On the essential spectrum of ideal magnetohydrodynamics. Dedicated to harold grad on the occasion of his sixtieth birthday

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.