Numerical Simulation Of Relativistic Electromagnetic Solitary Wave And Modulational Instability In Plasmas

The nonlinear interaction between an intense electromagnetic?EM?pulse and plasma is of great interest in various fundamental research and technological applications,including harmonic generation,self-focusing,wakefield generation,relativistic optical guiding,laser pulse frquency shifting,pulse compression,relativistic EM solitons propagation.Among the spectacular phenomena in the nonlinear interaction,relativistic EM solitary waves attract great attention due to their possible applications in inertial confinement fusion and the charged particle acceleration.It is reported that nearly 25-40 percent of the laser pulse energy goes into the generation of well localized concentrations of electromagnetic energy in the form of solitary waves or soliton-like structures,which can play a significant role in the laser plasma interaction process.In addition,as an important nonlinear process,modulational instability is closely related to the propagation of EM wave.The development of modulational instability may induce a variety of nonlinear behaviors such as field collapse and localization,filamentation,envelope solitons,envelope shocks,etc.Therefore,it is of great significance to study relativistic EM solitary waves and modulational instability in plasmas.In this paper,the propagation dynamics of EM solitary waves in uniform cold electronion plasmas is studied by one-dimensional?1D?particle-in-cell?PIC?simulation.Our simulation results show that the shape of the excited EM solitary wave,i.e.,the amplitude and width,can remain unchanged and is identical to the theoretical profile in a long-distance stable propagation.The velocity is also consistent with the theoretical one except a very slight reduction for the larger carrier wave frequency.For a simulation with the plasma density 10²³/m³and the dimensionless vector potential amplitude 0.18,it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than four times of the plasma frequency.While for the carrier wave frequency larger than that,it can excite a very weak Langmuir oscillation,which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability,so that the solitary wave begins to deform after a long enough distance propagation.The stable propagation distance before an obvious observation of instability increases?decreases?with the increase of the carrier wave frequency?vector potential amplitude?.Secondly,we studied the development and evolution of the plane wave modulational instability by 1D PIC simulation.The simulation study shows that the observed spatial wave number of the modulational instability has nothing to do with the carrier wave frequency and the dimensionless vector potential amplitude,but closely relates to the plasma density and is approximately equal to the spatial modulated wave number of Langmuir oscillation.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.In addition,our simulation results show that the instable growth rate is different at different positions of the plane wave,which is analyzed and demonstrated.Finally,we summarize the main results of this paper and give an outlook of the work in the future.