Continuous Energy#

MC/DC supports continuous energy (CE) neutron transport using pointwise nuclear data libraries. In CE mode, cross sections are represented as energy-dependent tabulated data rather than multigroup averages, enabling higher-fidelity simulations.

Data Libraries#

CE data is loaded from HDF5 files for each nuclide at a specified temperature. The environment variable MCDC_LIB must point to the library directory. Each nuclide file (e.g., U235-293.6K.h5) contains:

  • An energy grid (converted from MeV to eV on load),

  • Pointwise total, elastic, capture, inelastic, and fission cross sections,

  • Angular and energy distributions for secondary particles,

  • Prompt and delayed fission neutron multiplicities and spectra,

  • Delayed neutron precursor data (fractions, decay constants, and energy spectra).

Supported temperature points are 0.1, 233.15, 273.15, 293.6, 600.0, 900.0, 1200.0, and 2500.0 K. MC/DC selects the nearest available temperature for each nuclide.

Cross Section Evaluation#

Microscopic cross sections are evaluated by binary search on the energy grid followed by linear interpolation between bounding points. Macroscopic cross sections for a material are computed as the sum over constituent nuclides:

\[\Sigma(E) = \sum_i N_i \, \sigma_i(E)\]

where \(N_i\) is the atom density and \(\sigma_i(E)\) is the microscopic cross section of nuclide \(i\) at energy \(E\).

Collision Physics#

CE collision processing implements full center-of-mass (COM) kinematics:

  • Elastic scattering (MT-2): Thermal motion of the target nucleus is sampled from a Maxwellian distribution parameterized by \(\beta = \sqrt{A m / (2 k_B T)}\), where \(A\) is the mass ratio. Rejection sampling is used for the relative speed.

  • Inelastic scattering: Multiple MT channels with tabulated energy-angle distributions (Kalbach-Mann, evaporation, Maxwellian, N-body, level scattering).

  • Capture: Particle is absorbed; implicit capture can be enabled as a variance reduction technique.

  • Fission: Secondary particles are emitted using \(\nu(E)/k_\text{eff}\) scaling, with prompt and delayed components sampled separately.

Relativistic particle speed is computed as:

\[v = c \, \frac{\sqrt{E(E + 2m_n c^2)}}{E + m_n c^2}\]

Generating a Data Library from ACE Files#

MC/DC ships with a conversion tool in tools/data_library_generator/neutron/ that reads standard ACE-format nuclear data files and writes them into MC/DC’s per-nuclide HDF5 format. This is the primary path for creating CE libraries.

Prerequisites:

pip install ACEtk h5py numpy tqdm

You also need a set of ACE files from a source such as NJOY or an ENDF/B distribution.

Environment variables:

Variable

Description

MCDC_ACELIB

Path to the directory containing your ACE files.

MCDC_LIB

Path to the output directory where MC/DC HDF5 files will be written.

Running the generator:

export MCDC_ACELIB=/path/to/ace/files
export MCDC_LIB=/path/to/mcdc/library

cd tools/data_library_generator/neutron
python generate.py

By default, the tool converts only nuclides without a corresponding HDF5 file in $MCDC_LIB. Use --rewrite to regenerate all files or --verbose for detailed per-nuclide output:

python generate.py --rewrite --verbose

The generator processes each ACE file as follows:

  1. Reads the ACE header to determine nuclide identity and temperature.

  2. Extracts the principal cross-section block and writes HDF5 datasets grouped by reaction type.

  3. Extracts angular and energy distributions for each reaction channel.

  4. Extracts prompt and delayed \(\nu(E)\) data, precursor fractions, decay constants, and energy spectra for fissionable nuclides.

The resulting HDF5 file, such as U235-293.6K.h5, is ready for use with mcdc.Material().

Using CE Materials in an Input Deck#

Once the library is generated, set the MCDC_LIB environment variable and define materials with mcdc.Material():

import mcdc

# Define nuclides with atom densities (atoms/barn-cm)
fuel = mcdc.Material(
    nuclides=["U235", "U238", "O16"],
    density=[5.58e-4, 2.24e-2, 4.583e-2],
    temperature=293.6,
)

MC/DC will automatically look up the matching HDF5 file in $MCDC_LIB (e.g., U235-293.6K.h5) and load the pointwise cross sections.

Note on External Data Sources#

MC/DC’s internal HDF5 format is independent of the original data source. The shipped tool converts ACE data, but users can implement converters for other formats by following the same HDF5 schema used by generate.py.

The key HDF5 structure expected by MC/DC is:

<Nuclide>-<Temperature>K.h5
├── nuclide_name              (string)
├── temperature               (float, K)
├── atomic_weight_ratio       (float)
├── fissionable               (bool)
└── neutron_reactions/
    ├── xs_energy_grid         (1-D array, MeV)
    ├── elastic_scattering/
    │   └── MT-002/
    │       ├── xs             (1-D array, barns)
    │       ├── cosine/        (angular distribution)
    │       └── energy/        (energy distribution)
    ├── capture/
    │   └── MT-102/ ...
    ├── inelastic_scattering/
    │   └── MT-051/ ...
    └── fission/
        └── MT-018/
            ├── xs
            ├── cosine/
            ├── energy/
            ├── nu_total/
            ├── nu_prompt/
            ├── nu_delayed/
            └── delayed_neutron/ ...

A converter from OpenMC’s IncidentNeutron HDF5 format to this schema is a planned future addition. Contributions are welcome through Issue #333.