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Propagation of a solitary fission wave
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Image of FIG. 1.
FIG. 1.

Schematic representation of a solitary fission wave moving through fertile material. A fission wave moves through fertile material, breeding fissile material, and then consuming it. Under the proper conditions, the neutron flux profile will move at a constant velocity, v.

Image of FIG. 2.
FIG. 2.

Diffusive and reactive profiles. Top two plots show the terms in the numerator of Eq. (8) , and bottom left shows their difference. Bottom right plot shows the flux profile weighted by the mean neutron velocity. Dividing bottom left by bottom right gives constant wave velocity in cm/s, and this condition holds at every location. These profiles span the full extent of flux wave.

Image of FIG. 3.
FIG. 3.

Flux profiles for 3 time points. Dotted, dashed, and solid lines show fluxes at ∼140 years, 170 years, and 200 years.

Image of FIG. 4.
FIG. 4.

Neutron flux. The figure shows the computationally determined neutron flux (dashed line) as well as the flux as given by Eq. (7) using the K(ζ) and D(ζ) from the simulation results.

Image of FIG. 5.
FIG. 5.

Spatial dependence of V. Neutron flux wave (not shown) peak is centered at 9 m, at ∼200 years. This plot shows that the reaction term changes from positive to negative within the region of interest, which corresponds to the bistable class of reaction-diffusion problems (e.g., Ref. 7 ).


Generic image for table
Table I.

Reactor and simulation parameters. Not shown are concentrations of other materials, all are set to zero at beginning-of-life (BOL). 56Fe, 23Na, and 238U concentrations reflect a 12.5%, 43.75%, and 43.75% ratio by volume.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Propagation of a solitary fission wave