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On the Build-Up Factor from the Multi-Group Neutron Diffusion Equation with Cylindrical Symmetry

DOI: 10.4236/wjnst.2013.31001    4,312 Downloads   7,278 Views   Citations

ABSTRACT

We consider the time dependent neutron diffusion equation for one energy group in cylinder coordinates, assuming translational symmetry along the cylinder axis. This problem for a specific energy group is solved analytically applying the Hankel transform in the radial coordinate r. Our special interest rests in the build-up factor for a time dependent linear neutron source aligned with the cylinder axis, which in the limit of zero decay constant reproduces also the static case. The new approach to solve the diffusion equation by integral transform technique is presented and results for several parameter sets and truncation in the solution for the flux and build-up factor are shown and found to be compatible to those of literature [1,2].

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Fernandes, M. Vilhena, B. Bodmann and V. Borges, "On the Build-Up Factor from the Multi-Group Neutron Diffusion Equation with Cylindrical Symmetry," World Journal of Nuclear Science and Technology, Vol. 3 No. 1, 2013, pp. 1-5. doi: 10.4236/wjnst.2013.31001.

References

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[7] V. Borges, J. C. L. Fernandes, M. T. Vilhena, B. Bodmann and B. D. A. Rodriguez, “A Closed-Form Formulation for the Build-Up Factor and Absorbed for Photons and Electrons in the Compton Energy Range in Cartesian Geometry,” World Journal of Nuclear Science and Technology, Vol. 1, No. 2, 2012, pp. 23-28. doi:10.4236/wjnst.2012.21004
[8] C. Borges and W. Larsen, “The Transversed Integrated Scalar Flux of a Narrowly Focused Particle Beam,” SIAM Journal on Applied Mathematics, Vol. 55, No. 1, 1995, pp. 1-22.
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