Generalized Nelkin's expansion for plane lattices in a multigroup PN theory

Abstract

The decay λ of a burst of neutrons in a plane lattice with symmetric multilayered cells is computed in a P N multigroup theory versus the geometrical buckling k. For that purpose, the transport eigenvalue problem is transformed by Vladimirov's symmetric decomposition, and the space variable is eliminated by integration in each layer along the unit cell and by use of Bloch's theorem as boundary condition. A transmission operator for the unit cell generates a generalized eigenvalue problem defining numerically function λ(κ). Generalized Nelkin's coefficients ate computed for various water-beryllium lattices and compared to those obtained for the volume homogenized lattices.