Relativistic Effects on Plasma Oscillations and Two-Stream Instability. I

The general theory for high-temperature plasmas, in the presence of an external uniform magnetic field, is developed by means of a Laplace-transform technique. The dispersion relations for the longitudinal and the transverse oscillations, for a relativistic Maxwellian distribution with mass motion as well as for a non-Maxwellian distribution in the absence of magnetic field are derived. The stability of two streams is investigated in detail both in the nonrelativistic and in the extreme relativistic limits. The longitudinal and the transverse modes are uncoupled only when the stream velocity and the wave velocity are parallel.