Department of Mathematics,
Faculty of Physics, MSU
Read at 8-st semester.
2 hours of lectures per week, seminars
Special course aims to enhance common understanding of contemporary approaches to the study of non-equilibrium states of complex physical systems based on computer (numerical) experiment. In terms of content, it consists of three logically related parts, corresponding to the main stages of the process of mathematical modeling.
The first part provides a general description of the plasma as a new physical state of matter. We introduce the classical (Langmuir) Definition and basic classification of the plasma as a function of the main parameters - density and temperature. We consider it fundamental properties: quasi-neutrality, natural vibrations, Debye screening, collective interaction. We discuss the concept and criteria for the existence of ideal collisionless plasma - the main subject of numerical analysis.
The second part of the course covers the basics of plasma kinetics. It deals with the general background and basic concepts of the kinetic theory. Derivation of the dynamic equation for the particle distribution function in the collisionless approximation, discussed it (equation) the physical meaning and the form of amendments related to binary Coulomb collisions of particles. Further, based on the kinetic description of the Maxwell formalism and introduce the concept of the self-consistent field (Vlasov) plasma as the basic theoretical model. Discusses its characteristic features, justice conservation laws, types of equilibrium states. The physical adequacy and problems of analytic representation.
The content of the third part of the description method of large particles, which is one of the most effective ways of discrete approximation of the self-consistent formalism. Here we give a general description of the techniques discussed its physical justification and limits of applicability of a numerical investigation of nonlinear plasma physicist. Following is the basic concept of the method - the model of "cloud-in-cell". The concepts of form factor particulates, the transfer function of the nucleus of the grid; discusses the procedures specific to it and charge distribution of forces weighing; The specificity of the difference solution of the model equations. Finally, it discusses the general algorithm and non-physical (numerical) models the effects of "clouds".
