OpenMC Guide

Cross Sections

Understanding Cross Sections

Nuclear cross sections represent the probability of neutron interactions with atomic nuclei. Think of them as effective target areas - larger cross sections mean higher interaction probabilities. OpenMC uses these data to determine what happens when neutrons encounter different materials.

Cross sections vary dramatically with neutron energy and depend on the specific nuclide and reaction type. Understanding this behavior is crucial for accurate reactor modeling, which is why OpenMC uses continuous-energy data rather than simplified group averages.

Main Reaction Types

Absorption: Neutron disappears (fission, capture)
Scattering: Neutron changes direction/energy
Fission: Nucleus splits, produces new neutrons
Total: Sum of all possible interactions

Key Properties

Units: barns (10⁻²⁴ cm²)
Energy-dependent (thermal to fast)
Temperature-dependent (Doppler effect)
Isotope-specific

Nuclear Data Libraries

OpenMC requires nuclear data files that contain cross section information for all nuclides in your model. These libraries are based on evaluated nuclear data like ENDF/B-VIII.0 and are processed into HDF5 format for efficient access.

Getting Nuclear Data

python

# Download recommended nuclear data (one-time setup)
import openmc.data
openmc.data.download_endf_data(release='endfb80_hdf5')

# Downloads ENDF/B-VIII.0 data (~1.5 GB) into ~/.local/share/openmc

Using Custom Data Libraries

python

# Point to a specific cross sections file
import openmc

# Set cross sections path for all materials
openmc.config['cross_sections'] = '/path/to/cross_sections.xml'

# Or set for specific materials
materials = openmc.Materials()
materials.cross_sections = '/path/to/cross_sections.xml'

# Check what's available
print(f"Using cross sections: {openmc.config['cross_sections']}")

Data Requirements: Every nuclide in your materials must have corresponding cross section data. OpenMC will tell you if any data is missing when you run a simulation.

Temperature Effects

Cross sections change with temperature due to thermal motion of nuclei (Doppler broadening). This effect is most important for resonance reactions and significantly impacts reactor physics calculations.

Basic Temperature Handling

python

# Set material temperature
fuel = openmc.Material(name='Hot Fuel')
fuel.set_density('g/cm3', 10.4)
fuel.add_nuclide('U235', 0.045)
fuel.add_nuclide('U238', 0.955)
fuel.add_element('O', 2.0)
fuel.temperature = 900  # Kelvin

# OpenMC will interpolate cross sections to this temperature
# (if data is available at multiple temperatures)

Multiple Temperature Points

python

# Material with temperature-dependent data
hot_fuel = openmc.Material(name='Variable Temperature Fuel')
hot_fuel.set_density('g/cm3', 10.4)
hot_fuel.add_nuclide('U235', 0.045)
hot_fuel.add_nuclide('U238', 0.955)
hot_fuel.add_element('O', 2.0)

# Specify multiple temperatures for interpolation
hot_fuel.temperatures = [600, 900, 1200]  # K

# Configure simulation temperature handling
settings = openmc.Settings()
settings.temperature = {
    'method': 'interpolation',    # or 'nearest'
    'multipole': True            # Use windowed multipole data if available
}

Temperature effects are particularly important for U-238 resonance absorption and fuel Doppler feedback calculations. Proper temperature modeling can significantly impact calculated reactivity and safety parameters.

Thermal Scattering

For materials containing light nuclei (like hydrogen in water), thermal neutron scattering is affected by molecular binding. OpenMC uses S(α,β) thermal scattering data to account for these effects accurately.

python

# Water with thermal scattering (essential for accuracy)
water = openmc.Material(name='Light Water')
water.set_density('g/cm3', 1.0)
water.add_nuclide('H1', 2.0)
water.add_element('O', 1.0)
water.add_s_alpha_beta('c_H_in_H2O')    # Critical for thermal neutrons

# Graphite moderator
graphite = openmc.Material(name='Graphite')
graphite.set_density('g/cm3', 1.7)
graphite.add_element('C', 1.0)
graphite.add_s_alpha_beta('c_Graphite')

# Available thermal scattering data:
# c_H_in_H2O    - hydrogen in water
# c_Graphite    - graphite
# c_Be          - beryllium metal
# c_BeO         - beryllium oxide
# ... and others in your nuclear data library

Critical for Accuracy: Always include thermal scattering data for water, graphite, and other light-nucleus materials. Omitting this data can lead to significant errors in thermal neutron calculations.

Working with Cross Section Data

OpenMC provides tools to examine and understand cross section data programmatically. This is useful for validation, education, and understanding your simulation physics.

Basic Data Inspection

python

import openmc.data
import numpy as np
import matplotlib.pyplot as plt

# Load cross section data for a nuclide
u235_path = '/path/to/nuclear/data/U235.h5'
u235 = openmc.data.IncidentNeutron.from_hdf5(u235_path)

# Pick one of the available temperature evaluations (K)
temp = sorted(u235.temperatures)[0]
u235_data = u235[temp]

# Examine available reactions
print("Available reactions for U-235:")
for mt, rxn in u235.reactions.items():
    print(f"  MT {mt}: {rxn}")

# Plot total cross section vs energy
energies = np.logspace(-2, 7, 1000)  # 0.01 eV to 10 MeV
total_xs = u235_data.xs['total'](energies)

plt.figure(figsize=(10, 6))
plt.loglog(energies, total_xs, 'b-', linewidth=2)
plt.xlabel('Energy (eV)')
plt.ylabel('Cross Section (barns)')
plt.title('U-235 Total Cross Section')
plt.grid(True, which='both', alpha=0.3)
plt.show()

# Check cross section at specific energy
thermal_energy = 0.0253  # eV (thermal)
fast_energy = 1e6       # eV (1 MeV)

print(f"U-235 total XS at thermal: {u235_data.xs['total'](thermal_energy):.1f} barns")
print(f"U-235 total XS at 1 MeV:   {u235_data.xs['total'](fast_energy):.1f} barns")

Understanding Cross Section Behavior

python

# Compare different nuclides
u235 = openmc.data.IncidentNeutron.from_hdf5('/path/to/U235.h5')
u238 = openmc.data.IncidentNeutron.from_hdf5('/path/to/U238.h5')

energies = np.logspace(-2, 7, 1000)

# Use the coldest temperature evaluation for each nuclide
u235_data = u235[sorted(u235.temperatures)[0]]
u238_data = u238[sorted(u238.temperatures)[0]]

plt.figure(figsize=(12, 8))

# Fission cross sections
plt.subplot(2, 2, 1)
u235_fission = u235_data.xs['fission'](energies)
plt.loglog(energies, u235_fission, 'r-', label='U-235')
plt.xlabel('Energy (eV)')
plt.ylabel('Fission XS (barns)')
plt.title('Fission Cross Sections')
plt.legend()
plt.grid(True)

# Absorption cross sections
plt.subplot(2, 2, 2)
u235_abs = u235_data.xs['absorption'](energies)
u238_abs = u238_data.xs['absorption'](energies)
plt.loglog(energies, u235_abs, 'r-', label='U-235')
plt.loglog(energies, u238_abs, 'b-', label='U-238')
plt.xlabel('Energy (eV)')
plt.ylabel('Absorption XS (barns)')
plt.title('Absorption Cross Sections')
plt.legend()
plt.grid(True)

plt.tight_layout()
plt.show()

# This helps explain why U-235 is fissile and U-238 has strong resonances

Practical Tips

Here are essential tips for working effectively with cross sections in OpenMC:

Data Management

Start Simple: Use the default ENDF/B-VIII.0 data for most applications
Check Coverage: Ensure your data library includes all nuclides in your materials
Temperature Consistency: Use appropriate temperatures for your operating conditions
Thermal Scattering: Always include S(α,β) data for light-nucleus materials

Common Issues

python

# Check for missing cross section data
try:
    model = openmc.Model(geometry, materials, settings)
    model.run()
except Exception as e:
    if "does not contain cross sections" in str(e):
        print("Missing nuclear data - check your cross_sections.xml")
        print("Missing nuclide:", str(e).split("'")[1])
    else:
        raise e

# Verify thermal scattering is included
for material in materials:
    if 'H1' in material.nuclides:
        if not material.sab:
            print(f"Warning: {material.name} contains H1 but no S(a,b) data")
            
# Check temperature coverage
print("Material temperatures:")
for material in materials:
    if material.temperature:
        print(f"  {material.name}: {material.temperature} K")

Cross sections are the foundation of accurate neutron transport calculations. Understanding their behavior and proper usage is essential for reliable reactor physics analysis with OpenMC.

OpenMC Guide

Cross Sections

Understanding Cross Sections

Main Reaction Types

Key Properties

Nuclear Data Libraries

Getting Nuclear Data

Using Custom Data Libraries

Temperature Effects

Basic Temperature Handling

Multiple Temperature Points

Thermal Scattering

Working with Cross Section Data

Basic Data Inspection

Understanding Cross Section Behavior

Practical Tips

Data Management

Common Issues

Related Topics

Prerequisite

Materials

Next Steps

Cell Creation

Related

OpenMC Guide Overview

Monte Carlo Basics