N-group neutron transport theory: a criticality problem in slab geometry

Journal Article · Sun May 01 00:00:00 EDT 1977 · J. Math. Anal. Appl.; (United States)

DOI:https://doi.org/10.1016/0022-247X(77)90195-0· OSTI ID:7316089

Mullikin, T W ^[1]; Victory, D

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1. Purdue Univ., West Lafayette, IN

The steady-state equation for N-group neutron transport in slab geometry is written as an integral equation. A spectral analysis is made of the integral operator and related to the criticality problem. The method depends on a representation for the resolvent kernel for a subcritical slab and on analytic continuation in a complex parameter to characterize eigenvalues in terms of singularities of the resolvent. The analytic continuation is based on a bifurcation analysis of some nonlinear matrix integral equations whose solutions provide a matrix Wiener--Hopf factorization of the Fourier transform of the kernel of the transport operator.

• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Nuclear Criticality Safety Program (NCSP)
• DOE Contract Number: NONE
• OSTI ID: 7316089
• Journal Information: J. Math. Anal. Appl.; (United States), Journal Name: J. Math. Anal. Appl.; (United States) Vol. 58:3; ISSN JMANA
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOLTZMANN EQUATION
CRITICALITY
DIFFERENTIAL EQUATIONS
EQUATIONS
FOURIER TRANSFORMATION
INTEGRAL TRANSFORMATIONS
MATHEMATICAL MODELS
MULTIGROUP THEORY
NEUTRON TRANSPORT THEORY
Nuclear Criticality Safety Program (NCSP)
SLABS
TRANSFORMATIONS
TRANSPORT THEORY