PROBABILISTIC METHOD IN RADIATIVE TRANSFER AND NEUTRON TRANSPORT PROBLEMS

Abstract

For solving transfer problems in scattering atmospheres many exact and approximate methods hc1ve so far been proposed. Of them, the probabilistic method of Sobolev and Ueno have proved to be particularly successful in handling both time-dependent and time independent transfer and transport problems in plane-parallel atmospheres. In the present thesis, a scheme has been outlined to develop a probabilistic model of photon movement, capable of interpreting the transfer problems in spherical geometry. As the basic inspiration of the probabilistic method was drawn from Ambartzumian's physical method of principle of invariance, it has been thought worthwhile to examine the merits and limitations of all the methods whose origins can be traced back to Ambartzumian's physical or mathematical technique. In this category one can consider (a) the method of invariant imbedding, and (b) the combined operational method of Busbridge, in addition to the probabilistic method. So, a short critical review of these methods has been incorporated in this work. Application of the invariant imbedding method for solving certain scattering problems of spherical atmospheres has also been considered. The thesis has been divided mainly into two parts. Chapter I consists of three Chapters. Chapter I is devoted to clarification of the general notions and definitions of terms occurring in the description of the radiation field, introduction of the transfer equations used in the subsequent Chapters and a short account of the probabilistic method for solving the equations of transfer. Chapter II contains a critical appreciation of the above three methods in solving transfer equations in plane parallel medium. Attention has also been drawn to the basic features of Ambartzumian’s technique. In Chapter III, a review is given of the essential features of the method of invariant imbedding as it has been used to solve some of the specific problems of spherical geometry. Part II of the dissertation consists of two Chapters IV and V. Chapter IV is devoted to the development of a probabilistic model for transfer problem in can externally illuminated spherical shell atmosphere with 2 perfectly absorbing core. Chapter V contains the probabilistic scheme for solving transfer problems in spherical shell medium with an emitting source in the form of a black core. The particular case of central point source has also been considered. The matter contained in this part is original and has been proposed for the first time in this thesis.