Stochastic Methods in Reactor Physics

Course guarantor:

Ondřej Huml

Lecturer:

Ondřej Huml

Tutor:

Ondřej Huml

Supervisor:

Department of Nuclear Reactors

Synopsis:

The course is focused on numerical solution of neutron transport in reactor systems using stochastic Monte Carlo method. The course includes not only the theoretical basis of the Monte Carlo method (random sampling, computational geometry, interaction physics) but also practical demonstrations, exercises and individual work of students in solving model examples. In addition to theoretical knowledge, the students who complete the course will also have practical experience with different approaches to modeling the neutron-physical characteristics of nuclear facilities and their application to real reactor systems.

Requirements:

1. The student chooses an assignment that must be solved and defended in the form of an oral presentation.

2. The student must complete an online test.

A graded credit is awarded after both points are met and the grade depends on the result of the online test.

Syllabus of lectures:

1. Introductory lecture (1 lecture): introduction to the topic, incorporation of the lecture into the study and relations with other courses, course objectives, introduction to the structure of lectures and exercises, requirements for passing the subject, categorization of computational codes, differences between stochastic and deterministic codes, brief history of Monte Carlo method

2. Monte Carlo method theory (6 lectures): Monte Carlo analog and non-analog method, random variables (probability density function, cumulative density function), mean value, variance, random number generation, random sampling methods (direct inversion, rejection sampling)

3. Application of Monte Carlo method for neutron transport (6 lectures): computational geometry - principles of geometric model creation, stochastic geometry, collision physics in Monte Carlo method, neutron tracking,

computational quantities, results statistics, statistical estimates, computational modes (fixed source, criticality source - keff calculation), variance reduction methods

Syllabus of tutorials:

Practical examples from the simplest applications of Monte Carlo method (calculation of π value) in programming language C to complex models in stochastic codes (Serpent) for reactor calculations are presented. Students during the exercise create a model of the entire reactor core, gradually from the fuel rod, through the fuel assembly to the entire core. They will learn the basic concepts and rules of creating computational models in stochastic codes (Serpent). The basic processing of output data (bash, awk, Gnuplot) is also performed.

Study Objective:

detailed knowledge of mathematical modeling in nuclear reactor physics, statistic methods in nuclear reactor physics and nuclear reactor fuel burn-up modeling

orientation in the field, application of gained knowledge in other courses in the field of theoretical reactor physics

Study materials:

Haghighat A.: Monte Carlo Methods for Particle Transport, Boca Raton : CRC Press, Taylor & Francis Group, 2015, ISBN 978-1-4665-9254-4

Virius M.: Metoda Monte Carlo, ČVUT, 2012

Brown F.: Monte Carlo Techniques for Nuclear Systems - Theory Lectures., LA-UR-16-29043. LANL, 2016

Leppänen J.: Development of a New Monte Carlo Reactor Physics Code, VTT Technical Research Centre of Finland, 2007, ISBN 978-951-38-7019-5

Kalos M.H., Whitlock P.A.: Monte Carlo Methods, WILEY-VCH Verlag GmbH & Co. KgaA, Weinheim, 2008,

ISBN 978-3-527-40760-6

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: