DISPERSION RELATIONS IN A STATIONARY PLASMA,
Interim rept. no. 3,
RAYTHEON CO WALTHAM MASS
Pagination or Media Count:
Oscillations which are possible within a stationary, homogeneous, fully ionized, macroscopically neutral plasma of infinite extent are examined. In a field-free case, the dispersion relations for the longitudinal electron waves, the longitudinal ion waves, and the transverse electromagnetic waves are verified. For a longitudinal applied magnetic field, there are four dispersion relations, each representing a different type of plasma oscillation. Two of these are the same longitudinal electron and ion waves that are possible in the field-free case, and the remaining two are ordinary and extraordinary transverse waves which at high frequencies agree with the magneto-ionic theory of Appleton, at low frequencies agree with the magnetohydrodynamic theory of Alfven, and at intermediate frequencies have a form which does not agree with either of the earlier theories. With a transverse applied magnetic field, there are four solutions to the dispersion equation. One of these is the ordinary transverse wave of magneto-ionic theory, but the remaining three each represent complex coupled oscillations in the plane perpendicular to the applied field. After a great deal of analysis it is shown that one can arrange the solutions in a form such that one type of oscillation is identical to the extraordinary waves in magneto-ionic theory, another is quite similar to the longitudinal electron waves in the field free case, and the third coupled oscillation reduce to a longitudinal magnetohydrodynamic wave at low frequencies, an ordinary ionic wave at high frequencies, and a new type of wave at mid-frequencies.