Counterstreaming magnetized plasmas. I. Parallel wave propagation

The properties of longitudinal and transverse oscillations in magnetized counterstreaming Maxwellian plasmas of arbitrary composition and different thermal velocities for waves propagating parallel to the stream direction are investigated on the basis of the Maxwell equations and the relativistic Vlasov equation. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear parallel propagating plasma modes in the system. The dispersion relations hold for nonrelativistic values of the plasma temperatures, streaming velocities, and for any values of the relative intensities of the two streams and for all wave-number and frequency values of the oscillations. All dispersion relations are expressed in terms of the well-documented Fried and Conte plasma dispersion function and are thus valid for the whole complex-frequency plane, which assures the validity of growth and damping rates