The Qualitative Study Of Space Plasma Motion Models

Theoretical analysis, numerical simulation and experimental observation are three factors of modern scientific research. In recent years, most of reports in the space and the sun conference mainly focus on the analysis of all kinds of observed phenomena and the numerical simulation about some process. Few reports are about theory analysis of the basic plasma physics process. Compared with other factors, the theoretical analysis is a short leg of current space and astrophysical plasmas in research field. Therefore, in this paper, the dynamic system theory is the research tool, and nonlinear systems which originated from the actual space plasma nonlinear motion models are the research objects. We discussed the qualitative behavior of these nonlinear systems, and revealed the rich dynamical behavior contained in these models.Space plasma is a kind of conductor, this point determines its special response in many cases. It can be treated not only as partical in microcosmic theory, but also as fluid in macroscopic theory. The Debye length is a basic characteristic space scale. We can think roughly, that the plasma is composed of many Debye ball. When we analysed the physical process of plasma, we shoud compare the question’s characteristic space scale with the system’s Debye length. If the former is less than the latter, then the discussed physical process is happened mainly in the Debye ball. In this case, every electric particle can feel the coulomb potential of other electric particles, so we shoud consider the single particle process such as the two body coulomb collision. If the former is greater than the latter, then what the electric particle felt can be regard as some shielded coulomb potential. Under this condition, the single particle effect is no longer important, and the collective interactions which those of a large number of electric particles take part in, such as wave, is physical process that need to be valued. Therefore, the qualitative study of space plasmas particle dynamic model is dissertated systematically in this paper from microcosmic theory and macroscopic theory.Considerating the collision effect, we discussed the orbits of single particle nonlinear dynamic models in microcosmic theory. Some specific dynamic models of space plasmas and the basic research methods are introduced and discussed. On this basis, we established general nonlinear models. Using Mawhin’s continuation theorem and the first integral, the existence of periodic solutions and homoclinic solutions for some classes of nonlinear problem are discussed, and then by using them, we completed the study about the periodic orbit and the homoclinic orbit of sport model of single particle for space plasmas, the study about the periodic problem of drift motion of the guidance center in the earth’s magnetosphere electromagnetic field, the study about the periodic orbits of sport model of plasmas particle in the process of magnetosphere-ionosphere coupling, and the qualitative study about electric particles sporting in neutral sheet magnetic field of the distant magnetotail without the dawn-dusk electric field. Some results on the existence of periodic orbits and homoclinic orbits to the models are obtained, and the feasibility of our results is explained.Considerating the collectivity effect caused by long-range interaction of space particles, we discussed the qualitative study of nonlinear waves in space plasma. Using the geometry theorem of differential equation and the qualitative theorem, equilibrium points are considered. By the homoclinic orbits, some solitary waves and shock waves of nonlinear systems are studied, and the results are generalized. We completed the qualitative study of nonlinear ion-acoustic wave in space unmagnetized plasma, the qualitative study of nonlinear ion-acoustic wave in space magnetized plasma, the qualitative study of nonlinear drift wave in space inhomogeneous magnetized plasma, the qualitative study of nonlinear magnetosonic wave in the oblique propagation in a cold plasma, the qualitative study of Alfven wave in collisionless plasma, and the qualitative study of shock wave in fully ionized plasma.After the research on the above problems, our conclusions are consistent with the observation in laboratory and the phenomenon detected by space satellites. However, Space plasma motion is a complex and nonlinear multidimensional physical process, it contains many important physical mechanisms. These mechanisms are often linked with the frontier research in this field. The paper is only a beginning of the research in this field. The qualitative study of space plasma nonlinear dynamic system provides an imporant theoretical basis for reasonably explain the space physical process and the observations in space environment.