The properties of a relativistic plasma dispersion function (RPDF)
for an intrinsically extremely relativist, strongly magnetized, one-dimensional,
electron–positron plasma are discussed in detail. For a plasma with a mean
Lorentz factor 〈γ〉 [Gt ] 1 in its rest frame, the RPDF has a large peak >〈γ〉 at
a phase speed a fraction of order 1/〈γ〉 below the speed of light, and the
asymptotic value (infinite phase speed) is
〈γ−3〉 ∼ 1/〈γ〉. These features are not
particularly sensitive to the choice of distribution function. The RPDF is used
to discuss the properties of waves in such plasmas. Particular points discussed
are the implications of the RPDF for the maximum frequency for parallel
Langmuir waves, and for the reconnection between the Langmuir mode and the
Alfvén mode.