Hollow density profiles may occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the pellet fuelling scheme inefficient. In the present work, the particle transport driven by Ion Temperature Gradient/Trapped Electron (ITG/TE) mode turbulence in hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT, and magnetic shear are investigated. In addition, the effects of a fast species are studied and global ITG simulations in a simplified physics description are performed in order to investigate nonlocal effects. It is found that β in particular, has a stabilizing effect in the negative R/Ln region. Both nonlinear GENE and EDWM simulations show a decrease in inward flux for negative R/Ln and a change in the direction from inward to outward for positive R/Ln. Moreover, the addition of fast particles was shown to decrease the inward main ion particle flux in the positive gradient region further. This might have serious consequences for pellet fuelling of high β plasmas. Additionally, the heat flux in global ITG turbulence simulations indicates that nonlocal effects can play a different role from usual in connection with pellet fuelling.
References
1.
L.
Garzotti
, J.
Figueiredo
, C. M.
Roach
, M.
Valovič
, D.
Dickinson
, G.
Naylor
, M.
Romanelli
, R.
Scannell
, and G.
Szepesi
, “Microstability analysis of pellet fuelled discharges in MAST
,” Plasma Phys. Controlled Fusion
56
(3
), 035004
(2014
).2.
M.
Kotschenreuther
, G.
Rewoldt
, and W. M.
Tang
, “Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities
,” Comput. Phys. Commun.
88
(2
), 128
–140
(1995
).3.
D.
Tegnered
, H.
Nordman
, M.
Oberparleiter
, P.
Strand
, L.
Garzotti
, I.
Lupelli
, C. M.
Roach
, M.
Romanelli
, and M.
Valovic
, “Gyrokinetic simulations of transport in pellet fuelled discharges at JET
,” in 43rd European Physical Society Conference on Plasma Physics, Leuven, Belgium
, 2016
.4.
C.
Bourdelle
, X.
Garbet
, F.
Imbeaux
, A.
Casati
, N.
Dubuit
, R.
Guirlet
, and T.
Parisot
, “A new gyrokinetic quasilinear transport model applied to particle transport in tokamak plasmas
,” Phys. Plasmas
14
(11
), 112501
(2007
).5.
B.
Baiocchi
, C.
Bourdelle
, C.
Angioni
, F.
Imbeaux
, A.
Loarte
, and M.
Maslov
, “Transport analysis and modelling of the evolution of hollow density profiles plasmas in JET and implication for ITER
,” Nucl. Fusion
55
(12
), 123001
(2015
).6.
L.
Garzotti
, X.
Garbet
, P.
Mantica
, V.
Parail
, M.
Valovič
, G.
Corrigan
, D.
Heading
, T. T. C.
Jones
, P.
Lang
, H.
Nordman
, B.
Pégourié
, G.
Saibene
, J.
Spence
, P.
Strand
, J.
Weiland
, and Contributors to the EFDA-JET Workprogramme
, “Particle transport and density profile analysis of different jet plasmas
,” Nucl. Fusion
43
(12
), 1829
(2003
).7.
See http://genecode.org/ for further information about the GENE code.
8.
B. B.
Kadomtsev
and O. P.
Pogutse
, “Trapped particles in toroidal magnetic systems
,” Nucl. Fusion
11
(1
), 67
(1971
).9.
B.
Coppi
and F.
Pegoraro
, “Theory of the ubiquitous mode
,” Nucl. Fusion
17
(5
), 969
(1977
).10.
W.
Horton
, Jr., D.
Choi
, and W. M.
Tang
, “Toroidal drift modes driven by ion pressure gradients
,” Phys. Fluids
24
(6
), 1077
–1085
(1981
).11.
P. N.
Guzdar
, L.
Chen
, W. M.
Tang
, and P. H.
Rutherford
, “Ion temperature gradient instability in toroidal plasmas
,” Phys. Fluids
26
(3
), 673
–677
(1983
).12.
F.
Romanelli
, “Ion temperature-gradient-driven modes and anomalous ion transport in tokamaks
,” Phys. Fluids B: Plasma Phys.
1
(5
), 1018
–1025
(1989
).13.
H.
Biglari
, P. H.
Diamond
, and M. N.
Rosenbluth
, “Toroidal ion-pressure-gradient-driven drift instabilities and transport revisited
,” Phys. Fluids B: Plasma Phys.
1
(1
), 109
–118
(1989
).14.
T.
Dannert
and F.
Jenko
, “Gyrokinetic simulation of collisionless trapped-electron mode turbulence
,” Phys. Plasmas
12
(7
), 072309
(2005
).15.
A. M.
Dimits
, G.
Bateman
, M. A.
Beer
, B. I.
Cohen
, W.
Dorland
, G. W.
Hammett
, C.
Kim
, J. E.
Kinsey
, M.
Kotschenreuther
, A. H.
Kritz
et al., “Comparisons and physics basis of tokamak transport models and turbulence simulations
,” Phys. Plasmas
7
(3
), 969
–983
(2000
).16.
J.
Weiland
, Collective Modes in Inhomogeneous Plasmas: Kinetic and Advanced Fluid Theory (
CRC Press
, 1999
).17.
P. I.
Strand
, G.
Bateman
, A.
Eriksson
, W. A.
Houlberg
, A. H.
Kritz
, H.
Nordman
, and J.
Weiland
, “Comparisons of anomalous and neoclassical contributions to core particle transport in tokamak discharges
,” in 31th EPS Conference, London 2004, European Physical Society
(2004
), Vol. 28.18.
J.
Citrin
, F.
Jenko
, P.
Mantica
, D.
Told
, C.
Bourdelle
, J.
Garcia
, J. W.
Haverkort
, G. M. D.
Hogeweij
, T.
Johnson
, and M. J.
Pueschel
, “Nonlinear stabilization of tokamak microturbulence by fast ions
,” Phys. Rev. Lett.
111
(15
), 155001
(2013
).19.
F.
Merz
, “Gyrokinetic simulation of multimode plasma turbulence
,” Ph.D. thesis (Universitat Munster
, 2008
).20.
H.
Nordman
, A.
Skyman
, P.
Strand
, C.
Giroud
, F.
Jenko
, F.
Merz
, V.
Naulin
, T.
Tala
, and JET-EFDA Contributors
, “Fluid and gyrokinetic simulations of impurity transport at JET
,” Plasma Phys. Controlled Fusion
53
(10
), 105005
(2011
).21.
ASDEX Upgrade Team
, C.
Angioni
, A. G.
Peeters
, G. V.
Pereverzev
, F.
Ryter
, and G.
Tardini
, “Density peaking, anomalous pinch, and collisionality in tokamak plasmas
,” Phys. Rev. Lett.
90
(20
), 205003
(2003
).22.
C.
Angioni
and A. G.
Peeters
, “Direction of impurity pinch and auxiliary heating in tokamak plasmas
,” Phys. Rev. Lett.
96
(9
), 095003
(2006
).23.
X.
Garbet
, L.
Garzotti
, P.
Mantica
, H.
Nordman
, M.
Valovic
, H.
Weisen
, and C.
Angioni
, “Turbulent particle transport in magnetized plasmas
,” Phys. Rev. Lett.
91
(3
), 035001
(2003
).24.
C.
Angioni
, E.
Fable
, M.
Greenwald
, M.
Maslov
, A. G.
Peeters
, H.
Takenaga
, and H.
Weisen
, “Particle transport in tokamak plasmas, theory and experiment
,” Plasma Phys. Controlled Fusion
51
(12
), 124017
(2009
).25.
A.
Casati
, C.
Bourdelle
, X.
Garbet
, F.
Imbeaux
, J.
Candy
, F.
Clairet
, G.
Dif-Pradalier
, G.
Falchetto
, T.
Gerbaud
, V.
Grandgirard
et al., “Validating a quasi-linear transport model versus nonlinear simulations
,” Nucl. Fusion
49
(8
), 085012
(2009
).26.
M. J.
Pueschel
, M.
Kammerer
, and F.
Jenko
, “Gyrokinetic turbulence simulations at high plasma beta
,” Phys. Plasmas
15
, 102310
(2008
).27.
J. W.
Connor
, R. J.
Hastie
, and J. B.
Taylor
, “Shear, periodicity, and plasma ballooning modes
,” Phys. Rev. Lett.
40
(6
), 396
(1978
).28.
B.
Coppi
, “Topology of ballooning modes
,” Phys. Rev. Lett.
39
(15
), 939
(1977
).29.
A. M. M.
Todd
, M. S.
Chance
, J. M.
Greene
, R. C.
Grimm
, J. L.
Johnson
, and J.
Manickam
, “Stability limitations on high-beta tokamaks
,” Phys. Rev. Lett.
38
(15
), 826
(1977
).30.
F.
Jenko
and W.
Dorland
, “Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas
,” Plasma Phys. Controlled Fusion
43
(12A
), A141
(2001
).31.
A.
Skyman
, D.
Tegnered
, H.
Nordman
, and P.
Strand
, “Gyrokinetic modelling of stationary electron and impurity profiles in tokamaks
,” Phys. Plasmas
21
(9
), 092305
(2014
).32.
C.
Angioni
, J.
Candy
, M.
Fable
, E.
Maslov
, A. G.
Peeters
, R. E.
Waltz
, and H.
Weisen
, “Particle pinch and collisionality in gyrokinetic simulations of tokamak plasma turbulence
,” Phys. Plasmas
16
(6
), 060702
(2009
).33.
C.
Holland
, L.
Schmitz
, T. L.
Rhodes
, W. A.
Peebles
, J. C.
Hillesheim
, G.
Wang
, L.
Zeng
, E. J.
Doyle
, S. P.
Smith
, R.
Prater
et al., “Advances in validating gyrokinetic turbulence models against L-and H-mode plasmas
,” Phys. Plasmas
18
(5
), 056113
(2011
).34.
G.
Tardini
, J.
Hobirk
, V. G.
Igochine
, C. F.
Maggi
, P.
Martin
, D.
McCune
, A. G.
Peeters
, A. C. C.
Sips
, A.
Stäbler
, J.
Stober
, and ASDEX Upgrade Team
. “Thermal ions dilution and ITG suppression in ASDEX upgrade ion ITBS
,” Nucl. Fusion
47
(4
), 280
(2007
).35.
C.
Bourdelle
, G. T.
Hoang
, X.
Litaudon
, C. M.
Roach
, T.
Tala
, ITPA Topical Group on Transport
, ITB Physics
, and International ITB Database Working Group
, “Impact of the α parameter on the microstability of internal transport barriers
,” Nucl. Fusion
45
(2
), 110
(2005
).36.
M.
Romanelli
, A.
Zocco
, and F.
Crisanti
, and JET-EFDA Contributors
, “Fast ion stabilization of the ion temperature gradient driven modes in the joint European torus hybrid-scenario plasmas: A trigger mechanism for internal transport barrier formation
,” Plasma Phys. Controlled Fusion
52
(4
), 045007
(2010
).37.
J.
Garcia
, C.
Challis
, J.
Citrin
, H.
Doerk
, G.
Giruzzi
, T.
Görler
, F.
Jenko
, P.
Maget
, and JET Contributors
, “Key impact of finite-beta and fast ions in core and edge tokamak regions for the transition to advanced scenarios
,” Nucl. Fusion
55
(5
), 053007
(2015
).38.
C.
Estrada-Mila
, J.
Candy
, and R. E.
Waltz
, “Turbulent transport of alpha particles in reactor plasmas
,” Phys. Plasmas
13
(11
), 112303
(2006
).39.
J.
Citrin
, F.
Jenko
, P.
Mantica
, D.
Told
, C.
Bourdelle
, R.
Dumont
, J.
Garcia
, J. W.
Haverkort
, G. M. D.
Hogeweij
, T. Johnson
et al., “Ion temperature profile stiffness: Non-linear gyrokinetic simulations and comparison with experiment
,” Nucl. Fusion
54
(2
), 023008
(2014
).40.
Z.
Lin
, S.
Ethier
, T. S.
Hahm
, and W. M.
Tang
, “Size scaling of turbulent transport in magnetically confined plasmas
,” Phys. Rev. Lett.
88
, 195004
–195Apr
(2002
).41.
J.
Candy
, R. E.
Waltz
, and W.
Dorland
, “The local limit of global gyrokinetic simulations
,” Phys. Plasmas
11
(5
), L25
–L28
(2004
).42.
T.
Görler
, X.
Lapillonne
, S.
Brunner
, T.
Dannert
, F.
Jenko
, S. K.
Aghdam
, P.
Marcus
, B. F.
McMillan
, F.
Merz
, O.
Sauter
, D.
Told
, and L.
Villard
, “Flux- and gradient-driven global gyrokinetic simulation of tokamak turbulence
,” Phys. Plasmas
18
(5
), 056103
(2011
).43.
L.
Villard
, A.
Bottino
, S.
Brunner
, A.
Casati
, J.
Chowdhury
, T.
Dannert
, R.
Ganesh
, X.
Garbet
, T.
Görler
, V.
Grandgirard
, R.
Hatzky
, Y.
Idomura
, F.
Jenko
, S.
Jolliet
, S.
Khosh Aghdam
, X.
Lapillonne
, G.
Latu
, B. F.
McMillan
, F.
Merz
, Y.
Sarazin
, T. M.
Tran
, and T.
Vernay
, “Gyrokinetic simulations of turbulent transport: Size scaling and chaotic behaviour
,” Plasma Phys. Controlled Fusion
52
(12
), 124038
(2010
).44.
J. W.
Connor
, J. B.
Taylor
, and H. R.
Wilson
, “Shear damping of drift waves in toroidal plasmas
,” Phys. Rev. Lett.
70
(12
), 1803
–1805
(1993
).45.
J. Y.
Kim
and M.
Wakatani
, “Radial structure of high-mode-number toroidal modes in general equilibrium profiles
,” Phys. Rev. Lett.
73
(16
), 2200
–2203
(1994
).46.
F.
Romanelli
and F.
Zonca
, “The radial structure of the ion-temperature-gradient-driven mode
,” Phys. Fluids B: Plasma Phys.
5
(11
), 4081
–4089
(1993
).© 2017 Author(s).
2017
Author(s)
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