Effect of Energy Anisotropy on Ordinary Mode in Relativistic Regime

The dielectric constant and the dispersion relation of the Ordinary mode (O-mode) instability has been discussed by using the Vlasov kinetic model in the presence of the Heaviside distribution function. The Heaviside distribution includes relativistic effects for both the parallel and perpendicular streaming. It is noted that the relativistic effects play a destabilizing role for the O-mode at higher magnetic field in comparison to the non-relativistic case. The growth rate of O-mode instability is calculated analytically for different values of parallel and perpendicular streaming. It is shown that the parallel streaming destabilizes the O-mode where as the perpendicular streaming provides a stabilizing effect. The results of the non-relativistic O-mode instability have been retrieved under limiting case.