Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak
In addition to the analysis of magnetic perturbation amplitudes [2] a detailed investigation of the plasma motion affected by this external helical magnetic perturbation is carried out near the HYBTOK-II main resonance surface. Додатково до аналізу амплітуд магнітних збурень [2] виконано детальне до...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Zitieren: | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak / I.M. Pankratov, A.Ya. Omelchenko, V.V. Olshansky // Вопросы атомной науки и техники. — 2005. — № 2. — С. 20-22. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860132672958889984 |
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| author | Pankratov, I.M. Omelchenko, A.Ya. Olshansky, V.V. |
| author_facet | Pankratov, I.M. Omelchenko, A.Ya. Olshansky, V.V. |
| citation_txt | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak / I.M. Pankratov, A.Ya. Omelchenko, V.V. Olshansky // Вопросы атомной науки и техники. — 2005. — № 2. — С. 20-22. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | In addition to the analysis of magnetic perturbation amplitudes [2] a detailed investigation of the plasma motion affected by this external helical magnetic perturbation is carried out near the HYBTOK-II main resonance surface.
Додатково до аналізу амплітуд магнітних збурень [2] виконано детальне дослідження руху плазми, що викликано цим зовнішнім гвинтовим магнітним збуренням поблизу головної резонансної поверхні в HYBTOK-II.
Дополнительно к анализу амплитуд магнитных возмущений [2] выполнено детальное исследование движений плазмы под воздействием этого внешнего винтового магнитного возмущения вблизи главной резонансной поверхности в HYBTOK-II.
|
| first_indexed | 2025-12-07T17:45:30Z |
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MODELLING OF PLASMA MOTION RESPONSE INDUCED BY AN
EXTERNAL ROTATING HELICAL PERTURBATION IN THE HYBTOK-II
TOKAMAK
I.M. Pankratov, A.Ya. Omelchenko, V.V. Olshansky
Institute of Plasma Physics, NSC KIPT
Akademicheskaya str. 1, 61108, Kharkov, Ukraine, e-mail: pankratov@kipt.kharkov.ua
In addition to the analysis of magnetic perturbation amplitudes [2] a detailed investigation of the plasma motion
affected by this external helical magnetic perturbation is carried out near the HYBTOK-II main resonance surface.
PACS: 52.30.-q; 52.35.Vd; 52.35.We; 52.55.Fa
1. INTRODUCTION
Direct observations of tokamak plasma responses to
an externally applied rotating helical magnetic
perturbation have been performed on a small tokamak
HYBTOK-II (R=0.4m, a=0.11m) in order to clarify the
process of penetration of this external magnetic
perturbation into tokamak plasmas [1]. The radial profiles
of the radial and poloidal magnetic components of the
penetrating external field were measured using a small
magnetic probe inserted into the plasma. A comparison of
the theoretical treatment [2] with these HYBTOK-II
experiments shows a good qualitative agreement. In the
present paper a more detailed theoretical study of the
HYBTOK-II experiments is made.
2. MODEL
A model of a current carrying cylindrical plasma,
whose axis is taken as the z direction, is used. The
external axial magnetic field B z0 is large in comparison
with the poloidal magnetic field Bθ0 produced by the
axial current. The perturbation values depend on the
azimuthal angle θ , the coordinate z ( k=n/R ) and the
time t as exp [ i mθ−kz−ωt ] , m and n are poloidal
and toroidal numbers, respectively, R plays the role of
the tokamak major radius, ω is the frequency of the
external perturbation. The investigation is based on the
equations for perturbations of radial components of
plasma velocity V r
~ and magnetic field B r
~ (see [2])
d
dr
r ω ' ρ d
dr rV r
~−ω ' m2 ρi r 2
δ 2
F 2 r
μ0ω V r
~
¿i r 2
δ 2
ω '
ω
F r r2 d
2
F
dr2 3r dF
dr B r
~
μ0
,
(1)
d
dr
r d
dr rBr
~−m2−i r2
δ 2
ω '
ω Br
~=−i r 2
δ2
F r V r
~
ω
, (2)
where
ω '=ωm /r Er0 /B z0kV z0 ,
δ=1/ μ0 σ∣∣ω , (3)
F r =k⋅B0=
m
r
Bθ0−kB z0 . (4)
In Eqs. (1), (2) the terms kV z
~ and kB z
~ ( krm )
are neglected, ρ is the plasma mass density and σ∣∣ is
the parallel conductivity. We included the poloidal plasma
rotation connected with an equilibrium radial electric field
E r0 and the toroidal plasma rotation with a
homogeneous velocity V z0 . We assume that the
equilibrium quantities are slowly varying. Recall that the
ion gyroviscosity tensor π i compensates the drift
diamagnetic effect (see, e.g., [3,4]).
In this paper only the main HYBTOK-II resonant
mode (m/n=6/1) is investigated, when the value of
F r is equal to zero, F rres =0 , on the main
resonance surface r res=8 . 5 cm , where
q r res=6 /1 ( q r =rBz0 /RBθ0 ).
The typical HYBTOK-II parameters are used: the
toroidal magnetic field B z0 = 0.27 T, the plasma current
I p = 5 kA, the edge electron density
ne=1 . 5 ×1018 m−3 and the electron temperature
T e = 25 eV.
3. RESULTS AND DISCUSSION
Recall [2] that for the considered HYBTOK-II
experiments the resistive effects dominate in a broader
region than that defined by the Alfven resonances.
In Eqs. (1), (2) we neglect the ion diamagnetic drift.
As a result, Eqs. (1), (2) contain only the Doppler shifted
frequency ω ' as a key parameter. In Figs. 1-3 the results
of calculations for three Doppler shifted frequencies f '
= 10, 30 and 40 kHz are presented. For f=30 kHz we take
the skin depth value δ =1 cm. Note, that results of the
calculations depend on the local values of .
In Figs.1a,d, 2a,d, 3a,d the radial profiles of B r , θ
~
amplitudes and their phases ψ Br ,θ
are shown. These re
sults are in a good qualitative agreement with HYBTOK-II
experimental measurements ([1], Case I). The gap in the
profile of ∣Bθ
~∣ is clearly visible near r≈rres . The
minimum value of this gap is shifted to the plasma depth
from the surface r=r res . Some attenuation of ∣B r
~∣
20 Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 20-22
Z eff
and amplification of ∣Bθ
~∣ for rr res may be
explained by not only sideband modes occurring, but also
by the non-resonant J z
~ excitation.
Figs. 1b,e, 2b,e, 3b,e show the radial profiles of the
velocities V r , θ
~ . Because ∣B r
~∣ grows towards the
antenna, ∣V r
~∣ has a finite value at the plasma edge.
In Figures 2b, 3b ∣V r
~∣ ~0.4 km/s at r>10 cm.
In Figures 1e, 2e, 3e the maximum values of ∣V θ
~∣ are
max ∣V θ
~∣ ~2-3 km/s. The value of ∣V θ
~∣ grows, when
f ' drops. For example, max ∣V θ
~∣ ~10 km/s for f ' =1
kHz.
Figs. 1c, 2c, 3c show the magnetic island m/n=6/1
position and contour plots of the plasma fluxes (the
arrows show the direction of motion) in the poloidal
cross-section ( Δθ=π /3 ) near the main resonance
surface r res=8 . 5 cm for a certain moment of time. In
time this picture rotates as a unit. The calculated width of
the magnetic island is approximately 0.5 cm. When the
Doppler shifted frequency ω ' increases, the resonant
zone (resistive layer) size increases with respect to the
magnetic island width. The plasma vortexes occur. The
plasma moves across the resonant surface inwards
(outwards) of the discharge near O-point (X-point) of the
magnetic islands (compare with [5]). The last statement is
not concerned with the plasma inside four vortexes.
Sideband modes of m/n=5/1 and m/n=7/1 are resonant at
r res=7 cm and r res=9 . 5 cm , respectively. For
the wide resonant zone in a toroidal plasma a strong
coupling between m and m ± 1 modes through the plasma
21
0.2 0.4 0.6 0.8 1 1.2
7.5
8
8.5
9
9.5
r(
cm
)
0 2 4 6 8 10 12
-0.5
0.0
0.5
Re(Vr
~)
Im(Vr
~)
0.2 0.4 0.6 0.8 1 1.2
7.5
8
8.5
9
9.5
θ (rad)
r
(c
m
)
-10
-5
0
5
10
0 2 4 6 8 10 12
r(cm)
-2
-1
0
1
2
Re(Vθ
~)
Im(Vθ
~)
6 7 8 9 10
r (cm)
-25
0
25
50
75
100
125
150
175
ph
as
e
(d
eg
.)
ψ Bθ
ψ Br
6 7 8 9 10
0.1
1.0
10.0
|Br
~|
Br
vac
|Bθ
~|
a b c
d e f
10kHz
Fig.1. The resonant zone size, � 1 cm, is approximately two times magnetic island width. Two vortexes are
observed per one poloidal period of the magnetic perturbation
0 2 4 6 8 10 12
-0.5
0.0
0.5
Re(Vr
~)
Im(Vr
~)
0.2 0.4 0.6 0.8 1 1.2
7.5
8
8.5
9
9.5
θ (rad)
r
(c
m
)
-10
-5
0
5
10
6 7 8 9 10
r (cm)
-25
0
25
50
75
100
125
150
175
ph
as
e
(d
eg
.)
ψ Bθ
ψ Br
0 2 4 6 8 10 12
r(cm)
-1
0
1
Re(Vθ
~)
Im(Vθ
~)
6 7 8 9 10
0.1
1.0
10.0
|Br
~|
Br
vac
|Bθ
~|
a b c
d e f
30 kHz
Fig.2. The resonant zone size, � 2 cm, is approximately four times magnetic island width. Two vortexes are still
observed per one poloidal period of the magnetic perturbation
motion is possible (see, e.g.,[6]). The effect on the
poloidal rotation profile of an external rotating helical
magnetic perturbation was observed near resonant
surfaces in the HYBTOK-II experiment [7], but more
detailed experiments are needed.
In Figs.1f, 2f, 3f the 2-D profiles of the perturbed
current density J z
~ are presented. Here J z
~ ~10-15
kA/m2.
In the figures the values of B r , θ
~ , V r , θ
~ and J z
~
are normalized to the values B r
vac r res ,
V rA=Br
vac / μ0 ρ ∣r=rres
and B r
vac r res/ μ0 rres ,
respectively.
In Figs.1-3 the situation f ' >0 is presented. For f '
<0 (Eq.(3)) the same radial profiles of ∣Br , θ
~ ∣ are
observed, the values of Re V r
~ and Im V θ
~ change the
sign, and the phases ψ Br ,θ
decrease now towards the
plasma depth.
4. CONCLUSIONS
The present calculations reproduce not only the radial
profiles of amplitudes [2] but also the phase radial
profiles of externally induced magnetic perturbations in
the HYBTOK-II experiments.
The plasma vortexes with opposite direction of
rotation are found per one poloidal period of the external
perturbation ( Δθ=π /3 ). The cases with two vortexes
and the formation of four vortexes per one poloidal period
are considered.
ACKNOWLEDGEMENTS
The authors would like to thank Prof. S. Takamura for
fruitful discussion.
REFERENCES
1. Y.Kikuchi, Y. Uesugi, S. Takamura and A.G.Elfimov.
Direct observation of tokamak plasma responses to the
externally applied rotating helical magnetic field in the
small tokamak HYBTOK-II// Nucl. Fusion (44). 2004,
N6, p. S28-S36.
2. I.M. Pankratov, A.Ya. Omelchenko, V.V. Olshansky
and K.H. Finken. Investigation of plasma response
influence on the penetration of an external low
frequency helical perturbation into a tokamak edge
plasma// Nucl. Fusion (44). 2004, N 6, p. S37-S43.
3. B. Basu, B. Coppi. Moment equations treatment of the
reconnecting mode // Nucl. Fusion (17). 1977, N 6,
p. 1245-1255.
4. A.B. Mikhailovskii. Generalized MHD for numerical
stability analysis of high- performance plasmas in
tokamaks// Plasma Phys. Contr. Fusion (40). 1998,
N11, p.1907-1920.
5. T. Tuda, M. Kobayashi, G. Kurita, S. Takamura.
Interaction of externally applied helical field with
tokamak plasma// Contrib. Plasma Phys. (40). 2000,
N3-4, p. 256-259.
22
0 2 4 6 8 10 12
-0.5
0.0
0.5
Re(Vr
~)
Im(Vr
~)
0.2 0.4 0.6 0.8 1 1.2
7.5
8
8.5
9
9.5
θ (rad)
r
(c
m
)
-15
-10
-5
0
5
10
15
6 7 8 9 10
r (cm)
-25
0
25
50
75
100
125
150
175
ph
as
e
(d
eg
.)
ψ Bθ
ψ Br
6 7 8 9 10
0.1
1.0
10.0
|Br
~|
Br
vac
|Bθ
~|
0 2 4 6 8 10 12
r(cm)
-1
0
1
Re(Vθ
~)
Im(Vθ
~)d
a b
e
c
f
40 kHz
Fig.3. The resonant zone size, � 3 cm, is approximately six times magnetic island width. Formation of four
vortexes is observed per one poloidal period of the magnetic perturbation. Note, four vortexes per one
period were also observed during the stability analysis of the resistive tearing eigenmodes (see, e.g. [8])
6. J.M. Finn. Coupling of tearing modes in tokamaks//
Phys. Fluids (20), 1977, N10, p. 1749-1757.
7. V.P. Budaev, Y. Kikuchi, M. Toyoda, et al. Effect of
rotating helical magnetic field on the turbulence fractal
structure and transport in the tokamak edge//J. Nucl.
Mater.(313-316). 2003, p.1309-1313.
8. G. Bateman. MHD Instability. Cambridge: “MIT
Press”, 1979.
МОДЕЛИРОВАНИЕ ОТКЛИКА ПЛАЗМЫ, ИНДУЦИРОВАННОГО ВНЕШНИМ ВИНТОВЫМ
ВОЗМУЩЕНИЕМ В ТОКАМАКЕ HYBTOK-II
И.М. Панкратов, А.Я. Омельченко, В.В. Ольшанский
Дополнительно к анализу амплитуд магнитных возмущений [2] выполнено детальное исследование движений
плазмы под воздействием этого внешнего винтового магнитного возмущения вблизи главной резонансной
поверхности в HYBTOK-II.
МОДЕЛЮВАННЯ ВІДГУКУ ПЛАЗМИ, ІНДУКОВАНОГО ЗОВНІШНІМ ОБЕРТОВИМ ГВИНТОВИМ
ЗБУРЕННЯМ У ТОКАМАЦІ HYBTOK-II
І.М. Панкратов, А.Я. Омельченко, В.В. Ольшанський
Додатково до аналізу амплітуд магнітних збурень [2] виконано детальне дослідження руху плазми, що
викликано цим зовнішнім гвинтовим магнітним збуренням поблизу головної резонансної поверхні в HYBTOK-II.
23
|
| id | nasplib_isofts_kiev_ua-123456789-79313 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:45:30Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Pankratov, I.M. Omelchenko, A.Ya. Olshansky, V.V. 2015-03-31T08:20:18Z 2015-03-31T08:20:18Z 2005 Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak / I.M. Pankratov, A.Ya. Omelchenko, V.V. Olshansky // Вопросы атомной науки и техники. — 2005. — № 2. — С. 20-22. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.30.-q; 52.35.Vd; 52.35.We; 52.55.Fa https://nasplib.isofts.kiev.ua/handle/123456789/79313 In addition to the analysis of magnetic perturbation amplitudes [2] a detailed investigation of the plasma motion affected by this external helical magnetic perturbation is carried out near the HYBTOK-II main resonance surface. Додатково до аналізу амплітуд магнітних збурень [2] виконано детальне дослідження руху плазми, що викликано цим зовнішнім гвинтовим магнітним збуренням поблизу головної резонансної поверхні в HYBTOK-II. Дополнительно к анализу амплитуд магнитных возмущений [2] выполнено детальное исследование движений плазмы под воздействием этого внешнего винтового магнитного возмущения вблизи главной резонансной поверхности в HYBTOK-II. The authors would like to thank Prof. S. Takamura for fruitful discussion. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak Моделювання відгуку плазми, індукованого зовнішнім обертовим гвинтовим збуренням у токамаці HYBTOK-II Моделирование отклика плазмы, индуцированного внешним винтовым возмущением в токамаке HYBTOK-II Article published earlier |
| spellingShingle | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak Pankratov, I.M. Omelchenko, A.Ya. Olshansky, V.V. Magnetic confinement |
| title | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak |
| title_alt | Моделювання відгуку плазми, індукованого зовнішнім обертовим гвинтовим збуренням у токамаці HYBTOK-II Моделирование отклика плазмы, индуцированного внешним винтовым возмущением в токамаке HYBTOK-II |
| title_full | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak |
| title_fullStr | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak |
| title_full_unstemmed | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak |
| title_short | Modelling of plasma motion response induced by an external rotating helical perturbation in the HYBTOK-II tokamak |
| title_sort | modelling of plasma motion response induced by an external rotating helical perturbation in the hybtok-ii tokamak |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79313 |
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