NON-COHERENT SCATTERING IN SPHERICAL MEDIA

Abstract

The study of Radiative Transfer in media with curvature has received much attention in recent years, From the point of view of mathematical methods, the boundary value problems, encountered in the description of the process of radiative transfer in spherical media usually require solution of integral or integrodifferential equations of various complexity. In the last decade or so, attempts have been made to convert these problems into initial value ones. In this respect, modification and extension of what is now known as the Ambartzumian technique has proved singularly successful. This scheme can be subdivided into two basic groups-- namely (a) the physical method and (b) the mathematical method. The essential feature of the physical method lies in defining emergent intensity in terms of some intermediate functions using the total optical depth as a parameter. Integral or integro-differential equation for these intermediate functions are constructed in forms suitable for numerical solutions; simply by taking recourse to physical reasonings. On the other hand, development of Ambartzumian’s mathematical method was done through the study of the Newman series solution of auxiliary equation corresponding to the relevant integral equation of transfer for specific problems in plane parallel media. This scheme is due to Busbridge [13-16] and is now popularly known as the Combined Operations Method. In the present thesis, it has been shown that this method can be effectively utilised to solve various non-coherent scattering problems in spherical geometry. The subject matter of the thesis has been divided into two parts. Part I consists of two chapters. The fundamental physical quantities used in the thesis for the description of a non-coherent scattering radiation field have been introduced in Chapter I. Chapter II contains a brief survey of Ambartzumian' s physical and mathematical methods, The application of the mathematical technique as demonstrated by the combined operations method for solving the diffuse reflection problem in homogeneous, coherently scattering, spherical media has also been exposed. In Part II of the thesis, the combined operations method has been utilised to solve non-coherent scattering problems in homogenous spherical media and inhomogenous spherical shell media. In Chapter III, we consider the problems of diffuse reflection by a homogenous sphere. Chapter IV and V are concerned with the diffuse reflection and transmission problems in inhomogenous spherica1 shell media involving frequency--independent and frequency-dependent source functions respectively. In Chapter VI, we extend the scope of the combined operations method to tackle the same problems in spherical shell media involving macroscopic radial motion.