1. MONK® Status
Paul N Smith
28 June 2017

2. Background
MONK® is a Monte Carlo neutronics code for the solution of criticality safety and reactor physics problem.
MONK Version 10A was released in 2014 after an extensive programme of developments and enhancements over the previous version.
Significant further developments have been carried out since then culminating in MONK10B which was handed to our SSQA team on 13 June.
MONK10B scheduled for release in the summer.

3. MONK 10B Highlights Fission matrix module
Tallies the fission matrix, and calculates eigenvalues, eigenvectors and the dominance ratio.
Improvements to the burn-up credit capabilities, e.g.
better user image and robustness; and
greater control of isotopic content (e.g. for actinide-only BUC).
Improvements to the scattering kernel near epithermal resonances.
Improved tracking in CAD geometries:
better run-time performance and greater control over material contents.
A capability for creating copies of geometry components with reflections as well as rotations.
New nuclear data libraries (JEFF3.2 and ENDF/B-VII.1)
Cross-section tally module, to score shielded cross-sections.
Improved parallel processing, including:
splitting of looping calculations across multiple processors.

4. Fission Matrix – Introduction
In Monte Carlo criticality calculations the fission source distribution is not known a priori.
So we make an initial source “guess”;
and use the power iteration method to converge the source distribution during settling stages;
before beginning the scoring stages.
A converged fission source is required before scoring can begin.
This is the fundamental eigenvector of the fission kernel
i.e. the probability of a fission at position r being caused by a fission neutron born at position rʹ in the previous generation
keff is the fundamental eigenvalue of the fission kernel.
The rate of convergence depends on the dominance ratio
ratio of the first-order to the fundamental (zeroth-order) eigenvalue.
If this is high (→1) convergence is slow (difficult to isolate fundamental mode)
The fission matrix has the potential to help with the acceleration and automation of the settling process.

5. Fission Matrix – Example
MONK Validation Experiment No.89
LEU-COMP-THERM-048
Circular array of 3 wt% uranium dioxide fuel rods on square lattice
Nx x Ny x Nz = 54 x 54 x 1 (one region per pincell)

6. Fission Matrix – Results
MONK Validation Experiment No. 89
Nx x Ny x Nz = 54 x 54 x 1
First nine eigenmodes:
Mode
Eigenvalue 1 2 3 4 5 6 7 8
Dominance Ratio:

7. Burn-up – Introduction
MONK has included a multigroup, microscopic depletion capability for many years:
using the WIMS 172 group nuclear data libraries;
with user-defined materials to model spatial discretization.
MONK 10A (2014) introduced point energy microscopic burn-up:
using the BINGO nuclear data libraries and collision processor; giving
continuous energy cross-section data; and
run-time Doppler broadening (temperature distribution is important for BUC); with
an overlaid mesh for spatial discretization.
MONK 10B improves this functionality through:
improved algorithms;
better user image; and
additional options.

8. Spatially-dependent burn-up
A new burn-up methodology exists in MONK10, based on the concept of artificial materials:
a Cartesian burn-up (BU) mesh is superimposed over the geometry;
a Monte Carlo sampling algorithm determines which user-defined materials occur in each cell, and maps them to unique artificial materials;

9. Spatially-dependent burn-up
A new burn-up methodology exists in MONK10, based on the concept of artificial materials:
a Cartesian burn-up (BU) mesh is superimposed over the geometry;
a Monte Carlo sampling algorithm determines which user-defined materials occur in each cell, and maps them to unique artificial materials;

10. Spatially-dependent burn-up
A new burn-up methodology exists in MONK10, based on the concept of artificial materials:
a Cartesian burn-up (BU) mesh is superimposed over the geometry;
a Monte Carlo sampling algorithm determines which user-defined materials occur in each cell, and maps them to unique artificial materials;
the same algorithm also estimates the volume of each artificial material; and
the criticality and depletion calculations proceed using the artificial materials.
The artificial materials are generated in cycle 1 and stored in an archive file for subsequent cycles.

11. Burn-up Credit Burn-up credit calculations require:
A depletion calculation in a reactor model (the donor model); followed by
A criticality calculation using irradiation fuel compositions in a receiver model, e.g.:
a spent fuel transport flask; or
a spent fuel storage facility.
MONK 10A introduced the COWL facility:
Irradiated artificial material compositions are stored in the archive file by the donor calculation;
The receiver calculation reads one or more archive files to import material compositions.
The user specifies which user-defined materials to import from specified cells of the burn-up mesh in the donor calculation; and
MONK determines the mapping to the appropriate artificial materials.

12. COWL Improvements
The default behaviour of COWL is to import all nuclides from donor materials.
MONK 10B has been developed to allow greater control:
Specified nuclides can be excluded (i.e. import all except these)
Specified nuclides can be included (i.e. only import these)
Users can define lists of fission products and/or actinides to use in these options.
These developments make it simpler to do:
actinide-only burn-up credit; or
actinide plus specific fission products burn-up credit.
These approaches give less conservatism than not using burn-up credit but with a greater safety margin than full burn-up credit.
COWL has also been developed to include WIMS-BINGO nuclide mappings:
allows different nuclear data (WIMS or BINGO) to be used in donor and receiver models.

13. Cross-Section Tallying
The Monte Carlo methods used in MONK together with the continuous- energy BINGO libraries mean that neutron transport can be calculated very accurately,
taking resonance shielding in the resolved resonance range into account exactly.
(In the unresolved resonance range an enhanced resonance treatment is required for a small number of nuclides – a subgroup pre-shielding treatment is applied to the BINGO data for these nuclides.)
Deterministic codes (e.g. the WIMS general purpose reactor physics code) need to use approximate methods for resonance shielding, e.g.
equivalence theory; or
the subgroup method.
A new XT module in MONK 10B:
tallies the fluxes and reaction rates during the continuous energy Monte Carlo calculation; and
uses these to calculated appropriately-shielded cross-sections for use in deterministic codes.

14. Cross-Section Tallying – Example
The fission cross-section for 235U tallied by the MONK XT module in the WIMS 172 group scheme in a pincell model.
Original JEFF3.1.2 continuous energy cross-section shown for comparison.

15. Scattering Kernel
The scattering kernel determines the probability of a neutron scattering from energy E to E´ and Ω to Ω´
At sufficiently high energies the motion of the target nucleus can be neglected (asymptotic kernel).
At thermal energies crystalline structure and molecular rotations and vibrations are important:
Secondary momentum and energy determined from S(α,β) tables for certain bound nuclides.
At epithermal energies molecular effects are less important but target motion cannot be ignored.
Monatomic free gas model
Non-zero target velocity results in a small change in relative neutron energy. This effect is commonly neglected (constant cross-section approximation).
Constant cross-section approximation becomes inaccurate in the region of a resonance. This is most significant for heavy nuclides (A>200) with epithermal resonances with strong scatter and capture components (e.g. 238U).

16. Doppler Broadening Rejection Correction
The monatomic free gas model in the MONK scattering kernel has been modified using the DBRC method [Becker, Dagan, Lohnert (2009)]
After sampling the target nuclide velocity by rejection and additional rejection test is applied. The target velocity is accepted if
Note this requires the elastic scattering cross-section data at zero Kelvin.
Not currently part of a standard BINGO library.
Possible future development.
DBRC method will be available for evaluation in MONK 10B but will require an externally-supplied source of zero Kelvin cross-section data.

17. Part Reflection
The MONK geometry package allows a component of a model to be define once and used many times in an assembled model.
This leads to reduced modelling and verification effort and improved productivity and QA.
When parts are reused in this way they may be given optional rotations, or multiple successive rotations.
Not all desired transformations can ben achieved through rotation and translation so MONK 10B adds an option to reflect parts of the geometry.
Reflections can be combined to rotations and translations to give a flexible transformation capability.

18. CAD Improvements
MONK has the capability to import CAD models and perform Monte Carlo neutron tracking directly in that geometry
It is not necessary to convert to native MONK geometry.
Less efficient than simple body tracking or Woodcock tracking.
Run-time performance improvements in MONK 10B:
Other developments to the CAD functionality allow users greater control of materials:
Material names can be updated in different regions of a model to replace material contents as desired
Model
MONK 10A
FG/IGES
MONK 10B
Speed-up
factor
Transport Flask
39.0
15.0
2.6
Fuel Flask
262.8
52.9
4.95
Barrel Room
21.7
12.1
1.8

19. Parallel Looping MONK includes a powerful looping capability:
Parameters may be defined in the input file with a list of values; MONK will run a sequence of calculations using each value in the list.
Multiple looping parameters can be defined, and loops can be nested.
This allows sophisticated parameter surveys to be carried out within a single execution of MONK, using a single input file (generating multiple output files).
Iterations of the calculation are performed sequentially.
MONK 10B introduces the option to run a specific iteration of a looping calculation.
This allows multiple iterations to be distributed across multiple processors to run concurrently, either using a script or Visual Workshop:

20. Nuclear Data Libraries
MONK supports (and is supplied with) nuclear data libraries in a number of formats:
BINGO – continuous energy, with run-time Doppler broadening
DICE – hyper-fine 13,193 group scheme
WIMS – 172 group with broad group collision processing.
Data libraries are available for a wide range of evaluations, e.g.:
Legacy : JEF 2.2, ENDF/B-VI, JENDL-3
Added in MONK10A : JEFF 3.1, JEFF 3.1.1, JEFF 3.1.2, ENDF/B-VII.0
Added in MONK10B : JEFF 3.2, ENDF/B-VII.1
Current BINGO libraries have a base temperature of K
IAEA Transport Regulations are driving a requirement for libraries including temperatures down to -40 ºC.
This is fine for free-gas nuclides but S(α,β) data for bound nuclides are available at a limited number of temperatures. International research effort is attempting to address this limitation and MONK 10B is being developed to handle new low temperature data.

21. Summary
MONK is a Monte Carlo code for criticality safety (including burn-up credit) and reactor physics applications, with a long track record.
It is in continuous development by the ANSWERS Software Service to meet the requirements of users.
A forthcoming release (MONK10B) has new developments including:
Fission matrix module
Improvements to the burn-up credit capabilities
Improvements to the scattering kernel near epithermal resonances.
Improved tracking in CAD geometries:
A capability for creating copies of geometry components with reflections as well as rotations.
New nuclear data libraries (JEFF3.2 and ENDF/B-VII.1)
Cross-section tally module, to score shielded cross-sections.
Improved parallel processing

22. Contact the ANSWERS Software Service
Amec Foster Wheeler King’s Point House 5 Queen Mother Square, Poundbury, Dorchester, Dorset DT1 3BW United Kingdom T +44 (0) answerssoftwareservice.com amecfw.com