Electrical Dissipation Effects on Propagation of Magneto-hydrodynamic Waves in Anisotropic Media

Abstract

This paper deals with the investigation of the modification of magneto-hydrodynamic wave propagation by electrical dissipation and the Hall effect. A dispersion relation is obtained from magneto-hydrodynamic equations, Maxwell's equations and the generalized Ohm's law which includes the Hall effect. The effect of electrical dissipation is well represented by a magnetic Reynolds number defined for the Alfvén wave ; and the inclusion of the Hall effect is equivalent to taking account of the ion cyclotron motion. It is found that there exist three waves, in general, as in the case without electrical dissipation or the Hall effect. It is also found that, in a perfectly conducting medium, the slowest wave evanesces in a range of propagation direction determined from the frequency, due to ion cyclotron resonance. However, when the electrical conductivity of the medium is finite, three waves are observable in any direction, and with the decrease of electrical conductivity, one of the waves is reduced to an ordinary acoustic wave, whie the other two waves are reduced to electromagnetic waves.