Materials and Transport Data#

A mcdc.Material describes a physical medium. A nuclide or element composition establishes its native transport data. Materials can also carry particle-specific data that augments native interaction data, for example with semi-empirical information, or supports specialized and reduced transport treatments.

Native Composition and Data#

In MC/DC, native refers to data-library-backed transport physics derived from a material’s nuclide or element composition. The composition identifies the physical constituents whose library records provide the interaction data.

Define a native material with either nuclide or element atomic densities in atoms/(barn cm). Material temperature is specified in K:

fuel = mcdc.Material(
    name="UO2",
    nuclide_composition={
        "U235": 5.0e-4,
        "U238": 2.2e-2,
        "O16": 4.5e-2,
    },
    temperature=293.6,
)

Particle-specific Transport Data#

Particle-specific transport data is attached to the material that uses it. The transport physics determines when and how each dataset contributes to a particle interaction.

Neutron Multigroup Transport#

Neutron multigroup transport represents neutron energy with discrete groups and describes interactions using groupwise macroscopic data. It is widely used in general transport pedagogy and in nuclear engineering applications. mcdc.Material.multigroup() creates a material with mcdc.NeutronMultigroupData, which holds the cross sections, group speeds, production spectra, and delayed-precursor data. Macroscopic cross sections use cm-1, group speeds use cm/s, and precursor decay rates use s-1:

moderator = mcdc.Material.multigroup(
    name="Moderator",
    capture=np.array([0.1, 0.2]),
    scatter=np.array([
        [0.7, 0.1],
        [0.2, 0.5],
    ]),
    energy_grid=np.array([1.0e-5, 1.0, 20.0e6]),
)

Multigroup Energy Grids and Representation#

An explicit energy_grid contains G + 1 physical energy boundaries in eV. Group g covers energy_grid[g] <= E < energy_grid[g + 1]. The grid both maps continuous energy to a group and bounds continuous energy reconstructed from a group.

The grid may be omitted for standard multigroup transport when every material omits energy_grid.

For lower and upper group boundaries \(E_g\) and \(E_{g+1}\), the energy-representation policies are:

  • "midpoint": use the arithmetic midpoint, \(E=(E_g+E_{g+1})/2\);

  • "log_midpoint": use the geometric midpoint, \(E=\sqrt{E_g E_{g+1}}\);

  • "uniform": sample \(E\) uniformly between the two boundaries; and

  • "log_uniform": sample \(\log E\) uniformly between their logarithms, equivalently \(E=E_g(E_{g+1}/E_g)^\xi\) for \(\xi\sim\mathcal{U}(0,1)\).

The policies apply when transport reconstructs physical energy from a group, including after a hybrid multigroup interaction. The logarithmic policies require strictly positive energy boundaries. Midpoint policies reconstruct one deterministic value per group, while uniform policies sample a new value when continuous energy is reconstructed. Standard multigroup transport retains the group coordinate instead and does not apply a physical-energy reconstruction policy during particle transport.

MC/DC determines the neutron multigroup transport organization when the simulation is compiled. Standard neutron multigroup transport applies when every material uses neutron multigroup data without native composition and all materials either omit energy_grid or share the same explicit grid. In standard multigroup transport, particle energy uses a dimensionless group coordinate: energy 0.0 represents group 0, energy 1.0 represents group 1, and so forth.

Transport is hybrid when native composition data is present or multigroup materials use different grids. Every multigroup dataset participating in hybrid transport requires an explicit physical energy grid because continuous energy selects the applicable material-local group. In hybrid transport, particle energy remains physical energy in eV, and energy_grid maps it to a material-local group. The material’s energy_representation policy maps an outgoing group back to physical energy. If a particle lies outside that grid, MC/DC uses the material’s native neutron data when present; without a native composition, the material has zero interaction cross section at that energy.

Combining Native and Multigroup Data#

Construct mcdc.NeutronMultigroupData directly when attaching it to a material with a native composition:

hybrid_fuel = mcdc.Material(
    name="Hybrid fuel",
    nuclide_composition={"U235": 5.0e-4, "U238": 2.2e-2},
    neutron_multigroup=mcdc.NeutronMultigroupData(
        capture=np.array([0.10]),
        fission=np.array([0.20]),
        nu_p=np.array([2.50]),
        energy_grid=np.array([1.0e-5, 20.0e6]),
    ),
)

The explicit energy grid is required whenever a native composition and neutron multigroup data are combined. Its bounds identify the energy interval where the multigroup transport model is available.

See Standard Neutron Multigroup Sources for the corresponding source-energy convention.