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Engineering Online

NE 591 608 Monte Carlo Methods and Applications

3 Credit Hours

This course provides a detailed discussion over the fundamental concepts associated with the Monte Carlo (MC) method for particle/radiation transport. Students will be able to learn the fundamental and advanced topics on the application of MC to solve radiation transport problems in nuclear engineering. Applications of generalized MC techniques using the MCNP code to solve neutron, photon, and electron radiation transport problems typically encountered in reactor physics, shielding, criticality safety, and radiation dosimetry will be addressed. The students will also learn how to use the MCNP code to solve these problems. Students will improve their programming skills for Monte Carlo particle transport and statistical analysis.

Prerequisite

A basic understanding of nuclear reactor physics is highly recommended, as in NE 301 (Fundamentals of Nuclear Engineering), or an equivalent undergraduate course. Also, students in this class are expected to have a background in Probability and Statistics equivalent to ST 311 (Introduction to Statistics) and ST 371 (Introduction to Probability and Distribution Theory). Also, programming experience (e.g., Python, MATLAB) is highly recommended.

Course Objectives

Upon completion of this course, students will be able to:

  1. Analyze random variables and their relation to random numbers;
  2. Develop codes to sample random numbers using the fundamental formulation of MC;
  3. Generate random numbers using Pseudo-Random Number Generators (PRNGs) and test their randomness;
  4. Apply the fundamentals of probability and statistics to the design and interpretation of MC techniques for particle transport problems;
  5. Evaluate numerical integrals and reduce their variances using different MC approaches;
  6. Build MC models and write numerical codes to solve the fixed-source MC particle transport problem, and reduce the variance using various approaches;
  7. Apply MC in particle transport problems, such as geometry modeling, particle tracking, data, physical processes, scoring and tallying, and eigenvalue/criticality calculations;
  8. Use the MCNP v6.2 code for several representative real-world neutron transport problems, including building input decks, running the simulations, and interpreting the simulation results.
    Additionally, the graduate students completing this course (NE 570) will be able to:
  9. Implement advanced variance reduction techniques for fixed source MC particle transport, such as PDF biasing with Russian roulette, particle splitting with Russian roulette, weight-window technique, integral biasing, and hybrid method (CADIS and FW-CADIS). This will be evaluated in Homework 5.
  10. Solve more advanced radiation transport problems using the MCNP code, such as the deep penetration streaming problem with MC particle transport. This will be evaluated in computational project 6.
  11. Employ various types of advanced Monte Carlo particle biasing techniques to reduce the tally variance using a deep penetration streaming problem where students simulate gamma-ray radiation transport through a narrow streaming path from the source to a detector.
  12. Simulate an actual detector response and makes direct comparison between calculated and measured values for a benchmark calibration experiment.
  13. Build the entire 3-D radiation transport model in the MCNP code from scratch.

Course Requirements

Homework (30%, 5 assignments), Midterm Exam (25%), Computational Projects (45%, 5 assignments for NE 491 and 6 assignments for NE 591)

Course Outline

This course consists of 2 parts with 9 modules.

  • Part 1: Monte Carlo Theories for Radiation/Particle Transport
     I. Random Variables and Sampling (1 week)
  • Discrete and Continuous Random Variables
  • Random Numbers
  • Fundamental Formulation of Monte Carlo (FFMC)
  • Sampling Procedures for One-dimensional and Multi-dimensional Density Functions
    II. Random Number Generator (RNG) (1 week)
  • Random Number Generation Approaches
  • Pseudo-Random Number Generators (PRNGs)
  • Randomness Testing
    III. Fundamentals of Probability and Statistics (2.5 weeks)
  • Statistical Moments
  • Sample Statistics
  • Common Discrete and Continuous Distribution Functions
  • Limit Theorems
  • Relative Uncertainty and Confidence Levels
  • Normality Tests
    IV. Monte Carlo Integrals and Variance Reduction Techniques (1.5 weeks)
  • Numerical Integrals with Monte Carlo
  • Variance Reduction Techniques
    V. Fixed-Source Monte Carlo Particle Transport (2 weeks)
  • The Linear Boltzmann Equation (LBE)
  • MC for Simplified Particle Transport
  • Perturbation via Correlated Sampling
  • Statistical Reliability of MC Results
  • Variance Reduction for Fixed-Source Particle Transport
  • Part 2: Monte Carlo Applications with the MCNP Code
    VI. Geometry Modeling and Particle Tracking (2 weeks)
  • Generalized Geometry
  • Surfaces
  • Repeated structures geometry
  • Particle Tracking
    VII. Physics & Data in MCNP (2 weeks)
  • Source definition
  • Materials/Physics Input
  • Cross-sections
  • Scattering tables S(α; β)
    VIII. Scoring/Tallying (2 weeks)
  • Major Physical Quantities in Particle Transport
  • detector, reaction rates
  • Tallying in Steady-state System
  • Tallying in Time-dependent System
  • Variance reduction techniques in MCNP
    IX. Eigenvalue (Criticality) Monte Carlo Method (2 weeks)
  • Power Iteration for Eigenvalue Problems
  • Eigenvalue Calculation with MC
  • Derivation and Formulation of the Fission-Matrix (FM) Methodology
  • Application of the FM Method

Textbook

Haghighat, A. (2020). Monte Carlo methods for particle transport. Second Edition, ISBN 9780367188054, CRC Press.

Software Requirements

A programming tool such as Python or MATLAB.

Created 08/15/2024