Search

A solution of the neutron transport equation is obtained by expanding the flux Phi (r Omega ) at position r in direction Omega as a series of the form: Phi (r, Omega )= Sigma l=0N(2l+1) Sigma m=0lPlm(cos theta )( psi lm (r)cos(m phi )+ gamma lm(r)sin(m phi )) where Plm(cos theta ) is the associated Legendre polynomial of order l, m with theta and phi the axial and azimuthal angles, respectively, of Omega . psi lm(r) and gamma lm(r) satisfy first-order differential equations and are determined by eliminating terms with odd l and then using finite-difference or finite-element techniques on the resulting second-order system. Complicated algebra is involved in deriving this latter set of relations and FORTRAN subroutines have been written to calculate the necessary coefficients and specify the relevant differentials.