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Abstract
The relaxation of temperatures and velocities of the components of a quasi-equilibrium two-component homogeneous completely ionized plasma is investigated on the basis of a generalization of the Chapman-Enskog method applied to the Landau kinetic equation. The generalization is based on the functional hypothesis in order to account for the presence of kinetic modes of the system. In the approximation of a small difference of the component temperatures and velocities, it is shown that relaxation really exists (the relaxation rates are positive). The proof is based on the arguments that are valid for an arbitrary two-component system. The equations describing the temperature and velocity kinetic modes of the system are investigated in a perturbation theory in the square root of the small electron-to-ion mass ratio. The equations of each order of this perturbation theory are solved with the help of the Sonine polynomial expansion. Corrections to the known Landau results related to the distribution functions of the plasma and relaxation rates are obtained. The hydrodynamic theory based on these results should take into account a violation of local equilibrium in the presence of relaxation processes.
Highlights
In his known paper [1] Landau obtained a kinetic equation for a two-component fully ionized electron-ion plasma
The Landau equation takes into account only the short-range part of the Coulomb interaction because the Coulomb potential is artificially cut in the collision integral at the Debye radius
The relaxation of the temperatures and velocities of the components of a quasi-equilibrium twocomponent homogeneous fully ionized plasma described by the Landau kinetic equation is investigated
Summary
In his known paper [1] Landau obtained a kinetic equation for a two-component fully ionized electron-ion plasma. On the basis of his equation [1] Landau investigated the case in which the components are spatially homogeneous equilibrium subsystems with different temperatures Ta (t ) (a = e,i) and the temperature relaxation is observed This phenomenon is of great interest because of its fundamental importance for applications in plasma theory and condensed matter physics in general. Our consideration is based on the Chapman-Enskog method generalized to account for the relaxation phenomena (we use the term “relaxation phenomena” in the narrow sense of the word as nonequilibrium processes that can be observed in spatially uniform states) Such a theory should describe kinetic modes of the system. The problem of correction of the assumption (1.4) is considered as a very important one, and the distribution function fap (Te, υe) is calculated in a perturbation theory in a small difference of the component temperatures and velocities (let the corresponding small parameter be λ).
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