Collective modes in nonrelativistic electron-positron plasmas.

Abstract

The longitudinal and transverse collective modes in a nonrelativistic electron-positron plasma are studied in two cases: a static uniform magnetic field is present or absent. The dispersion relations for the longitudinal and transverse collective modes in the absence of a magnetic field and those for the longitudinal mode in the presence of a magnetic field (Bernstein mode) are found to be similar to those for the one-component electron plasma. The transverse modes in the presence of a magnetic field, on the other hand, are found to be quite different from the electron-ion plasma: The dispersion relations for the left- and right-circularly polarized waves propagating parallel to the magnetic field are found to be identical. In addition to the transverse plasma oscillations, the low-frequency Alfv\'en mode exists, while the whistler mode does not exist. For waves propagating perpendicular to the magnetic field, the extraordinary wave becomes a pure transverse mode. In the cold-plasma limit, there is only one resonance at the cyclotron frequency and one cutoff frequency for the extraordinary mode, in contrast to the electron-ion plasma, where there are two hybrid resonances and two cutoff frequencies.