Reflection and Transmission Functions in Reactor Physics

Citation

Pfeiffer, Wayne Wallace (1969) Reflection and Transmission Functions in Reactor Physics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/73BQ-HK18. https://resolver.caltech.edu/CaltechTHESIS:06072017-101556497

Abstract

The utility of reflection and transmission function (or collectively, response function) concepts in reactor physics is extensively investigated. Previously obtained differential (invariant imbedding) and functional (adding) equations for the response functions are re-derived in a unified manner. In addition a numerical halving technique is developed from the adding relations.

Existing response function calculations are summarized and extended by combining the invariant imbedding and functional equations. For deep-penetration shielding problems in slab geometry, this combined response function approach is shown to be more efficient than conventional Monte Carlo or discrete ordinates techniques. The response function approach is also shown to be efficient for a criticality search in slab geometry. As a step toward a more general treatment, invariant imbedding equations are derived, but not solved, in finite cylindrical geometry.

Finally the feasibility of performing response function experiments to obtain cross-section and criticality information is examined. The envisioned experimental set-up is described and calculations are carried out to verify the analytical procedures, with particular emphasis on the propagation of errors. Cross-sections can be determined using the halving scheme, which provides a theoretically sound technique for multiple scattering correction. Thus experiments may be done on moderately thick slabs. Criticality parameters can be obtained from measured response functions using the criticality search procedure. Because response function experiments are expected to be relatively quick and cheap compared to present cross-section and critical experiments, it is concluded that response function experiments should be carried out as soon as possible to determine whether they are as useful as our analysis indicates.

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