Even-parity Boltzmann transport equation applied for response (contributon) flux calculation based on the spatial channel theory

An even parity approach for the detection of main stream channels of response flux inside the material is presented. The product of forward and adjoint flux is called the response flux which plays an important role in assessing the performance of shielding materials. Based on two distinct maximum principles, even parity forward and adjoint fluxes (ψ and ψ†) are obtained respectively. Weak and strong points of shielding materials can be well understood using the spatial channel theory and this analysis is performed using the even parity Boltzmann transport equation. The PN method as well as the finite element method are employed to approximate the angular and spatial components of the fluxes, respectively. Also, we extend the concept of spatial channel theory to fissile materials. A number of test cases are provided to evaluate the performance of the proposed approach.