Two-Group Diffusion Theory for a Ring of Cylindrical Rods

Journal Article · Thu May 01 04:00:00 EDT 1958 · Nuclear Science and Engineering

OSTI ID:4336616

Avery, R. ^[1]

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1. Argonne National Laboratory (ANL), Argonne, IL (United States)

The conditions for criticality and resulting flux distribution are 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 Bessei 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), Argonne, 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-12-010098
• OSTI ID: 4336616
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Vol. 3; ISSN 0029-5639
• Publisher: Taylor & Francis
• Country of Publication: United States
• Language: English

Related Subjects

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BESSEL FUNCTIONS
BOUNDARY CONDITIONS
CRITICALITY
CYLINDERS
DIFFUSION
GROUP THEORY
MATHEMATICS
MECHANICAL STRUCTURES
NORDHEIM-SCALETTAR METHOD
Nuclear Criticality Safety Program (NCSP)
RODS
TRANSPORT THEORY