Abstract
It is shown that the monoenergetic neutron transport equation and the associated boundary conditions can be characterized by a Lagrangian. A proper choice of the trial function for this Lagrangian leads to the widely used spherical harmonics approximation as the Euler-Lagrange equations. Further, a set of boundary conditions for the spherical harmonic equations is the result of the logical application of the variational method. These variational boundary conditions appear to be significantly more accurate than the boundary conditions presently in general use. For example, the use of the variational boundary conditions at a free surface reduces the error (compared with the boundary conditions presently used) in the linear extrapolation distance for the Milne problem by several factors. In particular, the P-1 (diffusion) approximation yields a value of 0.7071 (in units of mean free paths) and the P-3 approximation yields a value of 0.7118, both comparing quite favorably with the exact value of 0.7104.
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