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, Beliën, van der Holst, and Keppens [Phys. Plasmas 11, 28 (2004)]. A further rearrangement of the system of equations for the coupled Alfvén 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 Alfvén 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.

Response to “Comment on ‘Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks’ ” [Phys. Plasmas 19, 064701 (2012)]

“…The new results on magnetohydrodynamic instabilities of such tokamak equilibria obtained in our paper but absent in the paper by Goedbloed et We are very pleased with the interest caused by our paper and are grateful to Professor Goedbloed for his comment. 1 We are really sorry that we have not noticed the work presented in Ref. 2 (henceforth referred to as I), although we have cited other relevant papers by the same authors.…”