Magnetofluid-dynamic spectrum and low shear stability.

For a perfectly conducting, cylindrical plasma equilibrium ("screw-pinch"), the spectrum contains four distinct continua, three of which can extend to the origin. This implies the existence of irreversible damping and heating in the nondissipative model. The continuum becomes (Suydam) unstable by instantly shedding an infinite number of point eigenvalues. More generally, any local instability implies an infinity of unstable eigenvalues. Spectral analysis of a new class of low shear, semilocal unstable modes provides a connection between Suydam modes, found only in sheared systems, and interchanges, found only in closed line (shearless) systems, and gives rise to the concept of an effective marginal stability threshold. Study of the spectrum should also provide a unified picture of many other plasma phenomena.