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 widespread 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 transslow Alfven continuum instabilities to both tokamaks, with possible implications for the LH transition, andmore »
 Authors:
 FOMInstitute DIFFERDutch 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 widespread 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 transslow Alfven continuum instabilities to both tokamaks, with possible implications for the LH 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 crosssection. 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.

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