Abstract
The two-fluid theory for a fully ionized, macroscopically neutral plasma is used to examine small-amplitude normal mode oscillations in an infinite, homogeneous medium for three cases: no applied magnetic field; a magnetic field in the direction of wave propagation; and a magnetic field perpendicular to the direction of wave propagation. In the field-free case, which has been treated in a similar way by Pai, the dispersion relations for the three simplest types of plasma oscillations—longitudinal electron waves, longitudinal ion waves, and transverse waves—are verified and the properties of each of these waves are described. In the second and third cases, the influence of an applied magnetic field on the normal mode solutions is studied and the results of this complete two-fluid theory are compared with the analogous results obtained in the simpler theories of Appleton (magneto-ionic theory) and of Alfvén (magnetohydrodynamics).
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