Alfvén continuum with toroidicity

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Abstract
The symmetry property of the magnetohydrodynamic (MHD) wave propagation operator is utilized to express the toroidal eigenmodes as a superposition of the mutually orthogonal cylindrical modes. Because of the degeneracy among cylindrical modes with the same frequency but resonant surfaces of different helicity, the toroidal perturbation produces a zeroth‐order mixing of the above modes. The toroidal eigenmodes of frequency ω20 have multiple resonant surfaces, with each surface shifted relative to its cylindrical position and carrying a multispectral content. Thus a single helicity toroidal antenna of frequency ω0 couples strongly to all different helicity resonant surfaces with matching local Alfvén frequency. Zeroth‐order coupling between modes in the continuum and global Alfvén modes also results from toroidicity and degeneracy. The perturbation technique used in this study is the MHD counterpart of the quantum‐mechanical methods and is applicable through the entire range of the MHD spectrum.