Superluminal electromagnetic solitary waves in electron-positron plasmas

Abstract

The propagation of an electromagnetic wave packet in an electron-positron plasma, in the form of coupled localized electromagnetic excitations, is investigated, from first principles. By means of the Poincaré section method, a special class of superluminal localized nonlinear stationary solutions, existing along a separatrix curve, are proposed as intrinsic electromagnetic modes in a relativistic electron-positron plasma. The ratio of the envelope time scale to the carrier wave time scale of these envelope solitary waves critically depends on the carrier's phase velocity. In the strongly superluminal regime, vph/c ≫ 1, the large difference between the envelope and carrier time scales enables us to carry out a multiscale perturbative analysis resulting in an analytical form of the solution envelope. The analytical prediction thus obtained is shown to be in agreement with the solution obtained via a direct numerical integration.