Propagation of Hydromagnetic Waves in Collisionless Plasma. I

Abstract

The propagation of hydromagnetic waves in collisionless plasma is investigated on the basis of the Chew-Goldberger-Low approximation. The dispersion relation for weak, plane disturbances in a uniform plasma is derived. It is found that there exist the fast and slow modes of magnetoacoustic waves as well as the Alfvén wave. However, under certain conditions the phase velocities of the slow and the Alfvén waves become imaginary: namely the system is not necessarily totally hyperbolic but can be partially elliptic. The conditions on the elliptic cases are investigated in detail, especially for the slow wave. Then the propagation of a wave diverging from a point source is investigated graphically as well as analytically.
The general theory of steady flow is also given, and some discussions are done for the two dimensional aligned field-flow in which the directions of magnetic field and flow are aligned everywhere.