Acceleration of Relativistic EM Solitons in Intense Laser -Plasmas

Relativistic EM solitons are localized structures self-trapped by a locally modified plasma refractive index via relativistic electron mass increase and an electron density drop due to the ponderomotive force of an intense laser light [1]. A train of relativistic EM solitons is typically found to form behind the intense laser pulse front. Relativistic electromagnetic (EM) solitons in laser driven plasmas were analytically predicted and found by PIC (particle-in-cell) simulations [2] [3], [4]. It has been estimated that, for ultra-short laser pulses, up to 40% of the laser energy can be trapped by relativistic solitons, creating a significant channel for laser beam energy conversion. In this paper, we treat a case of a linearly polarized laser light. In laser-plasma interactions, relativistic Lorentz force sets electrons into motion, generating coupled longitudinaltransverse wave modes. These modes in the framework of a weakly relativistic cold plasma approximation in onedimension, can be well described by a single dynamical equation of the generalized nonlinear Schrödinger type [1], with two extra nonlocal terms. A new analytical solution for the moving EM soliton case is calculated in the implicit form and the soliton motion effect on its self-frequency and amplitude is outlined and the influence of the soliton velocity on the EM solition stability is discussed. Moreover, it is shown that the soliton acceleration down-shifts the soliton eigen-frequency while decreases its amplitude. These results are compared with the one for a standing (nonmoving) relativistic EM soliton case, obtained by some of these authors [1]. Finally, numerical simulations of the model dynamical equation were performed in order to check the good agreement with our analytical results. In a weakly relativistic limit for | and | 1 | 1 |<< n δ , the wave equation for the vector potential envelope A is obtained