A comparison of compressible and incompressible magnetohydrodynamics in toroidal plasmas

Abstract

A comparison is made of the properties of compressible and incompressible magnetohydrodynamic (MHD) oscillations in toroidal plasmas. In the main part of the paper we deal with the compressible case, and it is shown that the Alfvén wave equation describing toroidal Alfvén eigenmodes (TAE modes) in a low-β tokamak [Berk et al., Phys. Fluids B 4, 1806 (1992)], including the toroidal coupling of the shear Alfvén continuum modes with poloidal mode numbers m and m±1, can be obtained by means of an inverse aspect ratio expansion of the usual set of compressible MHD equations. This method provides an alternative, and more straightforward, approach to the analysis of such modes as compared with previous studies based on reduced MHD, or on different formulations of MHD. In the case of incompressible MHD, it is found that the Alfvén continua are strongly modified by the finite value of the toroidal component of the plasma perturbation. In particular, a large frequency gap where global eigenmodes can be found appears already to lowest order in the inverse aspect ratio in the case of incompressible oscillations.