Deterministic Methods in Reactor Physics

Course guarantor:

Jan Frýbort

Lecturer:

Jan Frýbort, Pavel Suk

Tutor:

Jan Frýbort, Pavel Suk

Supervisor:

Department of Nuclear Reactors

Synopsis:

Course is intended to nuclear data processing for mathematical modeling in nuclear reactor physics, to analytical and numerical solution of various deterministic methods in reactor systems, statistic methods in nuclear reactor physics and to nuclear reactor burn-up modeling.

Stress is put on practical examples, exercises and individual students? work on solving given exercises. After passing the course the attendees obtain not only theoretical knowledge, but also practical experience with various methods and approaches to modeling of neutron-physical characteristics of nuclear facilities and their application on real reactor systems.

Requirements:

Syllabus of lectures:

1. Introduction to the topic of nuclear data

Scope: 2 lectures

Lecture topics:

Introductory lecture, introduction to the topic, integration of lectures into the study and connection to other subjects, teaching objectives and introduction of the assessment system using homework. Nuclear data for mathematical modeling in nuclear reactor physics - introduction to the theory of effective cross sections, experimental measurement of effective cross sections, determination of cross sections by calculation, libraries of evaluated nuclear data (JEFF, JENDL, ENDF/B), general overview and division of libraries as data sources,

2. Nuclear data for mathematical modeling in nuclear reactor physics

Scope: 3 lectures

Lecture topics:

Working with nuclear data libraries - programs for searching and visualizing library data, especially microscopic cross sections, Internet data sources, codes for special work with nuclear data, especially data conversion from general format to formats for computational codes (emphasis on data in ACE format for MCNP and Serpent), NJOY program (basic program for conversions and modifications of cross sections). Detailed description of the issue of group nuclear data.

3. Introduction to Mathematical Modeling in Nuclear Reactor Physics

Scope: 2 lectures

Lecture topics:

Basic approaches to neutron calculations of reactor systems, analytical and numerical solutions of diffusion and transport equations, choice of physical model, importance of benchmark tests in mathematical modeling of reactor systems.

4. Deterministic methods of mathematical modeling in nuclear reactor physics: fuel assembly level

Scope: 3 lectures

Lecture topics:

Definition of computational task, setting up the nuclear data adjustment system for self-shielding, iterative scheme for determining the multiplication coefficient, calculations of variations of input conditions, determination of reactivity coefficients, calculation uncertainty resulting from uncertainties of nuclear data, analysis of the sensitivity of the result to input data, calculations of fuel assembly burnup, Bateman equation and one-group nuclear data for burnup calculations.

5. Deterministic methods of mathematical modeling in nuclear reactor physics: core level

Scope: 3 lectures

Lecture topics:

Performing homogenization and parameterization of macroscopic nuclear data, introducing a two-step computational scheme, defining a computational model, and determining the basic characteristics of the fuel charge.

Syllabus of tutorials:

Topics of the exercises:

Processing and visualization of nuclear data. NJOY program, conversion of evaluated data to ACE format, creation of group data for user-specified group boundaries, export from NJOY to high-quality PS images for publications or presentations of results.

Nuclear data and fuel assembly calculations. Creation of a deterministic 2D model of a pressurized water reactor fuel assembly, definition of material and operational characteristics, options for nuclear data (self-shielding model, anisotropy of scattering), analysis of temperature feedback, determination of the sensitivity of the multiplication coefficient to nuclear data, analysis of calculation uncertainties.

Data homogenization and calculations of cores. Methods of performing homogenization and parameterization of macroscopic nuclear data, creation of a model of the entire core, performance of calculations and evaluation of results.

Study Objective:

Detailed knowledge of various types of nuclear data and their areas of application. Orientation in deterministic modeling of fuel assemblies and nuclear reactors for static cases and burnup calculations. Ability to independently process nuclear data and understand the calculation logic for alternative deterministic calculation programs.

Study materials:

LAMARSH, John R. Introduction to nuclear reactor theory. LaGrange Park: American Nuclear Society, 2002. ISBN 0-89448-040-5.

REUSS, Paul. Neutron physics. Les Ulis Cedex: EDP Sciences, 2008. ISBN 978-2-7598-0041-4.

HOFFMAN, Joe D. Numerical methods for engineers and scientists. 2nd ed., rev. and expanded. New York: Marcel Dekker, 2001. ISBN 0-8247-0443-6.

HÉBERT, Alain. Applied reactor physics. Québec: Presses internqationales Polytechnique, 2009. ISBN 978-2-553-01436-9.

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Jaderné inženýrství - Jaderné reaktory (compulsory elective course)