On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum *
نویسندگان
چکیده
The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{a>it, io%t) is investigated numerically and graphically. For sufficiently incommensurate frequencies coi, a>2 a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained. The equation considered is a model for the magneto-hydrodvnamic "continuum" in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently irrational magnetic surfaces.
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