Discrete spectra of compressional Alfvén eigenmodes in inhomogeneous magnetohydrodynamic plasma

The spectrum of the compressional Alfvén eigenmodes in a magnetohydrodynamic (MHD) current-carrying inhomogeneous plasma column is obtained analytically. A MHD model that is adequate for calculating the compressional Alfvén spectra in large tokamaks like the Joint European Torus (JET) [Plasma Physics and Controlled Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] and Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] is employed. It is shown that the radial nonuniformities of the plasma density give rise to various types of localization of the eigenmodes. Thus, the global, near-axis, near-wall, and annulus spectra are identified and studied. The eigenfrequencies and domains of localization of the various eigenmodes, as well as their range of existence in parameter and wavelength space, are determined and investigated. The effects of finite ion gyrofrequency on the MHD eigenmodes are examined, and a perturbation scheme for calculating the modified eigenfrequencies and localization domains is presented. Numerical calculations of a set of near-axis eigenmodes for the JET parameters is given as an example for the applicability of the MHD model. Finally, the relevancy of the eigenmodes to plasma heating in large tokamaks is discussed.