Elementary Model for Nuclear Fission Reactor

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This Demonstration considers a model for a nuclear reactor using collision probabilities.


The graphic shows a plane view of four spheres, S2 for sample, C3 for control device, D4 for detector and E5 for extraneous source, initially at the summits of a regular tetrahedron in a multiplicative medium. It is assumed that there are no leaks from the pile P1.

You can change some parameters, moving the sample S2 of coordinates out of the plane by sliding or in the plane by dragging the yellow circle centered at . Watch the effects on the collision probabilities , detection rates , neutron fluxes and global amplification and multiplication factors. Gray levels on the plane view and the bar chart reflect the fluxes. If you see a white flash, you are dead.

is the inverse mean free path or total macroscopic cross-section, is the multiplication factor and is the spontaneous source. For all , is the sum of and is the -weighted average over all regions. is the probability that a particle emitted in region first collides in region .


Contributed by: Pierre Albarède (March 2021)
Open content licensed under CC BY-NC-SA



The model is the integral stationary isotropic monokinetic transport equation [1], discretized over nine regions. The collision probability path integrals are approximated by choosing a single typical path, which increases the speed of the computation. Thus, the probability model reduces to the [2]. Shadows are not accounted for. Negative mean that the probability model breaks down (when two spheres come too close). Negative fluxes mean that the stationary hypothesis breaks down. The reference state is fully symmetric with respect to sphere exchange, except for the spontaneous source, that is concentrated in E5 and unitary. For more details, see a companion notebook in [3].


[1] J. Bussac and P. Reuss, Traité de neutronique: Physique et calcul des réacteurs nucléaires avec application aux réacteurs à eau pressurisée et aux réacteurs à neutrons rapides, 2e éd. corr., Paris: Hermann, 1985.

[2] Wikipedia. "Beer–Lambert Law." (Mar 12, 2021) en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law.

[3] P. Albarède. (Mar 12, 2021) pierre.albarede.free.fr.

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