Mode conversion of toroidal Alfven waves

The effects of electron inertia and mode conversion on the propagation of Alfven waves in toroidal magnetic fields are considered. When electron inertia is neglected, two singularities occur in the equation determining the radial and vertical wavefield dependencies. The inclusion of electron inertia resolves one singularity and is shown to lead to linear mode conversion in either a cold electron or warm electron approximation. The Alfven wave converts to an electrostatic wave which propagates back toward the inside of the torus in the cold electron approximation and through the ion cyclotron resonance toward the outside edge of the torus with warm electrons via the electrostatic ion cyclotron wave. Without damping, both lead to a discrete spectrum of eigenfrequencies, but with only weak damping, the electrostatic waves are absorbed and lead to a continuous spectrum of frequencies. The nature of the damping terms gives an indication of the type of energy absorption, whether Landau damping of electrons or ions or ion cyclotron damping. The second singularity in the equations is found to have only regular solutions and does not lead to mode conversion.