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Remembering Charles E. Till
Charles E. Till
Charles E. Till, an ANS member since 1963 and Fellow since 1987, passed away on March 22 at the age of 89. He earned bachelor’s and master’s degrees from the University of Saskatchewan and a Ph.D. in nuclear engineering from Imperial College, University of London. Till initially worked for the Civilian Atomic Power Department of the Canadian General Electric Company, where he was the physicist in charge of the startup of the first prototype CANDU reactor in Canada.
Till joined Argonne National Laboratory in 1963 in the Applied Physics Division, where he worked as an experimentalist in the Fast Critical Experiments program. He then moved to additional positions of increasing responsibility, becoming division director in 1973. Under his leadership, the Applied Physics Division established itself as one of the elite reactor physics organizations in the world. Both the experimental (critical experiments and nuclear data measurements) and nuclear analysis methods work were internationally recognized. Till led Argonne’s participation in the International Nuclear Fuel Cycle Evaluation (INFCE), and he was the lead U.S. delegate to INFCE Working Group 5, Fast Breeders.
M. M. R. Williams
Nuclear Science and Engineering | Volume 173 | Number 2 | February 2013 | Pages 182-196
Technical Note | doi.org/10.13182/NSE12-11
Articles are hosted by Taylor and Francis Online.
A method has been developed that provides analytic solutions for two-dimensional cell problems for the neutron transport equation. This is made possible by assuming an infinite, repeating lattice of rectangular regions. The solution is effected by means of a finite Fourier transform, the periodicity of which is related to the size of the unit cell. In order to drive the flux, we assume that the cell is composed of two regions: an inner circular region and the remaining exterior part. Different sources are placed in each region thereby leading to a situation rather like the conventional reactor cell problem but with no spatial variation of the cross sections. The method is illustrated by two examples: the Levermore-Pomraning equations and the two-group equations. In the former case, we have obtained the stochastically averaged flux within the cell and also the Pomraning χ-function. In addition, we have calculated the ratio of the spatially averaged flux in the outer region to that in the inner circular region, i.e., the disadvantage factor. Fluxes and disadvantage factors are also obtained for the two-group equations, and the rate of convergence is shown. These results are exact transport theory solutions and are offered as benchmarks for checking transport theory codes. The calculations are also repeated using diffusion theory. The SPN method, which we show to be exact for our problem, is used to demonstrate the rate of convergence of the PN method for two-dimensional cell problems.