# The MCU-RFFI/A Code

Abagjan L.P., Alekseev N.I., Bryzgalov V.I., Veretjonov V.V., Glushkov A.E., Gomin E.A., Gurevich M.I., Kalugin M.A., Majorov L.V., Marin S.V., Yudkevich M.S.

Software registration certificate N2010613419.

Passport of the code N61. In 2006 it was extended until 17.10.2016. In 2016 it was replaced by the passport N400 of 14.07.2016

The MCU-RFFI/A code is intended to solve neutron transport equations by means of the Monte-Carlo method using estimated nuclear data for systems with arbitrary three-dimensional geometry.

Main application fields:

- nuclear energy objects’ safety estimation
- neutron constants verification and validation
- calculation of neutron physic constants of nuclear reactors of different types
- verification of design codes for calculations of neutron physic characteristics of nuclear reactors

The MCU-RFFI/A code with the DLC/MCUDAT-1.0 neutron data library is licensed by Russian Safety Authority /Gosatomnadzor RF/ (Code Passport: MCU-RFFI/A code with DLC/MCUDAT-1.0 data library, passport’s registration number 61 of 17.10.1996) to calculate criticality of a wide class of systems multiplying neutrons with the following fuels: low and highly enriched uranium, plutonium, uranium and plutonium mixture (MOX); and such moderators as water, heavy water, graphite, hydride zirconium, etc.

The code allows one to take into account the effects of continuous change of the energy at collisions, and both continuous and step representation of cross-sections on energy. The calculations may be performed using the prompt and delayed neutron fission spectrum. For the unresolved resonance region the cross-sections are calculated by subgroup parameters or using Bondarenko’s f-factors. For the resolved resonance region both subgroup and pointwise descriptions of cross-sections are possible. Cross-sections of the most important nuclides are described by the “infinite” number of points, because at neutron history modelling in each energy point they are calculated by means of resonance parameters. This scheme lets one perform calculations directly using resonance parameters data with no preliminary preparations of cross-sections table, and lets one estimate temperature effects using analytical dependence of cross-sections on temperature. Collision modelling in the thermalization region is done according to the user’s choice: in multigroup approximation, or using the model of continuous energy change taking into account correlations between energy and angle change at scattering. Both cases take into account chemical bonds, nucleus thermal motion, and coherent effects for shape-elastic scattering.

The precision of criticality calculations by means of the Monte-Carlo method is limited only by the precision of the nuclear data library used.

The DLC/MCUDAT-1.0 neutron physic data base is the data support for the MCU-RFFI/A code. DLC/MCUDAT-1.0 includes:

- ACE - pointwise library obtained by means of the NJOY code from estimated nuclear data files
- BNAB/MCU - enlarged and modified version of 26-group constant system BNAB-78
- LIPAR - resonance parameters in the resolved resonance region
- TEPCON - multigroup cross-sections in the thermalization region
- VESTA - the library for modelling of neutron collisions with nucleus taking into account continuous change of neutron’s energy in the thermalization region, that is given in the form of the probability tables obtained from scattering laws S(a , b ).

The DLC/MCUDAT-1.0 constants library contains information on 131 isotopes.

The MCU-RFFI/A code allows one to calculate three-dimensional systems practically of any complication. The systems are described by means of combinatorial geometry as Boolean combinations of primitive bodies. The user has a choice of 13 types of bodies (cylinder, cone, sphere, parallelepiped and etc.). The possibility of using the symmetry of the system and lattices - that are generated by means of multiplication of some of the initial elements - makes it easier to describe the geometry and border conditions. The lattices may include heterogeneity as applications. The user ascribes to each geometry zone a number of attributes: material number, registration zone number, registration object number and etc. These attributes may be generated automatically for lattices and use minimal information provided by the user.

It is possible to take into account the following border conditions: leakage through the outer surface, white and mirror reflection, translational symmetry. The code lets one take into account the effects of double heterogeneity, when fuel assemblies consist of tens of thousands micro-spheres, and solve the problem of asymptotic lattice (Benua problem) and calculate neutron transport functionals for infinite uniform heterogeneous lattices with translational symmetry with leakage given by buckling vector.

Different flux functionals are calculated. The functionals are determined as flux integrals with given weight functions in registration zones, registration objects, and the system as a whole. The estimation of the functionals is possible by the track length and collision points.

The following values are calculated: neutron multiplication factor (by the number of collisions, number of absorptions, combined estimations), neutron flux density, nuclear reaction rates for separate nuclides and their mixture in the given space-energy intervals, few-group constant set for registration objects including diffusion coefficients based on the different definitions, spectral indexes, effective fraction of delayed neutrons, in some cases - currents and fluxes at cells’ surfaces.

The MCU-RFFI/A code is written in the Fortran-77 language. It relates to the class of the hardware independent. There are no principal limitations in memory volume.

The MCU-RFFI/A code is developed within the framework of the MCU project.

The MCU project includes the development of the applied codes to solve the transport equation by means of the Monte-Carlo method , development and adaptation of different constants data libraries, development of codes to work with the libraries, verification of the codes and constants by means of the comparison with experimental data, development of the CLAD library which contains description of benchmark experiments and results of calculations.

The MCU package is the set of modules that are compiled into specialized codes to solve different applied tasks. The architecture of the set includes the possibility to compile specialized codes that are similar to the MCU-RFFI/A code by means of using the alternative modules from the library of the package.

Module - is the collection of subroutines with functionality and interface determined by the package architecture. According to the purpose the modules are divided into the following types: C - control, T - transport, P - physic, G - geometry, Tl - tally, S - source, E - equipment.

Besides, the package has a preprocessor to compile working codes according to the names of the modules of different types, that are given at the package setup at the user’s PC and according to the user’s request.

The creation of the working code (W) is performed according to the formula:

W=C+T+P+G+Tl+S+E,

where C, T, P, G, Tl, S, E - names of the modules of the corresponding types.

The names given for package preprocessor specify the scheme of the task solving. All package modules of the same type are inter-changeable.

To modify the thermal neutron constants libraries TEPCON and VESTA the TERMAC and STEN codes are used. These codes are developed within the framework of the MCU project. The code GRAF provides geometry module input data check. The code performs visualization of geometry data of a variant in the form of two-dimensional sections with successive plotting of material and registration zones, and registration objects. The choice of the sections and types of regions are determined by the user in the interactive regime.

The current version of the CLAD library contains descriptions of more than 400 critical lattices and international tests in the MCU input language. The library includes the results of measurements at lattices and results of the corresponding calculations by means of the MCU-RFFI/A code.

The authors of the code are Abagjan L.P., Alexeyev N.I., Bryzgalov V.I., Veretenov V.V., Glushkov A.E., Gomin E.A., Gurevich M.I., Kalugin M.A., Maiorov L.V., Marin S.V., Judkevitch M.S.

Besides this Introduction, the description of the MCU-RFFI/A code includes the following chapters:

- Gomin E.A., Gurevich M.I., Maiorov L.V. Description of the usage and user guide.
- Alexeyev N.I., Veretenov V.V., Gurevich M.I. Geometric module SCG.
- Gurevich M.I., Alexeyev N.I. Geometric module NCG.
- Gurevich M.I. MCU-RFFI/A generation at the user’s PC.
- Abagjan L.P., Glushkov A.E., Judkevitch M.S. DLC/MCUDAT-1.0 neutron data library.
- Glushkov A.E., Gomin E.A. General description and algorithms of MCU-RFFI/A compound physic module.
- Gomin E.A., Gurevich M.I., Maiorov L.V. Architecture description.
- Abagjan L.P., Alexeyev N.I., Bryzgalov V.I. and others. Verification and quality assurance of the MCU-RFFI/A code in relation to the criticality calculations of neutron multiplying systems. RRC KI NRI report N36/1-133-96, Moscow, 1996.

The knowledge of chapters [1-3] is enough to create input data for MCU-RFFI/A. The first chapter contains the description of the algorithms used for neutron history modeling and neutron flux functionals estimation, the guide on the input data creation for all modules except geometric one, and the guide on the GRAF geometry visualization code. Information on geometry description and input data guide for SCG and NCG modules are given in chapters [2] and [3] accordingly.

The existence of two geometric modules is due to the following reasons. On the one hand, the SCG module is more reliable, because it has been in use for more than 10 years and tens of thousands variants have been calculated using this module (NCG has been in use for 4 years and hundreds variants have been calculated). On the other hand, NCG has many advantages in the input data simplicity and RAM memory economy. Full scope three-dimension models have been created by means of this module taking into account all the details of such complicated objects as reactors VVER-1000, RBMK-1000 and etc.

The chapter [4] describes the rules of generation of MCU-RFFI/A working versions considering the user’s suggestions and existing hardware. It also describes the MCUREP preprocessor that provides the generation.

The chapter [5] contains the description of the constants support of the code - constants library DLC/MCUDAT-1.0.

The chapter [6] contains detailed description of physical models of neutron interactions with nucleus, implemented in different sub-modules of the compiled physical module SOFIZM included into the code. These sub-modules are FARION (fast energy region), FIMBROEN (resonance energy region), two sub-modules for modeling of neutron interactions with matter in the thermalization region - MOFITTG and FIMTOEN, and the RAPAN code for calculations of the cross-sections by resonance parameters. The first thermalization sub-module lets one model neutron interaction with matter in multy-group transport approximation, the second one - considering continuous dependence of cross-sections on energy taking into account correlation between neutron energy change and change of its path direction. The calculation experience shows that the MOFITTG sub-module provides sufficient accuracy for most of practical applications.

As the code is intended only for eigenvalue problem solutions (criticality calculations) it includes the simplest SPNT source module that lets one model neutrons of the zero generation in one space point.

The chapter [7] contains the description of the code’s architecture intended mostly to help authors of separate modules.

The chapter [8] is the verification report containing the results of the calculations verifying the precision of effective multiplication factor and power distribution calculations stated in the code’s passport.

The MCU codes set has been developing in Russian Research Center “Kurchatov Institute” (Moscow, Russia) from the year 1982. Three versions of the code has been generated: MCU-1 (1985), MCU-2 (1990), MCU-3 (1993). On the base of updated modules of the MCU-3 package the MCU-RFFI code (1995) has been created. All these versions have been shareware and now are being used by many institutes of Russia.