Ordinary-Mode Electromagnetic Instability in Colliding Plasma Streams

The instability of the electromagnetic linearly polarized mode propagating perpendicular to the magnetic field is studied for a system composed of two colliding plasma streams, in each of which both the electrons and the ions are streaming at the same velocity. Based on the linearized Vlasov-Maxwell equations and allowing for anisotropic temperatures, it is found that in the presence of streaming ions the instability can occur in very low-$\beta$ plasmas. The higher the values of $\beta$, the streaming velocity, and the temperature ratios $\frac{T_{\parallel }e}{T_{\perp }e}$ and $\frac{T_{\perp }e}{T_{\perp }i}$, the more the plasma is susceptible to the electromagnetic instability. The ratio $\frac{T_{\parallel }i}{T_{\parallel }e}$ has negligible influence, except when the streaming velocity is smaller than the ion thermalspeed. It is found that for $\beta$ values of order unity, the streaming ions, while greatly enlarging the range of unstable wave numbers, contribute negligibly to the maximum growth rate, which is typically of the order of the electron cyclotron frequency. A comparison with the growth rates of the electrostatic two-stream instability is made.