ABSTRACT
Some treatments of compressional oscillations use a single-fluid MHD approach. This chapter argues that cylindrical symmetry allows an identical azimuthal Alfven oscillation to that for cold plasma. Just as in the case of cold plasma, it is possible to find circumstances in which the equations for hot plasma describe localized oscillations, confined to a particular magnetic shell or field line. In azimuthal transverse Alfven oscillations, the cylindrically symmetric magnetic shells slide past each other without compression. The motion is unaffected by the compressibility of the plasma. The other set of equations in this case describes a global compressional oscillation. The equations take the form of two pairs of coupled equations, with the magnitude of the coupling terms on the right-hand side determined by the field-line curvature and the transverse magnetic field gradient. In a dipole-like geometry, the cylindrically symmetric transverse Alfven wave behaves in the same way as in cold plasma.
