Ordinary-mode electromagnetic instability for counter-streaming plasmas with anisotropic temperatures

The instability of the ordinary electromagnetic mode propagating perpendicular to an external magnetic field is studied for two counter-streaming plasmas with anisotropic temperatures. A necessary and sufficient condition for this instability is derived and the growth rate is calculated. Although instability can occur in a plasma with low β^e, provided the streaming velocity is comparable to the parallel electron thermal velocity, β_e of the order of unity and large electron temperature anisotropy (T_e T_e) are required for large growth rates. These large growth rates are typically of the order of the electron cyclotron frequency. Comparison with the electrostatic two-stream instability is made.