Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and Their Relation to the MHD Continuum

摘要

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f( omega sub 1 t, omega sub 2 t) is investigated numerically and graphically. For sufficiently incommensurate frequencies omega sub 1 , omega sub 2 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. (ERA citation 08:006360)