On the essential spectrum of ideal magnetohydrodynamics. Dedicated to harold grad on the occasion of his sixtieth birthday
Author:
- 1 January 1985
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 38 (1) , 43-66
Abstract
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.Keywords
This publication has 22 references indexed in Scilit:
- Sufficient criterion for magneto-hydrodynamic stability and the low-shear limitPlasma Physics, 1981
- Unstable continuous spectrum and ballooning modesNuclear Fusion, 1979
- High mode number stability of an axisymmetric toroidal plasmaProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1979
- Theory of Ballooning Modes in Tokamaks with Finite ShearPhysical Review Letters, 1977
- The continuous MHD spectrum in toroidal geometriesNuclear Fusion, 1975
- Magnetofluid-Dynamic Spectrum and Low Shear StabilityProceedings of the National Academy of Sciences, 1973
- On the essential spectrum of an arbitrary operator. IJournal of Mathematical Analysis and Applications, 1966
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions IICommunications on Pure and Applied Mathematics, 1964
- Reducible Problems in Magneto-Fluid Dynamic Steady FlowsReviews of Modern Physics, 1960
- An energy principle for hydromagnetic stability problemsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1958