Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas
In the frame of one-fluid MHD the pressure perturbation resonant excitation by external low frequency helical magnetic perturbations near the plasma edge is investigated. The plasma rotation plays a key role in this phenomenon. The plasma response has been taken into account. These pressure perturba...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2012 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/109103 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas / I.M. Pankratov, I.V. Pavlenko, O.A. Pomazan, A.Ya. Omelchenko // Вопросы атомной науки и техники. — 2012. — № 6. — С. 61-63. — Бібліогр.: 8 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859658990246428672 |
|---|---|
| author | Pankratov, I.M. Pavlenko, I.V. Pomazan, O.A. Omelchenko, A.Ya. |
| author_facet | Pankratov, I.M. Pavlenko, I.V. Pomazan, O.A. Omelchenko, A.Ya. |
| citation_txt | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas / I.M. Pankratov, I.V. Pavlenko, O.A. Pomazan, A.Ya. Omelchenko // Вопросы атомной науки и техники. — 2012. — № 6. — С. 61-63. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | In the frame of one-fluid MHD the pressure perturbation resonant excitation by external low frequency helical magnetic perturbations near the plasma edge is investigated. The plasma rotation plays a key role in this phenomenon. The plasma response has been taken into account. These pressure perturbations may affect stability of the ballooning and peeling modes.
В рамках одножидкостной МГД исследовано резонансное возбуждение возмущений давления у края плазмы внешними низкочастотными винтовыми возмущениями магнитного поля. Вращение плазмы играет ключевую роль в этом явлении. Учтен отклик плазмы. Эти возмущения давления могут влиять на устойчивость баллонных и пилинг-мод.
У рамках однорідинної МГД досліджено резонансне збудження збурень тиску біля краю плазми зовнішніми низькочастотними гвинтовими збуреннями магнітного поля. Обертання плазми відіграє ключову роль у цьому явищі. Враховано відгук плазми. Ці збурення тиску можуть впливати на стійкість балонних та пілінг-мод.
|
| first_indexed | 2025-11-30T09:41:30Z |
| format | Article |
| fulltext |
ISSN 1562-6016. ВАНТ. 2012. №6(82) 61
EFFECT OF PLASMA ROTATION ON THE RESONANCE MAGNETIC
PERTURBATIONS AT THE EDGE OF TOKAMAK PLASMAS
I.M. Pankratov1,2, I.V. Pavlenko2, O.A. Pomazan2 and A.Ya. Omelchenko1
1Institute of Plasma Physics NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2V.N. Karazin Kharkov National University, Kharkov, Ukraine
E-mail: pankratov@kipt.kharkov.ua
In the frame of one-fluid MHD the pressure perturbation resonant excitation by external low frequency helical magnetic
perturbations near the plasma edge is investigated. The plasma rotation plays a key role in this phenomenon. The plasma
response has been taken into account. These pressure perturbations may affect stability of the ballooning and peeling modes.
PACS: 52.35.Bj, 52.55.Fa
INTRODUCTION
Control of Edge Localized Modes (ELMs) is a
critical issue of the present day large tokamaks and
future ITER operation [1, 2].
Experiments at DIII-D have shown that ELMs can be
suppressed by small external low frequency helical
magnetic perturbations [3, 4].
In Ref. [5] the influence of an external helical field
on the equilibrium of ideal plasma was investigated in
the frame of MHD theory. A perfect shielding of the
external resonant field was assumed.
Early in the frame of one-fluid MHD a possibility of
the pressure perturbation resonant excitation (due to the
plasma rotation) by external helical magnetic perturbations
near the plasma edge has been shown [6], when the plasma
response has being taken into account (a perfect shielding
is not assumed).
In the present paper, the influence of these pressure
perturbations on external helical magnetic field near the
plasma edge is investigated. Considered plasma
parameters are closed to DIII-D experiments [3, 4].
Poloidal and toroidal plasma rotations are taken into
account. The plasma response takes into account.
Note, that the toroidal rotation effects on ELM
behavior were observed in experiments [4, 7].
1. BASIC EQUATIONS
We start from the one-fluid MHD equations
[ ]1
i
d p
dt c
ρ = −∇ −∇ ⋅ + ×
V J Bπ ,
0 0,dp pdiv
dt
γ+ =V (1)
tc
rot
∂
∂
−=
BE 1 , JB
c
rot π4
= , 0=Bdiv , (2)
0=Jdiv , (3)
[ ]⎟
⎠
⎞
⎜
⎝
⎛ ×+= BVEJ
c
1σ , (4)
_____________________________________
where ρ is the plasma mass densities, p is the plasma
pressure, J is the current density, σ is the conductivity
and iπ is the ion gyroviscosity tensor, respectively.
We consider a current carrying toroidal plasma with
nested equilibrium circular magnetic surfaces ( 0ρ is the
radius of the magnetic surfaces, 0ω is the poloidal
angle in the cross-section const=ς , ς is the toroidal
angle). Each magnetic surface is shifted with respect to
the magnetic axis (ξ is the shift, R is the radius of the
magnetic axis). The equilibrium toroidal contravariant
component of the magnetic field, ( )gB πς 20 Φ′= , is
large with respect to the poloidal one,
( )gB πχθ 20 ′= , ( ) / ,q a χ′′= Φ Φ′ and χ ′ are the
radial derivatives of toroidal and poloidal fluxes,
respectively. The known expressions for metric tensor
are used [8].
On each magnetic equilibrium surface (see, e.g. [8])
we introduce a straight magnetic field line coordinate
system ( a ,θ ,ς ) a=0ρ , ( ) θλθω sin0 a+= ,
( ) Raaa −′−= )(ξλ , (5)
( )
2 2
00
1 ( ) ( )16 ( )
2 2
aa ba p b bdb
aR R R
χ χξ π
π π
− ⎡ ⎤′ ′⎛ ⎞ ⎛ ⎞′ = +⎢ ⎥⎜ ⎟ ⎜ ⎟
⎝ ⎠⎢ ⎥⎝ ⎠ ⎣ ⎦
∫ . (6)
Assuming periodicity in both θ and ζ , we take the
perturbations in the form
( ) ( ) ( )[ ]∑ −−=
nm
mn tnmiaXtaX
,
exp,,, ωζθζθ , (7)
where ω is the frequency of the external perturbation.
Assuming that magnetic perturbation 0≈ςB , for
perturbations with m >>1, nq >>1 from Eqs. (1) - (4)
in a linear approximation in 1/R the next equations were
found (derivatives with respect to radius are denoted
by the prime) [6]:
[ ]
0
2
0 1 1 0 1 12 2
0 0 0
2 0
1 1 1 12
0 0 0 0
4 4 2( ) ( ) ( ) ( ) ( / )
( ) ( ) ( )
8 4 4( 1 ) ( ) ( 1) ( 1) 0
( ) ( ) ( ) ( )
a
a a a m
m m m m m m m
m m m m m
BSqR iqR aRF a i a B mB p B B p a B B J a
B a B a c B a
apim a R i iS p ap ap m p m p
B a R B a a B a B a
θ θ θ
ζ ζ ζ
ζ ω ζ ζ
π π
π π πμ ξ
− + − +
− + − +
′ ′ ′ ′ ′⎡ ⎤+ + + + − + −⎣ ⎦
′
′ ′ ′− − + − − − + − + + = ,
(8)
62 ISSN 1562-6016. ВАНТ. 2012. №6(82)
2 2
0 0 1 1
0 0|| 0 0 1 12
0 0
( ) ( )( ) ( ) ,
1 1
a a a
a a a as m m s m m
m m Em m m m m
m
Bc B c aV aVip F a V V p p V V V
R B B R m m
ζ ω ρρ ω − +
− +
⎧ ⎫⎛ ⎞ ′ ′⎡ ⎤⎪ ⎪′ ′ ′= − + + + − − +⎨ ⎬⎜ ⎟ ⎢ ⎥Ω − +⎪ ⎪⎣ ⎦⎝ ⎠⎩ ⎭
(9)
2
0 2
m 2( ) ( )
4
a a a
i m m m m m
B ic mB F a V i a B mB
R a
ς θω
πσ
′⎡ ⎤= − − +⎣ ⎦ . (10)
____________________________________________
In Eqs. (8) - (10) ( ) ( )mF a m a nμ= − , qS a
q
′
= ,
0 ( ) / 2 ,B a aζ π′= Φ
00 ( ) / 2 ,B a Rω χ π′=
1/ ,qμ = ( ) 0,a
m maB imaBθ′ + =
2
2 2
2( ) ( ),s
m im m m
ca F a
R
ω ωΩ = − 2 0
0
0
,s
pc γ
ρ
= (11)
0 0 0
0||
0 0 0
( ) ,m a
m
B BF a EmV c
B R B a B
ς ςω ω= − + (12)
0 0 0
0||
0 0 0 0
( )[ ( )].m i a
im
B F a p EmV c c
B R a en B B
ςω ω
′
= − + − (13)
In our consideration all poloidal harmonic
amplitudes of perturbations have finite values. The
number of poloidal harmonics with finite values of
amplitudes depends on the antenna spectrum (external
perturbation). Equilibrium parameters are denoted by
the subscript 0. We took into account the equilibrium
poloidal plasma rotation due to the existence of an
equilibrium radial electric field E0a, the ion diamagnetic
drift and the parallel with respect to equilibrium
magnetic field plasma rotation with a velocity 0||V .
Fig.1. Equilibrium pressure gradients (in Pa)
For simplicity we consider case cs = 0 and 0ω = .
Near the plasma edge the inequality 1Sξ ′ >> (S ~ 4)
takes place. From Eqs. (8) - (10) we get in this case
_____________________________________
0
2
20
2
0
1 ( ) ,
( ) 4 ( )
a
m
m
im
a a
m m m
m im
ip Vp
ip R i c mB i a B mB
F a B a a
θ
ς
ω
ω πσ
′
= − =
⎡ ⎤′
′⎡ ⎤= + +⎢ ⎥⎣ ⎦
⎣ ⎦
(14)
2
2 2
1 ( ) ( ) ( ) 0,a a a
N N m N m m N m
N N N N N
d d m ma a B a B Q a B
a da da a a
⎛ ⎞
− − =⎜ ⎟
⎝ ⎠
(15)
where
( )
02
0
2
22
( )
( ) ( ) ( ) ( ) ( )
4 ( )
,
( ) ( ) ( )
4 ( )
m N
m N N m N m N N
N
m N m N N
N
Q a
B cK a A a mK a F a i A a
B a a
cmK a F a A a
a a
ς
πσ
πσ
=
⎛ ⎞
+⎜ ⎟
⎝ ⎠=
⎛ ⎞
+ ⎜ ⎟
⎝ ⎠
(16)
( ) 0|| 0
0
0 0
( )1 1( ) ( ) ,i i N
m N m N a N
i N pl
V dp T aaK a F a E a
R mc B p da ea
⎛ ⎞
= + −⎜ ⎟⎜ ⎟
⎝ ⎠
(17)
2 20
2
0
8( ) ( 1 ),N N
N
dp RA a a m S
B da aς
π μ ξ ′= − − pl/ .Na a a= (18)
Fig. 2. Equilibrium radial electric field
2. DISCUSSIONS
Poloidal modes m = 9…14 and toroidal mode n = 3
are considered. The profile ( )Nq ψ near plasma edge
close to the DIII-D experiments is used ([3, 4]). From
Eqs. (14), (15) the pressure perturbation is presented
in the next form:
( )
0 2
00
2
2 02
( ) ( ) ( ) ( ) ( )
4 ( )
( ) .
( ) ( ) ( )
4 ( )
m N m N m N m N N a
N m
m N N
N
m N m N N
N
B cmK a F a im K a F a A a
B a adp BRp a a
da a BcmK a F a A a
a a
ς
πσ
πσ
⎛ ⎞
−⎜ ⎟
⎝ ⎠=
⎛ ⎞
+ ⎜ ⎟
⎝ ⎠
(19)
The pressure perturbation resonant excitation by
external low frequency helical magnetic perturbations
near the plasma edge is possible when ( ) 0m NF a ≈ or
( ) 0m NK a ≈ (Eq. (19)). The case ( ) 0m NK a ≈ occurs
during the plasma rotation only. It may affect the
excitation of ballooning and peeling modes because of a
plasma pressure change. In Figs. 1, 2 the behaviors of
the equilibrium pressure gradients and equilibrium
radial electric field E0a are shown for typical DIII-D
ISSN 1562-6016. ВАНТ. 2012. №6(82) 63
experimental conditions ([3, 4]) as functions of the
normalized poloidal flux Nψ .
In Fig. 3 and Fig. 4 the radial profiles of ReQm
and ImQm are shown, respectively (m = 11).
Here 0 0B ς > . If 0|| 0V = the strong change in profile of
Qm(aN) is visible near 0.948Na ≈ where 11( ) 0NF a =
only. And effect of the resonance ( ) 0m NK a ≈ at
0.958Na ≈ is small. When 0|| 0V ≠ the effect of the
resonance ( ) 0m NK a ≈ at 0.958Na ≈ is strong and
depends on direction of rotation. Note that the position of
this resonance does not depend on m practically. But
position of ( ) 0m NF a ≈ resonance depends on m strongly.
Fig. 3. Radial profiles of ReQm
Note that
( ) 2
2
( )
( ) ( ) .
a
m m
a a
m m
irot i a B mB
aR
i d d ma aB aB
maR da da a
ς θ ′⎡ ⎤≈ − + =⎣ ⎦
⎡ ⎤⎛ ⎞= −⎜ ⎟⎢ ⎥
⎝ ⎠⎣ ⎦
B
(20)
Hence, parameter Qm is characteristic of the plasma
current response on penetration of external perturbation
(see Eq. (15)).
CONCLUSIONS
The strong influence of toroidal plasma rotation on
pressure perturbation resonant excitation by external
low frequency helical magnetic perturbations near the
plasma edge is shown. The plasma rotation and plasma
response play a key role in this phenomenon.
Fig. 4. Radial profiles of Im Qm
Obtained results may be used to control of the plasma
stability for experiments in tokamaks JET, DIII-D,
TEXTOR and future ITER operation.
REFERENCES
1. K. Kamiya, N. Asakura, J. Boedo, et al. Edge localized
modes: recent experimental findings and related issues //
Plasma Phys. Control. Fus. 2007, v. 49, №.7, p. S43-S62.
2. P-H. Rebut. From JET to the reactor // Plasma Phys.
Control. Fusion. 2006, v. 48, №12B, p. B1-B14.
3. T.E. Evans, R.A. Moyer, P.R. Thomas, et al. Suppression
of large edge localized modes in high confinement DIII-D
plasmas with a stochastic magnetic boundary // Phys. Rev.
Letters. 2004, v. 92, №.23, 235003.
4. T.E. Evans, M.E. Fenstermacher, R.A. Moyer, et al.
RMP ELM suppression in DIII-D plasmas with ITER
similar shapes and collisionalities // Nuclear Fusion,
2008, v. 48, №2, p. 024002.
5. J.−K. Park, M.J. Schaffer, J.E. Menard, A.H. Boozer.
Control of asymmetric magnetic perturbations in
tokamaks // Phys. Rev. Letter. 2007, v. 99, p. 95003.
6. I.M. Pankratov, A.Ya. Omelchenko. On possibility of
pressure perturbation resonant excitation by an external
low frequency helical field near edge plasma//PAST.
Series «Plasma Physics »(17), 2011, №. 1, p. 23-25.
7. N. Oyama, Y. Kamada, A. Isayama, et al. ELM
frequency dependence on toroidal rotation in grassy
ELM regime in JT-60U // Plasma Phys. Control.
Fusion. 2007, v. 49, №.3, p. 249-259.
8. A.B. Mikhailovskii. Instabilities of plasma in magne-
tic traps. Moscow: “Atomizdat”, 1978 (in Russian).
Article received 27.09.12
ВЛИЯНИЕ ВРАЩЕНИЯ ПЛАЗМЫ НА РЕЗОНАНСНЫЕ МАГНИТНЫЕ ВОЗМУЩЕНИЯ
ВБЛИЗИ КРАЯ ПЛАЗМЫ ТОКАМАКА
И.М. Панкратов, И.В. Павленко, О.А. Помазан, А.Я. Омельченко
В рамках одножидкостной МГД исследовано резонансное возбуждение возмущений давления у края
плазмы внешними низкочастотными винтовыми возмущениями магнитного поля. Вращение плазмы играет
ключевую роль в этом явлении. Учтен отклик плазмы. Эти возмущения давления могут влиять на
устойчивость баллонных и пилинг-мод.
ВПЛИВ ОБЕРТАННЯ ПЛАЗМИ НА РЕЗОНАНСНІ МАГНІТНІ ЗБУРЕННЯ
ПОБЛИЗУ КРАЮ ПЛАЗМИ ТОКАМАКА
І.М. Панкратов, І.В. Павленко, О.O. Помазан, О.Я. Омельченко
У рамках однорідинної МГД досліджено резонансне збудження збурень тиску біля краю плазми
зовнішніми низькочастотними гвинтовими збуреннями магнітного поля. Обертання плазми відіграє
ключову роль у цьому явищі. Враховано відгук плазми. Ці збурення тиску можуть впливати на стійкість
балонних та пілінг-мод.
|
| id | nasplib_isofts_kiev_ua-123456789-109103 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-30T09:41:30Z |
| publishDate | 2012 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Pankratov, I.M. Pavlenko, I.V. Pomazan, O.A. Omelchenko, A.Ya. 2016-11-20T19:27:21Z 2016-11-20T19:27:21Z 2012 Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas / I.M. Pankratov, I.V. Pavlenko, O.A. Pomazan, A.Ya. Omelchenko // Вопросы атомной науки и техники. — 2012. — № 6. — С. 61-63. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.35.Bj, 52.55.Fa https://nasplib.isofts.kiev.ua/handle/123456789/109103 In the frame of one-fluid MHD the pressure perturbation resonant excitation by external low frequency helical magnetic perturbations near the plasma edge is investigated. The plasma rotation plays a key role in this phenomenon. The plasma response has been taken into account. These pressure perturbations may affect stability of the ballooning and peeling modes. В рамках одножидкостной МГД исследовано резонансное возбуждение возмущений давления у края плазмы внешними низкочастотными винтовыми возмущениями магнитного поля. Вращение плазмы играет ключевую роль в этом явлении. Учтен отклик плазмы. Эти возмущения давления могут влиять на устойчивость баллонных и пилинг-мод. У рамках однорідинної МГД досліджено резонансне збудження збурень тиску біля краю плазми зовнішніми низькочастотними гвинтовими збуреннями магнітного поля. Обертання плазми відіграє ключову роль у цьому явищі. Враховано відгук плазми. Ці збурення тиску можуть впливати на стійкість балонних та пілінг-мод. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники ИТЭР и приложения для термоядерного реактора Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas Влияние вращения плазмы на резонансные магнитные возмущения вблизи края плазмы токамака Вплив обертання плазми на резонансні магнітні збурення поблизу краю плазми токамака Article published earlier |
| spellingShingle | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas Pankratov, I.M. Pavlenko, I.V. Pomazan, O.A. Omelchenko, A.Ya. ИТЭР и приложения для термоядерного реактора |
| title | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas |
| title_alt | Влияние вращения плазмы на резонансные магнитные возмущения вблизи края плазмы токамака Вплив обертання плазми на резонансні магнітні збурення поблизу краю плазми токамака |
| title_full | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas |
| title_fullStr | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas |
| title_full_unstemmed | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas |
| title_short | Effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas |
| title_sort | effect of plasma rotation on the resonance magnetic perturbations at the edge of tokamak plasmas |
| topic | ИТЭР и приложения для термоядерного реактора |
| topic_facet | ИТЭР и приложения для термоядерного реактора |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/109103 |
| work_keys_str_mv | AT pankratovim effectofplasmarotationontheresonancemagneticperturbationsattheedgeoftokamakplasmas AT pavlenkoiv effectofplasmarotationontheresonancemagneticperturbationsattheedgeoftokamakplasmas AT pomazanoa effectofplasmarotationontheresonancemagneticperturbationsattheedgeoftokamakplasmas AT omelchenkoaya effectofplasmarotationontheresonancemagneticperturbationsattheedgeoftokamakplasmas AT pankratovim vliânievraŝeniâplazmynarezonansnyemagnitnyevozmuŝeniâvblizikraâplazmytokamaka AT pavlenkoiv vliânievraŝeniâplazmynarezonansnyemagnitnyevozmuŝeniâvblizikraâplazmytokamaka AT pomazanoa vliânievraŝeniâplazmynarezonansnyemagnitnyevozmuŝeniâvblizikraâplazmytokamaka AT omelchenkoaya vliânievraŝeniâplazmynarezonansnyemagnitnyevozmuŝeniâvblizikraâplazmytokamaka AT pankratovim vplivobertannâplazminarezonansnímagnítnízburennâpoblizukraûplazmitokamaka AT pavlenkoiv vplivobertannâplazminarezonansnímagnítnízburennâpoblizukraûplazmitokamaka AT pomazanoa vplivobertannâplazminarezonansnímagnítnízburennâpoblizukraûplazmitokamaka AT omelchenkoaya vplivobertannâplazminarezonansnímagnítnízburennâpoblizukraûplazmitokamaka |