Calculation of multi-group migration areas in deterministic transport simulations

Abstract Recent work on the Cumulative Migration Method (CMM) has demonstrated that it is possible to define multi-group transport cross sections directly from Monte Carlo spectral calculations by utilizing edits of the energy-dependent neutron migration areas. However, it is difficult to demonstrate that downstream deterministic transport calculations actually preserve Monte Carlo migration areas. This paper addresses this issue by: 1) demonstrating the relationship of migration area with the concept of mean squared displacement, 2) deriving, and validating vs. Monte Carlo, an analytic expression for computing one-group migration areas for a homogeneous medium with energy-independent cross sections, 3) deriving, and validating vs. Monte Carlo, an analytic expression for computing multi-group migration areas for a homogenized medium with energy-dependent cross sections, and 4) rigorously proving that energy condensation of multi-group transport cross section must be inverse flux weighted in order to preserve Monte Carlo neutron migration areas.

[1]  S. Magazù,et al.  Mean square displacement evaluation by elastic neutron scattering self-distribution function. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  J. Rieger.  Conformation of liquid crystal side chain polymers in the smectic phase : models for anisotropic random walks , 1988 .

[3]  J. Dai.  Euler–Rodrigues formula variations, quaternion conjugation and intrinsic connections , 2015 .

[4]  Cassiano R. E. de Oliveira,et al.  Two-dimensional C5G7 MOX fuel assembly benchmark calculations using the FEM-PN code EVENT , 2004 .

[5]  R. A. Moore,et al.  A computer and analytic study of the metallic liquid–glass transition. II. Structure and mean square displacements , 1988 .

[6]  J. G. Dash,et al.  MEAN-SQUARE DISPLACEMENT OF DILUTE IRON IMPURITY ATOMS IN HIGH-PURITY BERYLLIUM AND COPPER , 1964 .

[7]  Elmer E Lewis,et al.  Fundamentals of Nuclear Reactor Physics , 2008 .

[8]  B. Forget,et al.  Cumulative migration method for computing rigorous diffusion coefficients and transport cross sections from Monte Carlo , 2018 .

[9]  E. Lewis,et al.  Benchmark specification for Deterministic 2-D/3-D MOX fuel assembly transport calculations without spatial homogenisation (C5G7 MOX) , 2001 .

[10]  Benoit Forget,et al.  The OpenMOC method of characteristics neutral particle transport code , 2014 .

[11]  Kord Smith,et al.  CASMO-5 Development and Applications , 2006 .

[12]  B. Forget,et al.  Generalized equivalence methods for 3D multi-group neutron transport , 2018 .

[13]  W. Stacey.  Nuclear Reactor Physics , 2001 .

[14]  Deokjung Lee,et al.  A new approach to three-dimensional neutron transport solution based on the method of characteristics and linear axial approximation , 2017, J. Comput. Phys..

[15]  Alain Hébert,et al.  A consistent technique for the pin-by-pin homogenization of a pressurized water reactor assembly , 1993 .

[16]  Paul K. Romano,et al.  OpenMC: A State-of-the-Art Monte Carlo Code for Research and Development , 2014, ICS 2014.

[17]  E. Fridman,et al.  On the use of the Serpent Monte Carlo code for few-group cross section generation , 2011 .

[18]  S. Magazù,et al.  Mean square displacements from elastic incoherent neutron scattering evaluated by spectrometers working with different energy resolution on dry and hydrated (H2O and D2O) lysozyme. , 2010, The journal of physical chemistry. B.

[19]  Amir H. Gandjbakhche,et al.  Scaling relationships for anisotropic random walks , 1992 .

[20]  J. Eduard Hoogenboom,et al.  GENERATION OF MULTI-GROUP CROSS SECTIONS AND SCATTERING MATRICES WITH THE MONTE CARLO CODE MCNP5 , 2007 .

[21]  A. Yamamoto,et al.  Convergence analysis of MOC inner iterations with large negative self-scattering cross-section , 2013 .

[22]  G. I. Bell,et al.  Introduction to Nuclear Reactor Theory , 1966 .

[23]  Nam Zin Cho,et al.  2D/1D fusion method solutions of the three-dimensional transport OECD benchmark problem C5G7 MOX , 2006 .

[24]  K. E. Bisshopp.  Rodrigues’ Formula and the Screw Matrix , 1969 .

[25]  Yoshihiro Yamane,et al.  Simplified Treatments of Anisotropic Scattering in LWR Core Calculations , 2008 .

[26]  B. Forget,et al.  Stabilization of multi-group neutron transport with transport-corrected cross-sections , 2019, Annals of Nuclear Energy.

[27]  Benoit Forget,et al.  Comet solutions to the 3-D C5G7 MOX benchmark problem , 2006 .

[28]  A. Figá-Talamanca,et al.  Harmonic analysis for anisotropic random walks on homogeneous trees , 1994 .

[29]  Andrew Siegel,et al.  ARRC: A random ray neutron transport code for nuclear reactor simulation , 2018 .

[30]  Nonlinear Brownian motion – mean square displacement , 2004 .

[31]  R Nossal,et al.  Scaling relationships for theories of anisotropic random walks applied to tissue optics. , 1993, Applied optics.

[32]  A. Yamamoto,et al.  Recent developments in the GENESIS code based on the Legendre polynomial expansion of angular flux method , 2017 .

[33]  Benoit Forget,et al.  The OpenMC Monte Carlo particle transport code , 2012 .

[34]  H. Nishi,et al.  Transport Criticality Analysis of FBR MONJU Initial Critical Core in Whole Core Simulation by NSHEX and GMVP , 2004 .

[35]  Kord Smith,et al.  Impact of inflow transport approximation on light water reactor analysis , 2015, J. Comput. Phys..

[36]  R.E. MacFarlane,et al.  The NJOY Nu-clear Data Processing System Version 91 , 1994 .

[37]  P J Prendergast,et al.  Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation. , 2007, Journal of biomechanics.