Neoclassical transport for Uragan-2M in the 1/ν regime
The 1/ν neoclassical transport (effective ripple, εeff) is studied for the torsatron Uragan-2M (see in [1]. For stellarators where the finite plasma pressure causes a weak influence on the equilibrium εeff can be computed using field line tracing code [2] in real space coordinates. Also, an optimizi...
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| Zitieren: | Neoclassical transport for Uragan-2M in the 1/ν regime / V.N. Kalyuzhnyj, S.V. Kasilov, W. Kernbihler, V.V. Nemov, B. Seiwald // Вопросы атомной науки и техники. — 2005. — № 1. — С. 30-32. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-784552015-03-18T03:01:56Z Neoclassical transport for Uragan-2M in the 1/ν regime Kalyuzhnyj, V.N. Kasilov, S.V. Kernbihler, W. Nemov, V.V. Seiwald, B. Magnetic confinement The 1/ν neoclassical transport (effective ripple, εeff) is studied for the torsatron Uragan-2M (see in [1]. For stellarators where the finite plasma pressure causes a weak influence on the equilibrium εeff can be computed using field line tracing code [2] in real space coordinates. Also, an optimizing procedure is carried out using the code [3] for optimizing stellarators with fixed coil design. Besides, possibilities of improving the neoclassical transport by changing the resulting vertical magnetic field are considered. Вивчено неокласичний перенос в режимі 1/ν («effective ripple», εeff) для торсатрону Ураган-2M [1]. Для стелараторів, де вплив кінцевого тиску плазми на рівновагу являється слабким , εeff може бути розраховано з застосуванням коду [2], що використовує інтегрування вздовж магнітних силових ліній в реальних просторових координатах. Застосовано також оптимізаційну процедуру, яка використовує код [3] для оптимізації стелараторів з фіксованими котушками. Крім того, розглянуто можливості зниження коефіцієнтів неокласичного переносу шляхом змінювання результуючого вертикального магнітного поля. Изучен неоклассический перенос в режиме 1/ν («effective ripple», εeff) для торсатрона Ураган-2M [1]. Для стеллараторов, где конечное давление плазмы оказывает слабое влияние на равновесие, εeff может быть рассчитан с применением кода [2], использующего интегрирование вдоль магнитных силовых линий в реальных пространственных координатах. Применена также оптимизационная процедура, использующая код [3] для оптимизации стеллараторов с фиксированными катушками. Рассмотрены также возможности снижения коэффициентов неоклассического переноса путем изменения результирующего вертикального магнитного поля. 2005 Article Neoclassical transport for Uragan-2M in the 1/ν regime / V.N. Kalyuzhnyj, S.V. Kasilov, W. Kernbihler, V.V. Nemov, B. Seiwald // Вопросы атомной науки и техники. — 2005. — № 1. — С. 30-32. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.55.Hc http://dspace.nbuv.gov.ua/handle/123456789/78455 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Magnetic confinement Magnetic confinement |
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Magnetic confinement Magnetic confinement Kalyuzhnyj, V.N. Kasilov, S.V. Kernbihler, W. Nemov, V.V. Seiwald, B. Neoclassical transport for Uragan-2M in the 1/ν regime Вопросы атомной науки и техники |
| description |
The 1/ν neoclassical transport (effective ripple, εeff) is studied for the torsatron Uragan-2M (see in [1]. For stellarators where the finite plasma pressure causes a weak influence on the equilibrium εeff can be computed using field line tracing code [2] in real space coordinates. Also, an optimizing procedure is carried out using the code [3] for optimizing stellarators with fixed coil design. Besides, possibilities of improving the neoclassical transport by changing the resulting vertical magnetic field are considered. |
| format |
Article |
| author |
Kalyuzhnyj, V.N. Kasilov, S.V. Kernbihler, W. Nemov, V.V. Seiwald, B. |
| author_facet |
Kalyuzhnyj, V.N. Kasilov, S.V. Kernbihler, W. Nemov, V.V. Seiwald, B. |
| author_sort |
Kalyuzhnyj, V.N. |
| title |
Neoclassical transport for Uragan-2M in the 1/ν regime |
| title_short |
Neoclassical transport for Uragan-2M in the 1/ν regime |
| title_full |
Neoclassical transport for Uragan-2M in the 1/ν regime |
| title_fullStr |
Neoclassical transport for Uragan-2M in the 1/ν regime |
| title_full_unstemmed |
Neoclassical transport for Uragan-2M in the 1/ν regime |
| title_sort |
neoclassical transport for uragan-2m in the 1/ν regime |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2005 |
| topic_facet |
Magnetic confinement |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/78455 |
| citation_txt |
Neoclassical transport for Uragan-2M in the 1/ν regime / V.N. Kalyuzhnyj, S.V. Kasilov, W. Kernbihler, V.V. Nemov, B. Seiwald // Вопросы атомной науки и техники. — 2005. — № 1. — С. 30-32. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT kalyuzhnyjvn neoclassicaltransportforuragan2minthe1nregime AT kasilovsv neoclassicaltransportforuragan2minthe1nregime AT kernbihlerw neoclassicaltransportforuragan2minthe1nregime AT nemovvv neoclassicaltransportforuragan2minthe1nregime AT seiwaldb neoclassicaltransportforuragan2minthe1nregime |
| first_indexed |
2025-07-06T02:32:55Z |
| last_indexed |
2025-07-06T02:32:55Z |
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1836863115639128064 |
| fulltext |
NEOCLASSICAL TRANSPORT FOR URAGAN-2M IN THE ν1 REGIME
V.N.Kalyuzhnyj1, S.V.Kasilov1, W.Kernbihler2, V.V.Nemov1, B.Seiwald2
1Institute of Plasma Physics, National Science Centre “ Kharkov Institute of Physics and
Technology”, Akademicheskaya 1, 61108 Kharkov, Ukraine;
2Institut fur Theoretishe Physik, Technische Universitat Graz, Petersgasse 16, A-8010 Graz, Austria
The 1/ν neoclassical transport (effective ripple, εeff) is studied for the torsatron Uragan-2M (see in [1]. For stellarators where
the finite plasma pressure causes a weak influence on the equilibrium εeff can be computed using field line tracing code [2] in real
space coordinates. Also, an optimizing procedure is carried out using the code [3] for optimizing stellarators with fixed coil design.
Besides, possibilities of improving the neoclassical transport by changing the resulting vertical magnetic field are considered.
PACS: 52.55.Hc
INTRODUCTION
The U-2M device (IPP, Kharkov) is an l=2 torsatron with
an additional toroidal magnetic field (mp=4, RT=170cm, mp is
a number of the field periods along the torus, RT is the big
radius of the torus). In the design phase of this device a big
number of various studies were carried out, the results are
summarized in [1]. At the same time, due to the flexibility of
the device magnetic system further investigations of
possibilities of improving the confinement properties is
possible and desirable.
The additional toroidal magnetic field in U-2M is
produced by a system of 16 toroidal field coils (TF coils)
uniformly distributed in angle along the major circumference
(4 coils in each field period). In accordance with [1] for the
"standard" configuration, which is considered here, the mean
current in such a coil is of ITFC=5/12 (in units of the helical coil
current). In this case the parameter kϕ=Bth/(Bth+Btt) is kϕ=0.375
(Bth and Btt are the toroidal components of the magnetic field
produced by helical and TF coils, respectively). The additional
control parameter for improving the effective ripple is the
difference of currents in adjacent TF coils [1], [4].
An important role in formation of the torsatron magnetic
configuration belongs to the vertical field coil (VF coil)
system. In the presented computations the VF coil system
variant [5] is used which makes it possible to suppress
significantly the island structure of the magnetic surfaces.
For the helical coils the magnetic field and its spatial
derivatives are calculated on the basis of the Biot-Savart law
modeling each helical coil by 24 current filaments distributed
in two layers. The magnetic fields produced by the TF and VF
coils are calculated using elliptic integrals (recalculating the
fields obtained in the local coordinate systems of each coil to
the general cylindrical coordinates).
COMPUTATIONS OF EFFECTIVE RIPPLE
AND OPTIMIZATION RUN
In view of the results of [4] the currents in the TF coils are
presented in a form ITFC±∆I with sign plus for the inner two
coils in each field period and with sign minus for the outer two
coils (further, ∆I is expressed in the units of the helical coil
current). In [4] a decrease in the effective ripple, εeff, was
found in U-2M for certain values of ∆I>0 (and vice versa an
increase in case of ∆I<0). Here the dependence of εeff on ∆I is
analyzed using methods which are valid (in contrast to [4])
over the entire magnetic configuration and allow in this case to
obtain the quantitative evaluation of εeff.
Optimization run [3] using NEO code [2] for the εeff
3/2
computation is performed with varying the ∆I parameter. Note
that computation of εeff
3/2 is more useful (as compared to εeff)
since for the 1/ν transport regime the transport coefficients are
proportional directly to εeff
3/2. To assess the necessary interval
of the ∆I variation, before the optimization run computations
of εeff
3/2 are made for the ∆I values of 0 and ±5/144. After that
a more detailed assessment of the configuration confinement
properties in case of 1/ν regime is performed using the
optimization procedure for the ∆I interval of -0.1÷0.1.
In the procedure the total stored energy in the plasma
volume is used as fitness parameter with an energy source,
Q(r)= Q0δ(r)/r, which is localized at the magnetic axis. It is
assumed that the temperature profile is defined by the heat
conductivity equation
0)(1
=+
∂
∂
∂
∂
⊥ rQ
r
Tr
rr
κ
(1)
with the boundary conditions T(a)=0 and (rdT/dr)=0
(here a is the boundary of the plasma). So, the heat
conductivity, κ
0
lim
→r
⊥, is proportional to εeff
3/2T7/2, and computation
of εeff
3/2 for sets of computed magnetic surfaces is an essential
part of the optimization procedure. The normalized stored
energy
92
0 0
23 )'('
')(∫ ∫ ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
a a
eff rr
drrndrrW
ε
(2)
can be obtained by integrating the temperature profile
resulting from (1) ( n is a normalized plasma density).
RESULTS
Fig.1 shows cross-sections of magnetic surfaces used for
the εeff
3/2 computations for ∆I=0 (in the ϕ=0 plane and after
half of the field period). A circle with a radius of 34 cm shows
the inner boundary of the vacuum chamber. Magnetic islands
of ι=4/5 can be seen close to the chamber boundary. Magnetic
surfaces for ∆I=5/144 and ∆I= -5/144 (not shown here) differ
from those in Fig.1 mainly by the sizes of the outermost
magnetic surfaces. For ∆I>0 (∆I<0) these sizes are smaller
(bigger) than those in Fig.1. The position of the islands for
these cases only slightly differ from that for ∆I=0. In the case
of ∆I=5/144 for the region outside the ι=4/5 islands the
magnetic configuration has entirely a structure of island chains
consisting of very big numbers of small islands.
30 Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 30-32
The results of the computations of εeff
3/2 for ∆I=0, ±5/144,
0.035 and 0.0375 are presented in Fig.2 (for the non- island
magnetic surfaces) as functions of the mean radius r of a
magnetic surface. The curves presented in Fig.2 have gaps
corresponding to the island surfaces. Different total intervals
in r for the curves correspond to different sizes of the
outermost magnetic surfaces. Surfaces outside the islands are
not fully inside the vacuum vessel and, therefore, suppressed
for computations of the total stored energy (nevertheless εeff
3/2
is shown for ∆I equal to 0 and -5/144 in Fig.2).
120 140 160 180 200 220
-40
-20
0
20
40
z
R
120 140 160 180 200 220
-40
-20
0
20
40
z
R
Fig. 1. “Standard” configuration of U-2M for ∆I=0
0 2 4 6 8 10 12 14 16 18
0.001
0.010
0.100
1.000
ε3/2
eff
r
1
1
2
3
3
4
5
Fig.2. Parameters εeff
3/2 as functions of r for various ∆I;
1: ∆I=0; 2: ∆I=5/144; 3: ∆I=-5/144;
4 and 5 (thin lines): ∆I=0.035 and 0.0375, respectively
(gaps in curves correspond to the island surfaces)
It follows from the results that for the small r for
∆I=5/144, 0.035 and 0.0375 the εeff
3/2 value is smaller by
one order of magnitude than that for ∆I=0. However, this
difference decreases when approaching the islands and in
the island vicinity becomes small. For ∆I=-5/144 the εeff
3/2
values are bigger than for ∆I=0. From the computations
also follows that in the islands εeff
3/2 reaches the values
0.2÷0.3 for all considered cases. The obtained results are
in a qualitative agreement with results of [4] for rather
small r/a (with a being the mean radius of the outermost
magnetic surface). Note that the εeff
3/2 values of 0.01÷0.1
which are characteristic for Fig.2 from r approximately 7
cm to r corresponding to the appearance of the island are
essentially bigger than those which are desirable from the
viewpoint of the stellarator optimization [6].
The optimization results are presented in Fig.3 in the
form of a normalized stored energy (2) as a function of
∆I. The results correspond to a model of the particle
density where constant and parabolic profiles are
assumed. A maximum in the stored energy is seen for
∆I≈0.035 that is rather close to the ∆I value 5/144
considered above.
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
50
60
70
80
90
100
110
120
130
∆ I
1
2
Fig.3. Normalized stored energy (in a. u.)
(see Eq.(2)) vs. change of ∆I;
1: n=const., 2: parabolic profile of n
The afore-presented results relate to the initial
"standard" configuration which is well centered with
respect to the vacuum chamber and is characterized by a
resulting vertical magnetic field B⊥ of B⊥/B0≈2.5% value
(B0 is the mean toroidal magnetic field). Further, the
calculations are performed for the changed value of B⊥,
namely, for B⊥=0 and B⊥/B0≈-2.5% in case of ∆I=0 (the
positive (negative) B⊥ value corresponds to the somewhat
un-compensated (over-compensated) vertical field of the
helical coils). For these changes an additional
homogeneous vertical magnetic field of the necessary
value is used. Due to the changes in B⊥/B0 the magnetic
axis turns out to be inward shifted with respect to its
position for B⊥/B0≈2.5%. Fig.4 shows the magnetic
surfaces corresponding to B⊥/B0≈-2.5%.
Computational results for εeff
3/2 corresponding to the
new values of B⊥/B0 are presented in Fig.5 (curves 3 and
4) as functions of r/a with a being the mean radius of the
outermost magnetic surface for B⊥/B0≈2.5%, ∆I=0. For
comparison curves 1 and 2 in the figure show some
results from Fig.2. Curve 5 shows the results
corresponding to B⊥/B0≈-2.5% when the B⊥/B0 value is
obtained by the corresponding increase in the currents of
the VF coils but not by the additional homogeneous
magnetic field.
It follows from Fig.5 that the inward-shifted magnetic
configurations have markedly smaller values of εeff
3/2 than
the configurations corresponding to B⊥/B0=2.5%. This
31
CONCLUSIONS can be explained by the fact that inward shifted stellarator
configurations turn out to be rather close to the so called
"σ-optimized" configurations (see, e.g., [7]).
The initial "standard" U-2M configuration is well centered
with respect to the vacuum chamber. It is found that for this
configuration the 1/ν transport is essentially bigger than that
which is desirable from the viewpoint of the stellarator
optimization [6]. Some improvement in this transport can be
achieved by a certain difference of currents in adjacent TF
coils. Markedly smaller 1/ν transport can be obtained by
changing the resulting vertical magnetic field in a way which
leads to an inward-shifted configuration. This way can be of
interest although the inward-shifted stellarator configuration
can posses a magnetic hill (instead of a magnetic well). From
recent experimental results [8] for LHD follows that MHD
stability as well as good transport properties can be obtained
simultaneously in inward-shifted configurations with a
magnetic hill.
120 140 160 180 200 220
-40
-20
0
20
40
z
R
ACKNOWLEDGEMENTS
This work has been partly carried out within the Association
EURATOM-OEAW. The content of the publication is the
sole responsibility of its authors and it does not necessarily
represent the views of the Commission or its service.
Fig. 4. “Inward-shifted” configuration of U-2M
REFERENCES
0.0 0.2 0.4 0.6 0.8 1.0 1.2
1E-4
0.001
0.01
0.1
1
r/a
ε3/2
eff
1
2
3
4
5
1
3
[1] O.S.Pavlichenko for the U-2M group. First results from the
URAGAN-2M torsatron// Plasma Phys. and Control. Fusion,
1993, v.35, B223.
[2] V.V.Nemov, S.V.Kasilov, W.Kernbichler, M.F.Hein.
Evaluation of 1/ν neoclassical transport in stellarators// Phys.
Plasmas, 1999, v.6, p.4622.
[3] B.Seiwald, V.V.Nemov, S.V.Kasilov, W.Kernbihler.
Optimization of stellarators with respect to neoclassical
transport in real space// Proc. of 29th EPS Conf. on Plasma
Phys. and Contr. Fusion, Montreux, 17-21 June 2002, ECA,
2002, v.26B, P-4.099.
[4] C.D.Beidler, et al. Physics studies for the Uragan-2M
torsatron// in Plasma Phys. and Contr. Nucl. Fusion Res. 1990
(Proc. of 13 IAEA Conf. on Nucl. Fusion, Washington), Vienna:
IAEA, 1991, v.2, p.663.
[5] V.E.Bykov, et al. Optimization studies of compact
torsatrons// in Plasma Phys. and Contr. Nucl. Fusion Res. 1988
(Proc. of 12th IAEA Conf. on Nucl. Fusion, Nice, 1988),
Vienna: IAEA, 1989, v.2, p.403.
Fig. 5. Parameters εeff
3/2 as functions of r/a;
1: ∆I=0, B⊥/B0=2.5%; 2: ∆I=5/144, B⊥/B0=2.5%; [6] G.Grieger, et al. Physics optimization of stellarators// Phys.
Fluids B, 1992, v.4, p.2081. 3: B⊥=0, ∆I=0; 4 and 5: B⊥/B0= -2.5%, ∆I=0
[7] H.E.Mynic. Improved theory of collisionless particle motion
in stellarators// Phys. Fluids, 1983, v.26, p.1008. Because of the vacuum chamber and islands the
confinement regions are smaller than it is seen from Figs.2 and
5. They can be characterized by the corresponding maximum
values of r/a which equal r/a≈0.82 for B⊥/B0=0, r/a≈0.47 for
B⊥/B0=-2.5%; r/a≈0.68 for B⊥/B0=2.5%, ∆I=5/144.
[8] O.Motojima, et al. Recent advances in the LHD experiment//
Nucl. Fusion, 2003, v.43, p.1674.
НЕОКЛАССИЧЕСКИЙ ПЕРЕНОС В РЕЖИМЕ 1/ν ДЛЯ УРАГАНА-2M
В.Н. Калюжный, С.В. Касилов, В. Кернбихлер, В.В. Немов, Б. Сейвальд
Изучен неоклассический перенос в режиме 1/ν («effective ripple», εeff) для торсатрона Ураган-2M [1]. Для стеллараторов, где
конечное давление плазмы оказывает слабое влияние на равновесие, εeff может быть рассчитан с применением кода [2],
использующего интегрирование вдоль магнитных силовых линий в реальных пространственных координатах. Применена
также оптимизационная процедура, использующая код [3] для оптимизации стеллараторов с фиксированными катушками.
Рассмотрены также возможности снижения коэффициентов неоклассического переноса путем изменения результирующего
вертикального магнитного поля.
НЕОКЛАСИЧНИЙ ПЕРЕНОС В РЕЖИМІ 1/ν ДЛЯ УРАГАНА-2M
В.М. Калюжний, С.В. Касілов, В. Кернбіхлер, В.В. Нємов, Б. Сейвальд
Вивчено неокласичний перенос в режимі 1/ν («effective ripple», εeff) для торсатрону Ураган-2M [1]. Для стелараторів, де вплив
кінцевого тиску плазми на рівновагу являється слабким , εeff може бути розраховано з застосуванням коду [2], що
використовує інтегрування вздовж магнітних силових ліній в реальних просторових координатах. Застосовано також
32
33
оптимізаційну процедуру, яка використовує код [3] для оптимізації стелараторів з фіксованими котушками. Крім того,
розглянуто можливості зниження коефіцієнтів неокласичного переносу шляхом змінювання результуючого вертикального
магнітного поля.
INTRODUCTION
RESULTS
CONCLUSIONS
ACKNOWLEDGEMENTS
REFERENCES
|