Positron sound waves and nonlinear Landau damping of intense transverse EM waves in an isotropic EPI plasma

Relativistically hot electron–positron–ion (EPI) plasmas in the presence of relativistic intense electromagnetic (EM) radiation that are not in thermal equilibrium are studied by following a modified plasma particle distribution function. By means of a kinetic description, soliton solution is obtained for a small amplitude EM wave, whereas for large amplitude EM waves a cusp soliton solution is obtained. A general expression of positron density oscillations is obtained for long wavelength in comparison with the Debye length of electrons, and is discussed for special cases. Dispersion relations for a new type of longitudinal waves with slow damping is formulated as a consequence of resonant wave–particle interaction, and the necessary conditions for the existence of positron sound waves are obtained. Furthermore, for ultrarelativistic electrons and non-relativistic positrons, quasi positron sound waves dispersion relation in the intermediate wave range is obtained. It is shown that the modulation of amplitude of relativistic EM waves leads to instability for the rare plasma. Finally, we have obtained the relativistic kinetic nonlinear Schrödinger equation (KNLS) with local and non-local nonlinearities. The KNLS equation depicts nonlinear Landau damping rates for intense EM waves, and these damping rates are also examined.