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On the essential spectrum of ideal magnetohydrodynamics. Dedicated to harold grad on the occasion of his sixtieth birthday
Author(s) -
Hameiri Eliezer
Publication year - 1985
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160380104
Subject(s) - ballooning , magnetohydrodynamics , eigenvalues and eigenvectors , essential spectrum , spectrum (functional analysis) , rotational symmetry , mathematics , magnetic field , physics , continuous spectrum , spectral line , mode (computer interface) , simple (philosophy) , stability (learning theory) , mathematical analysis , classical mechanics , mechanics , plasma , quantum mechanics , tokamak , computer science , philosophy , epistemology , machine learning , operating system
The essential spectrum of magnetohydrodynamics (MHD) is shown to arise from waves propagating one‐dimensionally along magnetic field lines. Different polarizations of these waves give rise to the “Alfven” and “ballooning” spectra. The essential spectrum of an axisymmetric equilibrium when a single azimuthal mode number is considered consists of the Alfven spectrum only, while the ballooning modes appear as intervals of accumulation of discrete eigenvalues with different mode numbers. We derive some necessary and one sufficient conditions for stability and show some examples where the criteria coincide to yield a simple condition for stability.