https://doi.org/10.1140/epjh/s13129-025-00111-z
Regular Article
Heisenberg's reactor equation and his last reactor project B8: calculating criticality for a fully tampered cylindrical core
Department of Physics, University of Houston, 77401, Houston, Tx, USA
a
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Received:
12
February
2025
Accepted:
10
October
2025
Published online:
1
December
2025
Abstract
I study Heisenberg's 1939 chain reaction equation as an eigenvalue problem for nonspherical shapes and apply it to calculate the criticality condition of the cylindrical 1945 Haigerloch reactor experiment B8. I also discuss Heisenberg's B8 criticality analysis where he relied on his 1939 spherical result that the neutron current ratio is infinite at criticality. I show that that result holds for a sphere but not for a cylinder. His wrong expectation for a cylinder has recently been assumed in simulations of B8. Heisenberg and Wirtz applied an inconsistent mix of spherical and axial extrapolations to B8 that led Heisenberg to predict that they needed a radial increase of 20 cm to reach criticality. The B8 reactor was designed with the height twice the radius, H = 2R, so that a sphere of radius R fits perfectly inside the cylinder, apparently with the application of his 1939 spherical calculation in mind. I solve Heisenberg's reactor equation for axial symmetry and the full tamper boundary condition. Diffusion theory with the tamper then predicts that the reactor should have been slightly subcritical, while Heisenberg's albedo boundary condition predicts slight supercriticality. Diffusion theory therefore predicts that the reactor was very near to criticality. I also consider how the reactor's designers may have arrived at a nearly correct size of B8 without doing a correct cylindrical calculation.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
