A MODIFIED P-3-LIKE APPROXIMATION TO THE TRANSPORT-EQUATION

Standard P-N theory is well developed as an approximation to the neutr on transport equation. However, this theory contains no physics in the sense that it simply represents the angular flux as a sum of polynomi als in angle. Thus, standard P-N theory (with N finite) cannot qualita tivelJ? predict correct asymptotic transport behavior except in the li mit of pure scattering. In this paper, we modify standard P-N theory b y incorporating certain transport physics, namely, the Case discrete m odes, into a modified P-N expansion of the angular flux. The theory re sulting from using this modified P-N-like expansion predicts the exact transport asymptotic growth/decay length, since it contains the discr ete Case eigenvalue. Such modified P-3-like equations and associated b oundary conditions are derived in planar geometry according to a recen tly introduced variational calculus. Analyses and numerical calculatio ns reveal that this modified P-3-like theory possesses the following f eatures: (a) It reduces to standard P-3 theory in the limit of pure sc attering,. (b) it conserves neutrons but exhibits a scalar flux discon tinuity at a material interface; (c) it is shown numerically to be exc eedingly accurate, much more accurate than standard P-3 theory, in pre dicting various transport theory behavior for homogeneous problems; an d (d) for heterogeneous problems, it is necessary that each material r egion in the system be sufficiently large for this theory to predict b etter results than standard P-3 theory.