[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956915","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Advanced Neutronics\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          4\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemester:\n          Semestre 2\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ELecture:\u003C\/span\u003E\n                                      \u003Cspan\u003E30\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003EPractical study :\u003C\/span\u003E\n                                      \u003Cspan\u003E0\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003EDirected study:\u003C\/span\u003E\n                                      \u003Cspan\u003E9\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003EProject :\u003C\/span\u003E\n                                      \u003Cspan\u003E21\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Nuclear physics\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Introduction to neutronics\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; General knowledge: differential equations, linear algebra, linear operators, probabilities and statistics, eigenvalue problems, Laplace and Fourier transforms.\u003C\/p\u003E\n\u003Cp\u003E- Bases of scientific programming\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThe course is composed of class covering both deterministic and Monte Carlo methods for the simulation of neutron transport, practical works in order for the students to get familiar with the simulation software and with the practical implementation of the main simulation methods, and a personal project whereby the students learn how to manipulate codes and algorithms in order to compute the quantities of interest. The personal project can focus on the use of existing production-level simulation codes developed at CEA, like APOLLO (deterministic solver) or TRIPOLI (Monte Carlo solver), or on the development of a simplified transport code, in order to have a hands-on experience on numerical methods.\u003C\/p\u003E\n\u003Cp\u003EClasses will cover:\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EFor the deterministic methods:\u003C\/li\u003E\n\u003Cli\u003EThe study of the fundamental mode and PN expressions of the Boltzmann equation\u003C\/li\u003E\n\u003Cli\u003EThe basic calculation scheme based on the diffusion approximation and the SPN method.\u003C\/li\u003E\n\u003Cli\u003EThree major deterministic numerical methods developed to solve the Boltzmann equation: the collision probability method (Pij), the method of characteristics, (MOC), and the discrete ordinate method (SN).\u003C\/li\u003E\n\u003Cli\u003EFor the Monte Carlo methods:\u003C\/li\u003E\n\u003Cli\u003EThe integral formulation of the Boltzmann equation and its relation to the stochastic interpretation in terms of a random walk\u003C\/li\u003E\n\u003Cli\u003ESampling techniques and pseudo-random number generation\u003C\/li\u003E\n\u003Cli\u003EVariance-reduction methods\u003C\/li\u003E\n\u003Cli\u003EEigenvalue problems and power iteration\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThe course \u201cadvanced neutronics\u201d extends the course \u201cintroduction to neutronics\u201d, with special emphasis on numerical simulation methods to model neutron transport in nuclear systems. Emphasis is given to the different approaches that can be used to describe the neutron transport equation in matter: the physical and mathematical modeling choices and the corresponding numerical methods and algorithms developed for this purpose. In particular, both deterministic and Monte Carlo methods will be presented and their respective merits and drawbacks thoroughly discussed. The course includes practical works on production-level simulation software developed at CEA, and a personal project devoted to the simulation of neutron transport for radiation shielding or reactor physics applications.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EOrganisation g\u00e9n\u00e9rale et modalit\u00e9s p\u00e9dagogiques\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Students are encouraged to participate strongly in the course via exercises integrated into the course and tutorials. Exercises to prepare at home.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; The supervised practical work is part of the educational device aimed at establishing a back-and-forth between theory and practice promoting faster and more effective assimilation of the course.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EComp\u00e9tences\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EReactor physics:\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Define the neutron quantities of interest of a core calculation (other than the flux and the reaction rates) and give characteristic orders of magnitude: hot point factors, reactivity coefficients, anti-reactivity margin, residual heat, neutron fluence.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Explain the following physical effects on reactivity in UOx and MOx fuel cell configurations:\u003C\/p\u003E\n\u003Cp\u003E-The phenomenon of resonant isotopes self-shielding.\u003C\/p\u003E\n\u003Cp\u003E-Temperature effects: Doppler effect and moderator effect.\u003C\/p\u003E\n\u003Cp\u003E-The soluble boron efficiency.\u003C\/p\u003E\n\u003Cp\u003E-The vacuum fraction effect in a MOx fuel configuration.\u003C\/p\u003E\n\u003Cp\u003E-The fuel effect depletion (burnup calculation).\u003C\/p\u003E\n\u003Cp\u003EModeling:\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Present the deterministic and Monte Carlo calculation methods, and introduce the main steps of the neutron calculation scheme used for the PWR and FBR cores; using different methods of solving the Boltzmann equation and adopting certain equivalences in space and energy\u2026.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Establish the integral-differential and integral forms of the Boltzmann equation.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Explain what the fundamental mode is and its importance in neutronics for core calculations.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; State and explain the principles of modeling in a core computation: self-shielding of cross sections, equivalence, homogenization of initially heterogeneous media, condensation of cross sections, use of a degraded transport operator.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Specify which physical quantities are key for core calculations.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Show that the modeling of a core computation leads to solving a nonlinear problem.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Specify what it means to build a multi-parameter library.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Justify the implementation of a calculation scheme by a few appropriate orders of magnitude (calculation time, number of unknowns to calculate).\u003C\/p\u003E\n\u003Cp\u003ESimulation methods:\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Distinguish the problems to be solved: stationary and unsteady, with fixed source and with eigenvalues (calculation of the neutron multiplication factor, of the fundamental mode, of the harmonics of the flux).\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Establish the PN equations.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Write and solve the core calculation equations in diffusion and SPN approximations.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Compare the deterministic and stochastic Monte Carlo calculation approaches and justify their use. Explain their respective advantages and disadvantages, highlight their complementarity.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Solve on simple configurations the transport equation by the method of characteristics, the collision probability method and the Monte Carlo method.\u003C\/p\u003E\n\u003Cp\u003E-\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Analyze the convergence of deterministic and stochastic calculation algorithms.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003EPaul Reuss, Neutron Physics, Les Ulis, INSTN\/EDPSciences, 2008.\u0026nbsp;\u003C\/li\u003E\n\u003Cli\u003EJ. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis, John Wiley \u0026amp; Sons, 1976.\u003C\/li\u003E\n\u003Cli\u003EAlain H\u00e9bert, Applied Reactor Physics, Montr\u00e9al, Presses internationales Polytechnique, 2009.\u003C\/li\u003E\n\u003Cli\u003ET. J. Akai, \u201cApplied Numerical Methods for Engineers\u201d, 1994, J. Wiley \u0026amp; Sons Inc.\u003C\/li\u003E\n\u003Cli\u003Ellya M. Sobol, A Primer for the Monte Carlo Method, London, CRC Press, 1994.\u003C\/li\u003E\n\u003Cli\u003EJ. Spanier and E. M. Gelbard, Monte-Carlo Principles and Neutron Transport Problems, USA, Addison-Wesley Publishing Company, 1969.\u003C\/li\u003E\n\u003Cli\u003ENeutronics, A Nuclear Energy Division Monograph, ouvrage collectif, Paris, Saclay, Les \u00c9ditions du Moniteur\/CEA, 2015.\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]