OpenMC Documentation

OpenMC provides a rich Python API designed for programmatic pre-processing (generating input files) and post-processing (analyzing results). Using the Python API allows you to leverage the Python ecosystem (like NumPy) and provides high-level scientific capabilities that are not available in the standalone C++ version.

Key capabilities provided by the API include:

• Geometry & Modeling: Defining dimensions with variables, convenience functions for complex shapes (e.g., hexagonal regions), and plotting individual universes during geometry creation.
• Nuclear Data: A fully-featured interface via openmc.data and automated multi-group cross section generation via openmc.mgxs.
• Physics & Simulation: Depletion capabilities via openmc.deplete, $k_{\text{eff}}$ search via openmc.search_for_keff, and random sphere packing for TRISO particle locations via openmc.model.pack_spheres.
• Material Management: Creating materials based on natural elements or specific uranium enrichment levels.

Version 0.5.4 introduced several functional improvements:

• Particle Tracking: Ability to write particle track files, which also allows for more graceful handling of lost particles.
• Data Management: A new script is available to download ACE data from NNDC. Additionally, cross_sections.xml now supports mixed ASCII/binary formats.
• Randomness: Support for multiple random number generator streams.
• Utilities: The mesh tally plotting utility has been converted to use Tkinter instead of PyQt.
• Source Handling: Source sites located outside the geometry are now resampled, and expanded options for writing the source bank are available. The ability to use a source file as a starting source has also been re-enabled.
• Performance: Avoids $S(\alpha, \beta)$ recalculation when the same nuclide and $S(\alpha, \beta)$ table are accessed.
• Backend: The XML-Fortran backend has been replaced by FoX XML.

OpenMC executes Monte Carlo simulations by tracking one particle at a time per program instance. The execution lifecycle is divided into three main phases: Initialization, Transport Simulation, and Finalization.

1. Initialization

Before tracking begins, OpenMC performs the following:

• Reads input files to build data structures for geometry, materials, and tallies.
• Initializes the pseudorandom number generator.
• Loads continuous-energy or multi-group cross section data.
• Initializes special energy grid treatments (e.g., union energy grids or lethargy bins) if specified.
• For multi-group problems, combines nuclide cross sections into material-specific data.
• Samples source sites (coordinates, direction, and energy) for fixed source or eigenvalue problems.

2. Transport Simulation (Particle Life Cycle)

For each particle, the following loop occurs:

1. Initialization: Particle properties are set from a sampled source site.
2. Location: The current cell is determined based on coordinates.
3. Cross Sections: Energy-dependent cross sections for the current material are determined.
4. Boundary Check: The distance to the nearest cell boundary is calculated.
5. Collision Sampling: The distance to the next collision is sampled using the total material cross section $\Sigma_t$.
6. Movement:
   • If the boundary is closer than the collision, the particle moves to the boundary and the process repeats from step 2.
   • If the collision is closer, the particle undergoes a collision.
7. Nuclide Selection: In continuous-energy simulations, a specific nuclide is sampled based on total cross sections. (In multi-group, this is pre-combined).
8. Reaction Sampling: A specific reaction is sampled based on microscopic (or material-specific multi-group) cross sections.
9. Reaction Outcome:
   • Scattering (Elastic/Inelastic): Outgoing energy and angle are sampled. In continuous-energy, $(n,xn)$ reactions create secondary particles added to a bank. In multi-group, particle weight is increased instead. The particle continues from step 3.
   • Absorption/Fission: The particle dies. If fission occurs, fission sites are stored in a fission bank.

3. Finalization

After all particles are processed:

• Tallies are processed to calculate sample means and variances.
• Results and (optionally) source files are written to disk.
• Memory is freed.

Variance reduction techniques in OpenMC are used to combat high attenuation between source and detector regions, which otherwise leads to high uncertainties in low-flux areas. OpenMC provides three primary strategies:

1. Weight Windows (MAGIC method): An iterative technique using spatial flux information from a normal Monte Carlo solve to generate weight windows for subsequent iterations. It uses a mesh to split particles in low-flux regions and terminate them in high-flux regions.
2. Weight Windows (FW-CADIS method): A more numerically efficient method that generates weight windows based on spatial adjoint flux information. It uses an internal random ray multigroup transport solver to generate adjoint flux maps.
3. Source Biasing: Modifies the sampling of the external source distribution (space, angle, energy, or time) to preferentially track particles toward regions of interest, applying a weight adjustment to maintain statistical fairness.

Key Distinction: Source biasing changes how particles are born, while weight windows apply population control (splitting and Russian roulette) during transport. For problems with high attenuation in optically thick regions, weight windows are generally more effective.

Random Ray is a stochastic transport method in OpenMC that is closely related to the deterministic Method of Characteristics (MOC). Unlike Monte Carlo (MC), where each ray represents a single neutron, in Random Ray, each ray represents a characteristic line through the simulation geometry.

Key characteristics include:

• Analytical Solution: The transport equation is written as an ordinary differential equation along the ray and solved analytically (using a multigroup approach for energy discretization).
• Spatial/Angular Distribution: Rays are selected to explore the simulation problem with a statistically equal distribution in space and angle, meaning they are not affected by the material characteristics of the problem.
• Variance: Random ray provides approximately even variance throughout the entire global simulation domain, unlike Monte Carlo which can struggle with numerical efficiency in low-flux regions.