Ideal and resistive magnetohydrodynamic modes

This paper gives a further discussion of the analytical properties of both discrete and continuous Alfven wave spectra in an incompressible as well as compressible plasma. Although the continuous MHD modes produced by a well-behaved initial perturbation decay according to a power law, some singular solutions exist and are found to behave differently. In particular, it is possible to exhibit the existence of a new continuous mode which decays exponentially, and not as an inverse power of time, and this exponential damping is not the consequence of a continuous variation of the magnetic field. Even the set of discrete magnetohydrodynamic modes is shown to be empty unless certain conditions are satisfied. Next, we consider resistive modes and give explicit solutions for them which are valid in the neighborhood of the Alfven resonance layer and discuss their implications for plasma heating schemes. Finally, we study discrete and continuous Alfven wave spectra in a compressible plasma and discuss how they behave differently from those in an incompressible plasma. In particular, we show that though compressibility of the plasma is responsible for the slow mode continuum, strong compressibility will eliminate it. The discrete modes in a compressible plasma undergo an exponential damping even in an ideal plasma if the compressibility is strong.