Growth rates of envelope modulations of electromagnetic waves in relativistic temperature electron-positron plasmas, stimulated by weak or finite phonon damping

We study the modulational instability of an electron-positron plasma with r elativistic temperatures and phonon damping. It is shown that when the phon on damping is O(1) or O(epsilon), a modulational instability appears even f or classical temperatures. When the phonon damping is O(epsilon(2))), we fi nd that in the non-relativistic limit, previous results are recovered, and for ultrarelativistic temperatures, the instability occurs in a wider band around the relativistic plasma frequency.