Two-Group Diffusion Theory for a Ring of Cylindrical Rods

Technical Report · Sat Jun 01 04:00:00 EDT 1957

DOI:https://doi.org/10.2172/4339952· OSTI ID:4339952

Avery, R. ^[1]

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1. Argonne National Lab. (ANL), Lemont, IL (United States)

The conditions for criticality and the resulting flux distribution have been obtained in the two-group diffusion theory approximation for a ring of N equally spaced, identical cylindrical rods embedded symmetrically in a radially bare cylinder. The system is uniform axially and of either finite or infinite height. Either or both of the two media of the system may be multiplying. The method used is a generalization of the Nordheim-Scalettar method for the solution of the control rod problem of similar geometry. In satisfying each of the various boundary conditions use is made of the Bessel function addition theorems to center all terms in the general solution at the appropriate line of symmetry. The results are obtained in terms of a Fourier expansion of the angular dependence of the flux about each rod, which in application must be cut off after some early term in the infinite series. The order of the critical determinant is equal to twice the number of angular terms retained.

• Research Organization: Argonne National Laboratory (ANL), Lemont, IL (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Nuclear Criticality Safety Program (NCSP); US Atomic Energy Commission (AEC)
• DOE Contract Number: W-31109-ENG-38
• NSA Number: NSA-11-011393
• OSTI ID: 4339952
• Report Number(s): ANL-5729
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Bessel Function
CONTROL ELEMENTS
CRITICALITY
CYLINDERS
DIFFUSION
DISTRIBUTION
EQUATIONS
Flux Distribution
GROUP THEORY
NEUTRON FLUX
NORDHEIM-SCALETTAR METHOD
Nuclear Criticality Safety Program (NCSP)
REACTORS
RODS
Reactor Core
TRANSPORT THEORY