Unstable continuous spectrum in magnetohydrodynamics

The continuous spectrum need not be stable for an equilibrium with flow. The case of a noncircular, rotating ϑ pinch is shown to have an unstable continuum with the instability interpreted as a parametric instability arising from coupling between the rotation frequency and the plasma wave frequencies. On the other hand, equilibria with sub-Alfvénic flow parallel to the magnetic field in incompressible plasmas, as well as static equilibria, have a stable continuum. A formulation to determine the continuous spectrum is given in terms of characteristic surfaces for the equations and does not involve the use of any particular system of coordinates.