Parametric instabilities of circularly polarized Alfvén waves in a relativistic electron-positron plasma

Dispersion relation and nonlinear evolution of the parametric instabilities of circularly polarized Alfvén waves in a relativistic electron-positron plasma are investigated by theoretical and numerical approaches. In the nonrelativistic limit, when [Formula presented] the characteristics of the instabilities are similar to those in an electron-ion plasma, except that the modulational instability takes place only if [Formula presented] where [Formula presented] and [Formula presented] denote the plasma frequency and the acoustic speed, and [Formula presented] [Formula presented] indicate the frequency and the wave number of the parent wave. On the other hand, when [Formula presented] two new types of instabilities emerge between the parallel or antiparallel propagating Alfvén-like waves and the parallel propagating Langmuir-like wave. The weakly relativistic effect is discussed for all the instabilities. The one-dimensional full particle simulation and bicoherence analysis of the simulation result suggest that successive decay via the interaction between the parallel propagating Langmuir-like wave and antiparallel propagating Alfvén-like wave can efficiently generate a continuum of low frequency electromagnetic waves, which can interact with energetic particles.