Effect of Sheared Magnetic Field on E × B Drift Instability in Plasma
DOI:
https://doi.org/10.15407/ujpe68.7.448Keywords:
magnetic shear, drift instability, collision frequency, density gradientAbstract
The influence of the magnetic shear on ion drift waves has been investigated for plasmas in the plane slab geometry with a density gradient. A differential equation is derived to describe the mode structure along the density gradient. The magnetic shear localizes the mode around a mode-rational surface, which is perpendicular to the magnetic field. The non-local growth rate turned out to be smaller as compared to the shearless one. The magnetic shear stabilizes long wavelength modes (kρi < 1 ), whereas it destabilizes, as the mode tends toward the short wavelength region, where the density gradient provides a destabilizing effect for the magnetic shear-driven resistive drift mode. However, the effect due to the collision frequency is significantly low in our analysis. The combined effects of E×B flows and the magnetic shear enhance the confinement over a narrow radial region with an internal transport barrier, where stability is attained.
References
N.A. Krall, A. Simon, W.B. Thomson. Advances in Plasma Physics (New York, 1968).
C.I. Weng, C.S. Ma. Linear theory of the E × B instability. Chinese J. Phys. 13 (1), 44 (1975).
H. Romero, G. Ganguli, Y.C. Lee, P.J. Palmadesso. Electron-ion hybrid instabilities driven by velocity shear in a magnetized plasma. Phys. Fluids B: Plasma Phys. 4 (7), 1708 (1992).
https://doi.org/10.1063/1.860028
R.J. Groebner, K.H. Burrell, R.P. Seraydarian. Role of edge electric field and poloidal rotation in the L-H transition. Phys. Rev. Lett. 64 (25), 3015 (1990).
https://doi.org/10.1103/PhysRevLett.64.3015
G. Ganguli, Y.C. Lee, P.J. Palmadesso. Kinetic theory for electrostatic waves due to transverse velocity shears. The Physics of Fluids 31 (4), 823 (1988).
https://doi.org/10.1063/1.866818
S. Sen, M.G. Rusbridge, R.J. Hastie. Collisionless drift waves in the H mode edge (plasma). Nuclear Fusion 34 (1), 87 (1994).
https://doi.org/10.1088/0029-5515/34/1/I06
C.R. De Vore. Current-driven resistive drift instabilities in sheared magnetic fields. Nuclear Fusion 21 (1), 105 (1981).
https://doi.org/10.1088/0029-5515/21/1/011
L. Chen, P.N. Guzdar, J.Y. Hsu, P.K. Kaw, C. Oberman, R. White. Theory of dissipative drift instabilities in sheared magnetic fields. Nuclear Fusion 19 (3), 373 (1979).
https://doi.org/10.1088/0029-5515/19/3/009
W. Horton. Drift waves and transport. Rev. Mode. Phys. 71 (3), 735 (1999).
https://doi.org/10.1103/RevModPhys.71.735
J.D. Huba, S.L. Ossakow, P. Satyanarayana, P.N. Guzdar. Linear theory of the E × B instability with an inhomogeneous electric field. JGR: Space Physics 88 (A1), 425 (1983).
https://doi.org/10.1029/JA088iA01p00425
M.A. Pedrosa et al. Sheared flows and turbulence in fusion plasmas. Plasma Phys. Controll. Fusion 49 (12B), B303 (2007).
https://doi.org/10.1088/0741-3335/49/12B/S28
V. Rozhansky, E. Kaveeva, S. Voskoboynikov, D. Coster, X. Bonnin, R. Schneider. Modelling of electric fields in tokamak edge plasma and LH transition. Nuclear Fusion 42 (9), 309 (2002).
https://doi.org/10.1088/0029-5515/42/9/309
V.N. Rai, F.Y. Yueh, J.P. Singh. Laser-induced breakdown spectroscopy of liquid samples. Laser Induced Breakdown Spectroscopy (Elsevier Amsterdam, 2007) [ISBN: 9780080551012].
M. Greenwald. Density limits in toroidal plasmas. Plasma Phys. Controll. Fusion 44 (8), R27 (2002).
https://doi.org/10.1088/0741-3335/44/8/201
B.A. Carreras, L. Garcia, M.A. Pedrosa, C. Hidalgo. Critical transition for the edge shear layer formation: Comparison of model and experiment. Phys. Plasmas 13 (12), 122509 (2006).
https://doi.org/10.1063/1.2405344
M.A. Pedrosa et al. Threshold for sheared flow and turbulence development in the TJ-II stellarator. Plasma Phys. Controll. Fusion 47 (6), 777 (2005).
https://doi.org/10.1088/0741-3335/47/6/004
R. Bharuthram, M.A. Hellberg, R.D. Lee. The cross field current-driven ion-acoustic instability in a collisional plasma. Theor. Nucl. Phys. 28 (3), 385 (1982).
https://doi.org/10.1017/S0022377800000374
M. Gregoire, P. Rolland. Shear stabilization of drift dissipative instabilities. Nuclear Fusion 13 (6), 867 (1973).
https://doi.org/10.1088/0029-5515/13/6/011
C.L. Chang, J.F. Drake, N.T. Gladd, C.S. Liu. Unstable dissipative drift modes in a sheared magnetic field. The Physics of Fluids 23 (10), 1998 (1980).
https://doi.org/10.1063/1.862876
J. Boedo et al. Enhanced particle confinement and turbulence reduction due to E × B shear in the TEXTOR tokamak. Nuclear Fusion 40 (7), 1397 (2000).
https://doi.org/10.1088/0029-5515/40/7/309
S. Khrapak, V. Yaroshenko. Ion drift instability in a strongly coupled collisional complex plasma. Plasma Phys. Controll. Fusion 62 (10), 105006 (2020).
https://doi.org/10.1088/1361-6587/aba7f8
R.J. Taylor et al. H-mode behavior induced by cross-field currents in a tokamak. Phys. Rev. Lett. 63 (21), 2365 (1989).
https://doi.org/10.1103/PhysRevLett.63.2365
Y. Zhang, S.I. Krasheninnikov, A.I. Smolyakov. Different responses of the Rayleigh-Taylor type and resistive drift wave instabilities to the velocity shear. Physics of Plasmas 27 (2), 020701 (2020).
https://doi.org/10.1063/1.5130409
P.J. Catto et al. Parallel velocity shear instabilities in an inhomogeneous plasma with a sheared magnetic field. The Physics of Fluids 16 (10), 1719 (1973).
https://doi.org/10.1063/1.1694200
R. Singh, R. Singh, H. Jhang, P.H. Diamond. Momentum transport in the vicinity of qmin in reverse shear tokamaks due to ion temperature gradient turbulence. Phys. Plasmas 21 (1), 012302 (2014).
https://doi.org/10.1063/1.4861625
S. Ku et al. Physics of intrinsic rotation in flux-driven ITG turbulence. Nuclear Fusion 52 (6), 063013 (2012).
https://doi.org/10.1088/0029-5515/52/6/063013
R.L. Tanna et al. Overview of operation and experiments in the ADITYA-U tokamak. Nuclear Fusion 59 (11), 112006 (2019).
T. Ohkawa, R.L. Miller. Creation of localized sheared flow by ion trapping. Phys. Plasmas 12 (9), 094506 (2005).
https://doi.org/10.1063/1.2047629
M. Okabayashi, V. Arunasalam. Nuclear Fusion 17 (3), 497 (1977).
https://doi.org/10.1088/0029-5515/17/3/010
W. Tang, R. White, P. Guzdar. Impurity effects on iondrift-wave eigenmodes in a sheared magnetic field. The Physics of Fluids 23 (1), 167 (1980).
https://doi.org/10.1063/1.862835
Y. Saxena, P. John. Dispersion and spectral characteristics of crossfield instability in collisional magnetoplasma. Pramana 8 (2), 123 (1977).
https://doi.org/10.1007/BF02868062
J. C. Perez, W. Horton, K. Gentle, W. Rowan, K. Lee, R.B. Dahlburg. Drift wave instability in the Helimak experiment. Phys. Plasmas 13 (3), 032101 (2006).
https://doi.org/10.1063/1.2168401
K.H. Burrel. Effects of E × B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices Phys. Plasmas 4 (5), 1499 (1997).
https://doi.org/10.1063/1.872367
P. Satyanarayana, G. Ganguli, S. Ossakow. Influence of magnetic shear on the collisional current driven ion cyclotron instability. Plasma Phys. Controll. Fusion 26 (11), 1333 (1984).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
