Thermal radiation of an inhomogeneous plasma layer

This study discusses the radiation from an arbitrary inhomogeneous isotropic layer (of a plasma, for example, when the radiation frequency greatly exceeds the electron cyclotron frequency). With the fluctuation-theory method we obtain a formula for radiation intensity that depends on the solutions of two linear homogeneous second-order differential equations whose coefficients are determined by the distributions of density and temperature in the layer. We discuss in detail: 1) Radiation from a semi-infinite homogeneous dielectric; 2) Radiation from a layer with a smoothly changing dielectric permeability when the geometrical-optics method is applied; 3) Radiation from a layer with a smoothly changing dielectric permeability when there are regions inside the layer in which the real portion of dielectric permeability vanishes and the geometrical-optics method is inapplicable owing to the smallness of the imaginary portion. The formula for radiation intensity remains finite but exponentially small even when the imaginary portion of the dielectric permeability approaches zero. If the wave length of the radiated wave is of the order of the thickness of the inhomogeneous transparent layer inside which dielectric permeability vanishes, the radiation intensity is of the order of the radiation intensity of a black body.