A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at , thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C1 code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if β is sufficiently high to provide the necessary drive for the instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.
References
1.
R. J.
Hastie
, “Sawtooth instability in tokamak plasmas
,” Astrophys. Space Sci.
256
(1/2
), 177
–204
(1997
).2.
B. B.
Kadomtsev
, “Disruptive instability in tokamaks
,” Sov. J. Plasma Phys.
1
, 389
(1975
).3.
TEXTOR Team
, in Plasma Physics and Controlled Nuclear Fusion Research (Proceedings of the 12th International Conference Nice (1988))
, IAEA Vienna
, 1988
, Vol. 1
, p. 331
.4.
J.
Blum
, E.
Lazzaro
, J.
O'Rourke
, B.
Keegan
, and Y.
Stephan
, “Problems and methods of self-consistent reconstruction of tokamak equilibrium profiles from magnetic and polarimetric measurements
,” Nucl. Fusion
30
, 1475
–1492
(1990
).5.
M.
Yamada
, F. M.
Levinton
, N.
Pomphrey
, R.
Budny
, J.
Manickam
, and Y.
Nagayama
, “Investigation of magnetic reconnection during a sawtooth crash in a high-temperature tokamak plasma
,” Phys. Plasmas
1
(10
), 3269
(1994
).6.
A.
Letsch
, H.
Zohm
, F.
Ryter
, W.
Suttrop
, A.
Gude
, F.
Porcelli
, C.
Angioni
, and I.
Furno
, “Incomplete reconnection in sawtooth crashes in ASDEX Upgrade
,” Nucl. Fusion
42
, 1055
–1059
(2002
).7.
I. T.
Chapman
, “Controlling sawtooth oscillations in tokamak plasmas
,” Plasma Phys. Controlled Fusion
53
, 013001
(2011
).8.
J.
Stober
, A. C. C.
Sips
, C.
Angioni
, C. B.
Forest
, O.
Gruber
, J.
Hobirk
, L. D.
Horton
, C. F.
Maggi
, M.
Maraschek
, P.
Martin
et al., “The role of the current profile in the improved H-mode scenario in ASDEX Upgrade
,” Nucl. Fusion
47
, 728
–737
(2007
).9.
A. C. C.
Sips
, “Advanced scenarios for ITER operation
,” Plasma Phys. Controlled Fusion
47
, A19
–A40
(2005
).10.
A. C. C.
Sips
, R.
Arslanbekov
, C.
Atanasiu
, W.
Becker
, G.
Becker
, K.
Behler
, K.
Behringer
, A.
Bergmann
, R.
Bilato
, D.
Bolshukhin
et al., “Steady state advanced scenarios at ASDEX Upgrade
,” Plasma Phys. Controlled Fusion
44
, B69
–B83
(2002
).11.
E.
Joffrin
, A. C. C.
Sips
, J. F.
Artaud
, A.
Becoulet
, L.
Bertalot
, R.
Budny
, P.
Buratti
, P.
Belo
, C. D.
Challis
, F.
Crisanti
et al., “The hybrid scenario in JET: Towards its validation for ITER
,” Nucl. Fusion
45
, 626
–634
(2005
).12.
S.
Ide
and JT-60 Team
, “Overview of JT-60U progress towards steady-state advanced tokamak
,” Nucl. Fusion
45
, S48
–S62
(2005
).13.
C. C.
Petty
, J. E.
Kinsey
, C. T.
Holcomb
, J. C.
DeBoo
, E. J.
Doyle
, J. R.
Ferron
, A. M.
Garofalo
, A. W.
Hyatt
, G. L.
Jackson
, T. C.
Luce
et al., “High-beta, steady-state hybrid scenario on DIII-D
,” Nucl. Fusion
56
, 016016
(2016
).14.
A.
Bock
, E.
Fable
, R.
Fischer
, M.
Reich
, D.
Rittich
, J.
Stober
, M.
Bernert
, A.
Burckhart
, M.
Dunne
, B.
Geiger
et al., “Non-inductive improved H-Mode operation at ASDEX Upgrade
,” Nucl. Fusion
(published online).15.
O.
Gruber
, R. C.
Wolf
, R.
Dux
, C.
Fuchs
, S.
Günter
, A.
Kallenbach
, K.
Lackner
, M.
Maraschek
, P. J.
McCarthy
, H.
Meister
et al., “Stationary H-Mode discharges with internal transport barrier on ASDEX Upgrade
,” Phys. Rev. Lett.
83
, 1787
–1790
(1999
).16.
A.
Staebler
, A. C. C.
Sips
, M.
Brambilla
, R.
Bilato
, R.
Dux
, O.
Gruber
, J.
Hobirk
, L. D.
Horton
, C. F.
Maggi
, A.
Manini
et al., “The improved H-mode at ASDEX Upgrade: A candidate for an ITER hybrid scenario
,” Nucl. Fusion
45
, 617
–625
(2005
).17.
C. C.
Petty
, M. E.
Austin
, C. T.
Holcomb
, R. J.
Jayakumar
, R. J.
La Haye
, T. C.
Luce
, M. A.
Makowski
, P. A.
Politzer
, and M. R.
Wade
, “Magnetic-flux pumping in high-performance, stationary plasmas with tearing modes
,” Phys. Rev. Lett.
102
, 045005
(2009
).18.
S. C.
Jardin
, N.
Ferraro
, and I.
Krebs
, “Self-organized stationary states of tokamaks
,” Phys. Rev. Lett.
115
, 215001
(2015
).19.
R. E.
Denton
, J. F.
Drake
, and R. G.
Kleva
, “The m=1 convection cell and sawteeth in tokamaks
,” Phys. Fluids
30
(5
), 1448
(1987
).20.
V. S.
Lukin
, “Computational study of the internal kink mode evolution and associated magnetic reconnection phenomena
,” Ph.D. thesis (Princeton University
, 2008
).21.
F. D.
Halpern
, D.
Leblond
, H.
Lütjens
, and J.-F.
Luciani
, “Oscillation regimes of the internal kink mode in tokamak plasmas
,” Plasma Phys. Controlled Fusion
53
, 015011
(2011
).22.
J. A.
Breslau
, M. S.
Chance
, J.
Chen
, G. Y.
Fu
, S.
Gerhardt
, N.
Gorelenkov
, S. C.
Jardin
, and J.
Manickam
, “Onset and saturation of a non-resonant internal mode in NSTX and implications for AT modes in ITER
,” Nucl. Fusion
51
, 063027
(2011
).23.
W. A.
Cooper
, J. P.
Graves
, A.
Pochelon
, O.
Sauter
, and L.
Villard
, “Tokamak magnetohydrodynamic equilibrium states with axisymmetric boundary and a 3D helical core
,” Phys. Rev. Lett.
105
, 035003
(2010
).24.
W. A.
Cooper
, J. P.
Graves
, and O.
Sauter
, “Helical ITER hybrid scenario equilibria
,” Plasma Phys. Controlled Fusion
53
, 024002
(2011
).25.
E.
Strumberger
, S.
Günter
, and C.
Tichmann
, “MHD instabilities in 3D tokamaks
,” Nucl. Fusion
54
, 064019
(2014
).26.
D.
Brunetti
, W. A.
Cooper
, J. P.
Graves
, F.
Halpern
, C.
Wahlberg
, H.
Lütjens
, and J. F.
Luciani
, “MHD properties in the core of ITER-like hybrid scenarios
,” J. Phys.: Conf. Ser.
401
, 012003
(2012
).27.
D.
Brunetti
, J. P.
Graves
, W. A.
Cooper
, and D.
Terranova
, “Ideal saturated MHD helical structures in axisymmetric hybrid plasmas
,” Nucl. Fusion
54
, 064017
(2014
).28.
P. M.
Bellan
, Spheromaks: A Practical Application of Magnetohydrodynamic Dynamos and Plasma Self–Organization
(Imperial College Press
, 2000
).29.
S. C.
Hsu
and P. M.
Bellan
, “Experimental identification of the kink instability as a poloidal flux amplification mechanism for coaxial gun spheromak formation
,” Phys. Rev. Lett.
90
, 215002
(2003
).30.
S.
Ortolani
and D. D.
Schnack
, Magnetohydrodynamics of Plasma Relaxation
(World Scientific
, 1993
).31.
D.
Bonfiglio
, S.
Cappello
, and D. F.
Escande
, “Dominant electrostatic nature of the reversed field pinch dynamo
,” Phys. Rev. Lett.
94
, 145001
(2005
).32.
S.
Cappello
, D.
Bonfiglio
, and D. F.
Escande
, “Magnetohydrodynamic dynamo in reversed field pinch plasmas: Electrostatic drift nature of the dynamo velocity field
,” Phys. Plasmas
13
, 056102
(2006
).33.
P.
Piovesan
, D.
Craig
, L.
Marrelli
, S.
Cappello
, and P.
Martin
, “Measurements of the MHD dynamo in the quasi-single-helicity reversed-field pinch
,” Phys. Rev. Lett.
93
, 235001
(2004
).34.
P.
Piovesan
, D.
Bonfiglio
, M.
Cianciosa
, T.
Luce
, N.
Taylor
, D.
Terranova
, F.
Turco
, R.
Wilcox
, A.
Wingen
, S.
Cappello
et al., “Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas
,” Nucl. Fusion
57
(7
), 076014
(2017
).35.
S. C.
Jardin
, N.
Ferraro
, J.
Breslau
, and J.
Chen
, “Multiple timescale calculations of sawteeth and other global macroscopic dynamics of tokamak plasmas
,” Comput. Sci. Discovery
5
, 014002
(2012
).36.
37.
S.
Jardin
, “A triangular finite element with first-derivative continuity applied to fusion MHD applications
,” J. Comput. Phys.
200
, 133
–152
(2004
).38.
R. J.
Hastie
and T. C.
Hender
, “Toroidal internal kink stability in tokamaks with ultra flat q profiles
,” Nucl. Fusion
28
, 585
–594
(1988
).39.
F. L.
Waelbroeck
and R. D.
Hazeltine
, “Stability of low-shear tokamaks
,” Phys. Fluids
31
(5
), 1217
(1988
).40.
F. L.
Waelbroeck
, “Nonlinear growth of the quasi-interchange instability
,” Phys. Fluids B: Plasma Phys.
1
, 499
–505
(1989
).41.
N.
Ferraro
and S.
Jardin
, “Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
,” J. Comput. Phys.
228
, 7742
–7770
(2009
).42.
43.
F. D.
Halpern
, H.
Lütjens
, and J.-F.
Luciani
, “Diamagnetic thresholds for sawtooth cycling in tokamak plasmas
,” Phys. Plasmas
18
(10
), 102501
(2011
).44.
S.
Günter
, Q.
Yu
, K.
Lackner
, A.
Bhattacharjee
, and Y.-M.
Huang
, “Fast sawtooth reconnection at realistic Lundquist numbers
,” Plasma Phys. Controlled Fusion
57
, 014017
(2015
).45.
Q.
Yu
, S.
Günter
, and K.
Lackner
, “Numerical modelling of sawtooth crash using two-fluid equations
,” Nucl. Fusion
55
, 113008
(2015
).46.
A.
Sykes
and J. A.
Wesson
, “Relaxation instability in tokamaks
,” Phys. Rev. Lett.
37
, 140
–143
(1976
).47.
L. A.
Charlton
, B. A.
Carreras
, J. A.
Holmes
, and V. E.
Lynch
, “Tokamak m=1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations
,” Phys. Fluids
31
(2
), 347
–358
(1988
).48.
S.
Migliuolo
, “Theory of ideal and resistive m=1 modes in tokamaks
,” Nucl. Fusion
33
, 1721
–1754
(1993
).49.
E.
Strumberger
and S.
Günter
, “CASTOR3D: Linear stability studies for 2D and 3D tokamak equilibria
,” Nucl. Fusion
57
(1
), 016032
(2017
).50.
N. Z.
Taylor
, T. C.
Luce
, R. J.
La Haye
, C. C.
Petty
, and P.
Piovesan
, “Magnetic flux conversion in the DIII-D high-beta hybrid scenario
,” in 58th Annual Meeting of the APS Division of Plasma Physics
, October 2016
, Vol. 61
.© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.
