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

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, Belien, 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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3694872]