On the maximum longitudinal electric field of a large amplitude electron plasma wave excited by a short electromagnetic radiation pulse

The excitation of large amplitude plasma oscillations by the ponderomotive force exerted by a short electromagnetic (e.m.) radiation pulse on the electrons, is described within a one-dimensional, relativistic, cold plasma model. The quasistatic approximation, which assumes that the fluid variables follow adiabatically the temporal evolution of the field variables, is assumed to be valid. For a fixed rectangular profile of the e.m. wavepacket, travelling with group velocity upsilon(g) < c, the analytical solution of the problem is obtained. It is shown that, after the transit of the pulse, the coherent longitudinal electric field (travelling with phase velocity upsilon(phi)=upsilon(g)) can reach values higher than E(st)MAX=square-root 2 (m(e)comega(pe))/e)(gamma(phi)-1)1/2, where gamma(phi)=(1-upsilon(phi)2/c2)-1/2, up to E(MAX)= square-root 2 (m(e)comega(pe)/e)(gamma(phi)2upsilon(phi)/c)(3-upsilon(phi)2/c2 - square-root 5-2upsilon(phi)2/c2 + upsilon(phi)4/c4)1/2. However, this is only a transient dynamics which leads inevitably to the wavebreaking at a distance of approximately one wavelength from the beginning of the pulse. Actually, only for E < E(st)MAX stationary plasma oscillations can be sustained.