No abstract

Higher-order neutron fluxes (i.e., higher-order harmonics) are widely applied in perturbation theory and modal kinetics, and they are important for research on the physical characteristics of accelerator-driven subcritical reactors (ADSRs). This paper presents a computational scheme for reconstructing the neutron flux in the steady state according to the biorthogonal properties of the forward and adjoint neutron fluxes, which can be used to analyze how higher-order harmonics affect the steady-state neutron flux under λ - and prompt α -modes. Simulation results indicated that a modal synthesis method based on λ - and prompt α -modes can effectively reconstruct the steady-state neutron flux and core power in an ADSR with a power reconstruction accuracy of within 5%. The higher-order harmonics can be classified into three types according to their physical characteristics: the first type contributes significantly to the steady-state neutron flux, the second type contributes almost nothing to the steady-state neutron flux, and the third type contributes nothing to the steady-state neutron flux. The external neutron source contributes only to specific harmonic expansion orders, which are characterized by significant axial and radial symmetry for both the λ - and prompt α -modes.

An al go rithm for the Monte Carlo sim u la tion of elec tron mul ti ple elas tic scat ter ing based on the frame work of SuperMC (Super Monte Carlo sim u la tion pro gram for nu clear and ra di ation pro cess) is pre sented. This pa per de scribes ef fi cient and ac cu rate meth ods by which the mul ti ple scat ter ing an gu lar de flec tions are sam pled. The Goudsmit-Saunderson the ory of mul ti ple scat ter ing has been used for sam pling an gu lar de flec tions. Dif fer en tial cross-sec tions of elec trons and pos i trons by neu tral at oms have been cal cu lated by us ing Dirac par tial wave pro gram ELSEPA. The Legendre co ef fi cients are ac cu rately com puted by us ing the Gauss-Legendre in te gra tion method. Fi nally, a novel hy brid method for sam pling an gu lar dis tri bu tion has been de vel oped. The model uses ef fi cient re jec tion sam pling method for low en ergy elec trons (<500 keV) and larger path lengths (>500 mean free paths). For small path lengths, a sim ple, ef fi cient and ac cu rate an a lyt i cal dis tri bu tion func tion has been pro posed. The later uses ad just able pa ram e ters de ter mined from the fit ting of Goudsmith-Saunderson an gu lar dis tri bu tion. A dis cus sion of the sam pling ef fi ciency and ac cu racy of this newly de veloped al go rithm is given. The ef fi ciency of re jec tion sam pling al go rithm is at least 50 % for elec tron ki netic en er gies less than 500 keV and lon ger path lengths (>500 mean free paths). Monte Carlo Sim u la tion re sults are then com pared with mea sured an gu lar dis tri bu tions of Ross et al. The com par i son shows that our re sults are in good agree ment with ex per i men tal mea sure ments.Key words: Monte Carlo, mul ti ple scat ter ing, Goudsmit-Saunderson, SuperMC, dif fer en tial cross-sec tion, an gu lar dis tri bu tion, ELSEPA M. A. Wasaye, et al.: The Hy brid Model for Sam pling Mul ti ple Elas tic .