Dispersion in an intrinsically relativistic, one-dimensional, strongly magnetized pair plasma

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〉 ≫ 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.