# The MCU-REA/2 Code

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

Software registration certificate N2010613420.

MCU-REA/2 is intended for modeling of transport of neutrons, photons, electrons and positrons by analog and non-analog Monte Carlo methods on the basis of the evaluated nuclear data in systems with three-dimensional geometry.

**Ability
to model transport of various kinds of radiations by means of
non-analog Monte Carlo methods is the major difference of the code
from all previous codes of the MCU family.**

The basic scopes of the code:

the decision of the homogeneous and non-uniform equation of neutron transport and calculation of neutron-physical characteristics of systems with a given isotopic structure of materials;

calculation of fast neutron flux and evaluation of the flux at a surface and in thickness of reactor pressure vessel provided that sources of neutrons are given, for example, calculated by means of engineering codes;

calculation of a ratio between power distribution in a fuel assembly and a signal of the sensors of control and protection system.

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

**Constant data library of the code**

Constant maintenance of the code is provided by the bank of neutron-physical data DLC/MCUDAT-2.2 that consists of the following parts.

ACE - library 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-93;

MULTIC the 301-group library containing, in particular, the data on temperature dependence of subgroup parameters in the region of non-resolved resonances;

LIPAR - resonant parameters in the region of resolved resonances;

KORT – pointwise library of neutron-physical constants in the region of low energies (the top boundary - 5 eV),

TEPCON - multigroup sections in the thermal region;

VESTA - data for continuous energy simulation of scattering in thermal region in the form of probability tables received from laws of scattering S (alfa,beta);

DOSIM - cross-sections of dosimetry reactions;

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

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

PHOTONK - library of kerma-factors for photons.

Besides, the EGS-4 code, intended for modelling of electron-photon cascades, uses the internal library of constants.

For updating libraries of constants of thermal neutrons TEPCON and VESTA the TERMAC and STEN codes developed within the framework of the MCU project are used.

**Modeling of particle transport**

The code allows taking into account effects of continuous change of particle’s energy at collisions, and also both continuous, and stepwise dependence of cross-sections on energy.

At modelling of neutron transport the following effects are taken into account.

At generation of fission neutrons the use of fission spectrum of prompt and delayed neutrons is supposed.

In fast energy region the anisotropy of elastic scattering in system of the centre of mass is taken into account, there is an opportunity to carry out modelling of inelastic collisions considering the laws contained in files of the evaluated nuclear data.

In the region of the non-resolved resonances cross-sections are calculated using subgroup parameters or Bondarenko f-factors, in both cases considering temperature dependence of used parameters.

In the region of the resolved resonances both subgroup and pointwise representation of cross-sections may be used. Cross-sections of the most important nuclides are described by "infinite" number of points, because at modelling they are calculated using resonant parameters in each energy point. Such scheme allows to carry out calculations directly using the data on resonant parameters without preliminary preparation of tables of cross-sections and to evaluate temperature effects through analytical dependences of cross-sections on temperature.

Modelling of collisions in the thermal area is carried out either in multigroup transport approximation, or using the model of continuous change of energy considering correlations between change of energy and scattering angles. In both cases chemical bounds, thermal movement of nucleus and coherent effects for elastic scattering are taken into account.

The photon physics treatment in MCU-REA/2 includes:

• coherent scattering;

• incoherent scattering;

• photoelectric effect;

• pair production.

The electron and positron physics treatment in MCU-REA/2

includes:

• Bremsstrahlung;

• positron annihilation;

• Moeller (e-e-) and Bhabha (e+e-) scattering.

**Geometry of modeled systems**

The code allows calculating three-dimensional systems of practically any complexity.

The system is represented as a set of homogeneous geometrical zones, each of which is described as Boolean combination of a set of simple bodies (a method of combinatory geometry). There are 19 types of bodies (cylinders, a cone, a sphere, parallelepipeds etc.). The description of geometry of systems containing regularly repeating elements, is facilitated by the use of the duplication methods, allowing to set a repeating element only once. For the systems containing elements with complicated internal structure, there is an opportunity of their multilevel hierarchical description. The use of hierarchy reduces the amount of input and saves computer memory. The correct use of symmetry and boundary conditions also facilitates the task of geometry.

*The method of combinatory geometry* allows to describe systems,
which borders consist of pieces of planes or square-law surfaces.

*The Woodcock method* also realized in the code, allows to
remove this restriction.

*The special algorithm* enables to take into account effects of
double heterogeneity when fuel elements contain tens thousand
micro-rods.

To each geometrical zone the user attributes a number of attributes: number of a material, number of a tally zone (any association of geometrical zones from identical materials), number of tally object (for example, a cell or an assembly) and so forth. These attributes may be generated automatically using the minimal information set by the user.

To check input data describing a geometry of a modelled system, it is possible to view the image of the given system as flat cross-sections with the consecutive image of material zones, tally zones and tally objects. Generation of colour and black-and-white images is possible. The choice of cross-sections, types of areas, numbers of colours and the output of the picture (the screen or a file on a disk) are defined by the user in the interactive mode.

**Scope of the code**

The code allows calculating systems with an external neutron source and without it (criticality task).

The following boundary conditions may be used: leakage through an external surface, white and mirror reflection, translational symmetry. The code allows to calculate functionals of neutron flux for infinite homogeneous heterogeneous lattices with translational symmetry with the leakage given by a buckling vector.

Various functionals of the neutron flux are calculated. The functionals are determined as integrals of flux with the given weight functions in tally zones, tally objects and in a system as a whole. The evaluation of functionals is possible using the length of the path or points of collisions.

The following values are calculated.

For neutrons:

neutron multiplication factor (by the number of collisions, number of absorptions, combined estimations);

effective fraction of delayed neutrons;

neutron flux density, nuclear reaction rates for separate nuclides and their mixture in the given spatial-energy intervals;

few-group constant set for tally objects including diffusion coefficients based on the different definitions;

For photons:

photon fluxes and reaction rates for separate nuclides and their mixtures in specified spatial-energy intervals;

electron and positron fluxes and reaction rates for separate nuclides and their mixtures in specified spatial-energy intervals;

distribution of the electric charge in zones;

energy absorbed by materials.

For the decision of tasks with strong decrease of flux non-analog methods of modelling ALIGR, weight window and splitting-roulette are realized.

**Technical features of realization of the code**

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 on memory.