On the existence of eigenmodes of linear quasi-periodic differential equations and their relation to the MHD continuum

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f(ω1t,ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2 a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained. The equation considered is a model for the magneto-hydrodynamic 'continuum' in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently irrational magnetic surfaces. (orig.)