On some peculiarity in behavior of plasma with an arbitrary degree of degeneracy of electron gas in thin layer

Abstract

In this study we considered the response of electron plasma with an arbitrary degree of degeneration to an alternating electromagnetic field. The electromagnetic field directed perpendicularly to the boundary of the plasma layer. We present an analytic solution of the boundary problem. The kinetic Boltzmann-Vlasov equation with the Bhatnagar–Gross–Krook collision integral and the Maxwell equation for the electric field are used. We consider the mirror boundary conditions for the reflections of electrons from the layer boundary. The boundary problem may be reduced to a one-dimensional problem with a single velocity. Separation of variables allow reducing the problem equations to a characteristic system of equations. The eigensolutions of the initial system, which correspond to the continuous spectrum, are Van Kampen mode. The eigensolutions corresponding to the adjoint and discrete spectra are Drude and Debye modes. We can construct the general solution. The Debye mode determines the plasma screening of the electric field. The behavior of this mode was analyzed. It depends on the parameters of the problem. In case of sufficiently high degrees of the electron gas degeneracy, the range of the Debye mode existence has a substantially nontrivial character, in which the ranges of existence and absence of this mode alternate with increasing electric field frequency.