Shear Alfven Mode Resonances in Nonaxisymmetric Toroidal Low-Pressure Plasmas. I. Mode Equations in Arbitrary Geometry

Field line coordinates are used to obtain a concise set of three coupled partial differential equations for the modes in ideal magnetohydrodynamic plasmas of arbitrary geometry. Zero plasma pressure is assumed throughout. The shear Alfven continuum and the pressureless remnant of the ballooning continuum are readily obtained in a unifying manner. The qualitative differences and similarities of both spectra are discussed. The equations are suitable, in particular, for the study of the spatial dependence of continuum modes close to singular magnetic surfaces or field lines.