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The spark of the Super: Teller–Ulam and the birth of the H-bomb—rivalry, credit, and legacy at 75 years
In early 1951, Los Alamos scientists Edward Teller and Stanislaw Ulam devised a breakthrough that would lead to the hydrogen bomb [1]. Their design gave the United States an initial advantage in the Cold War, though comparable progress was soon achieved independently in the Soviet Union and the United Kingdom.
Thomas Folk, Siddhartha Srivastava, Dean Price, Krishna Garikipati, Brendan Kochunas
Nuclear Science and Engineering | Volume 198 | Number 11 | November 2024 | Pages 2096-2119
Research Article | doi.org/10.1080/00295639.2024.2303544
Articles are hosted by Taylor and Francis Online.
Accurately predicting errors incurred in a cross-section model for two-step reactor analysis enables the development of optimal case matrices and more efficient cross-section models. In a companion paper, we developed a systematic methodology for the partial derivatives cross-section model through rigorous analytic error analysis. In this paper, we verify our methodology against the conventional “brute force” numerical approach using a typical pressurized water reactor (PWR) lattice. By successfully reproducing known results, we gain confidence in our methodology’s application to advanced reactor environments, where optimal case matrices are generally not known. Our error methodology relies on accurately estimating bounds on the derivatives of the cross-section functions, a task we achieve through an order of convergence study. We use these derivative bounds in derived error expressions to obtain pointwise and setwise cross-section error bounds and verify these results with reference solutions of various two-group cross sections. We then propagate the cross-section error bounds to reactivity error using first-order perturbation theory and analyze their combined effect. Application of this approach to our test problem corroborates our prior qualitative findings with quantitative evidence and reveals the relative magnitudes of interpolation and model form error sources across diverse PWR cross-section functionalizations. Our results suggest systematic pathways for improving case matrix construction to minimize the overall error. These findings also confirm what is well known to the light water reactor design community, which is that interpolation error of cross sections for standard interpolation procedures and case matrix structures is on the order of 10 pcm or less. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multi-lattice problems, and investigating historical effects within the macroscopic depletion model.