# Monte Carlo Techniques for Nuclear Systems - Theory Lectures

## Abstract

These are lecture notes for a Monte Carlo class given at the University of New Mexico. The following topics are covered: course information; nuclear eng. review & MC; random numbers and sampling; computational geometry; collision physics; tallies and statistics; eigenvalue calculations I; eigenvalue calculations II; eigenvalue calculations III; variance reduction; parallel Monte Carlo; parameter studies; fission matrix and higher eigenmodes; doppler broadening; Monte Carlo depletion; HTGR modeling; coupled MC and T/H calculations; fission energy deposition. Solving particle transport problems with the Monte Carlo method is simple - just simulate the particle behavior. The devil is in the details, however. These lectures provide a balanced approach to the theory and practice of Monte Carlo simulation codes. The first lectures provide an overview of Monte Carlo simulation methods, covering the transport equation, random sampling, computational geometry, collision physics, and statistics. The next lectures focus on the state-of-the-art in Monte Carlo criticality simulations, covering the theory of eigenvalue calculations, convergence analysis, dominance ratio calculations, bias in Keff and tallies, bias in uncertainties, a case study of a realistic calculation, and Wielandt acceleration techniques. The remaining lectures cover advanced topics, including HTGR modeling and stochastic geometry, temperature dependence, fission energy deposition, depletion calculations, parallelmore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Monte Carlo Methods, Codes, and Applications Group; Univ. of New Mexico, Albuquerque, NM (United States). Nuclear Engineering Dept.

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1334102

- Report Number(s):
- LA-UR-16-29043

TRN: US1700794

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 22 GENERAL STUDIES OF NUCLEAR REACTORS; MONTE CARLO METHOD; COMPUTERIZED SIMULATION; LECTURES; NEUTRON TRANSPORT THEORY; EIGENVALUES; HTGR TYPE REACTORS; GEOMETRY; ENERGY ABSORPTION; FISSION; ENERGY LOSSES; RANDOMNESS; CRITICALITY; REVIEWS; STATISTICS; SAMPLING; DOPPLER BROADENING; REACTOR PHYSICS; COLLISIONS; M CODES; STOCHASTIC PROCESSES; TEMPERATURE DEPENDENCE; CONVERGENCE; MATRICES; SAFETY; PARALLEL PROCESSING; THERMAL HYDRAULICS; neutron transport; random sampling

### Citation Formats

```
Brown, Forrest B.
```*Monte Carlo Techniques for Nuclear Systems - Theory Lectures*. United States: N. p., 2016.
Web. doi:10.2172/1334102.

```
Brown, Forrest B.
```*Monte Carlo Techniques for Nuclear Systems - Theory Lectures*. United States. doi:10.2172/1334102.

```
Brown, Forrest B. Tue .
"Monte Carlo Techniques for Nuclear Systems - Theory Lectures". United States. doi:10.2172/1334102. https://www.osti.gov/servlets/purl/1334102.
```

```
@article{osti_1334102,
```

title = {Monte Carlo Techniques for Nuclear Systems - Theory Lectures},

author = {Brown, Forrest B.},

abstractNote = {These are lecture notes for a Monte Carlo class given at the University of New Mexico. The following topics are covered: course information; nuclear eng. review & MC; random numbers and sampling; computational geometry; collision physics; tallies and statistics; eigenvalue calculations I; eigenvalue calculations II; eigenvalue calculations III; variance reduction; parallel Monte Carlo; parameter studies; fission matrix and higher eigenmodes; doppler broadening; Monte Carlo depletion; HTGR modeling; coupled MC and T/H calculations; fission energy deposition. Solving particle transport problems with the Monte Carlo method is simple - just simulate the particle behavior. The devil is in the details, however. These lectures provide a balanced approach to the theory and practice of Monte Carlo simulation codes. The first lectures provide an overview of Monte Carlo simulation methods, covering the transport equation, random sampling, computational geometry, collision physics, and statistics. The next lectures focus on the state-of-the-art in Monte Carlo criticality simulations, covering the theory of eigenvalue calculations, convergence analysis, dominance ratio calculations, bias in Keff and tallies, bias in uncertainties, a case study of a realistic calculation, and Wielandt acceleration techniques. The remaining lectures cover advanced topics, including HTGR modeling and stochastic geometry, temperature dependence, fission energy deposition, depletion calculations, parallel calculations, and parameter studies. This portion of the class focuses on using MCNP to perform criticality calculations for reactor physics and criticality safety applications. It is an intermediate level class, intended for those with at least some familiarity with MCNP. Class examples provide hands-on experience at running the code, plotting both geometry and results, and understanding the code output. The class includes lectures & hands-on computer use for a variety of Monte Carlo calculations. Beginning MCNP users are encouraged to review LA-UR-09-00380, "Criticality Calculations with MCNP: A Primer (3nd Edition)" (available at http:// mcnp.lanl.gov under "Reference Collection") prior to the class. No Monte Carlo class can be complete without having students write their own simple Monte Carlo routines for basic random sampling, use of the random number generator, and simplified particle transport simulation.},

doi = {10.2172/1334102},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2016},

month = {11}

}