The Problem of Oscillations in a Plasma Channel with an Arbitrary Degree of Degeneracy of the Electron Gas

The paper states the boundary problem of oscillations of electron plasma in a layer of the conducting medium. Within the research we considered plasma with an arbitrary degree of degeneracy of the electron gas, the external electric field being perpendicular to the boundary of the medium. We applied mirror boundary conditions for boundary layer reflection of electrons. When setting the problem, we used the Vlasov --- Boltzmann kinetic equation with the BGK collision operator, i. e. Bhatnagar --- Gross --- Krook operator, and the Maxwell equation for the electric field. Reducing the boundary problem to the one-dimensional and one-velocity problem was crucial. For this purpose, we used the method of successive approximations, as well as linearization of the equations with respect to the absolute distribution of Fermi --- Dirac electrons and the law of conservation of the number of particles. The statement of the problem described above makes it possible to obtain an analytical solution for the distribution function and for the electric field

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