On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma
In the frame of one-fluid MHD a possibility of the pressure perturbation resonant excitation by external low frequency helical magnetic perturbations near the plasma edge is shown. The plasma rotation plays the key role in this phenomenon. The plasma response has being taken into account. These pres...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2011
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| Цитувати: | On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma / I.M. Pankratov, A.Ya. Omelchenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 23-25. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-906112016-01-04T15:46:39Z On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma Pankratov, I.M. Omelchenko, A.Ya. Магнитное удержание In the frame of one-fluid MHD a possibility of the pressure perturbation resonant excitation by external low frequency helical magnetic perturbations near the plasma edge is shown. The plasma rotation plays the key role in this phenomenon. The plasma response has being taken into account. These pressure perturbations may affect on the ballooning and peeling modes stability. У рамках однорідинної МГД показана можливість резонансного 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. В рамках одножидкостной МГД показана возможность резонансного возбуждения 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. 2011 Article On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma / I.M. Pankratov, A.Ya. Omelchenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 23-25. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.35.Bj, 52.55.Fa http://dspace.nbuv.gov.ua/handle/123456789/90611 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Магнитное удержание Магнитное удержание |
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Магнитное удержание Магнитное удержание Pankratov, I.M. Omelchenko, A.Ya. On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma Вопросы атомной науки и техники |
| description |
In the frame of one-fluid MHD a possibility of the pressure perturbation resonant excitation by external low frequency helical magnetic perturbations near the plasma edge is shown. The plasma rotation plays the key role in this phenomenon. The plasma response has being taken into account. These pressure perturbations may affect on the ballooning and peeling modes stability. |
| format |
Article |
| author |
Pankratov, I.M. Omelchenko, A.Ya. |
| author_facet |
Pankratov, I.M. Omelchenko, A.Ya. |
| author_sort |
Pankratov, I.M. |
| title |
On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma |
| title_short |
On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma |
| title_full |
On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma |
| title_fullStr |
On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma |
| title_full_unstemmed |
On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma |
| title_sort |
on possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2011 |
| topic_facet |
Магнитное удержание |
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http://dspace.nbuv.gov.ua/handle/123456789/90611 |
| citation_txt |
On possibility of pressure perturbation resonant excitation by an external low frequency helical field near edge plasma / I.M. Pankratov, A.Ya. Omelchenko // Вопросы атомной науки и техники. — 2011. — № 1. — С. 23-25. — Бібліогр.: 10 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT pankratovim onpossibilityofpressureperturbationresonantexcitationbyanexternallowfrequencyhelicalfieldnearedgeplasma AT omelchenkoaya onpossibilityofpressureperturbationresonantexcitationbyanexternallowfrequencyhelicalfieldnearedgeplasma |
| first_indexed |
2025-07-06T18:48:16Z |
| last_indexed |
2025-07-06T18:48:16Z |
| _version_ |
1836924479559696384 |
| fulltext |
ON POSSIBILITY OF PRESSURE PERTURBATION RESONANT
EXCITATION BY AN EXTERNAL LOW FREQUENCY HELICAL
FIELD NEAR EDGE PLASMA
I.M. Pankratov, A.Ya. Omelchenko
Institute of Plasma Physics, NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: pankratov@kipt.kharkov.ua
In the frame of one-fluid MHD a possibility of the pressure perturbation resonant excitation by external low
frequency helical magnetic perturbations near the plasma edge is shown. The plasma rotation plays the key role in this
phenomenon. The plasma response has being taken into account. These pressure perturbations may affect on the
ballooning and peeling modes stability.
PACS: 52.35.Bj, 52.55.Fa
1. INTRODUCTION
Control of Edge Localized Modes (ELMs) is a critical
issue of the present day large tokamaks and future ITER
operation. ELMs are short bursts of particles and energy
at tokamak edge plasma observed in H-mode operation
[1, 2]. Melting, erosion and evaporation of divertor target
plates may occur as results of these bursts.
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2011. № 1. 23
Series: Plasma Physics (17), p. 23-25.
Many experiments in DIII-D have shown that ELMs
can be suppressed by small external low frequency helical
magnetic perturbations [3, 4]. Until now, understanding of
the underlying physics of ELMs and their suppressions
has been far from complete.
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.
In the present paper, a possibility of the pressure
perturbation resonant excitation by external low
frequency helical magnetic perturbations near the plasma
edge is shown. A perfect shielding is not assumed. This
pressure perturbation resonant excitation strongly depends
on a plasma rotation. The plasma response takes into
account.
Note, that ELM frequency dependence on the toroidal
rotation in JT-60U was shown [6].
2. BASIC EQUATIONS
We start from the one-fluid MHD equations
1
i
d
p
dt c
V
J B , (1)
00 Vpdiv
dt
dp , (2)
the Maxwell’s equations
tc
rot
B
E
1
, JB
c
rot
4
, , (3)
, (4)
0Bdiv
0
______________________________________________
Jdiv
and Ohm’s Law ( - conductivity)
BVEJ
c
1 , (5)
where is the plasma mass densities, p is the plasma
pressure, is the current density, is the ion
gyroviscosity tensor, respectively.
J
i
We consider a current carrying toroidal plasma with
nested equilibrium circular magnetic surfaces ( 0 is the
radius of the magnetic surfaces, 0 is the poloidal angle
in the cross-section const , is the toroidal angle).
Each magnetic surface is shifted with respect to the
magnetic axis ( is the shift, is the radius of the
magnetic axis). The equilibrium toroidal contravariant
component of the magnetic field,
R
gB 20 , is
large with respect to the poloidal one, gB 20 ,
and are the radial derivatives of toroidal and
poloidal fluxes, respectively; /)(aq is the safety
factor, q/1 . The known expressions for metric tensor
are used [7].
On each magnetic equilibrium surface (see, e.g. [7])
we introduce a straight magnetic field line coordinate
system ( ,a , ) a0 , sin0 a
Raaa )( , (6)
dbb
R
b
bp
R
a
aR
a
a
0
2
0
2
2
)(
)(16
2
)(1
. (7)
Assuming that perturbation we get equations
r perturbations (m >>1, nq >>1). From Eq.(4) by usual
approximation in 1/R one finds
0B
fo
way [7] in a linear
2
11 12 12 22
0
00
1 8
2 4
( , ) 0,
a
a
g p
L g g B g g B
a ag g
pp J
W a L B B
c p c ap g
/
a
(8)
where
( / ) ( / )L ,
ggpc )0(0
2 )(4)/( ,
24
gJJ 2//0 ,
0 1( , ) ( ) ( , )W a W a W a ,
0
20 0
0 2 2
0 0
2
( ) 1
( )
p ap SR
W a
RB a B a
,
0
1 2
0
2
( , ) cos
( )
p S
W a
aB a
, q
S a
q
.
Equilibrium parameters denotes by the subscript 0.
_______________________________________
Assuming periodicity in both and , we take the
perturbations in the form
nm
mn tnmiaXtaX
,
exp,,, , (9)
where is the frequency of the external perturbation.
In our consideration all poloidal harmonic amplitudes
of perturbations have finite values. The amount of
poloidal harmonics with finite values of amplitudes
depends on the antenna spectrum (external perturbation).
Early the case was studied for one dominant poloidal
external mode and neighboring poloidal modes were
considered as small [8].
Using Eq. (9), Eq. (8) (derivatives with respect to
radius a denote by the prime) becomes
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)
( ) ( ) ( ) ( )
a
a a a m
m m m m m m m
m m m m m
BSqR iqR aR
F 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 i
S p ap ap m p m p
B a R B a a B a B a
.0
(10)
In Eq. (10) ( )mF a m n ,
0 ( ) / 2 ,B a a
00 ( ) / 2 ,B a R ( )aaB 0.m mimaB
_ _____________________________________
In the similar way from Eq. (2), using the parallel (with
respect to equilibrium magnetic field) momentum from
Eq. (1), we get for pressure perturbation ( 0div V )
the next equation:
(11)
Here
2
2 2 a
2
( ) ( ),s
m im m m
c
a F
R
2 0
0
0
,s
p
c
(12)
0 0 0
0
0 0
( )
,m
m
B BF a Em
V c
B R B a B
0
a (13)
0 0 0
0
0 0 0
( )
[ (m i
im
B F a p Em
V c c
B R a en B B
0
)]a
m
. (14)
______________________________________________
We took into account the equilibrium poloidal plasma
rotation due to the existence of an equilibrium radial
electric field E0a and the ion diamagnetic drift; and the
parallel with respect to equilibrium magnetic field plasma
rotation with a velocity . Recall that
(see, e.g. [7, 9]).
0V
a a a
m Em pV V V
From the radial component of Faraday’s Law and
Ohm’s Law Eq. (5) we find
2
0 2
m 2
( ) ( )
4
a a
i m m m m m
B ic m aB F a V i a B mB
R a
. (15)
____________________________________________
Equations (10), (11) and (15) describe the affect of an
external helical field on the ballooning and peeling modes
due to the direct change of the edge plasma pressure. This
affect has a resonant character.
3. DISCUSSIONS
When
2
2
2
( ) ( ) 0,s
m im m m
c
a F
R
2 a (16)
the resonant excitation of pressure perturbation takes
place.
Note, that during the plasma eigenmodes stability
analysis for a pressure perturbation (Eq. (1.98) of [10])
the nonresonant term occurred. 2 2 2 2( / ) ( )s mc R F a
For more typical situation, when
0
0
( ) a
m s
Ea
F a c c
mR B
,
t
he resonant excitation takes place, if
0 0 0
0
0 0
( )m a
B BF a Em
V c
B R B a B
0
(17)
or
0 0 0
0
0 0 0
( )
[ (m i
B F a p Em
V c c
B R a en B B
0
)]a . (18)
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 aVi
p F a V V p p V V V
R B B R m m
Resonant conditions (17) and (18) useful to present in
next form, respectively:
0
0
0
aE
k V k c
B
, (19)
0
0
0 0 0
( )ip E
k V k c c
en B B
25
0a . (20)
In the case 0 (e.g. for DIII-D) resonant conditions
(17) and (18) convenient to present the next way:
0
0
0
( )
( ( ) / ) aE aa
a n m V c
R
B
, (21)
0 0
0
0 0
( ( ) / ) ( )aE pa
a n m V c c
R B
0
i
en B
. (22)
Note, that for DIII-D edge plasma parameters [3, 4] the
resonant conditions (21) and (22) may be realized.
4. CONCLUSIONS
A possibility of the pressure perturbation resonant
excitation by external low frequency helical magnetic
perturbations near the plasma edge is shown. This
phenomenon occurs during the plasma rotation. It may
affect on the ballooning and peeling modes excitation
because of a plasma pressure change.
The equations that describe this influence on the
ballooning and peeling modes excitation are derived on
the basis of MHD equations when all poloidal harmonic
amplitudes of external perturbations have finite values.
Plasma rotation and plasma response are taken into
account.
Expected result may be used for interpretation of the
plasma stability 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. Fusion. 2007, v. 49, N 7,
p. S43-S62.
2. P-H. Rebut. From JET to the reactor // Plasma Phys.
Control. Fusion. 2006, v. 48, N 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, N 23,
235003.
4. T.E. Evans, R.A. Moyer, K.H. Burrell, et al. Edge
stability and transport control with resonant magnetic
perturbations in collisionless tokamak plasmas //
Nature Physics. 2006, v. 2, N 6, p.419-423.
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, р. 195003.
6. 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, N 3, p. 249-259.
7. A.B. Mikhailovskii. Instabilities of plasma in magnetic
traps. Moscow: ”Atomizdat”, 1978 (in Russian).
8. I.M. Pankratov, A.Ya. Omelchenko. Influence of an
external low frequency helical perturbation on the
ballooning modes // Problems of Atomic Science and
Technology. Series «Plasma Physics (14)», 2008. N 6,
p. 25-27.
9. A.I. Smolyakov, X. Garbet, C. Bourdelle. On the
parallel momentum balance in low pressure plasmas
with an inhomogeneous magnetic field // Nucl. Fusion.
2009, v. 49, N 12, p. 125001.
10. A.B. Mikhailovskii. Reviews of Plasma Physics.
Moscow: “Atomizdat”, 1979, v. 9, p. 3 (in Russian).
Article received 10.10.10
О ВОЗМОЖНОСТИ РЕЗОНАНСНОГО ВОЗБУЖДЕНИЯ ВОЗМУЩЕНИЯ ДАВЛЕНИЯ ВНЕШНИМ
НИЗКОЧАСТОТНЫМ ВИНТОВЫМ ПОЛЕМ ВБЛИЗИ КРАЯ ПЛАЗМЫ
И.М. Панкратов, А.Я. Омельченко
В рамках одножидкостной МГД показана возможность резонансного возбуждения 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.
ПРО МОЖЛИВІСТЬ РЕЗОНАНСНОГО ЗБУДЖЕННЯ ЗБУРЕННЯ ТИСКУ ЗОВНІШНІМ
НИЗЬКОЧАСТОТНИМ ГВИНТОВИМ ПОЛЕМ БІЛЯ КРАЮ ПЛАЗМИ
І.М. Панкратов, О.Я. Омельченко
У рамках однорідинної МГД показана можливість резонансного 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.
where is the frequency of the external perturbation.
Here
We took into account the equilibrium poloidal plasma rotation due to the existence of an equilibrium radial electric field E0a and the ion diamagnetic drift; and the parallel with respect to equilibrium magnetic field plasma rotation with a velocity. Recall that (see, e.g. [7, 9]).
REFERENCES
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