# The MCU-PD Code

Alekseev N.I., Bikeev A.S., Bolshagin S.N., Bryzgalov V.I., Gomin E.A., Gorodkov S.S., Gurevich M.I., Kalugin M.A., Kulakov A.S., Marin S.V., Oleynik D.S., Prjanichnikov A.V., Sergeev G.S., Sukhino-Khomenko E.A., Shkarovsky D.A., Yudkevich M.S.

Passport of the code N456 (24.10.2018).

1. Code Title

MCU-PD

2. Computer

The code is designed as a machine-independent. It is tested on the personal and multiprocessor computers.

3. FORMULATION

The code is designed to address the analog and non-analog Monte Carlo heterogeneous transport equation for neutrons, photons, electrons and positrons. For neutrons code allows one to solve the homogeneous equation (the problem of critical systems, multiplication of neutrons). Mathematically, this means that for the system the kinetic equation with given boundary conditions, describing the distribution of particle flux in it, is solved.

The code provides the calculated predictions of the isotopic composition of the materials of the reactor and its multiplying properties depending on the duration of the campaign.

For each of the reactor calculated by the Monte Carlo method the homogeneous equation is solved for the neutron transport using the evaluated nuclear data and the detailed description of the laws of interaction of neutrons with matter, without the simplifications in describing the geometry and taking into account various boundary conditions: flow through the outer surface, white and mirror reflections, translational symmetry, rotation symmetry. In addition, it is possible to calculate the neutron flux functionals for finite and infinite inhomogeneous heterogeneous arrays with translational symmetry and the leakage, given by the buckling vector, in particular, to solve the problem of the asymptotic lattice (the Benoit problem).

4. METHOD OF SOLUTION

Traditional analog Monte Carlo method is used to solve the homogeneous kinetic equation in the approximation of constant number of neutrons M (defined by the user) in generations. The solution in this approximation converges to the exact solution with increasing M.

In the simulation of neutron histories code allows continuous, pointwise and stepwise description of the cross sections on energy and takes into account the continuous change of energy in collisions.

Code MCU-PD allows calculating the three-dimensional system of almost any complexity.

The system is represented as a union of homogeneous geometric areas, each of which is described as a boolean combination of a set of simple bodies (the method of combinatorial geometry). The user has 19 types of bodies (cylinder, cone, sphere, boxes, etc.). Description of the geometry of systems containing recurring elements, facilitates the use of breeding methods that allow to specify a repeating element only once. For systems containing elements with complex internal structure there is a possibility of multi-level hierarchical description. A hierarchy assignments geometry reduces the amount of given information and reduces the requirements for the amount of RAM. Proper accounting of symmetry and boundary conditions also facilitates the task geometry.

In describing geometrical areas by means of the method of combinatorial geometry all their boundaries consist of pieces of planes and surfaces of the second order, so if you have parts with more complex boundary surfaces need to be approximated by a very large number of zones. The implemented Woodcock method allows one to remove this limitation.

A special algorithm allows to take into account the effects of double heterogeneity, when the fuel elements contain tens of thousands of microrods.

To the each geometric area the user assigns a number of attributes: material number, zone tally number (an arbitrary union of geometric areas), object tally number (eg, cell or cassette), etc. These attributes can be generated automatically using a minimum amount of information given by the user.

To verify the input data describing the geometry of the simulated system, we can visualize the image of a given system in the form of flat sections with a consistent image of the materials, zones and objects. Color and black and white images are available. The choice of cross sections, the types of areas, the number of colors are set by the user interactively.

Code calculates the following quantities: neutron multiplication factor, effective fraction of delayed neutrons; small group set of constants (including the diffusion coefficients), neutron fluxes and reaction rates in materials, zones, and objects in a given by the user bins of energy.

Neutron multiplication factor is estimated by collisions, absorptions, track length, and some combined estimates are also used.

Calculations can be carried out using fission spectrum of prompt and delayed neutrons. In the fast energy region the anisotropy of the elastic scattering in the center of mass is taken into account, it is possible to carry out simulation of inelastic collisions by the laws contained in the files of evaluated neutron data.

In the unresolved resonance energy region cross sections are calculated by subgroup parameters or using Bondarenko f-factors. In the region of allowed resonances may be used either subgroups, or pointwise description of the cross sections. Cross sections of the most important nuclides are described by "infinite" number of points, as the simulation in each energy point is calculated from the resonance parameters. This scheme allows calculations directly using data on the resonance parameters without preliminary preparation of tables of cross sections and to assess temperature effects through the analysis of cross sections depending on the temperature.

The type of simulation of collisions in the thermalization energy region is selected by the user. It may be multigroup transport approximation, or the model of continuous change of energy in terms of correlation between the change in energy and angle of scattering. Both cases account for chemical bonding, thermal motion of the nuclei, and for elastic scattering and coherent effects.

MCU-PD allows for calculation of the scattering law for the desired temperature during the initial input data for the calculated option. This ensures the adequacy of the evaluated nuclear data files of information on the temperature dependence of the scattering laws.

Calculation of changes in the isotopic composition of the reactor during the campaign is conducted at the given energy dependence of the average power in the system on time. When solving differential equations of the changes in the isotopic composition of materials depending on time one-group cross sections of neutron-physical reactions averaged by the burnable area are used. The user specifies the time intervals at the beginning of which these cross sections should be calculated. The general scheme of calculation is as follows. For a given initial state of the system the criticality problem is calculated by means of the Monte Carlo method. At this calculation single-group cross-section and the power for all burnable material are received. Then, for each burnable material analytically the burnup equation is solved for the first time interval and the average density of the isotope in material depending on time is determined. Then again criticality equation is solved for the new isotopic composition of the system and new values of cross sections are calculated, as well as the energy distribution function in materials. The process is repeated cyclically for all time intervals until the end of the campaign. Burning materials may contain fissile isotopes or absorbers. The code determines the content of all isotopes of actinides and fission products with half-lives of more than one day. Burnable absorbers can be virtually any traditional and advanced materials.

The accuracy of criticality calculations by means of the Monte Carlo method is limited mainly by the accuracy of nuclear data libraries.

The code MCU-PD is equipped with the data bank MDBPD50, consisting of the following sections:

- ACE/MCU - a library of cross sections of interaction of neutrons with nuclei in the epithermal energy region in the Pointwise representation, obtained from the files ENDF/B-VII and other sources;

- BNAB/MCU - expanded and modified version of the 26-group system of constants BNAB-93;

- LIPAR - resonance parameters of nuclides in the allowed resonances;

- MULTIC - 301-group library, containing, inter alia, data on temperature dependence of the parameters of a subgroup of nuclides in unresolved resonances;

- KORT - pointwise neutron-physical constants in the low-energy (upper limit - 5 eV),

- TEPKON - 40-group cross sections for thermalization of the boundary of 1 eV;

- VESTA - for modeling the collision of neutrons with nuclei of inhibitors in the light of continuous changes in the neutron energy in the thermalization; presented in the form of probability tables derived from the scattering law S (???);< br> - BOFS - generalized phonon spectra inhibitors;

- DOSIM - activation cross sections in the Pointwise representation;

- ABBNL - 40 group cross sections, used to obtain cross-sections "of the total isotope";

- PHOTONS - multigroup cross sections for generation of photons in the interaction of neutrons with matter on the basis of data libraries DLC-41/VITAMIN-S and DLC-184/VITAMIN-B6;

- PHOTONT - multigroup cross section of interaction of photons with matter on the basis of data libraries DLC-41/VITAMIN-S and DLC-184/VITAMIN-B6;

- BURN - contains information for burnup tasks: half-lives of nuclei, yields of fission fragments, chains of radioactive transformations, etc.;

- PHOTDATA - cross sections of interaction of photons with matter in the pointwise representation in the energy region from 100 eV to 100 MeV;

- SHELLDATA-contains data about atoms, according to LLNL Evaluated Atomic Data Library;

- ELECDATA - cross sections of interaction of electrons with matter in the pointwise representation in the energy region from 100 eV to 100 MeV;

- POSIDATA - cross sections of interaction of positrons with matter in the pointwise representation in the energy region from 100 eV to 100 MeV;

- NEUTRONK - Kerma factors for neutrons with energies from 10.5 eV to 20 MeV in the pointwise representation;

- PHOTONK - Kerma factors for photons in a panel presentation for the energy region up to 20 MeV.

MDBPD50 contains information for 375 isotopes.

5. LIMITATIONS

The code have no fundamental limitations on the complexity of simulated systems.

6. TYPICAL CALCULATION TIME

The calculation time depends on the isotopic composition of the materials of the reactor, the complexity of the geometry of the simulated system and the necessary statistical error of estimated functionals.

The calculation time depends on the users' qualifications when choosing the physical model, initial data to describe the geometry and the choice of time step of burnup.

7. FEATURES OF THE PROGRAM

MCU-PD code is the development of MCU software MCU-REA/1 and MCU-REA/2, certified by Rostehnadzor for calculations of neutron-physical characteristics of different types of reactors.

Working version of the code for each computer and its operating system is generated from the modules of the MCU-5 package using its preprocessor. Initial text files of the modules are stored in the preprocessor's input language. The preprocessor translates modules to the text file in the Fortran-90/95 language. Parameters defining the amount of memory needed to solve a certain class of problems, as well as functional features of the code may be reset by the user at the stage of generation.

Looking at the features of the code in comparison with the codes of the previous version of the MCU family, we note the possibility of parallel computing using multiprocessor systems, the possibility of simulation of photons, electrons and positrons, the transition to the use of dynamic memory, which makes the code much more economical in memory consumption. < br> In addition, there is the possibility to calculate the scattering law for the desired temperature during the initial data input according to the input data.

Significantly expanded data bank.

8. SUPPORT AND RELATED CODES

MCU Office, which is a graphical interface for MCU. Its main functions are as follows:

- Visualization of input data for geometric module NCG and the generation of error messages, if any;

- Possibilities to edit MCU input data file;

- View files created with MCU at calculation;

- Run a task in a separate window;

There are additional features:

- Generation of a working version of the MCU;

- Comparison of two pictures;

- Displays reaction rates obtained in the calculation using different colors within the picture;

- Displays reaction rates obtained in the process of calculation, as well as numbers of materials, areas, facilities, and other information as text over the picture;

- etc.

9. STATE

Code is deposited in OFAP YAR in November 2009 (inv. number 685 OFAP YAR).

There is full documentation on the code [1].

10. LINKS

1. Development of a MCU-PD for the calculation of neutron-physical characteristics of the active zones of the VVER-1200 NPP-2006, realizing for the neutron transport equation and Monte Carlo method based on the information stored in the files of evaluated nuclear data. Report RRC KI Inv. № 36-03/18-08, Moscow, 2009.

11. TECHNICAL REQUIREMENTS

Texts code MCU-PD with a library MDBPD50 and description of the code take about 2.2 GB hard drive, the recommended minimum amount of RAM - 1 GB on a single core processor.

12. PROGRAMMING LANGUAGES

Fortran-90/95.

Initial text files of the code modules are in the source language of the preprocessor of the MCU package, which generates text files in the Fortran-90/95 language.

Graphical visualization is written in C + +.

13. OPERATING SYSTEM

MS-DOS (version higher than 3.3); WINDOWS 95, 98, NT, 2000, XP, Server 2003.