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Title: Comment on 'Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks'[Phys. Plasmas 18, 092103 (2011)]

Abstract

It is shown that some of the main results of the recent paper by Lakhin and Ilgisonis [Phys. Plasmas 18, 092103 (2011)], viz. the derivation of the equations for the continuous spectra of poloidally and toroidally rotating plasmas and their special solution for large aspect ratio tokamaks with large parallel flows were obtained before by Goedbloed, Belieen, van der Holst, and Keppens [Phys. Plasmas 11, 28 (2004)]. A further rearrangement of the system of equations for the coupled Alfven and slow continuous spectra clearly exhibits: (a) coupling through a single tangential derivative, which is a generalization of the geodesic curvature; (b) the 'transonic' transitions of the equilibrium, which need to be carefully examined in order to avoid entering hyperbolic flow regimes where the stability formalism breaks down. A critical discussion is devoted to the implications of this failure, which is generally missed in the tokamak literature, possibly as a result of the wide-spread use of the sonic Mach number of gas dynamics, which is an irrelevant and misleading parameter in 'transonic' magnetohydrodynamics. Once this obstacle in understanding is removed, further application of the theory of trans-slow Alfven continuum instabilities to both tokamaks, with possible implications for the L-H transition, andmore » astrophysical objects like 'fat' accretion disks, with a possible new route to magnetohydrodynamic turbulence, becomes feasible.« less

Authors:
 [1]
  1. FOM-Institute DIFFER-Dutch Institute for Fundamental Energy Research, Edisonbaan14, Nieuwegein, 3439 MN (Netherlands)
Publication Date:
OSTI Identifier:
22072513
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 19; Journal Issue: 6; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCRETION DISKS; ASPECT RATIO; EQUATIONS; MACH NUMBER; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; ROTATING PLASMA; SPECTRA; STABILITY; TOKAMAK DEVICES; TURBULENCE

Citation Formats

Goedbloed, J. P. Comment on 'Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks'[Phys. Plasmas 18, 092103 (2011)]. United States: N. p., 2012. Web. doi:10.1063/1.3694872.
Goedbloed, J. P. Comment on 'Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks'[Phys. Plasmas 18, 092103 (2011)]. United States. doi:10.1063/1.3694872.
Goedbloed, J. P. 2012. "Comment on 'Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks'[Phys. Plasmas 18, 092103 (2011)]". United States. doi:10.1063/1.3694872.
@article{osti_22072513,
title = {Comment on 'Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks'[Phys. Plasmas 18, 092103 (2011)]},
author = {Goedbloed, J. P.},
abstractNote = {It is shown that some of the main results of the recent paper by Lakhin and Ilgisonis [Phys. Plasmas 18, 092103 (2011)], viz. the derivation of the equations for the continuous spectra of poloidally and toroidally rotating plasmas and their special solution for large aspect ratio tokamaks with large parallel flows were obtained before by Goedbloed, Belieen, van der Holst, and Keppens [Phys. Plasmas 11, 28 (2004)]. A further rearrangement of the system of equations for the coupled Alfven and slow continuous spectra clearly exhibits: (a) coupling through a single tangential derivative, which is a generalization of the geodesic curvature; (b) the 'transonic' transitions of the equilibrium, which need to be carefully examined in order to avoid entering hyperbolic flow regimes where the stability formalism breaks down. A critical discussion is devoted to the implications of this failure, which is generally missed in the tokamak literature, possibly as a result of the wide-spread use of the sonic Mach number of gas dynamics, which is an irrelevant and misleading parameter in 'transonic' magnetohydrodynamics. Once this obstacle in understanding is removed, further application of the theory of trans-slow Alfven continuum instabilities to both tokamaks, with possible implications for the L-H transition, and astrophysical objects like 'fat' accretion disks, with a possible new route to magnetohydrodynamic turbulence, becomes feasible.},
doi = {10.1063/1.3694872},
journal = {Physics of Plasmas},
number = 6,
volume = 19,
place = {United States},
year = 2012,
month = 6
}
  • The equations for the continuous spectra derived in our paper [V. P. Lakhin and V. I. Ilgisonis, Phys. Plasmas 18, 092103 (2011)] can be reduced to the matrix form used by Goedbloed et al.[Phys. Plasmas 11, 28 (2004)]. It is shown that the assumptions made in our paper provide the elliptic flow regime and guarantee the existence of plasma equilibrium with nested magnetic surfaces of circular cross-section. The new results on magnetohydrodynamic instabilities of such tokamak equilibria obtained in our paper but absent in the paper by Goedbloed et al. are emphasized.
  • A theory for localized low-frequency ideal magnetohydrodynamical (MHD) modes in axisymmetric toroidal systems is generalized to take into account both toroidal and poloidal equilibrium plasma flows. The general set of equations describing the coupling of shear Alfven and slow (sound) modes and defining the continuous spectrum of rotating plasmas in axisymmetric toroidal systems is derived. The equations are applied to study the continuous spectra in large aspect ratio tokamaks. The unstable continuous modes in the case of predominantly poloidal plasma rotation with the angular velocity exceeding the sound frequency are found. Their stabilization by the shear Alfven coupling effect ismore » studied.« less
  • This Comment discusses the representations of infinite sums of Bessel functions that occur in plasma problems involving collisionless plasmas treated from a plasma kinetic viewpoint. In addition, the influence of such summation techniques on dispersion relations for plasma waves involving a background magnetic field is discussed.
  • The relevance of linear 'corner modes' for the description of coherent electrostatic structures, as proposed by Valentini et al.[Phys. Plasmas 19, 092103 (2012)], is questioned. Coherency in their on-dispersion simulation is instead found to be caused by particle trapping in agreement with Schamel's nonlinear wave model [Phys. Plasmas 19, 020501 (2012)]. The revealed small amplitude structures are hence of cnoidal electron hole type exhibiting vortices in phase space. They are ruled by trapping nonlinearity rather than by linearity or quasi-linear effects, as commonly assumed. Arguments are presented, which give preference to these cnoidal hole modes over Bernstein-Greene-Kruskal modes. To fullymore » account for a realistic theoretical scenario, however, at least four ingredients are mandatory. Several corrections of the conventional body of thought about the proper kinetic wave description are proposed. They may prove useful for the general acceptance of this 'new' nonlinear wave concept concerning structure formation, updating several prevailing concepts such as the general validity of a linear wave Ansatz for small amplitudes, as assumed in their paper. It is conjectured that this nonlinear trapping model can be generalized to the vortex structures of similar type found in the more general setting of driven turbulence of magnetized plasmas. They appear as eddies in both, the phase and the position spaces, embedded intermittently on the Debye length scale.« less
  • The recently developed analytical theory of external kink modes in large aspect ratio tokamaks with large current gradients is extended to include effects due to locally large pressure gradients and a conducting wall. The results are presented in terms of simple integrals over the equilibrium profiles. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.