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Abstract:
The continuous spectrum formed by the accumulation points of eigenfrequencies of modes with large axial and/or azimuthal mode numbers (so-called "ballooning modes") is studied in axially periodic circular cylinders with magnetic shear, assuming incompressibility. A singular layer analysis about the radius where the modes are localized leads to an eigenvalue problem for a second order ordinary differential equation in a stretched radial coordinate. This equation is the Fourier transform of the fourth order equation along magnetic field lines that arises from the so-called "ballooning representation." Both equations therefore describe the radial variation of the perturbation rather than that along the field lines. The following results are readily obtained from the second order equation: The accumulation continua, if there are any, have no stable parts. They are traced out by the eigenvalues as the singular radius runs through the interval where Suydam's criterion is violated. There is one such eigenvalue for each radial mode number. (C) 2003 American Institute of Physics.
