Analytical solution of a plasma oscillation problem in a half-space subject to diffusive boundary conditions

The boundary value problem on the behavior (oscillations) of electron plasma with an arbitrary degree of degeneracy of the electron gas in the half-space subject to diffusive boundary conditions is solved analytically. The kinetic Boltzmann–Vlasov equation with the Bhatnagar–Gross–Krook (BGK) collision integral and the Maxwell equation for the electric field are used. The distribution of electrons and the electric field inside the plasma are obtained as expansions in the eigensolutions of the original system of equations. The coefficients of these equations are found using the boundary conditions.