1, ...) of the
first wall.
Fig.4. Divertor field line length dependence, Vst=1.5
Fig.5. Divertor field line length dependence, Vst=2
To achieve a long field line length, it is necessary to
ensure that field lines starting near the helical stripes do
not prematurely intercept the first wall. By starting points
near these helical stripes and following the field line, it
becomes apparent where and by what extent the first-wall
boundary should be move out to extend the length of the
field line. Ultimately, the field line will stop wrapping
around the plasma and begin wrapping around a coil, thus
setting an upper bound on the maximum field line length.
As shown in Figure 11, the field line starts with a
length (L) of zero and distance (DL) of zero. A value DL
less than zero indicates that the field line is on the plasma
side of the first wall. Positive value of DL indicates that
the field line has intercepted and is outside the first wall.
The field line does few excursion inside and outside the
first wall with deviation less than 10 cm and at a distance
of 47 m along the field line, it intercepts the first wall and
does not return. The lesson here is that by locally pushing
out the first wall boundary by not more than 11cm, this
field line length could be increased from 7m to 47m.
The other possibility to increase the divertor field line length is
to use bz field correction and Kϕ correction. We have studied
a possibility of increasing the DFL length (Lmax) with the
relatively small (≤10%) increase of the coefficient K ϕ and
selection of a suitable vertical correcting magnetic field ∆bZ.
Fig.6. V=0.5, first wall cross-section, divertor field line
length dependencies L≥6 m (+)
Fig.7. V=1, first wall cross-section, divertor field line
length dependencies (L≥6 m -largest bubbles)
Fig. 8. Vector poloidal field, V=0.5, scale 0.11 T /cm
14
-14
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2
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U
L,
m
Series1
Series2
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
U
L,
m Series1
Series2
-0,5
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0
0,1
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-0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7
R, m
Z,
m
Series7
Series8
Series9
Series10
Series11
+
+
+
+
+
+
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+
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R , m
Z,
m
Series 1
Ser ies 2
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+
+
-1
-0,8
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-0,4
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0
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-1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1
R, m
Z,
m
Series1
Series2
Series3
Series4
+
+
+
+
-
-
-
-
(Notice, that the value of Kϕ equals to the ratio of the toroidal
magnetic field (Bmc) in the modular coils (MC) to the total
toroidal field (B0) created by MC and coils of an additional
toroidal field (TF)). It has been shown that the above-
mentioned increase in Kϕ leads to the significant
(approximately in 2 times) increase of the DFL length
(maximum values of the length Lmax were increased
from 12.6 m (for Kϕ = 1.126) to 27 m (for Kϕ = 1.2).
Such an increase of Kϕ leads to the insignificant
(approximately by 10%) decrease of LCMS sizes and to
the increase of values of rotational transform angles t.
Fig.9. Field line path, (Vst=1.5,Ust=0.64 ), R,Z plane,
Rcf=1.3Rfw, L=+11.3 m, First wall cross-sections:
V=0.25,0.5, 0.75 , 1
0
0,2
0,4
0,6
0,8
1
1,2
0 0,5 1 1,5 2 2,5 3
V
U*
Series1
Series2
S
Fw1+
Fd+
Fd- Fw2
Fw3
Fw4
Fw5
Fig.10. (Vst=1,Ust=0.3 ), (U* =θ/2π, V) plane,
Rcf=1.3Rfw, L=+47.22 m, positive direction L=-6.82 m,
negative direction
Fig 11. Field line deviations with respect to the first wall
(Vst=1, Ust=0.3)
CONCLUSION
1. Parameters and behavior of divertor field lines in the
gap between the LCMS and FW are studied.
Magnetic surfaces in the edge region are not smooth
surfaces. Isolated island structure is present. Long
length field lines in the island's structure were
observed. A steep drop in field line length was seen
outside the region where long field line length were
observed.
2. A new, comparatively simple method (method -
starting from and finishing on the first wall) was
proposed. The method allowed to determine the
regions, where field lines have maximum length.
These regions correspond to tips of the magnetic
configuration.
3. It has been found that, because of the complicated
spatial vessel configuration, the field lines crossing
the first wall surface, before going out of the volume
enclosed by the modular coils, make multiple
crossings over the first wall. The recommendations
are given for the correction of the vacuum vessel and
FW shape in order to perform an optimum
arrangement of deviator system components.
ДОСЛІДЖЕННЯ ДИВЕРТОРНИХ СИЛОВИХ ЛІНІЙ В СТЕЛАРАТОРІ NCSX
В.А. Рудаков, О.В. Георгієвський, У. Реєрсен
Представлені розрахунки диверторних силових ліній для стеларатора NCSX. Зроблені пропозиції щодо корекції
вакуумної камери з метою оптимального розташування диверторних пристроїв.
ИССЛЕДОВАНИЕ ДИВЕРТОРНЫХ СИЛОВЫХ ЛИНИЙ В NCSX СТЕЛЛАРАТОРЕ
В.А. Рудаков, А.В. Георгиевский, У. Рейерсен
Представлены расчеты диверторных силовых линий для стелларатора NCSX. Сделаны рекомендации по
коррекции вакуумной камеры с целью оптимального расположения диверторных устройств.
15
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0 5 10 15 20 25 30 35 40 45 50
L, m
DL
, m
Var 1
2 3 4 5 6 7 8 9 10
11
12 13Fw1 Fw2 Fw3 Fw4 Fw5
Fw6
Fw7 Fw8
Fw9
Fw10
Fw11
-1
-0,8
-0,6
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-0,2
0
0,2
0,4
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1
-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8
R, m
Z,
m
Series1
Series2
Series3
Series4
Series5
S
Fd
0.75
1
1.25
1.5
1.75
2
2.252.5
2.75
3
3.25
3.5
Fig.5. Divertor field line length dependence, Vst=2
Fig.9. Field line path, (Vst=1.5,Ust=0.64 ), R,Z plane, Rcf=1.3Rfw, L=+11.3 m, First wall cross-sections: V=0.25,0.5, 0.75 , 1
Conclusion
В.А. Рудаков, О.В. Георгієвський, У. Реєрсен
В.А. Рудаков, А.В. Георгиевский, У. Рейерсен
|
| id | nasplib_isofts_kiev_ua-123456789-110141 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:27:06Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Rudakov, V.A. Georgiyevskiy, A.V. Reiersen, W. 2016-12-30T11:15:55Z 2016-12-30T11:15:55Z 2003 Investigation of divertor field lines in the NCSX stellarator / V.A. Rudakov, A.V. Georgiyevskiy, W. Reiersen // Вопросы атомной науки и техники. — 2003. — № 1. — С. 7-12. — англ. 1562-6016 PACS: 52.55.Hc https://nasplib.isofts.kiev.ua/handle/123456789/110141 Divertor field lines calculations for NCSX stellarator are presented. The recommendations are given for the correction of the vacuum vessel and FW shape in order to perform an optimum arrangement of divertor system components. Представлені розрахунки диверторних силових ліній для стеларатора NCSX. Зроблені пропозиції щодо корекції вакуумної камери з метою оптимального розташування диверторних пристроїв. Представлены расчеты диверторных силовых линий для стелларатора NCSX. Сделаны рекомендации по коррекции вакуумной камеры с целью оптимального расположения диверторных устройств. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Investigation of divertor field lines in the NCSX stellarator Дослідження диверторних силових ліній в стелараторі NCSX Исследование диверторных силовых линий в NCSX стеллараторе Article published earlier |
| spellingShingle | Investigation of divertor field lines in the NCSX stellarator Rudakov, V.A. Georgiyevskiy, A.V. Reiersen, W. Magnetic confinement |
| title | Investigation of divertor field lines in the NCSX stellarator |
| title_alt | Дослідження диверторних силових ліній в стелараторі NCSX Исследование диверторных силовых линий в NCSX стеллараторе |
| title_full | Investigation of divertor field lines in the NCSX stellarator |
| title_fullStr | Investigation of divertor field lines in the NCSX stellarator |
| title_full_unstemmed | Investigation of divertor field lines in the NCSX stellarator |
| title_short | Investigation of divertor field lines in the NCSX stellarator |
| title_sort | investigation of divertor field lines in the ncsx stellarator |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110141 |
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