General Principles of Neutron Transport

This chapter describes the basic theory underlying the neutron transport equation and the principal approximations used in this equation’s applications to reactor physics. In addition to presenting detailed classical derivations of various forms of the transport equation, we discuss several important topics in a more rigorous manner than is found in typical derivations. For instance, we include (i) a discussion of the lack of smoothness of the angular flux in multidimensional geometries (this has a negative impact on numerical simulations); (ii) derivations of the transport equation in specialized 1-D, 2-D, and 3-D geometries; (iii) a derivation of the time-dependent integral transport equation; (iv) an asymptotic derivation of the point kinetics equation; and (v) an asymptotic derivation of the multigroup P₁ and diffusion equations. The basic approach taken by the authors in this chapter is theoretical, in the hope that this will complement more intuitive presentations of related topics found in other chapters of this handbook.