Corresponding author: Gennady M. Zherdev ( jerdev@ippe.ru ) Academic editor: Georgy Tikhomirov
© 2018 Gennady M. Zherdev, Tamara S. Kislitsyna, Mark N. Nikolayev.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Zherdev G, Kislitsyna T, Nikolayev M (2018) ROCOCO system of combined neutron constants – current status and results of testing using geometrical module of the MMK code. Nuclear Energy and Technology 4(3): 217222. https://doi.org/10.3897/nucet.4.31861

Results of studies aimed at the further refinement of the ROCOCO system (routine for calculation and organization of combined constants including crosssections in group and subgroup representation with detailed description of energy dependence of neutron crosssections) (
Results of calculations are compared with data obtained using the MCNP5 precision program (
New ROCOCO combined system of neutron constant preparation, further refinement, introduction in the practice of calculations, MonteCarlo method, results of comparative calculations, potential of development
As compared with the ROCOCO system presented during the Neutronics Seminar in 2015 (
It was discovered that two subgroups are sufficient for describing the effect of selfscreening of crosssections within the range of unresolved resonances. Special simplified algorithm was developed for obtaining twosubgroup parameters of the resonance structure of crosssections on the basis of the data on selfscreening factors. Within the range of resolved resonances twosubgroup approximation fairly often proves to be insufficient and in that case previous universal algorithm (
A number of ambiguities were identified and eliminated in the process of operation of the ROCOCO complex in subroutines of the complex, number of error messages accompanied with output of information helping to reveal and remove the causes of these errors was increased. Several errors were found as well in the input data and were also removed.
Additional version of the COLIBRY library (combined library) was formed on the basis of ENDF/BVII evaluated data library. This version includes the data for the most important nuclides, including the data for 15 actinides and 81 nonfissionable isotopes. The version is linked to ROCOCO programs and was successfully tested on a small number of principal tests.
Geometrical modules of the MMK code were earlier combined with KENOVA code (
The following registration procedures were also introduced in the ROCOCOMMK code:
Microscopic crosssections of fission, capture (without fission), elastic and inelastic scattering, formation of secondary fission neutrons, formation of secondary neutrons in (n,2n) reactions, etc., energy release averaged by the registration zones;
Rates of the processes characterized by the above listed constants averaged over the registration zones with uncertainties (only for nuclides identified in the prescribed calculation job);
Multigroup spectra of neutron and gammaquanta fluxes averaged over the zones;
Energy release and contribution of separate nuclides in it;
Effective fractions of delayed neutrons for precursor groups.
Possibility of registration of a number of other functionals including average neutron lifetime, number of collisions, absorptions, number of neutrons leaking from the system, neutron leakage spectrum, etc., is provided as well. Registration is performed either “by the free path”, or “by the collision”, or “by the absorptions”. Combined estimations of the above functionals are not provided in the present version.
The complex is designed in the form of two independent program modules – the module of preparation of constants for calculations and module of modeling trajectories and registration. Calculation is performed in two stages. All data required for calculations are prepared during the first stage in accordance with isotopic composition, temperature and other parameters prescribed in the job description in the format and in the order optimal for simulation. All the data are stored in the external library. This library can be both in binary and in text form. The latter simplifies installation of the complex on different platforms and maintenance of the block of constants.
Results of calculation of infinite multiplying media performed using ROCOCO in comparison with calculations performed using precision MCNP5 code tied to the same ROSFOND library were presented in (
Results of calculation of keff for multidimensional multiplying systems.
Model  MMKRF  MCNP5  Discrepancy from MCNP5 (ROSFOND)  Ratio of calculation time using MCNP5 to that for ROCOCOMMK  

ROCOCOMMK  MCNP5 (ENDF/BVII)  
BIGTEN  0.99430(7)  0.99497(7)  –0.01±0.01%  0.01±0.01%  3.84 
BFS971  0.99481(12)  0.99511(12)  –0.03±0.02%  0.02±0.02%  6.56 
BFS801  1.00231(18)  1.00216(22)  0.01±0.03%  –0.15±0.03%  2.65 
BFS801 (elem.)  1.00265(18)  0.05±0.03%  3.94 
Results of calculations obtained using ROCOCOMMK are compared in Table
Comparison with calculation results obtained using MMK_C.
Model  ROCOCOMMK  MMK_C (ROSFOND)  Discrepancy from ROCOCOMMK  Ratio of calculation time using MMK_C to that for ROCOCOMMK 

BIGTEN  0.99430(7)  0.99660 (6)  –0.23±0.01%  18.5 
BFS801  1.00231(18)  1.00233(57)  0.002±0.03%  21.3 
Testing operational modes of ROCOCO in the systems with zones with different temperatures of the medium was performed using calculation model of BN800 fast reactor. 41 zones with seven temperature values were used in the model. Here, fissionable isotopes were present in the zones with only two different temperatures. Calculation performed using ROCOCOMMK with detailed description of neutron crosssections produced the result equal to k_{eff} = 0.99753(18). Multigroup (299 groups) calculation using MMKKENO with constants prepared by CONSYST system on the basis of BNABRF produced k_{eff} = 1.00120(14). Although statistically significant, discrepancy of – 0.37±0.22% proved to be of small significance. Expenditures of computation time for calculation with detailed description of crosssections proved, naturally, to be higher – by 2.3 times. No significant discrepancies in the distribution of energy release for reactor zones were identified, and, thus, this testing also produced positive result.
Temperature dependences of multiplication factor for BN800 model calculated using MMKKENO and ROCOCOMMK are compared in Figure
For the purpose of expansion of the field of application the MMKRF code was incorporated in the SCALA system (
Radiation characteristics of irradiated fuel, dpa numbers, etc., are calculated within the SCALA system simultaneously with calculation of nuclide composition.
The layout of the SCALA system with incorporated ROCOCOMMK code is represented in Figure
Experience of application of ROCOCOMMK demonstrated that performance of registration procedures occupies significant fraction of total calculation time. Obviously, this effect is manifested especially strongly in the calculations of geometrically complex systems, such as, for instance, BFS801. In such case registration of not only fluxes and energy release, but of microconstants, reaction rates, etc., required five times more time compared to the time required for calculation of only k_{eff}, energy release and group fluxes for zones. Time expenditures for registration in the calculation of more simple systems are significantly smaller (Table
Time (min) expended for execution of calculation job depending on the set of registered functionals.
System  Only k_{eff}  k_{eff}, group fluxes and energy release  k_{eff}, group fluxes, energy release and microconstants for nuclides  
By collisions  By absorptions  By freepaths  
BIGTEN  41.2  41.4  61.8  66.1  66.2 
BFS971  68.2  72.1  136.8  140.7  155.9 
BFS801  63.8  65.9  148.7  177.6  377.6 
It was precisely the time expended for registration that drove us to reject (at least temporarily) from combining registration procedures.
Figure
For the examined models the fraction of time expended for registration of crosssections can constitute from 30 to 56% and more, i.e. more than half of the calculation time may be spent for registration. For strongly heterogenous system registration time can reach or even exceed the time expended for simulation (by five times for BFS801, see Fig.
Incorporation of ROCOCOMMK in the SCALA system allows recording heterogeneously blocked (taking into account the detailed energy dependences) constants calculated using this code in the library in GMF format (
Narrow resonance;
“Weak diffusion”, i.e. neglecting the effects of current on the resonance structure of the flow;
“Standard spectrum” according to which group sections are averaged по.
Testing ROCOCOMMK performance in solving (n, γ)problems appears to be one of the first priority tasks. Let us remind, that ROCOCO complex supplies all the constants necessary for that. Gammaquanta are described in ROCOCO in 127group approximation with the use of macroconstants. They are assigned group numbers from 301st to 427th. Simulation of free path, collisions of the gammaquantum and consequences of this collision are already incorporated in ROCOCO operational procedures.
The necessity of modernization of 127group system of BNAB constants for the purpose of accounting for Xray radiation emitted during deceleration of photoelectrons, Compton electrons and positronelectron pairs should also be mentioned in connection with gammatask. The necessity of accounting for the bremsstrahlung became apparent in the calculations of radiation environment in SNF storage facility of the Bilibino NPP. Since generation of hard bremsstrahlung is mainly determined by the atomic number of the medium in which electrons are decelerated, inclusion of these data in the library for gammaquanta will not require modernization of the structure of this library.
For the purpose of further reduction of calculation time we intend as well to anticipate the possibility of combining all “group” nuclides, i.e. nuclides for which resonance selfscreening is not significant, in one macronuclide. Energyangular distributions of elastically scattered neutrons for this nuclide can be described in P5approximation using three discrete scattering angles with preset probabilities, similarly to how it is done in KENOVa and in ROCOCO in the description of gammaquanta scattering.
Algorithm for generating twosubgroup parameters tested in ROCOCOMMK could find its application in the anticipated modernization of СONSYST for obtaining twosubgroup macroconstants. Transition to twosubgroup approximation would allow correct accounting for the boundary resonance effects and angular dependence of resonance structure of the flux inside the group and, consequently, group constants as well.
Creation on the basis of ROCOCOMMK (or independently from it) of the program for calculation of BFS assembly cell allowing preparation of heterogeneously blocked (taking into account the detailed picture of crosssections) homogenized constants including transport crosssections determined from the condition of conservation of the ratio of neutron flow through the cell and gradient of the flux for its subsequent use in diffusion codes, such as TRIGEX (
Functionality of the combined ROCOCO nuclear constant supply system as the physical module of the engineering MonteCarlo nuclear reactor calculation code – the ROCOCOMMK code – was demonstrated. Difference between the results of calculation performed with detailed followup of neutron energy in the description of crosssections using the above code and the results of calculations using reference MCNP5 code does not exceed the uncertainties caused by the inaccuracy of knowledge of neutron data. Expenditures of CPU time on the calculation in the case of application of ROCOCOMMK are lower (in many cases significantly lower) then the expenditures of time for similar calculation using MCNP. Certain ways are examined for application of ROCOCOMMK in engineering calculations. Potential of future development was outlined.
The authors wish to express their gratitude to G.N. Mansurov for assistance in the organization of testing and development, as well as for recommendations and suggestions for improvement of the code; to K.F. Raskach for his assistance in mastering the OOBG module extracted from MMKKENO; to Yu.E. Golovko for the recommendations on the selection of models for testing and assistance in operating the DICE database and search for the required information in the database; to O.N. Andrianova for the provided calculation jobs and assistance in the operation of MCNP code; to V.N. Koscheev for consultations on ROSFOND and ENDF/BVII libraries and NJOY code, as well as for the comments on the results of test calculations; to V.B. Polevoy for the suggested tests of simple models, for crosstesting using MMKFK code and for the comments on the documentation for SCALA complex with ROCOCOMMK system.