Modulational instability of a circularly polarized wave in a magnetized electron-positron plasma with relativistic thermal energies

A circularly polarized electromagnetic wave, propagating in the direction of an external magnetic field in an electron-positron plasma, is known to be unstable for frequencies less than half the plasma frequency. This has been shown by taking into account weakly relativistic effects on particle motion in the wave field, and nonrelativistic temperatures. Here, we include fully relativistic effects on the thermal motion of the particles, and show that in the ultrarelativistic limit the system is unstable for all frequencies satisfying omega much less than eta omega(c) and omega(p) much less than (eta)(1/2)omega(c), where omega(c) is the gyrofrequency, omega(p) is the plasma frequency, and eta is the ratio between the rest energy density and the enthalpy of the system. In the limit of nonrelativistic thermal motions, the results obtained previously are recovered.