Electric field near the surface of a plasma with an arbitrary degree of degeneracy as a response to an external alternating electric field

We analytically solve a boundary value problem for the behavior (oscillation) of an electron plasma with an arbitrary degree of degeneracy of the electron gas in a half-space with mirror boundary conditions. We apply the Vlasov–Boltzmann kinetic equation with a collision integral of the Bhatnagar–Gross–Krook type and a Poisson equation for the electric field. We obtain the electron distribution function and the electric field inside the plasma as expansions in eigensolutions of the initial equation system. We find the expansion coefficients using the boundary conditions. We analyze the behavior of the electric field near interfaces for frequencies close to the plasma oscillation frequency.