Relativistic streaming effects on electromagnetic instability in magnetoplasmas

The electromagnetic waves propagating transverse to the direction of streaming of the contrastreaming plasmas in the presence of a uniform magnetic field are investigated. For electron plasmas these waves become unstable only for some bounded values of the streaming velocity U₀, namely, U_minc2k2ωpe2<13 and $\frac{k^2{V}_{te}^2}{{\Omega }_e^2}\ll 1$ (k being the characteristic wave number, $V_{te}$ the electron thermal velocity, Ωₑ the electron cyclotron frequency, and ${\omega }_{pe}$ the electron plasma frequency). The magnetic field however reduces the region of instability no matter what the streaming velocity is. The effect of nonrelativistic-ion streaming is destabilizing while that of the ion temperature is stabilizing. In the presence of a strong magnetic field, the effect of relativistic-ion streaming is also stabilizing.