Relativistic solitary waves modulating long laser pulses in plasmas

Abstract

This article discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From the mathematical point of view they are exact solutions of the 1-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of traveling wave solutions with velocity $V$ and vector potential frequency $\omega$, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. By using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a great variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values, and classify them according to: (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric $V-\omega$ plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.

arXiv comment20 pages, 10 figures

References in corpus (5)

• Three Dimensional Relativistic Electromagnetic Sub-cycle Solitons
• Dynamics of relativistic solitons
• Observation of post-soliton expansion following laser propagation through an underdense plasma
• Fluid simulation studies of the dynamical behaviour of one dimensional relativistic electromagnetic solitons
• Stability of nonlinear one-dimensional laser pulse solitons in a plasma

Cited by in corpus (4)

• Relativistic breather-like solitary waves with linear polarization in cold plasmas
• Transition from wakefield generation to soliton formation
• Modelling relativistic solitary wave interactions in over-dense plasmas: a perturbed nonlinear Schröndinger equation framework
• Relativistic quasi-solitons and embedded solitons with circular polarization in cold plasmas