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 ${U}_{0}$, namely, ${U}_{min}l{U}_{0}l{U}_{max}$. For relativistic streaming velocities, the electron thermal effects are destabilizing whereas for nonrelativistic streaming these are stabilizing unless $\frac{{c}^{2}{k}^{2}}{{\ensuremath{\omega}}_{\mathrm{pe}}^{2}}l\frac{1}{3}$ and $\frac{{k}^{2}{V}_{\mathrm{te}}^{2}}{{\ensuremath{\Omega}}_{e}^{2}}\ensuremath{\ll}1$ ($k$ being the characteristic wave number, ${V}_{\mathrm{te}}$ the electron thermal velocity, ${\ensuremath{\Omega}}_{e}$ the electron cyclotron frequency, and ${\ensuremath{\omega}}_{\mathrm{pe}}$ 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.