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Ways to generate multigroup cross sections

Generate and compare OpenMC multigroup cross sections (MGXS) with material_wise, stochastic_slab, and infinite_medium, as preparation for a later Pac-Man FW-CADIS simulation.

Ways to generate multigroup cross sections
├── 1. Build the continuous-energy model
├── 2. Generate MGXS libraries
├── 3. Read the MGXS libraries
├── 4. Total and absorption cross sections
├── 5. P0 scattering matrices
├── 6. Sanity checks
├── 7. (n,tot) in concrete
├── 8. Reproducibility and convergence
│   └── 8.1 Independent-seed reproducibility at 20,000 particles per batch
├── 9. Additional bootstrap
└── 10. Reuse these libraries in FW-CADIS

This notebook generates MGXS libraries for later use in FW-CADIS and compares their cross sections, computation times, statistical stability, independent-seed reproducibility, and additional bootstrapping.

Of the three openmc.Model.convert_to_multigroup() methods:

  • material_wise runs continuous-energy transport in the original Pac-Man geometry; its flux-weighted cross sections therefore depend on that geometry and source. The geometry comes from ../3_geometry/pacman_geometry_csg.xml.

  • stochastic_slab is independent of the simulation geometry, as it uses a surrogate randomized slab geometry.

  • infinite_medium is independent of the simulation geometry, as it uses independent homogeneous-medium calculations.

The latter two still depend on the material definitions, energy-group structure, and calculation inputs. The imported Pac-Man geometry also provides the spatial model for the additional bootstrapping demonstration.

1. Build the continuous-energy model

import copy
import json
import os
import sys
import time
from pathlib import Path

import matplotlib.pyplot as plt
import numpy as np
import openmc
import pandas as pd

from openmc_workbench_config import DATA_ROOT

# Make the OpenMC executable discoverable from the Jupyter kernel.
os.environ['PATH'] = (
    str(Path(sys.executable).parent) + os.pathsep + os.environ['PATH']
)

openmc.config['cross_sections'] = (
    DATA_ROOT / 'endf-b8.1' / 'cross_sections.xml'
)

GEOMETRY_FILE = Path('../3_geometry/pacman_geometry_csg.xml')
PNNL_FILE = DATA_ROOT / 'pnnl_v2.json'
OUTPUT_DIR = Path('1_1_ways_to_convert_to_multigroup_outputs').resolve()
MGXS_DIR = OUTPUT_DIR / 'mgxs'
MGXS_DIR.mkdir(parents=True, exist_ok=True)

# Change to True when ready to run.
GENERATE_MGXS = False
RUN_CONVERGENCE = False
GENERATE_BOOTSTRAP_WINDOWS = False
GENERATE_BOOTSTRAP_MGXS = False
with PNNL_FILE.open() as file:
    pnnl = json.load(file)

materials_by_name = {}
for name in ('Concrete, Ordinary (NIST)', 'Air (dry, near sea level)'):
    entry = pnnl['materials'][name]
    mat = openmc.Material(name=name)
    for element, fraction in entry['elements'].items():
        mat.add_element(element, fraction, percent_type=pnnl['percent_type'])
    mat.set_density(pnnl['density_units'], entry['density'])
    materials_by_name[name] = mat

concrete = materials_by_name['Concrete, Ordinary (NIST)']
air = materials_by_name['Air (dry, near sea level)']
materials = openmc.Materials([concrete, air])

geometry = openmc.Geometry.from_xml(
    path=GEOMETRY_FILE,
    materials=openmc.Materials(),
)
cells = {cell.name: cell for cell in geometry.get_all_cells().values()}
cells['WALL_CSG'].fill = concrete
cells['OPEN_CSG'].fill = air
cells['LOWER_SLAB'].fill = concrete
cells['UPPER_SLAB'].fill = concrete
settings = openmc.Settings()
settings.run_mode = 'fixed source'
settings.batches = 50
settings.particles = 20_000
settings.source = openmc.IndependentSource(
    space=openmc.stats.Point((0.0, 0.0, 0.0)),
    angle=openmc.stats.Isotropic(),
    energy=openmc.stats.Discrete([2.5e6], [1.0]),
    particle='neutron',
)

# Mesh from the completed bootstrap run, not a MGXS energy discretization.
MESH_DIMENSION = (28, 31, 6)
LOWER_LEFT = (-1400.0, -1550.0, -300.0)
UPPER_RIGHT = (1400.0, 1550.0, 300.0)

flux_mesh = openmc.RegularMesh(name='Global flux monitor')
flux_mesh.dimension = MESH_DIMENSION
flux_mesh.lower_left = LOWER_LEFT
flux_mesh.upper_right = UPPER_RIGHT

flux_tally = openmc.Tally(name='global_flux')
flux_tally.filters = [openmc.MeshFilter(flux_mesh)]
flux_tally.scores = ['flux']

ce_model = openmc.Model(
    geometry=geometry,
    materials=materials,
    settings=settings,
    tallies=openmc.Tallies([flux_tally]),
)

2. Generate MGXS libraries

Each method uses a separate copy of the CE model. The baseline MGXS libraries use 20,000 particles per batch and an explicit random seed so they can be compared with independently seeded runs in Section 8.

The generated HDF5 files are saved under 1_1_ways_to_convert_to_multigroup_outputs/mgxs/ for reuse by the later FW-CADIS notebook.

%%time
methods = ['material_wise', 'stochastic_slab', 'infinite_medium']
BASE_PARTICLES = 20_000
BASE_SEED = 1
timing_rows = []

if GENERATE_MGXS:
    for method in methods:
        rr_model = copy.deepcopy(ce_model)
        rr_model.tallies = openmc.Tallies()

        start = time.perf_counter()
        rr_model.convert_to_multigroup(
            method=method,
            mgxs_path=MGXS_DIR / f'mgxs_{method}.h5',
            overwrite_mgxs_library=True,
            particles=BASE_PARTICLES,
            seed=BASE_SEED,
        )
        timing_rows.append({
            'Method': method,
            'Particles per batch': BASE_PARTICLES,
            'Seed': BASE_SEED,
            'Wall time (s)': time.perf_counter() - start,
        })

if timing_rows:
    display(pd.DataFrame(timing_rows))
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=59.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=3.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=12.
  warn(msg, IDWarning)

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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:35:08
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
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 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.6360e+00 seconds
   Reading cross sections          = 2.5364e+00 seconds
 Total time in simulation          = 9.3349e+01 seconds
   Time in transport only          = 9.2713e+01 seconds
   Time in active batches          = 9.3349e+01 seconds
   Time accumulating tallies       = 5.8851e-01 seconds
   Time writing statepoints        = 8.4184e-03 seconds
 Total time for finalization       = 1.9175e-05 seconds
 Total time elapsed                = 9.5992e+01 seconds
 Calculation Rate (active)         = 42850 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=117.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=61.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=70.
  warn(msg, IDWarning)

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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:36:46
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.6418e+00 seconds
   Reading cross sections          = 2.5553e+00 seconds
 Total time in simulation          = 1.7286e+02 seconds
   Time in transport only          = 1.7228e+02 seconds
   Time in active batches          = 1.7286e+02 seconds
   Time accumulating tallies       = 5.0967e-01 seconds
   Time writing statepoints        = 1.0005e-02 seconds
 Total time for finalization       = 2.1692e-05 seconds
 Total time elapsed                = 1.7551e+02 seconds
 Calculation Rate (active)         = 23140.1 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=118.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=119.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=128.
  warn(msg, IDWarning)

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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:39:44
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.5028e+00 seconds
   Reading cross sections          = 2.4166e+00 seconds
 Total time in simulation          = 4.8557e+01 seconds
   Time in transport only          = 4.8387e+01 seconds
   Time in active batches          = 4.8557e+01 seconds
   Time accumulating tallies       = 1.4007e-01 seconds
   Time writing statepoints        = 9.4285e-03 seconds
 Total time for finalization       = 2.0904e-05 seconds
 Total time elapsed                = 5.1066e+01 seconds
 Calculation Rate (active)         = 41188.3 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=138.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=139.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=148.
  warn(msg, IDWarning)

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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:40:37
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for C13

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 4.1302e-01 seconds
   Reading cross sections          = 3.9210e-01 seconds
 Total time in simulation          = 6.6675e+01 seconds
   Time in transport only          = 6.6542e+01 seconds
   Time in active batches          = 6.6675e+01 seconds
   Time accumulating tallies       = 1.0675e-01 seconds
   Time writing statepoints        = 8.0764e-03 seconds
 Total time for finalization       = 1.7972e-05 seconds
 Total time elapsed                = 6.7089e+01 seconds
 Calculation Rate (active)         = 29996.4 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000
Loading...
CPU times: user 1.26 s, sys: 350 ms, total: 1.61 s
Wall time: 6min 39s

3. Read the MGXS libraries

OpenMC numbers the energy groups from high to low energy, whereas HDF5 stores the group boundaries in ascending order.

mglib, mgxs = {}, {}

for method in methods:
    mglib[method] = openmc.MGXSLibrary.from_hdf5(
        MGXS_DIR / f'mgxs_{method}.h5'
    )
    mgxs[method] = {xs.name: xs for xs in mglib[method].xsdatas}

ref_method = methods[0]
edges = mglib[ref_method].energy_groups.group_edges

for method in methods[1:]:
    assert np.array_equal(mglib[method].energy_groups.group_edges, edges)
    assert mgxs[method].keys() == mgxs[ref_method].keys()

df_groups = pd.DataFrame({
    'Group (high to low)': np.arange(1, len(edges)),
    'Lower energy (eV)': edges[:-1][::-1],
    'Upper energy (eV)': edges[1:][::-1],
})
display(df_groups)
Loading...

4. Total and absorption cross sections

Compare each material and energy group with material_wise as the reference. The percentage difference is undefined when the reference value is zero.

rows = []

for material in mgxs[ref_method]:
    for reaction in ('total', 'absorption'):
        row_values = {
            method: getattr(mgxs[method][material], reaction)[0]
            for method in methods
        }
        reference = row_values[ref_method]

        for g in range(len(reference)):
            row = {
                'Material': material,
                'Reaction': reaction,
                'Group': g + 1,
            }
            for method in methods:
                row[method] = row_values[method][g]
            for method in methods[1:]:
                row[f'{method} difference (%)'] = (
                    100 * (row_values[method][g] - reference[g]) / reference[g]
                    if reference[g] != 0 else np.nan
                )
            rows.append(row)

df_xs = pd.DataFrame(rows)
display(df_xs)
Loading...

5. P0 scattering matrices

The first [0] selects the temperature dataset; [:, :, 0] selects the isotropic scattering moment. Rows correspond to incoming groups and columns to outgoing groups.

rows = []

for material in mgxs[ref_method]:
    scatter = {
        method: mgxs[method][material].scatter_matrix[0][:, :, 0]
        for method in methods
    }
    for g_in in range(scatter[ref_method].shape[0]):
        for g_out in range(scatter[ref_method].shape[1]):
            reference = scatter[ref_method][g_in, g_out]
            row = {
                'Material': material,
                'Incoming group': g_in + 1,
                'Outgoing group': g_out + 1,
            }
            for method in methods:
                row[method] = scatter[method][g_in, g_out]
            for method in methods[1:]:
                value = scatter[method][g_in, g_out]
                row[f'{method} difference (%)'] = (
                    100 * (value - reference) / reference
                    if reference != 0 else np.nan
                )
            rows.append(row)

df_scatter = pd.DataFrame(rows)
display(df_scatter)
Loading...

6. Sanity checks

rows = []

for method in methods:
    for material, xs in mgxs[method].items():
        total = xs.total[0]
        absorption = xs.absorption[0]
        scatter = xs.scatter_matrix[0]

        rows.append({
            'Method': method,
            'Material': material,
            'Groups': len(total),
            'Scattering shape': str(scatter.shape),
            'All finite': (
                np.isfinite(total).all()
                and np.isfinite(absorption).all()
                and np.isfinite(scatter).all()
            ),
            'Nonfinite total': (~np.isfinite(total)).sum(),
            'Nonfinite absorption': (~np.isfinite(absorption)).sum(),
            'Nonfinite scattering': (~np.isfinite(scatter)).sum(),
            'Negative total': (total < 0).sum(),
            'Negative absorption': (absorption < 0).sum(),
            'Negative P0 scattering': (scatter[:, :, 0] < 0).sum(),
            'Zero total': (total == 0).sum(),
            'Zero absorption': (absorption == 0).sum(),
        })

df_diagnostics = pd.DataFrame(rows)
display(df_diagnostics)
Loading...

7. (n,tot) in concrete

concrete_name = next(
    name for name in mgxs[ref_method] if 'Concrete' in name
)
# MGXS dataset names are normalized; CE material names are not.
concrete = next(
    mat for mat in ce_model.geometry.get_all_materials().values()
    if 'concrete' in mat.name.lower()
)
reference = mgxs[ref_method][concrete_name].total[0][::-1]

fig, (ax, ax_diff) = plt.subplots(
    2, 1, figsize=(9, 7), sharex=True,
    layout='constrained', height_ratios=[2, 1],
)

# CE cross sections are computed directly from the selected ENDF/B-VIII.1 data.
openmc.plot_xs(
    {concrete: ['total']},
    axis=ax,
    temperature=294.0,
    ce_cross_sections=str(openmc.config['cross_sections']),
)
ax.lines[-1].set(
    label='ENDF/B-VIII.1 (CE)', color='0.5', linewidth=1,
)

for method in methods:
    values = mgxs[method][concrete_name].total[0][::-1]
    ax.stairs(values, edges, label=method, linewidth=2)

    if method != ref_method:
        ax_diff.stairs(
            100 * (values - reference) / reference,
            edges,
            label=method,
            linewidth=2,
        )

ax.set(
    ylabel=r'$\Sigma_t$ (cm$^{-1}$)',
    title='Ordinary concrete — neutron total cross section',
)
ax.set_yscale('log')
ax.legend()

ax_diff.axhline(0, color='0.5', linewidth=1)
ax_diff.set(
    xlabel='Neutron energy (eV)',
    ylabel='MGXS difference (%)',
)
ax_diff.legend()
ax_diff.set_xscale('symlog', linthresh=0.625)
ax_diff.set_xlim(edges[0], edges[-1])
ax_diff.set_xticks([0, 1, 1e2, 1e4, 1e6])
plt.show()
<Figure size 900x700 with 2 Axes>

8. Reproducibility and convergence

Generate independent MGXS libraries with increasing numbers of particles per batch and different random seeds. The 20,000-particle convergence run is an independent redo of the original 20,000-particle calculation, not a restart.

First, compare successive particle levels (20,000 → 40,000 → 80,000) as an indication of statistical stability. Then compare the two independent 20,000-particle results to examine run-to-run reproducibility at fixed statistics.

%%time
CONVERGENCE_METHODS = methods
CONVERGENCE_PARTICLES = [20_000, 40_000, 80_000]
CONVERGENCE_DIR = MGXS_DIR / 'convergence'
CONVERGENCE_DIR.mkdir(parents=True, exist_ok=True)

if RUN_CONVERGENCE:
    for method_index, method in enumerate(CONVERGENCE_METHODS):
        for level_index, particles in enumerate(CONVERGENCE_PARTICLES):
            path = CONVERGENCE_DIR / f'mgxs_{method}_{particles}.h5'
            model = copy.deepcopy(ce_model)
            model.tallies = openmc.Tallies()
            seed = 10_001 + 1000 * method_index + 137 * level_index

            model.convert_to_multigroup(
                method=method,
                mgxs_path=path,
                overwrite_mgxs_library=True,
                particles=particles,
                seed=seed,
            )
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=215.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=159.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=168.
  warn(msg, IDWarning)

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                  ####################     %%%%%%%%%%%%%%%%%
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                       ############     %%%%%%%%%%%%%%%
                          ########     %%%%%%%%%%%%%%
                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:42:04
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Simulating batch 200
 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.5192e+00 seconds
   Reading cross sections          = 2.4344e+00 seconds
 Total time in simulation          = 1.3358e+02 seconds
   Time in transport only          = 1.3306e+02 seconds
   Time in active batches          = 1.3358e+02 seconds
   Time accumulating tallies       = 4.6858e-01 seconds
   Time writing statepoints        = 9.1104e-03 seconds
 Total time for finalization       = 1.8754e-05 seconds
 Total time elapsed                = 1.3610e+02 seconds
 Calculation Rate (active)         = 29945.3 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=273.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=217.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=226.
  warn(msg, IDWarning)

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                  ####################     %%%%%%%%%%%%%%%%%
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                       ############     %%%%%%%%%%%%%%%
                          ########     %%%%%%%%%%%%%%
                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:44:22
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Simulating batch 200
 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.6383e+00 seconds
   Reading cross sections          = 2.5388e+00 seconds
 Total time in simulation          = 2.6312e+02 seconds
   Time in transport only          = 2.6228e+02 seconds
   Time in active batches          = 2.6312e+02 seconds
   Time accumulating tallies       = 7.6691e-01 seconds
   Time writing statepoints        = 1.1087e-02 seconds
 Total time for finalization       = 2.4905e-05 seconds
 Total time elapsed                = 2.6576e+02 seconds
 Calculation Rate (active)         = 30404.7 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=331.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=275.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=284.
  warn(msg, IDWarning)

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                ####################     %%%%%%%%%%%%%%%%%%%%%%
                #####################     %%%%%%%%%%%%%%%%%%%%%
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                #######################     %%%%%%%%%%%%%%%%%%
                 #######################     %%%%%%%%%%%%%%%%%
                 ######################     %%%%%%%%%%%%%%%%%
                  ####################     %%%%%%%%%%%%%%%%%
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                       ############     %%%%%%%%%%%%%%%
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                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:48:50
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Simulating batch 200
 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.6743e+00 seconds
   Reading cross sections          = 2.5771e+00 seconds
 Total time in simulation          = 4.8970e+02 seconds
   Time in transport only          = 4.8909e+02 seconds
   Time in active batches          = 4.8970e+02 seconds
   Time accumulating tallies       = 5.5220e-01 seconds
   Time writing statepoints        = 9.0599e-03 seconds
 Total time for finalization       = 2.2402e-05 seconds
 Total time elapsed                = 4.9239e+02 seconds
 Calculation Rate (active)         = 32672.8 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=389.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=333.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=342.
  warn(msg, IDWarning)

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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:57:05
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Simulating batch 200
 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.6121e+00 seconds
   Reading cross sections          = 2.5199e+00 seconds
 Total time in simulation          = 1.5700e+02 seconds
   Time in transport only          = 1.5618e+02 seconds
   Time in active batches          = 1.5700e+02 seconds
   Time accumulating tallies       = 7.6011e-01 seconds
   Time writing statepoints        = 9.2923e-03 seconds
 Total time for finalization       = 1.9566e-05 seconds
 Total time elapsed                = 1.5962e+02 seconds
 Calculation Rate (active)         = 25478.2 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=447.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=391.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=400.
  warn(msg, IDWarning)

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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 00:59:46
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

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 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.6557e+00 seconds
   Reading cross sections          = 2.5629e+00 seconds
 Total time in simulation          = 3.6796e+02 seconds
   Time in transport only          = 3.6756e+02 seconds
   Time in active batches          = 3.6796e+02 seconds
   Time accumulating tallies       = 3.0200e-01 seconds
   Time writing statepoints        = 1.1232e-02 seconds
 Total time for finalization       = 2.5262e-05 seconds
 Total time elapsed                = 3.7062e+02 seconds
 Calculation Rate (active)         = 21741.8 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=505.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=449.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=458.
  warn(msg, IDWarning)

                                %%%%%%%%%%%%%%%
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                 ######################     %%%%%%%%%%%%%%%%%
                  ####################     %%%%%%%%%%%%%%%%%
                    #################     %%%%%%%%%%%%%%%%%
                     ###############     %%%%%%%%%%%%%%%%
                       ############     %%%%%%%%%%%%%%%
                          ########     %%%%%%%%%%%%%%
                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:05:59
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

 Simulating batch 1
 Simulating batch 2
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 Creating state point statepoint.200.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.7257e+00 seconds
   Reading cross sections          = 2.6395e+00 seconds
 Total time in simulation          = 7.1052e+02 seconds
   Time in transport only          = 7.0977e+02 seconds
   Time in active batches          = 7.1052e+02 seconds
   Time accumulating tallies       = 6.6097e-01 seconds
   Time writing statepoints        = 1.0007e-02 seconds
 Total time for finalization       = 1.9946e-05 seconds
 Total time elapsed                = 7.1325e+02 seconds
 Calculation Rate (active)         = 22518.8 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=506.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=507.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=516.
  warn(msg, IDWarning)

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                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:17:54
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

 Simulating batch 1
 Simulating batch 2
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 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.6009e+00 seconds
   Reading cross sections          = 2.4974e+00 seconds
 Total time in simulation          = 5.7805e+01 seconds
   Time in transport only          = 5.7609e+01 seconds
   Time in active batches          = 5.7805e+01 seconds
   Time accumulating tallies       = 1.6179e-01 seconds
   Time writing statepoints        = 1.0103e-02 seconds
 Total time for finalization       = 1.8033e-05 seconds
 Total time elapsed                = 6.0414e+01 seconds
 Calculation Rate (active)         = 34598.8 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=526.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=527.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=536.
  warn(msg, IDWarning)

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                  ####################     %%%%%%%%%%%%%%%%%
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                       ############     %%%%%%%%%%%%%%%
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                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:18:57
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for C13

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

 Simulating batch 1
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 Simulating batch 100
 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 4.7389e-01 seconds
   Reading cross sections          = 3.7646e-01 seconds
 Total time in simulation          = 5.0877e+01 seconds
   Time in transport only          = 5.0714e+01 seconds
   Time in active batches          = 5.0877e+01 seconds
   Time accumulating tallies       = 1.3780e-01 seconds
   Time writing statepoints        = 7.4003e-03 seconds
 Total time for finalization       = 1.5463e-05 seconds
 Total time elapsed                = 5.1352e+01 seconds
 Calculation Rate (active)         = 39310.5 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=546.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=547.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=556.
  warn(msg, IDWarning)

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                  ####################     %%%%%%%%%%%%%%%%%
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                       ############     %%%%%%%%%%%%%%%
                          ########     %%%%%%%%%%%%%%
                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:19:50
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

 Simulating batch 1
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 Simulating batch 100
 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.2875e+00 seconds
   Reading cross sections          = 2.2661e+00 seconds
 Total time in simulation          = 1.0727e+02 seconds
   Time in transport only          = 1.0703e+02 seconds
   Time in active batches          = 1.0727e+02 seconds
   Time accumulating tallies       = 2.0649e-01 seconds
   Time writing statepoints        = 9.5881e-03 seconds
 Total time for finalization       = 1.9952e-05 seconds
 Total time elapsed                = 1.0957e+02 seconds
 Calculation Rate (active)         = 37288.1 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=566.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=567.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=576.
  warn(msg, IDWarning)

                                %%%%%%%%%%%%%%%
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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:21:42
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for C13

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

 Simulating batch 1
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 Simulating batch 100
 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 4.6705e-01 seconds
   Reading cross sections          = 3.7911e-01 seconds
 Total time in simulation          = 1.0879e+02 seconds
   Time in transport only          = 1.0856e+02 seconds
   Time in active batches          = 1.0879e+02 seconds
   Time accumulating tallies       = 2.0411e-01 seconds
   Time writing statepoints        = 7.7896e-03 seconds
 Total time for finalization       = 1.6491e-05 seconds
 Total time elapsed                = 1.0926e+02 seconds
 Calculation Rate (active)         = 36769.4 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=586.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=587.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=596.
  warn(msg, IDWarning)

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                     ###############     %%%%%%%%%%%%%%%%
                       ############     %%%%%%%%%%%%%%%
                          ########     %%%%%%%%%%%%%%
                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:23:33
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading H1 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H1.h5
 Reading H2 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/H2.h5
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Na23 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Na23.h5
 Reading Mg24 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg24.h5
 Reading Mg25 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg25.h5
 Reading Mg26 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Mg26.h5
 Reading Al27 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Al27.h5
 Reading Si28 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si28.h5
 Reading Si29 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si29.h5
 Reading Si30 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Si30.h5
 Reading K39 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K39.h5
 Reading K40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K40.h5
 Reading K41 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/K41.h5
 Reading Ca40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca40.h5
 Reading Ca42 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca42.h5
 Reading Ca43 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca43.h5
 Reading Ca44 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca44.h5
 Reading Ca46 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca46.h5
 Reading Ca48 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ca48.h5
 Reading Fe54 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe54.h5
 Reading Fe56 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe56.h5
 Reading Fe57 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe57.h5
 Reading Fe58 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Fe58.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for H1

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

 Simulating batch 1
 Simulating batch 2
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 Simulating batch 100
 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 2.4019e+00 seconds
   Reading cross sections          = 2.3094e+00 seconds
 Total time in simulation          = 2.0012e+02 seconds
   Time in transport only          = 1.9996e+02 seconds
   Time in active batches          = 2.0012e+02 seconds
   Time accumulating tallies       = 1.2689e-01 seconds
   Time writing statepoints        = 9.9668e-03 seconds
 Total time for finalization       = 2.0137e-05 seconds
 Total time elapsed                = 2.0253e+02 seconds
 Calculation Rate (active)         = 39975.1 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000


/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=606.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=607.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=616.
  warn(msg, IDWarning)

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                 ######################     %%%%%%%%%%%%%%%%%
                  ####################     %%%%%%%%%%%%%%%%%
                    #################     %%%%%%%%%%%%%%%%%
                     ###############     %%%%%%%%%%%%%%%%
                       ############     %%%%%%%%%%%%%%%
                          ########     %%%%%%%%%%%%%%
                                      %%%%%%%%%%%

                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:26:57
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 Reading cross sections XML file...
 Reading C12 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C12.h5
 Reading C13 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/C13.h5
 Reading N14 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N14.h5
 Reading N15 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/N15.h5
 Reading O16 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O16.h5
 Reading O17 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O17.h5
 Reading O18 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/O18.h5
 Reading Ar36 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar36.h5
 WARNING: Negative value(s) found on probability table for nuclide Ar36 at 294K
 Reading Ar38 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar38.h5
 Reading Ar40 from
 /home/idies/workspace/Storage/pchin/persistent/data/endf-b8.1/neutron/Ar40.h5
 Minimum neutron data temperature: 294 K
 Maximum neutron data temperature: 294 K
 Preparing distributed cell instances...
 Writing summary.h5 file...
 Maximum neutron transport energy: 20000000 eV for C13

 ===============>     FIXED SOURCE TRANSPORT SIMULATION     <===============

 Simulating batch 1
 Simulating batch 2
 Simulating batch 3
 Simulating batch 4
 Simulating batch 5
 Simulating batch 6
 Simulating batch 7
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 Creating state point statepoint.100.h5...

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 4.6713e-01 seconds
   Reading cross sections          = 3.8352e-01 seconds
 Total time in simulation          = 2.3320e+02 seconds
   Time in transport only          = 2.3296e+02 seconds
   Time in active batches          = 2.3320e+02 seconds
   Time accumulating tallies       = 2.0949e-01 seconds
   Time writing statepoints        = 9.5207e-03 seconds
 Total time for finalization       = 1.9821e-05 seconds
 Total time elapsed                = 2.3367e+02 seconds
 Calculation Rate (active)         = 34304.8 particles/second

 ============================>     RESULTS     <============================

 Leakage Fraction            = 0.00000 +/- 0.00000

CPU times: user 3.91 s, sys: 453 ms, total: 4.36 s
Wall time: 48min 48s

# Statistical stability: compare adjacent particle levels for each cross section.
# Percent changes with a near-zero higher-statistics value are left undefined.
MIN_REFERENCE_XS = 1e-6  # cm^-1
rows = []

for method in CONVERGENCE_METHODS:
    files = {
        n: CONVERGENCE_DIR / f'mgxs_{method}_{n}.h5'
        for n in CONVERGENCE_PARTICLES
    }
    if not all(path.exists() for path in files.values()):
        continue

    libs = {
        n: openmc.MGXSLibrary.from_hdf5(path)
        for n, path in files.items()
    }
    for lib in libs.values():
        assert np.array_equal(lib.energy_groups.group_edges, edges)

    xs_sets = {
        n: {xs.name: xs for xs in lib.xsdatas}
        for n, lib in libs.items()
    }

    for low_n, high_n in zip(CONVERGENCE_PARTICLES[:-1],
                             CONVERGENCE_PARTICLES[1:]):
        assert xs_sets[low_n].keys() == xs_sets[high_n].keys()
        for material in xs_sets[low_n]:
            for quantity in ('total', 'absorption', 'P0 scattering'):
                xs_low = xs_sets[low_n][material]
                xs_high = xs_sets[high_n][material]
                if quantity == 'P0 scattering':
                    low = xs_low.scatter_matrix[0][:, :, 0].ravel()
                    high = xs_high.scatter_matrix[0][:, :, 0].ravel()
                else:
                    low = getattr(xs_low, quantity)[0]
                    high = getattr(xs_high, quantity)[0]
                num_groups = len(xs_sets[low_n][material].total[0])

                for i, (a, b) in enumerate(zip(low, high)):
                    rows.append({
                        'Method': method,
                        'Material': material,
                        'Quantity': quantity,
                        'Particles (low)': low_n,
                        'Particles (high)': high_n,
                        'Incoming group': (i // num_groups + 1
                                           if quantity == 'P0 scattering'
                                           else i + 1),
                        'Outgoing group': (i % num_groups + 1
                                           if quantity == 'P0 scattering'
                                           else np.nan),
                        'Low value (cm^-1)': a,
                        'High value (cm^-1)': b,
                        'Absolute change (cm^-1)': abs(b - a),
                        'Relative change (%)': (
                            100 * abs(b - a) / abs(b)
                            if abs(b) >= MIN_REFERENCE_XS else np.nan
                        ),
                    })

df_convergence = pd.DataFrame(rows)
if not df_convergence.empty:
    df_convergence_summary = (
        df_convergence.groupby(
            ['Method', 'Material', 'Quantity',
             'Particles (low)', 'Particles (high)'],
            as_index=False,
        ).agg(
            Max_absolute_change=('Absolute change (cm^-1)', 'max'),
            Max_relative_change_percent=('Relative change (%)', 'max'),
            Median_relative_change_percent=('Relative change (%)', 'median'),
            Count_with_relative_change=('Relative change (%)', 'count'),
        )
    )
    display(df_convergence_summary)
    display(df_convergence)
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8.1 Independent-seed reproducibility at 20,000 particles per batch

Compare the original MGXS libraries (seed BASE_SEED) with the separate 20,000-particle libraries generated in Section 8. Both runs use the same CE model, MGXS method, and particles per batch, but different random seeds.

# Compare the original 20,000-particle library with its independent repeat.
rows = []

for method_index, method in enumerate(CONVERGENCE_METHODS):
    repeat_path = CONVERGENCE_DIR / f'mgxs_{method}_{BASE_PARTICLES}.h5'
    if not repeat_path.exists():
        continue

    repeat_lib = openmc.MGXSLibrary.from_hdf5(repeat_path)
    assert np.array_equal(repeat_lib.energy_groups.group_edges, edges)
    repeat_xs = {xs.name: xs for xs in repeat_lib.xsdatas}
    assert mgxs[method].keys() == repeat_xs.keys()
    repeat_seed = 10_001 + 1000 * method_index

    for material, original_xs in mgxs[method].items():
        other_xs = repeat_xs[material]
        for quantity in ('total', 'absorption', 'P0 scattering'):
            if quantity == 'P0 scattering':
                original = original_xs.scatter_matrix[0][:, :, 0]
                repeated = other_xs.scatter_matrix[0][:, :, 0]
            else:
                original = getattr(original_xs, quantity)[0]
                repeated = getattr(other_xs, quantity)[0]

            for index in np.ndindex(original.shape):
                a, b = original[index], repeated[index]
                rows.append({
                    'Method': method,
                    'Material': material,
                    'Quantity': quantity,
                    'Particles per batch': BASE_PARTICLES,
                    'Original seed': BASE_SEED,
                    'Repeat seed': repeat_seed,
                    'Incoming group': index[0] + 1,
                    'Outgoing group': (index[1] + 1
                                       if quantity == 'P0 scattering'
                                       else np.nan),
                    'Original (cm^-1)': a,
                    'Repeat (cm^-1)': b,
                    'Absolute difference (cm^-1)': abs(b - a),
                    'Relative difference (%)': (
                        100 * abs(b - a) / abs(a)
                        if abs(a) >= MIN_REFERENCE_XS else np.nan
                    ),
                })

df_reproducibility = pd.DataFrame(rows)
if not df_reproducibility.empty:
    df_reproducibility_summary = (
        df_reproducibility.groupby(
            ['Method', 'Material', 'Quantity'], as_index=False,
        ).agg(
            Max_absolute_difference=('Absolute difference (cm^-1)', 'max'),
            Median_relative_difference_percent=('Relative difference (%)', 'median'),
            Max_relative_difference_percent=('Relative difference (%)', 'max'),
            Count_with_relative_difference=('Relative difference (%)', 'count'),
        )
    )
    display(df_reproducibility_summary)
    display(df_reproducibility)
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9. Additional bootstrap

OpenMC’s bootstrapping procedure first generates MGXS with stochastic_slab, then uses a random-ray calculation to generate preliminary FW-CADIS weight windows.

%%time
BOOTSTRAP_RR_DIR = OUTPUT_DIR / 'bootstrap_random_ray'
BOOTSTRAP_RR_DIR.mkdir(parents=True, exist_ok=True)
BOOTSTRAP_WW_FILE = BOOTSTRAP_RR_DIR / 'weight_windows.h5'
BOOTSTRAP_MGXS_FILE = MGXS_DIR / 'mgxs_material_wise_bootstrapped.h5'

if GENERATE_BOOTSTRAP_WINDOWS:
    rr_model = copy.deepcopy(ce_model)
    rr_model.tallies = openmc.Tallies()
    rr_model.convert_to_multigroup(
        method='stochastic_slab',
        mgxs_path=MGXS_DIR / 'mgxs_stochastic_slab.h5',
    )
    rr_model.convert_to_random_ray()

    # Use the original CE tally mesh for both source regions and windows.
    ww_mesh = copy.deepcopy(
        ce_model.tallies[0].find_filter(openmc.MeshFilter).mesh
    )
    rr_settings = rr_model.settings
    rr_settings.batches = 300
    rr_settings.inactive = 180
    rr_settings.particles = 2_000
    rr_settings.random_ray['source_region_meshes'] = [
        (ww_mesh, [rr_model.geometry.root_universe])
    ]
    rr_settings.weight_window_generators = [
        openmc.WeightWindowGenerator(
            mesh=ww_mesh,
            energy_bounds=edges,
            method='fw_cadis',
            max_realizations=rr_settings.batches,
        )
    ]
    rr_model.export_to_model_xml(path=BOOTSTRAP_RR_DIR / 'model.xml')
    rr_model.run(cwd=BOOTSTRAP_RR_DIR)

if GENERATE_BOOTSTRAP_MGXS:
    if not BOOTSTRAP_WW_FILE.exists():
        raise FileNotFoundError(BOOTSTRAP_WW_FILE)

    model = copy.deepcopy(ce_model)
    model.tallies = openmc.Tallies()
    model.convert_to_multigroup(
        method='material_wise',
        mgxs_path=BOOTSTRAP_MGXS_FILE,
        overwrite_mgxs_library=True,
        particles=20_000,
        weight_windows_file=BOOTSTRAP_WW_FILE.resolve(),
        max_history_splits=500,
    )
Existing MGXS library file "/home/idies/workspace/Storage/pchin/persistent/openmc-workbench/5_variance_reduction/pacman_fw_cadis_runs/mgxs/mgxs_stochastic_slab.h5" will be used
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                 | The OpenMC Monte Carlo Code
       Copyright | 2011-2026 MIT, UChicago Argonne LLC, and contributors
         License | https://docs.openmc.org/en/latest/license.html
         Version | 0.16.0
     Commit Hash | 617d35a5063c57796b43428bc401e627d2011046
       Date/Time | 2026-11-11 01:30:53
   MPI Processes | 1
  OpenMP Threads | 72

 Reading model XML file 'model.xml' ...
 WARNING: The maximum number of specified tally realizations (300) is greater
          than the number of active batches (120).
 Reading cross sections HDF5 file...
 Loading cross section data...
 Loading Concrete__Ordinary__NIST__1 data...
 Loading Air__dry__near_sea_level__2 data...
 Preparing distributed cell instances...
 Writing summary.h5 file...

 =====>     FIXED SOURCE TRANSPORT SIMULATION (RANDOM RAY SOLVER)     <=====


 ======================>     FORWARD FLUX SOLVE     <=======================

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 Creating state point statepoint.forward.300.h5...

 =====================>     SIMULATION STATISTICS     <=====================

 Total Iterations                  = 300
 Number of Rays per Iteration      = 2000
 Inactive Distance                 = 4220.189569201839 cm
 Active Distance                   = 21100.947846009192 cm
 Source Regions (SRs)              = 5208
 SRs Containing External Sources   = 1
 Total Geometric Intersections     = 2.2910e+08
   Avg per Iteration               = 7.6367e+05
   Avg per Iteration per SR        = 146.63
 Avg SR Miss Rate per Iteration    = 0.0000%
 Energy Groups                     = 2
 Total Integrations                = 4.5820e+08
   Avg per Iteration               = 1.5273e+06
 Volume Estimator Type             = Hybrid
 Adjoint Flux Mode                 = OFF
 Source Shape                      = Flat
 Sample Method                     = PRNG
 Transport XS Stabilization Used   = NO

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 3.2989e-01 seconds
   Reading cross sections          = 2.6527e-03 seconds
 Total simulation time             = 1.2062e+01 seconds
   Transport sweep only            = 1.0417e+01 seconds
   Source update only              = 1.2123e-01 seconds
   Tally conversion only           = 1.9472e-01 seconds
   MPI source reductions only      = 0.0000e+00 seconds
   Other iteration routines        = 1.3289e+00 seconds
 Time in active batches            = 5.1937e+00 seconds
 Time writing statepoints          = 2.8183e-01 seconds
 Total time for finalization       = 1.6355e-01 seconds
 Time per integration              = 2.2735e-08 seconds

 ======================>     ADJOINT FLUX SOLVE     <=======================


 =====>     FIXED SOURCE TRANSPORT SIMULATION (RANDOM RAY SOLVER)     <=====

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 Creating state point statepoint.300.h5...
 Exporting weight windows to weight_windows.h5...

 =====================>     SIMULATION STATISTICS     <=====================

 Total Iterations                  = 300
 Number of Rays per Iteration      = 2000
 Inactive Distance                 = 4220.189569201839 cm
 Active Distance                   = 21100.947846009192 cm
 Source Regions (SRs)              = 5208
 SRs Containing External Sources   = 5208
 Total Geometric Intersections     = 2.2910e+08
   Avg per Iteration               = 7.6367e+05
   Avg per Iteration per SR        = 146.63
 Avg SR Miss Rate per Iteration    = 0.0000%
 Energy Groups                     = 2
 Total Integrations                = 4.5820e+08
   Avg per Iteration               = 1.5273e+06
 Volume Estimator Type             = Hybrid
 Adjoint Flux Mode                 = ON
 Source Shape                      = Flat
 Sample Method                     = PRNG
 Transport XS Stabilization Used   = NO

 =======================>     TIMING STATISTICS     <=======================

 Total time for initialization     = 0.0000e+00 seconds
   Reading cross sections          = 0.0000e+00 seconds
 Total simulation time             = 1.1211e+01 seconds
   Transport sweep only            = 1.0420e+01 seconds
   Source update only              = 4.4928e-02 seconds
   Tally conversion only           = 4.8271e-02 seconds
   MPI source reductions only      = 0.0000e+00 seconds
   Other iteration routines        = 6.9755e-01 seconds
 Time in active batches            = 4.7869e+00 seconds
 Time writing statepoints          = 3.0749e-01 seconds
 Total time for finalization       = 3.8240e-01 seconds
 Time per integration              = 2.2741e-08 seconds

/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=683.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=627.
  warn(msg, IDWarning)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another Filter instance already exists with id=636.
  warn(msg, IDWarning)
Fetching long content....
if BOOTSTRAP_WW_FILE.exists():
    ww_rows = []
    for index, ww in enumerate(
        openmc.WeightWindowsList.from_hdf5(BOOTSTRAP_WW_FILE)
    ):
        lower = np.asarray(ww.lower_ww_bounds)
        upper = np.asarray(ww.upper_ww_bounds)
        positive = lower[np.isfinite(lower) & (lower > 0)]
        ww_rows.append({
            'Window': index,
            'Mesh dimensions': str(ww.mesh.dimension),
            'Number of bounds': lower.size,
            'Finite lower fraction': np.isfinite(lower).mean(),
            'Nonpositive lower bounds': (lower <= 0).sum(),
            'Upper below lower': (upper < lower).sum(),
            'Minimum positive lower bound': (
                positive.min() if positive.size else np.nan
            ),
            'Maximum positive lower bound': (
                positive.max() if positive.size else np.nan
            ),
        })
    df_bootstrap_windows = pd.DataFrame(ww_rows)
    display(df_bootstrap_windows)

if BOOTSTRAP_MGXS_FILE.exists():
    boot_lib = openmc.MGXSLibrary.from_hdf5(BOOTSTRAP_MGXS_FILE)
    assert np.array_equal(boot_lib.energy_groups.group_edges, edges)
    boot_xs = {xs.name: xs for xs in boot_lib.xsdatas}
    assert boot_xs.keys() == mgxs['material_wise'].keys()

    rows = []
    for material in boot_xs:
        for quantity in ('total', 'absorption', 'P0 scattering'):
            old = mgxs['material_wise'][material]
            new = boot_xs[material]
            if quantity == 'P0 scattering':
                a = old.scatter_matrix[0][:, :, 0].ravel()
                b = new.scatter_matrix[0][:, :, 0].ravel()
            else:
                a = getattr(old, quantity)[0]
                b = getattr(new, quantity)[0]
            ngroups = len(old.total[0])
            for i, (x, y) in enumerate(zip(a, b)):
                rows.append({
                    'Material': material,
                    'Quantity': quantity,
                    'Incoming group': (i // ngroups + 1
                                       if quantity == 'P0 scattering'
                                       else i + 1),
                    'Outgoing group': (i % ngroups + 1
                                       if quantity == 'P0 scattering'
                                       else np.nan),
                    'Unweighted material-wise (cm^-1)': x,
                    'Bootstrapped material-wise (cm^-1)': y,
                    'Absolute change (cm^-1)': abs(y - x),
                    'Change (%)': (100 * (y - x) / x
                                   if abs(x) >= 1e-6 else np.nan),
                    'Both finite': np.isfinite(x) and np.isfinite(y),
                })

    df_bootstrap_comparison = pd.DataFrame(rows)
    display(df_bootstrap_comparison)
/home/idies/miniconda3/envs/openmc-mpi/lib/python3.14/site-packages/openmc/mixin.py:72: IDWarning: Another MeshBase instance already exists with id=1.
  warn(msg, IDWarning)
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10. Reuse these libraries in FW-CADIS

The generated libraries are saved in 1_cross_sections/1_1_ways_to_convert_to_multigroup_outputs/mgxs/. From a later notebook run in 5_variance_reduction/, for example, use ../1_cross_sections/1_1_ways_to_convert_to_multigroup_outputs/mgxs/mgxs_material_wise.h5 to access the material-wise MGXS library.

Cross sections
Survey ways to plot cross sections with OpenMC
Materials
Survey ways to define multi-element materials