The Study Of The Cutoff Rigidity In Middle-High Latitudes Of The Magnetosphere And The Diffusion Coefficients Matrix Of The Fokker-Planck Equation

The transportation, acceleration and loss of the energetic particles in the magnetosphere is a basic problem of space physics, it is also the key to establish numerical forecasting model for space weather. The complexity of the magne-tosphere and the variability of the interplanetary conditions make this problem exteremely difficult.In this work we study this problem in depth with theory, observation and numerical simulations. There are two main parts in this thesis.In the first part the cutoff rigidity at the high latitudes is studied. We define the cosmic rays’ window (CRWs) with which the high energy particles can enter into the magnetosphere space, and study the relationships between the area of CRWs and interplanetary conditions as well as the geomagnetic activity index. The area of CRWs is related to the solar wind parameters, such as interplanetary magnetic field Bz and solar wind pressure Pdyn, among which the area of CRWs has the strongest negative correlation with Bz, the second strongest negative correlation with Pdyn, and weaker one with other solar wind parameters.We simulate three geomagnetic storms and find that, usually the AE index and the area of the CRWs have a positive correlation, but the Dst index show similar corelation only when the storms is strong, while during moderate and weak magnetic storms there are no correlation. Therefore, the Dst index can not be used as the forecast index as energetic particles access into the magnetosphere at high latitudes. During the study, we find that high-energy particles’ cutoff latitude can be fitted by the ellipse fit very well, the equations of the ellipse are given with the analytical expressions of the elliptic parameters.In the second part, using energetic particles transport equation, the Fokker-Planck equation, we study the transport of energetic particles in the magneto-sphere in theory, and we study in detail the numerical solution method of the equation. We study in detail the five dimensional diffusion coefficients. It is found that the pitch angle diffusion coefficient Dμμ and the cross diffusion coef- ficient DYμ are basically in the same order of magnitude and both of them are important for the transport of the energetic particles. Especially when the pitch angle cosine is ±1, that is, when the particle’s pitch angle is 0° or 180°, the loss of the particles at the mirror point can be affected significantly by this effect. So that the cross diffusion coefficients can result in the change in the position of the particles in the magnetic equatorial plane, particles may be vibrate in the magnetic equator plane and can be accelerated by the electric field. Our result is important to study the magnetosphere particles loss by entering into the atmosphere and bounce back or forth at the magnetic mirrors.