Beams in Magnetised Pair Plasmas

The radiative instability was considered in the context of pulsar radio emission by Goldreich & Keeley (1971) and rederived and extended by Asseo, Pellat, & Sol (1983) and by Asseo (1995). Their results can be generalised and reproduced by replacing the thin cylindrical ring of charged particles by an infinitesimally thin current carrying sheet in either planar or cylindrical geometry, suggesting that the local ring geometry may not be essential for the instability. It may be useful to further investigate the generalised dispersion equation given below.