The spectrum of incompressible waves and instabilities of two-dimensional plasma
geometries with background flow is calculated. The equilibrium is solved numerically
by the recently developed program FLow Equilibrium Solver (FLES). The
spectra of the equilibria are computed by means of another new program, the
INcompressible 2-dimensional FLow Eigenvalue Solver (IN2FLES). Magnetic instabilities
and instabilities driven by the two-dimensionality and the flow are found.
For linear equilibria, the eigenvalues for elliptical geometries remain close to the
curves on which the eigenvalues for circular geometries lie. These curves may be
found for unbounded domains by a calculation in Fourier space [see Lifschitz, A.
In: Proceedings of 1995 International Workshop on Operator Theory and Applications
(ed. R. Mennicken and C. Tretter), pp. 97–117, Birkhäuser, Boston, 1998]. Here
the relation between a new continuous spectrum of unbounded domains and the
discrete spectrum of bounded domains is investigated. Finally, it is found that the
two-dimensionality and the background flow may lead to an overstable cluster-point.