The Absolute Statistical Equili-Brium Of The Incompressible Hall Magnetohydrodynamics Based On Exact Solutions

The MHD turbulence is a non-linear physical phenomenon prevalent in the plasma.In astronomical and spatial plasma physics,the study of MHD turbulence has important physical significance.Solar wind,motivating of geothermal energy,as well as some new energy generation and interstellar dielectric diffusion are all the behavior of MHD turbulence.In this paper,some physical properties of MHD turbulence are explored by studying the incompressible Hall magnetohydrodynamics model(an approximate model of plasma two-fluid model).Compared with the two-fluid model,the incompressible Hall magnetohydrodynamics model has the advantage that it can be used to study the two-fluid effect but does not have complex computational problems,and can be used to study small-scale physical behavior.The incompressible Hall magnetohydrodynamics equations have complex nonlinear properties,and we know that traveling wave method is a basic and effective method for solving nonlinear problems.Therefore,we obtain the exact solution of the incompressible ideal Hall magnetic fluid by our traveling wave method,the fluctuating velocity and magnetic field components along the direction of the wave vector are arbitrary constants.The perpendicular components of the velocity and magnetic field are both helical waves.Moreover,the amplitude of the velocity perpendicular to the wave vector is related with the wave number and the circular frequency.And because of the magnetism of the plasma,the external magnetic field is unable to enter the plasma.However,there is a traveling wave in the plasma,and there is a magnetic field in the propagation direction.The magnetic field is generated by the plasma itself.Therefore,whether or not the uniform external magnetic field exists,there is no effect on the form of the traveling wave solution of the incompressible ideal Hall MHD.Then,based on the exact traveling wave solution,we calculate the statistical equilibrium of the incompressible ideal Hall MHD.