Chapter 3. Neutron Diffusion Theory

  1. Prof. Weston M. Stacey

Published Online: 10 MAY 2007

DOI: 10.1002/9783527611041.ch3

Nuclear Reactor Physics, Second Edition

Nuclear Reactor Physics, Second Edition

How to Cite

Stacey, W. M. (2007) Neutron Diffusion Theory, in Nuclear Reactor Physics, Second Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527611041.ch3

Author Information

  1. Georgia Institute of Technology, Nuclear & Radiological Engineering, 900 Atlantic Drive, NW, Atlanta, GA 30332-0425, USA

Publication History

  1. Published Online: 10 MAY 2007
  2. Published Print: 2 FEB 2007

ISBN Information

Print ISBN: 9783527406791

Online ISBN: 9783527611041



  • nuclear reactor physics;
  • neutron diffusion theory;
  • neutron diffusion equation;
  • nonmultiplying media;
  • diffusion kernels;
  • distributed sources;
  • Albedo boundary condition;
  • neutron migration lengths;
  • homogeneous reactor;
  • reflected reactor;
  • homogenization;
  • heterogeneous fuel–moderator assembly;
  • control rods;
  • Nodal approximation;
  • transport methods


This chapter contains sections titled:

  • Derivation of One-Speed Diffusion Theory

    • Partial and Net Currents

    • Diffusion Theory

    • Interface Conditions

    • Boundary Conditions

    • Applicability of Diffusion Theory

  • Solutions of the Neutron Diffusion Equation in Nonmultiplying Media

    • Plane Isotropic Source in an Infinite Homogeneous Medium

    • Plane Isotropic Source in a Finite Homogeneous Medium

    • Line Source in an Infinite Homogeneous Medium

    • Homogeneous Cylinder of Infinite Axial Extent with Axial Line Source

    • Point Source in an Infinite Homogeneous Medium

    • Point Source at the Center of a Finite Homogeneous Sphere

  • Diffusion Kernels and Distributed Sources in a Homogeneous Medium

    • Infinite-Medium Diffusion Kernels

    • Finite-Slab Diffusion Kernel

    • Finite Slab with Incident Neutron Beam

  • Albedo Boundary Condition

  • Neutron Diffusion and Migration Lengths

    • Thermal Diffusion-Length Experiment

    • Migration Length

  • Bare Homogeneous Reactor

    • Slab Reactor

    • Right Circular Cylinder Reactor

    • Interpretation of Criticality Condition

    • Optimum Geometries

  • Reflected Reactor

    • Reflected Slab Reactor

    • Reflector Savings

    • Reflected Spherical, Cylindrical, and Rectangular Parallelepiped Cores

  • Homogenization of a Heterogeneous Fuel–Moderator Assembly

    • Spatial Self-Shielding and Thermal Disadvantage Factor

    • Effective Homogeneous Cross Sections

    • Thermal Utilization

    • Measurement of Thermal Utilization

    • Local Power Peaking Factor

  • Control Rods

    • Effective Diffusion Theory Cross Sections for Control Rods

    • Windowshade Treatment of Control Rods

  • Numerical Solution of Diffusion Equation

    • Finite Difference Equations in One Dimension

    • Forward Elimination/Backward Substitution Spatial Solution Procedure

    • Power Iteration on Fission Source

    • Finite-Difference Equations in Two Dimensions

    • Successive Relaxation Solution of Two-Dimensional Finite-Difference Equations

    • Power Outer Iteration on Fission Source

    • Limitations on Mesh Spacing

  • Nodal Approximation

  • Transport Methods

    • Transmission and Absorption in a Purely Absorbing Slab Control Plate

    • Escape Probability in a Slab

    • Integral Transport Formulation

    • Collision Probability Method

    • Differential Transport Formulation

    • Spherical Harmonics Methods

    • Discrete Ordinates Method