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

Abstract

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 2omega(2)(p)>omega20, the characteristics of the instabilities are similar to those in an electron-ion plasma, except that the modulational instability takes place only if v(2)(s)<omega(2)(0)/k(2)(0), where omega(p) and v(s) denote the plasma frequency and the acoustic speed, and omega(0), k(0) indicate the frequency and the wave number of the parent wave. On the other hand, when 2omega(2)(p)<omega20, 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.