Landau's Problem of Degenerate Plasma Oscillations in Slab with Specular   Boundary Conditions
  In the present paper the linearized problem of plasma oscillations in slab (particularly, thin films) in external longitudinal alternating electric field is solved analytically. Specular boundary conditions of electron reflection from the plasma boundary are considered. Coefficients of continuous and discrete spectra of the problem are found, and electron distribution function on the plasma boundary and electric field are expressed in explicit form. Absorption of energy of electric field in slab is calculated. 
A.V. Latyshev and A.A. Yushkanov
math-ph math.MP physics.optics physics.plasm-ph