Hrinishyn O. Effects of long-range in plasma kinetics and hydrodynamics

Українська версія

Thesis for the degree of Doctor of Philosophy (PhD)

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  • 104 - Фізика та астрономія


Specialized Academic Board

ДФ 08.051.015

Oles Honchar Dnipro National University


The study of nonequilibrium processes is a central task of statistical physics and is contributed by the dissertation. Such a study is possible only on the basis of a reduced description of nonequilibrium states, in which the system is described by a relatively small set of parameters - the parameters of the reduced description (RDP). The reduced description is based on the Liouville equation or kinetic equations (Boltzmann, Landau, etc.). The current trend is to expand the standard sets of RDPs, in order to take into account the new degrees of freedom of the system. Here, first of all, we should mention the description of relaxation processes in the narrow sense of the term as processes that can take place in spatially homogeneous states of the system. Near equilibrium, these processes correspond to the kinetic modes of the system and the relaxation degrees of freedom. Classical research of these processes belongs to Landau, who studied the relaxation of temperatures of plasma components, and Grad, who developed the theory of Maxwell's relaxation. The ideas of these studies are still a working tool for the latest research. An important disadvantage of these studies is the lack of a small parameter in the calculations and the solution of the kinetic equation based on it, as well as the disregard for violation of local equilibrium in the systems in the presence of relaxation processes. Elimination of these shortcomings is an urgent task of modern theory of nonequilibrium processes. Scientific novelty of the results obtained in the dissertation: 1. For the first time, the Lorentz model of the kinetic equation of fully ionized plasma is generalized in order to take into account the effects of longrange Coulomb electronion interaction and consider the ion system as an equilibrium subsystem. 2. The properties of the collision integral and the spectral properties of the corresponding collision operator of the model are investigated. The modes of the system and the characteristic times of their evolution are studied. 3. In the method of the reduced description the basic relations of hydrodynamics of the electronic subsystem of plasma taking into account relaxation processes of equalization of temperatures and macroscopic velocities of electrons and ions for the states close to completion of relaxation processes are developed. 4. On the basis of the spectral theory of the collision integral operator, the evolution of plasma and the possibility of its reduced description by energy and momentum densities or the corresponding temperature and macroscopic velocity of electrons for states far from the completion of relaxation processes are studied for the first time. For the first time, the expediency of describing the modes of a system by irreducible polynomials is shown. 5. For the first time, a functional hypothesis for the reduced description of plasma by electron energy and momentum densities in the presence of a constant homogeneous external electric field and assumptions about the times of evolution of plasma modes is proved. 6. Method for the approximate calculation of objects of theory by using truncated expansions in Sonine polynomials has been developed for the generalized Lorentz model. 7. Within the framework of the generalized Lorentz model, for the first time exact expressions for the mobility of plasma electrons, its conductivity were obtained and calculated approximately. The effect of temperature difference of the components of the equilibrium plasma is substantiated in the presence of external electric field.


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