Multiple Timescale Expansions for Neutron Kinetics - II: Illustrative Application to P₁ and P₃ Equations

Closed-form expressions for three-timescale approximations are developed for the one-group time-dependent P₁ and P₃ equations for a homogeneous multiplying medium in planar geometry with two effective groups of delayed neutrons. The development of these three-scale approximations does not rely on imposing separation of space and time. The differences between the three-scale approximations for the P₁, P₃, and diffusion equations, respectively, are analyzed in detail. In particular, the results obtained using the three-scale approximations for the P₁ and P₃ equations underscore their efficiency and accuracy, particularly for the shortest timescales and in the presence of large reactivity insertions.