Bernstein modes in a weakly relativistic electron-positron plasma.

The form of the propagating electrostatic Bernstein mode in a relativistic electron-positron plasma is markedly different from that in the classical plasma, once the momentum-dependent cyclotron frequency is accounted for in full inside the integrations. Given that particles in different parts of momentum space "see" a different cyclotron frequency, there is no simple global singularity which reproduces the classical dispersion features.