Study Of The Modulational Collapse Dynamics In Non-equilibrium Distributed Plasmas

The plasma turbulence and its evolution are attractive subjects in plasma physics.Based on Zakharov's model,a large number of turbulence and related physical phenomena have been explained very well,such as the Langmuir amplitude modulational observed in space and the solitary waves in the laser plasma,etc.Many results indicated that the plasma turbulence will be easily excited by the nonlinear coupling of multi-scale modes,and the modulational instability is an important feature in inducing instabilities by plasma waves,especially that the nonlinear modulational collapse is one of the important mechanisms to induce the plasma turbulence cascade.The physical processes of fast electron emission and flare observed in astronomical and laboratory plasmas discover that plasma distribution always deviate equilibrium statistical distribution.Non-equilibrium statistical mechanics,such as Kappa distribution and q-distribution,have been developed as a very useful tool to describe the complex systems.Therefore,this paper focused on the nonlinear modulational collapse processes,induced by wave-wave and wave-particle interactions,in the nonequilibrium distribution of space or laser plasma.Firstly,the governing equations of the self-generated magnetic field in the plasma with Kappa distribution are given and the low frequency nonlinear flow induced by wave-wave and wave-particle interactions is presented.The collapse dynamics of the self-generated magnetic field in the quasi-static approximation is studied by using the finite difference method.The results show that the modulational instability will lead the envelope of the low frequency electromagnetic field to collapse,in which the local high ponderomotive force makes the plasma density to strongly localize,and the nonlinear density cavitons are formed in small scales;The envelope of the selfgenerated magnetic field runs into highly intermittent turbulent flux with time;The characteristic time scale of the envelope self-magnetic fields depends on the superthermal particles: decreasing the superthermal index,namely increasing the superthermal particles,can make the self-generated magnetic field to be collapsed faster,grown stronger and more strongly localized.Secondly,based on the fluid theory,the two-temperature-electron Zakharov equations are derived by using the method of two time scale,which are used to describe the nonlinear wave-wave interactions among the Langmuir wave,electromagnetic wave and electric acoustic wave in two-temperature-electrons plasma.The governing equations are solved by the numerical difference method.The results show that Langmuir wave,electromagnetic wave and electric acoustic waves can be evolved into modulational instability,and the electromagnetic field is collapsed into a highly localized nonlinear structure;At the same time,Langmuir wave transfers from the longest wavelength modes(smallest wave number)to the shortest wavelength modes(largest wave number),and then runs into turbulence;The electric acoustic waves eventually collapse into cavity structures,which can effectively accelerate the electrons because it has the characteristics of high energy and time scales.On the other hand,the numerical solution of the differential equation method is used to study the evolution of the standing wave solutions of the generalized two-temperature-electron Zakharov equations.Researches show that the time evolution of the wave packet electric field in x-direction is presented on the standing wave amplitude modulation,the dipole oscillator structure is presented in y-direction component.Eventually it also presents that they will form the nonlinear cavity structures and then collapses to a highly localized nonlinear structures.In addition,the generalized nonlinear Schr?dinger equation,describing the low frequency ion acoustic wave instability,is a scalar degradation from the generalized Zakharov equation.It also can be used to analyze the modulation of wave field,selfdefocusing and turbulence instabilities in laser plasma.It shows that self-defocusing instability will occur in the certain parameters no matter there is external potential field or not;It is found that a large localized pulse can suffer self-defocusing and lead to the shortest-wavelength modes(largest wave number).The Gaussian waveform will be evolved into a pattern of strong turbulence with broad spectrum.Moreover,the total energy of the system will preserve conservation in the case of potential and nonpotential with time.And the external potential will suppress the development of selfdefocusing.