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A variational solution of the one group neutron transport equation with isotropic scattering in long, homogeneous, circular cylinders.

McGill University
Publication Date
  • Mathematics.


An investigation is made of the usefulness of a variational method for the calculation of the neutron flux distribution in a cylinder. In particular the method is applied to a long homogeneous cylinder which captures and isotropically scatters neutrons and which is subject to an incurrent of neutrons with an angular distribution proportional to the cosine of the angle between the normal to the surface and the direction of neutron travel. Tables and figures are given to illustrate the accuracy of the “method for cylinders with radii up to four mean free paths and which range from almost purely capturing to nearly purely scattering. The calculations are done with trial functions that are polynomials in the square of the distance from the cylinder axis with various number of terms, up to nine, included.

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