Radiation output of a spherical homogeneous plasma: Analytical models of computing the spectral brightness of plasma objects with various configurations

Analytical relationships between the photon-emission probability from a surface and the optical thickness along with analytical relationships between the spectral brightness of a homogeneous plasma of spherical geometry are derived with taking into account the radiation absorption. The photon-emission probability and the spectral brightness are also obtained for a plasma of cylindrical geometry and a plasma consisting of spherical layers. The relationships are given in the integral form, while attempts to find them analytically, i.e., to calculate the integrals, failed. However, they can be computed numerically. The formula for spectral brightness is derived for the case of radiation of two flat layers, which differ by the structure, thickness, and thermodynamic and spectral characteristics. The expressions for the spherical and flat layers are compared. The ratio of the dimensions permitted to approximate the flat case by the spherical case is found. The criteria of applicability and accuracy of such approximation have been elaborated. As examples of the application of the expressions derived, the radiation spectra of the aluminum, carbon, copper, and oxygen plasmas were calculated and plotted.