Long waves in a relativistic pair plasma in a strong magnetic field

The properties of low-frequency waves in a one-dimensional, relativistic electron-positron plasma in a strong external magnetic field typical of pulsar magnetospheres are discussed. Approximate dispersion relations are derived for a broad class of distribution functions that have an intrinsically relativistic spread in energies. The effects of the non-neutrality, associated with rotation, and of the relative motion of the plasma species are discussed briefly. In the plasma rest frame only three wave modes need be considered. The magnetosonic $\mathrm{}\left(t\right)\mathrm{}$ mode becomes firehose unstable as the magnetic field weakens, and this occurs in the wind zone of the pulsar. The Alfvén $\mathrm{}\left(A\right)\mathrm{}$ mode exists only below a maximum frequency, and is weakly damped only for sufficiently strong magnetic fields. The Langmuir-$O$ mode is approximately longitudinal near its cutoff frequency, and approximately transverse at high frequencies. We argue that the emission zone is within $\sim {10}^2$ pulsar radii, and that only $t,$ $A,$ and Langmuir waves may participate in the formation of the observed radio spectrum.