Accession Number : AD0616662

Title :   NEUTRON BRANCHING PROCESSES.

Descriptive Note : Revised ed.,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Mullikin,T. W.

Report Date : 20 DEC 1960

Pagination or Media Count : 33

Abstract : The paper presents a study of the neutron population in a nuclear reactor as a branching process. Results are presented concerning the extinction probability of a supercritical reactor near the critical dimension, extending results of T. E. Harris. Parts of the theory of branching processes are presented; these are developed in a general setting in Harris's forthcoming monograph on this subject. The results of this paper apply to spheres, to infinite slabs, and to rods, with the assumptions that the neutron energy is constant and that the collision-fission process is isotropic. The assumption of homogeneity is also made, although similar results can be obtained in nonhomogeneous cases of restricted types; e.g., in the sphere the variation of physical properties should depend only on the radial coordinate. One consequence of this analysis is the determination of a new computational method for estimating the critical dimension and the steady-state flux for the above-mentioned reactors. This replaces the eigenvalue problem of transport theory by a nonlinear functional equation that can be solved by iteration. (Author)

Descriptors :   (*NEUTRON TRANSPORT THEORY, NUCLEAR REACTORS), (*NUCLEAR REACTORS, NEUTRON TRANSPORT THEORY), MATHEMATICAL MODELS, NEUTRON FLUX, ITERATIONS, PROBABILITY, DECAY SCHEMES

Distribution Statement : APPROVED FOR PUBLIC RELEASE