Dispersion in an intrinsically relativistic, one-dimensional, electron–positron
pair plasma (a pulsar plasma) is treated exactly, generalizing earlier results
that applied in the low-frequency limit and that neglected the cyclotron resonance.
The general theory involves two additional relativistic plasma dispersion functions,
evaluated at the normal and anomalous Doppler resonances. These two functions
are associated with the non-gyrotropic and gyrotropic parts of the response respectively.
The functions are evaluated for bell-type and Jüttner distributions. Wave
dispersion is discussed for a non-gyrotropic pulsar plasma with a highly relativistic
Alfvén speed. Emphasis is placed on crossings of the light line, defined in terms
of the parallel phase velocity. Subluminal waves exist only for sufficiently small
angles of propagation, and are confined to frequencies below about the mean gyrofrequency of the relativistic particles.
Large amplitude electromagnetic solitons in a fully relativistic magnetized electron-positron-pair plasma
