The Theoretical Study On The Relativistic Electromagnetic Soliton And Magnetosonic Soliton In The Plasmas

During the laser pulse interaction with the plasma that has strongnonlinearity under condition of relativistic intensity, a large number of interestingnonlinear phenomenons will occur. Among of them, the relativisticelectromagnetic solitons (RES) have attracted great attention and play animportant role in the strongly nonlinear interaction between intenseelectromagnetic radiation and plasmas due to their application and appearance inthe laser heating and laser induced fusion. On the other hand, the robust behaviorof relativistic electromagnetic solitons is of concern for astrophysics andcosmology. There are also many interesting nonlinear structures in themagnetized relativistic plasma, such as relativistic magnetosonic soliton wave(RMS) with robust characteristic, which will be important in the magnetizedfusion. Then both the RES occurring from the interaction of intense laser pulsewith plasma and the RMS generated by the magnetized relativistic plasma havean important impact on the fusion. So we studied these relativistic solitary wavestructures and properties in this thesis.Firstly, in the electron-positron-ion plasma, we have derived a set of coupledequations about vector potential and scalar potential of the circularly polarizedelectromagnetic wave describing the one-dimensional RES. The change ofproportion of ions in the plasma has effects on the properties and maximumvelocity of RES. The relations between the maximum velocity of RES and theother free parameters are presented and discussed.Secondly, basing on the continuity and momentum equations of electronsand the Maxwell equations describing the intense electromagnetic field, we havederived a Davey-Stewartson (DS) equation with the help of multiple scalemethod to study the two-dimensional RES for the limit of weak nonlinearity. Thecondition of RES appearance is found by considering the modulation instabilityof a plane wave solution of the DS equation. A two-dimensional dromion solitonsolution is derived for the vector potential of the RES.Subsequently, we study the RMS in the magnetized relativistic plasmas byusing the continuity and momentum equations of both electrons and ion. In the...