Surface and discrete Alfven waves in a current carrying plasma

MHD surface waves propagating on the interface between a constant density current-free plasma and a vacuum have recently been shown to be strongly affected by finite frequency effects, i.e. the inclusion of the Hall term in the Ohm's Law. Two distinct modes exist, depending on the sign of m, the azimuthal mode number in cylindrical geometry. The authors incorporate the effects of an axial plasma current and investigate the dispersion relation of the resulting modes of a plasma cylinder of uniform density with variable vacuum width. For wave frequency omega << Omega i (the ion-cyclotron frequency) the current introduces an asymmetry in the dispersion relation with respect to the sign of k, the axial wavenumber. An unstable branch also appears, related to the external kink mode. They also find eigenmodes of the discrete Alfven wave (DAW), both stable and unstable. However, the existence of these modes depends strongly on the shear of the magnetic field. At frequency omega approximately= Omega i, the surface wave is not much affected by the current; however, the DAW modes, or ion-cyclotron waves, are eliminated below a limiting frequency due to the effects of the current.