SELF-MODULATION OF A STRONG ELECTROMAGNETIC-WAVE IN A POSITRON-ELECTRON PLASMA-INDUCED BY RELATIVISTIC TEMPERATURES AND PHONON DAMPING

The modulational instability of a linearly polarized, strong, electrom agnetic wave in a (unmagnetized) positron-electron plasma is analyzed using relativistic two-fluid hydrodynamics to properly account for phy sical regimes of very high temperatures. The effect of phonon damping is also included in the treatment. The theory can be reduced to a pair of extended Zakharov equations. The envelope modulation is then studi ed by deriving the corresponding nonlinear Schrodinger (NLS) equation, using multiscale perturbation analysis. According to the intensity of the damping three different types of NLS are obtained. The main resul ts are (a) that relativistic temperatures modify the stability result found in the literature for low temperature, zero damping, e(+)-e(-) p lasmas, and (b) that phonon damping also produces substantial changes in the NLS, which then predict unstable envelopes. This work extends p revious analyses, showing that if the phonon damping is O(epsilon(0)) or O(epsilon(1)) (epsilon is the perturbation parameter), a modulation al instability appears in the electron-positron case in al ranges of t emperature and wave frequencies. Thus presence of some amount of sound absorption helps to produce an envelope decay. When the phonon dampin g is very small [O(epsilon(2))] the self-modulational instability occu rs in a finite band near the reduced plasma frequency, for ultrarelati vistic temperatures.