Beam instabilities in the strongly magnetized electron–positron plasma
of a pulsar magnetosphere are considered. We analyse the resonance conditions and
estimate the growth rates of the Cherenkov and cyclotron instabilities of the ordinary
(O), extraordinary (X) and Alfvén modes in two limiting regimes: kinetic and
hydrodynamic. The importance of the different instabilities as a source of 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, Cherenkov-type instabilities occur in
the hydrodynamic regime, while cyclotron-type instabilities occur in the kinetic
regime. We argue that electromagnetic cyclotron-type instabilities on the X, O and
probably Alfvén waves are more likely to develop in the pulsar magnetosphere.
Beam instabilities in a magnetized pair plasma