Stabilization of a model magnetic island in tokamaks by localized electron cyclotron current drive (ECCD) has been studied using a fluid-kinetic hybrid model coupled with ray tracing and Fokker−Planck equations. Even though a gyrokinetic toroidal code at present is not able to simulate the long-time evolution of tearing modes, which starts from small perturbation and evolves to the Rutherford regime, we can still calculate a model magnetic island and its stabilization by ECCD. Gyrokinetic simulations find that the model magnetic island can be fully stabilized by the ECCD with the 1 MW 68 GHz X2-mode in HL-2A-like equilibrium, while the model magnetic island in the DIII-D tokamak is only partially stabilized with the same ECCD power. A helicoidal current drive is more efficient than a continuous ECCD to stabilize the model magnetic island. Simulation results further indicate that, without external current drive, thermal ion kinetic effects could also reduce the magnetic island width and the linear growth rate of tearing modes.
References
1.
G.
Giruzzi
, M.
Zabiego
, T. A.
Gianakon
, X.
Garbet
, A.
Cardinali
, and S.
Bernabei
, Nucl. Fusion
39
, 107
(1999
).2.
J.
Walker
, Phys. Rev. E
98
, 033209
(2018
).3.
]
R. J.
La Haye
, Phys. Plasmas
13
, 055501
(2006
).4.
E.
Kim
, Phys. Rev. E
76
, 025401
(2007
).5.
R. J.
La Haye
, R.
Prater
, R. J.
Buttery
, N.
Hayashi
, A.
Isayama
, M. E.
Maraschek
, L.
Urso
, and H.
Zohm
, Nucl. Fusion
46
, 451
(2006
).6.
Y. R.
Lin-Liu
, V. S.
Chan
, and R.
Prater
, Phys. Plasmas
10
, 4064
(2003
).7.
R. I.
Pinsker
, Phys. Plasmas
8
, 1219
(2001
).8.
R.
Fitzpatrick
, Nucl. Fusion
33
, 1049
(1993
).9.
Q.
Hu
, Q.
Yu
, B.
Rao
, Y. H.
Ding
, X. W.
Hu
, and G.
Zhuang
, and J-TEXT Team,
Nucl. Fusion
52
, 083011
(2012
).10.
M.
Garcia-Munoz
, H.-U.
Fahrbach
, S. D.
Pinches
, V.
Bobkov
, M.
Brudgam
, M.
Gobbin
, S.
Gunter
, V.
Igochine
, Ph.
Lauber
, M. J.
Mantsinen
, M.
Maraschek
, L.
Marrelli
, P.
Martin
, P.
Piovesan
, E.
Poli
, K.
Sassenberg
, G.
Tardini
, H.
Zohm
, and ASDEX Upgrade Team,
Nucl. Fusion
49
, 085014
(2009
).11.
G.
Gantenbein
, H.
Zohm
, G.
Giruzzi
, S.
Günter
, F.
Leuterer
, M.
Maraschek
, J.
Meskat
, Q.
Yu
, ASDEX Upgrade Team, and ECRH-Group,
Phys. Rev. Lett.
85
, 1242
(2000
).12.
C. C.
Petty
, R. J.
La Haye
, T. C.
Luce
, D. A.
Humphreys
, A. W.
Hyatt
, J.
Lohr
, R.
Prater
, E. J.
Strait
, and M. R.
Wade
, Nucl. Fusion
44
, 243
(2004
).13.
A.
Isayama
, Y.
Kamada
, T.
Ozeki
, S.
Ide
, T.
Fujita
, T.
Oikawa
, T.
Suzuki
, Y.
Neyatani
, N.
Isei
, K.
Hamamatsu
, Y.
Ikeda
, K.
Takahashi
, K.
Kajiwara
, and JT-60 Team,
Nucl. Fusion
41
, 761
(2001
).14.
Z.
Chang
, J. D.
Callen
, E. D.
Fredrickson
, R. V.
Budny
, C. C.
Hegna
, K. M.
McGuire
, M. C.
Zarnstorff
, and TFTR Group,
Phys. Rev. Lett.
74
, 4663
(1995
).15.
R. J.
La Haye
, P. A.
Politzer
, and D. P.
Brennan
, Nucl. Fusion
48
, 015005
(2008
).16.
X. R.
Duan
, Y.
Liu
, M.
Xu
, L. W.
Yan
, Y.
Xu
, X. M.
Song
, J. Q.
Dong
, X. T.
Ding
, L. Y.
Chen
, B.
Lu
, D. Q.
Liu
et al., Nucl. Fusion
57
, 102013
(2017
).17.
Y.
Liu
, Phys. Rev. E
84
, 016403
(2011
).18.
M.
Kong
, T. C.
Blanken
, F.
Felici
, C.
Galperti
, E.
Maljaars
, O.
Sauter
, T.
Vu
, F.
Carpanese
, A.
Merle
, J.-M.
Moret
, F.
Pesamosca
, E.
Poli
, M.
Reich
, A. A.
Teplukhina
, TCV Team, and EUROfusion MST1 Team,
Nucl. Fusion
59
, 076035
(2019
).19.
B. A.
Hennen
, E.
Westerhof
, P. W. J. M.
Nuij
, J. W.
Oosterbeek
, M. R.
de Baar
, W. A.
Bongers
, A.
Bürger
, D. J.
Thoen
, M.
Steinbuch
, and TEXTOR Team,
Plasma Phys. Controlled Fusion
52
, 104006
(2010
).20.
G.
Gantenbein
, A.
Keller
, F.
Leuterer
, M.
Maraschek
, W.
Suttrop
, H.
Zohm
, and ASDEX Upgrade Team,
“Investigations on m = 2, n = 1 tearing mode stabilisation with ECRH at ASDEX Upgrade
,” in Proceedings of the 30th EPS Conference on Controlled Fusion and Plasma Physics, St. Petersburg, Russia, 2003
, edited by R.
Koch
and S.
Lebedev
(European Physical Society, Geneva, 2003
), Vol. 27A, p. P-1.187 (CD-ROM).21.
R. J.
La Haye
, S.
Günter
, D. A.
Humphreys
, J.
Lohr
, T. C.
Luce
, M. E.
Maraschek
, C. C.
Petty
, R.
Prater
, J. T.
Scoville
, and E. J.
Strait
, Phys. Plasmas
9
, 2051
(2002
).22.
R.
Prater
, R.
LaHaye
, T. C.
Luce
, C. C.
Petty
, E. J.
Strait
, J. R.
Ferron
, D. A.
Humphreys
, A.
Isayama
, J.
Lohr
, K.
Nagasaki
, P. A.
Politzer
, M. R.
Wade
, and A. S.
Welander
, Nucl. Fusion
47
, 371
(2007
).23.
Q.
Yu
, X. D.
Zhang
, and S.
Gnter
, Phys. Plasmas
11
, 1960
(2004
).24.
J.
Li
, X.
Ji
, J.
Dong
, Y.
Hu
, S.
Liu
, L.
Yan
, and HL-2A Contributors,
Phys. Plasmas
26
, 032505
(2019
).25.
T. G.
Jenkins
and E. D.
Held
, J. Comput. Phys.
297
, 427
(2015
).26.
S.
Wang
, Z. W.
Ma
, and W.
Zhang
, Phys. Plasmas
23
, 052503
(2016
).27.
J.
Pratt
, G. T.
Huijsmans
, and E.
Westerhof
, Phys. Plasmas
23
, 102507
(2016
).28.
O.
Fvrier
, P.
Maget
, H.
Lutjens
, and P.
Beyer
, Plasma Phys. Controlled Fusion
59
, 044002
(2017
).29.
A. M.
Popov
, R. J.
La Haye
, Y. Q.
Liu
, M.
Murakami
, N. N.
Popova
, and A. D.
Turnbull
, Phys. Plasmas
9
, 4229
(2002
).30.
T. G.
Jenkins
, S. E.
Kruger
, C. C.
Hegna
, D. D.
Schnack
, and C. R.
Sovinec
, Phys. Plasmas
17
, 012502
(2010
).31.
H.
Cai
, S.
Wang
, Y.
Xu
, J.
Cao
, and D.
Li
, Phys. Rev. Lett.
106
, 075002
(2011
).32.
H.
Cai
and G.
Fu
, Phys. Plasmas
19
, 072506
(2012
).33.
W. A.
Hornsby
, P.
Migliano
, R.
Buchholz
, S.
Grosshauser
, A.
Weikl
, D.
Zarzoso
, F. J.
Casson
, E.
Poli
, and A. G.
Peeters
, Plasma Phys. Controlled Fusion
58
, 014028
(2016
).34.
Z.
Lin
, T. S.
Hahm
, W. W.
Lee
, W. M.
Tang
, and R. B.
White
, Science
281
, 1835
(1998
).35.
Z.
Lin
, W. M.
Tang
, and W. W.
Lee
, Phys. Rev. Lett.
78
, 456
(1997
).36.
W.
Zhang
, Z.
Lin
, and L.
Chen
, Phys. Rev. Lett.
101
, 095001
(2008
).37.
H. S.
Zhang
, Z.
Lin
, and I.
Holod
, Phys. Rev. Lett.
109
, 025001
(2012
).38.
Z.
Wang
, Z.
Lin
, I.
Holod
, W. W.
Heidbrink
, and B.
Tobias
, Phys. Rev. Lett.
111
, 145003
(2013
).39.
Z.
Lin
, I.
Holod
, L.
Chen
, P. H.
Diamond
, T. S.
Hahm
, and S.
Ethier
, Phys. Rev. Lett.
99
, 265003
(2007
).40.
J.
McClenaghan
, Z.
Lin
, I.
Holod
, and W.
Deng
, Phys. Plasmas
21
, 122519
(2014
).41.
D. J.
Liu
, W. L.
Zhang
, J.
McClenaghan
, J. Q.
Wang
, and Z.
Lin
, Phys. Plasmas
21
, 122520
(2014
).42.
J. C.
Li
, C. J.
Xiao
, Z. H.
Lin
, and K. J.
Wang
, Phys. Plasmas
24
, 082508
(2017
).43.
X. Q.
Xue
, Phys. Rev. E
78
, 016406
(2008
).44.
45.
O.
Fevrier
, P.
Maget
, H.
Lütjens
, J. F.
Luciani
, J.
Decker
, G.
Giruzzi
, M.
Reich
, P.
Beyer
, E.
Lazzaro
, and S.
Nowak
, Plasma Phys. Controlled Fusion
58
, 045015
(2016
).46.
I.
Holod
, W. L.
Zhang
, Y.
Xiao
, and Z.
Lin
, Phys. Plasmas
16
, 122307
(2009
).47.
J.
Bao
, D.
Liu
, and Z.
Lin
, Phys. Plasmas
24
, 102516
(2017
).48.
W. W.
Lee
, J. Comput. Phys.
72
, 243
(1987
).49.
A.
Brizard
and T.
Hahm
, Rev. Mod. Phys.
79
, 421
(2007
).50.
A. M.
Dimits
and W. W.
Lee
, J. Comput. Phys.
107
, 309
(1993
).51.
S. E.
Parker
and W. W.
Lee
, Phys. Fluids B
5
, 77
(1993
).52.
W.
Deng
, Z.
Lin
, and I.
Holod
, Nucl. Fusion
52
, 023005
(2012
).53.
W.
Zhang
, S.
Wang
, and Z. W.
Ma
, Phys. Plasmas
24
, 062510
(2017
).54.
M.
Maraschek
, G.
Gantenbein
, Q.
Yu
, H.
Zohm
, S.
Günter
, F.
Leuterer
, A.
Manini
, ASDEX Upgrade Team, and ECHR Group,
Phys. Rev. Lett.
98
, 025005
(2007
).55.
J.
Wang
, C.
Xiao
, X.
Wang
, X.
Ji
, and Y.
Liu
, Plasma Phys. Controlled Fusion
54
, 122001
(2012
).56.
J. C.
Li
, X. Y.
Gong
, J. Q.
Dong
, P. W.
Zheng
, S. D.
Song
, Q. D.
Gao
, and D.
Du
, Phys. Plasmas
22
, 062512
(2015
).57.
W. W.
Heidbrink
, M. E.
Austin
, C. S.
Collins
, T.
Gray
, B. A.
Grierson
, G. J.
Kramer
, M.
Lanctot
, D. C.
Pace
, M. A.
Van Zeeland
, and A. G.
Mclean
, Nucl. Fusion
55
, 083023
(2015
).58.
L. L.
Lao
, H. S.
John
, R. D.
Stambaugh
, A. G.
Kellman
, and W.
Pfeiffer
, Nucl. Fusion
25
, 1611
(1985
).59.
Y.
Liu
, R. J.
Hastie
, and T. C.
Hender
, Phys. Plasmas
19
, 092510
(2012
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
