ESTIMATES OF CRITICAL DIMENSIONS OF SPHERICAL AND SLAB REACTORS

Abstract

UNDER THE ASSUMPTIONS OF CONSTANT ENERGY OF NEUTRONS AND ISOTROPY OF THE COLLISION-FISSION PROCESS, THE DETERMINATION OF THE CRITICAL MASS OF SPHERICAL AND SLAB REACTORS IS EQUIVALENT TO THE DETERMINATION OF TWO OF THE EIGENVALUES OF A LINEAR INTEGRAL OPERATOR T. In the theory of radiative transfer in homogeneous plane parallel atmospheres with isotropic scattering, this same operator is an important one known as the truncated Hopf operator. The theory also applies to stratified slab and spherical reactors in which the physical properties can change from stratum to stratum. This observation is developed and then applied to reactors with a homogeneous core surrounded by a homogeneous reflector. Numerical results are given for the bare homogeneous reactors. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1962
Accession Number
AD0270639

Entities

People

  • T.w. Mullikin

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Atmospheres
  • Collisions
  • Eigenvalues
  • Homogeneous Reactors
  • Integrals
  • Mathematics
  • Observation
  • Physical Properties
  • Radiative Transfer
  • Reflectors
  • Scattering

Fields of Study

  • Mathematics
  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.
  • Thermal Physics or Thermal Science.