M2 Nuclear Engineering

Basics of U chemistry. Basics of Radiation Protection. PWR functional description. Basics of system thermodynamics, of neutronics, thermal hydraulics, fuel cycle

General physics, thermodynamics, fluid mechanism and heat transfert.

No specific prerequisite. Interest for both economy and electricity supply is desirable.

Mathematics: Notions of differential equations, numerical analysis, linear algebra

Physics: Notions of thermal-hydraulics, neutronics, thermics. Notions of nuclear reactor operation.

This course is an introduction to multiphysics and to the quantification of uncertainty in the frame of nuclear reactor modeling.

The couplings between the usual modeling of each of the nuclear reactor core physics domains will be recalled. The different approaches to deal with couplings will be presented, in connection with the objectives of computer simulation, in particular the nuclear safety demonstration.

A practical work session will allow, through the construction of a code coupling, to address the challenges related to the implementation of such calculations. The behavior of a simulated nuclear reactor core, during simple multiphysics transients, will also be observed on this occasion.

We will introduce the concepts of convergence and stability, which are key for multiphysics simulations. The most used coupling algorithms and time schemes will be presented.

The course will also tackle the theoretical concepts related to the treatment of uncertainties, from the description of the sources of uncertainty (probability laws, covariance, correlation), to the propagation of uncertainties and to sensitivity studies via surrogate models (neural networks, kriging).

Finally, we will present the recent advances in Monte Carlo codes that pave the way for multiphysics transient simulations. We will also discuss the challenges that still need to be overcome.

- Describe the steps between the observation of a physical phenomenon and its simulation.

- Explain the terms used to describe multiphysics calculations (coupling, one-way coupling, partitioned, monolithic, explicit, implicit etc.).

- Describe the couplings between the physics involved in the usual modeling of nuclear reactor cores.

- Describe the main approaches used to take into account these couplings, the most used multiphysics models.

- Discuss these approaches and models, their use and their asset.

- Explain the impact of coupled calculations on the development of computer codes.

- Describe a simple multiphysics transient.

- Describe the issues of stability and precision in the development of multiphysics calculation schemes.

- Discuss the advantages of the most common time schemes used in multiphysics calculations.

- Clarify how to implement these time schemes in a code coupling.

- Point out the differences and advantages of the most common coupling algorithms (Gauss-Seidel, Newton, JFNK, Anderson).

- Spell out the nature of the uncertainties under discussion.

- Explain the difference between interaction and correlation (whatever its nature) between variables in order to be able to sort out what methods might be of use.

- Explain the basic probability concepts that describe randomness (location and dispersion parameters for instance).

- Describe a probability law with its basic statistical properties (mean, variance, mode…) and compare one law to another one of the same kind.

- Spell out the concept of experimental estimators along with their underlying biases and variance terms and compute simple ones (mean, variance…) when dealing with provided samples.

- Explain the role of the central limit theorem when computing the average of a sample and use it to estimate a rough 95% confidence interval for the sample mean.

- Choose a strategy to generate a design-of-experiment, when no data are available, in order to pursue the requested analysis.

- Explain the basic blocks of uncertainty quantification for a generic problem.

- Briefly detail the purpose of a sensitivity analysis and the various possible techniques that can be used, depending on the aim of the analysis.

- Explain the generic concept of surrogate models (from the training, quality assessment to the prediction step) and be able to mention different models.

- Adapt the aforementioned blocks and possibly combine them for a given problem that would take under consideration specific issues (CPU/time consumption for a code, number of input variables...).

- Explain the effects of the statistical uncertainty on the results provided by a Monte Carlo code when its output is provided to another simulation code.

- Name et explain the variance-reduction techniques that can be used in order to reduce the statistical uncertainty.

- Identify/Construe the specific issues concerning the coupling of a Monte Carlo code (as a solver for neutron transport) with external codes providing the reactivity feedbacks due to temperature and density effects, or mechanical deformations.

- Explain the stability of the coupling scheme: illustrate the effects of the statistical noise (induced by Monte Carlo simulations) on the transmission of the information between the codes and on the overall stability.

- Discuss the role of parallel simulations and the performances in terms of computation time and memory occupation.

Course and practical work. Student participation is encouraged.

- Judge of the relevance of a model of a nuclear reactor core.

- Identify the methods that can be used to assess the uncertainty of a simulation.

- Debate the issues and challenges of current R&D on these issues.

The previous semester module « Thermal-Hydraulics » (S3-D-O-R-FLUI) is a convenient prerequisite.

Basics knowledge acquired in nuclear physics (beta-neutron decay, precursors properties…), Neutronics 1, Thermalhydraulics, PWR Functional Description, Introduction to Safety.

The module is structured in three parts: a thermo-hydraulic section applied to PWRs, a neutronics and reactor core control section, and an immersive component on the EVOC digital platform (EVOC nuclear system, experimental reactor).

This course focuses on reactor physics and on the physical, thermal, hydraulic and neutronic phenomena that occur during the operation of nuclear reactors. The use of simulation and modelling enables students to study the couplings between phenomena, to address their dynamic and time-dependent aspects, and to develop a solid understanding of the relevant orders of magnitude.

Describe the thermo-hydraulic behaviour of the primary circuit of a PWR under normal and accidental operating conditions, and break down the main steps of the start-up sequence.
Describe the phases of the accidents studied on the simulator.
Explain the physical phenomena governing the evolution of the system and justify the actions of the reactor protection system.
Use steam tables.
Perform energy and mass balances.

For reactor kinetics and xenon/samarium poisoning, be able to develop a model:
• Write the systems of differential equations, providing the physical meaning of each term.
• Derive numerical values for the model from nuclear data and reactor-specific information.

Explain the Nordheim function and its graphical representation: vertical asymptotes, oblique asymptote, and intersections with both axes.
Use the Nordheim curve to qualitatively and quantitatively describe the kinetic behaviour of the reactor in the following cases: reactor trip (SCRAM), negative reactivity step (rod-drop test), positive reactivity pulse.

Describe the kinetic behaviour of the reactor at low flux during the subcritical approach, the evolution of flux near criticality, and the divergence phase.

Present the time evolution of xenon and samarium poisoning, with correct orders of magnitude (in time constants and pcm), in the following situations: start-up with fresh or spent fuel, SCRAM, negative power step (load reduction).

Explain the influence of fuel burnup on xenon and samarium poisoning phenomena.

Explain the phenomenology of spatial–temporal xenon oscillations in a PWR. Present the influence of the key parameters: geometric dimensions, flux level, presence of MOX fuel, Doppler effect, and power distribution within the core.

Analyse transients taking into account the temperature effects of both moderator and fuel in a PWR.

Perform reactivity balances for a PWR with correct orders of magnitude in different operating conditions: reactor start-up and power ramp-up, power transients.

Note: Numerical method issues (implicit vs. explicit method, choice of time step) will be discussed during the course but are not defined as learning outcomes.

The specific tools used are:
• SOFIA PWR simulator
• C-PWR PWR simulator: temperature effects
• JANIS: used for searching nuclear data (cross sections, fission yields, decay periods)
• National Nuclear Data Center NuDat 2.8: search for nuclear data (Sn, Q values for the study of delayed-neutron emission)
• DESMOS: online function-analysis software, used for manipulating the Nordheim function
• Software developed at INSTN: Prke, XesmCalc, DiffTools, Sphère

The module alternates short course refreshers (15-minute segments), demonstrations, hands-on practical work carried out by the students, and guided exercises.

– Identify the different functionalities of research reactors
– Analyse the operation of research reactors
– Know how to start up a research reactor of the ISIS type while complying with safety rules
– Describe the role of delayed neutrons in reactor kinetics
– Explain the reactivity changes induced by temperature effects and by modifications of the moderation ratio

« Neutron physics » (Paul Reuss)

« Physics of nuclear kinetics » (G. Robert Keepin, 1965)

« Dynamics of nuclear reactors » (David L. Hetrick)

« Beta-delayed neutron emission evaluation » (IAEA Headquaters, Vienna, Austria, 10-12 october 2011):

https://inis.iaea.org/collection/NCLCollectionStore/_Public/43/041/43041197.pdf?r=1&r=1

« Delayed neutron data for the major actinides » (NEA/WPEC-6, 2002): 

https://www.oecd-nea.org/science/wpec/volume6/volume6.pdf

-      Nuclear physics 

-      Introduction to neutronics

-      General knowledge: differential equations, linear algebra, linear operators, probabilities and statistics, eigenvalue problems, Laplace and Fourier transforms.

- Bases of scientific programming

The 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.

Classes will cover:

• For the deterministic methods:
• The study of the fundamental mode and PN expressions of the Boltzmann equation
• The basic calculation scheme based on the diffusion approximation and the SPN method.
• Three 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).
• For the Monte Carlo methods:
• The integral formulation of the Boltzmann equation and its relation to the stochastic interpretation in terms of a random walk
• Sampling techniques and pseudo-random number generation
• Variance-reduction methods
• Eigenvalue problems and power iteration

The course “advanced neutronics” extends the course “introduction to neutronics”, 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.

-      Students are encouraged to participate strongly in the course via exercises integrated into the course and tutorials. Exercises to prepare at home.

-      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.

Reactor physics:

-      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.

-      Explain the following physical effects on reactivity in UOx and MOx fuel cell configurations:

-The phenomenon of resonant isotopes self-shielding.

-Temperature effects: Doppler effect and moderator effect.

-The soluble boron efficiency.

-The vacuum fraction effect in a MOx fuel configuration.

-The fuel effect depletion (burnup calculation).

Modeling: 

-      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….

-      Establish the integral-differential and integral forms of the Boltzmann equation.

-      Explain what the fundamental mode is and its importance in neutronics for core calculations.

-      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.

-      Specify which physical quantities are key for core calculations.

-      Show that the modeling of a core computation leads to solving a nonlinear problem.

-      Specify what it means to build a multi-parameter library.

-      Justify the implementation of a calculation scheme by a few appropriate orders of magnitude (calculation time, number of unknowns to calculate).

Simulation methods: 

-      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).

-      Establish the PN equations.

-      Write and solve the core calculation equations in diffusion and SPN approximations.

-      Compare the deterministic and stochastic Monte Carlo calculation approaches and justify their use. Explain their respective advantages and disadvantages, highlight their complementarity.

-      Solve on simple configurations the transport equation by the method of characteristics, the collision probability method and the Monte Carlo method.

-      Analyze the convergence of deterministic and stochastic calculation algorithms.

• Paul Reuss, Neutron Physics, Les Ulis, INSTN/EDPSciences, 2008. 
• J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, 1976.
• Alain Hébert, Applied Reactor Physics, Montréal, Presses internationales Polytechnique, 2009.
• T. J. Akai, “Applied Numerical Methods for Engineers”, 1994, J. Wiley & Sons Inc.
• llya M. Sobol, A Primer for the Monte Carlo Method, London, CRC Press, 1994.
• J. Spanier and E. M. Gelbard, Monte-Carlo Principles and Neutron Transport Problems, USA, Addison-Wesley Publishing Company, 1969.
• Neutronics, A Nuclear Energy Division Monograph, ouvrage collectif, Paris, Saclay, Les Éditions du Moniteur/CEA, 2015.

Basics Math knowledge is necessary for this course: integrals and derivatives, vectors and tensors.

Bachelor level in solid state physics and chemistry
Basics on materials science.

• Lectures (21 hours) & Exercises (6h)

a-Atomic scale process 

b- Irradiation effects on various components of today’s nuclear reactors (Generations II and III)

c- Peculiar features of fuel of today’s nuclear reactors (Generations II and III)

d- Metallic materials for innovative advanced reactors

• Lab. Works (12h)

a- Labwork at the JANNuS facilities and use of the SRIM simulation code

b- SEM and XRD labworks: Phase identification and steels microstructure identification.

Materials for PWR and innovative advanced nuclear reactors (metals and ceramics) with an emphasis on their behaviour under and after irradiation, from atomic scale processes to macroscopic properties. The aim of this course is to give an overall knowledge on the materials used in power nuclear reactors (Gen. II& III and innovative advanced reactors). The course describes the main materials used, for structural components, fuel cladding and fuel pellets. The course addresses specifically the radiation effects in materials. This course is particularly focused on the detailed process of radiation damage at the microscopic scale. At a higher scale, the radiation effects on the main components (structure and fuel elements) are detailed.

The lectures are conventional lectures but with intense interactions. During the course, quiz and short exercises are provided. Furthermore, exercises sessions are also given. During the labwork sessions, a software (SRIM) is used and several experiments are done using SEM and XRD devices.

Lemaignan C. (2010) Nuclear Materials and Irradiation Effects. In: Cacuci D.G. (eds) Handbook of Nuclear Engineering. Springer, Boston, MA

Was S. G. (2017) Fundamentals of Radiation Materials Science, Metals and Alloys, 2nd Edition, Springer, Boston, MA

Motta A. T., Olander D. R. (2017) Light Water Reactor Materials, Volume I: Fundamentals, 1st Edition, La Grange Park, Illinois : American Nuclear Society

Lemaignan C. (2004) Science des matériaux pour le nucléaire, EDP Sciences, Collection Génie Atomique

Mathematics: differential equations, linear algebra, linear operators, probability.
Basics of nuclear physics: nuclear reactions induced by neutrons, decay processes, cross-sections definitions, kinematics.

Mathematics: differential equations, linear algebra, linear operators, probability.
Quantum Mechanics, Electrodynamics.

Le cours se divise en deux grandes parties : la première présente les outils fondamentaux de la physique nucléaire, tandis que la seconde se concentre sur leurs applications à la physique des réacteurs. Dans un premier temps, les étudiants acquièrent les notions de sections efficaces, de forces fondamentales, de structure et de potentiels nucléaires, de modélisation micro et macroscopique, ainsi que de cinématique nucléaire. Ces bases permettent ensuite d’aborder l’étude des interactions entre les photons, neutrons, protons, particules alpha et électrons dans la matière. La seconde partie approfondit la compréhension des processus de décroissance radioactive, des désintégrations alpha, bêta et gamma, du comportement des neutrons à différentes énergies et du processus de fission nucléaire. Enfin, elle introduit le formalisme résonant de Breit-Wigner, essentiel à l’analyse des sections efficaces dans les phénomènes de résonance.

Ce cours, accompagné de travaux dirigés, vise à donner aux étudiants les outils conceptuels et pratiques nécessaires pour comprendre les phénomènes fondamentaux de la physique nucléaire et leur manifestation dans les systèmes macroscopiques tels que les matériaux et les réacteurs. À travers l’étude des forces nucléaires, des propriétés du noyau, des modèles de réaction et des processus de désintégration, les étudiants apprendront à analyser et résoudre des problèmes de physique subatomique. Ils seront capables de réaliser des calculs de cinématique à un et deux corps, de décrire les interactions des rayonnements avec la matière, de modéliser les processus radioactifs et de maîtriser le vocabulaire spécifique de la neutronique. Le développement de l’autonomie scientifique, de la rigueur analytique et de la clarté dans la présentation du raisonnement fait également partie intégrante des objectifs du cours.

L’enseignement alterne cours magistraux et travaux dirigés. Les séances de cours exposent les concepts théoriques essentiels et leurs fondements expérimentaux, tandis que les travaux dirigés offrent un espace de réflexion et de discussion autour des problèmes proposés une semaine à l’avance. Les étudiants y présentent leurs solutions et débattent collectivement, sous la supervision de l’enseignant, dans le but de renforcer leur compréhension, leur autonomie et leur capacité à raisonner scientifiquement.

À l’issue du cours, les étudiants seront capables de calculer des grandeurs pertinentes en physique nucléaire et en neutronique, d’appliquer les modèles de réactions et de désintégrations pour résoudre des problèmes subatomiques, et d’interpréter les résultats à l’aide du vocabulaire scientifique approprié. Ils sauront également travailler de manière autonome, mobiliser leurs connaissances dans le contexte de la physique des réacteurs et communiquer leurs analyses avec précision et rigueur.

Nuclear physics: radioactivity, emission intensity, directly and indirectly ionizing particles, beta particles, x-rays, gamma-rays, cross sections of interaction.

• Interaction of radiation with matter:
  • Interaction of photon with matter:
  •Interaction of light and heavy charge particles with matter
  •Interaction of neutrons with matter: elastic and inelastic scattering, capture, fission, transmission law.

Prerequisites for « Introduction to Safety »:
Basic knowledge on PWR (components, systems and operation).

Prerequisites for « Criticality-Safety »:
Basics Neutronics.
« Introduction to Safety » course is also a prerequisite.

Nuclear physics: radioactivity, emission intensity, directly and indirectly ionizing particles, beta particles, x-rays, gamma-rays, cross sections of interaction.

• Interaction of radiation with matter:
  • Interaction of photon with matter:
  •Interaction of light and heavy charge particles with matter
  •Interaction of neutrons with matter: elastic and inelastic scattering, capture, fission, transmission law.

Prerequisites for « Introduction to Safety »:
Basic knowledge on PWR (components, systems and operation).

Prerequisites for « Criticality-Safety »:
Basics Neutronics.
« Introduction to Safety » course is also a prerequisite.

Probability, Statistics

Basics of U chemistry. Basics of Radiation Protection. PWR functional description. Basics of system thermodynamics, of neutronics, thermal hydraulics, fuel cycle

General physics, thermodynamics, fluid mechanism and heat transfert.

No specific prerequisite. Interest for both economy and electricity supply is desirable.

Mechanics of material

Fundamentals of:
•mechanics of solids and structures,
•waves and vibrations.
Basics in numerical methods

Good level in applied mathematics (analysis, algebra, optimization)
Basic knowledge in software engineering and programming
Elasticity (3D, beams, plates and shells)
Heat conduction
Plasticity
Linear dynamics
Non-linear dynamics
Fatigue and fracture

Linear Algebra, Differential Equation

Basic knowledge in software engineering and programming

Basics Math knowledge is necessary for this course: integrals and derivatives, vectors and tensors.

Nuclear physics: radioactivity, emission intensity, directly and indirectly ionizing particles, beta particles, x-rays, gamma-rays, cross sections of interaction.

• Interaction of radiation with matter:
  • Interaction of photon with matter:
  •Interaction of light and heavy charge particles with matter
  •Interaction of neutrons with matter: elastic and inelastic scattering, capture, fission, transmission law.

Prerequisites for « Introduction to Safety »:
Basic knowledge on PWR (components, systems and operation).

Prerequisites for « Criticality-Safety »:
Basics Neutronics.
« Introduction to Safety » course is also a prerequisite.

Probability, Statistics

Basics of U chemistry. Basics of Radiation Protection. PWR functional description. Basics of system thermodynamics, of neutronics, thermal hydraulics, fuel cycle

General physics, thermodynamics, fluid mechanism and heat transfert.

No specific prerequisite. Interest for both economy and electricity supply is desirable.

General knowledge in neutronics, thermal-hydraulic, mechanics

Elementary knowledge of reliability engineering, calculus, matrix theory, probability and statistics.

Linear Algebra, Differential Equation

Basics Math knowledge is necessary for this course: integrals and derivatives, vectors and tensors.

Nuclear physics: radioactivity, emission intensity, directly and indirectly ionizing particles, beta particles, x-rays, gamma-rays, cross sections of interaction.

• Interaction of radiation with matter:
  • Interaction of photon with matter:
  •Interaction of light and heavy charge particles with matter
  •Interaction of neutrons with matter: elastic and inelastic scattering, capture, fission, transmission law.

Prerequisites for « Introduction to Safety »:
Basic knowledge on PWR (components, systems and operation).

Prerequisites for « Criticality-Safety »:
Basics Neutronics.
« Introduction to Safety » course is also a prerequisite.

Probability, Statistics

Basics of U chemistry. Basics of Radiation Protection. PWR functional description. Basics of system thermodynamics, of neutronics, thermal hydraulics, fuel cycle

General physics, thermodynamics, fluid mechanism and heat transfert.

No specific prerequisite. Interest for both economy and electricity supply is desirable.

Students should be familiar with basic concepts of nuclear physics such as: size, charge and mass of the nucleus; the binding energy in ground state nuclei; excitation energy. They should understand radioactive decays.

Students should be familiar with derivatives of common analytic function and have sufficient knowledge in mathematics to solve simple linear differential equation of the first and second order.

Pre-requisite are the fundamentals of the engineering sciences (physics, chemical engineering, mechanical engineering), and a good knowledge of the fundamentals of radioactivity (from the nature of radioactivity emissions to basic principles of radioprotection)

Pre-requisite are the fundamentals of the engineering sciences (physics, chemical engineering, mechanical engineering), and a good knowledge of the fundamentals of radioactivity (from the nature of radioactivity emissions to basic principles of radioprotection)

Nuclear physics: radioactivity, emission intensity, directly and indirectly ionizing particles, beta particles, x-rays, gamma-rays, cross sections of interaction.

• Interaction of radiation with matter:
  • Interaction of photon with matter:
  •Interaction of light and heavy charge particles with matter
  •Interaction of neutrons with matter: elastic and inelastic scattering, capture, fission, transmission law.

Prerequisites for « Introduction to Safety »:
Basic knowledge on PWR (components, systems and operation).

Prerequisites for « Criticality-Safety »:
Basics Neutronics.
« Introduction to Safety » course is also a prerequisite.

Probability, Statistics

Basics of U chemistry. Basics of Radiation Protection. PWR functional description. Basics of system thermodynamics, of neutronics, thermal hydraulics, fuel cycle

General physics, thermodynamics, fluid mechanism and heat transfert.

No specific prerequisite. Interest for both economy and electricity supply is desirable.

Students should be familiar with basic concepts of nuclear physics such as: size, charge and mass of the nucleus; the binding energy in ground state nuclei; excitation energy. They should understand radioactive decays.

Students should be familiar with derivatives of common analytic function and have sufficient knowledge in mathematics to solve simple linear differential equation of the first and second order.

Quantum chemistry, electronic structure

Solution chemistry

Solution Chemistry

Solution chemistry

Solution chemistry.

Inorganic Chemistry