Beam Instabilities in Magnetized Pair Plasma

Beam instabilities in the strongly magnetized electron-positron plasma of pulsar magnetospheres are considered. We analyze the resonance conditions and estimate the growth rates of the Cherenkov and cyclotron instabilities of the ordinary (O), extraordinary (X) and Alfv\'{e}n modes in two limiting regimes: kinetic and hydrodynamic. As a preliminary step, we reconsider wave dispersion and polarization properties in a one dimensional pair plasma taking into account relativistic thermal effects. We then find the location of the Cherenkov and cyclotron resonance of the X, O and Alfv\'{e}n waves with the particles from the primary beam. The importance of the different instabilities as a source of the coherent pulsar radiation generation is then estimated taking into account the angular dependence of the growth rates and the limitations on the length of the coherent wave-particle interaction imposed by the curvature of the magnetic field lines. We conclude, that in the pulsar magnetosphere the Cherenkov-type instabilities occur in the hydrodynamic regimes, while the cyclotron-type instabilities occur in the kinetic regime. We argue, that electromagnetic cyclotron-type instabilities on the X, O and probably Alfv\'{e}n waves are more likely to develop in the pulsar magnetosphere.