# Napredne metode za analizo termičnih sipalnih presekov

### Oznaka in naziv projekta

NC-0012 Napredne metode za analizo termičnih sipalnih presekov

NC-0012 Advances in Thermal Scattering Law Analysis

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### Projektna skupina

Vodja projekta: **prof. dr. Luka Snoj**

### Vsebinski opis projekta

Problem identification In nuclear reactors, neutrons are slowed down to low energies where the chemical structure of materials plays a central role in the neutron physics. The corresponding thermal neutron scattering cross sections are conventionally tabulated for energies below 4 eV and are used as input in the calculation of the reactor physical parameters [1, 2]. The thermal neutron scattering cross sections, as provided in nuclear data libraries, such as commonly employed ENDF/B or JEFF libraries, are nuclide specific and are generated from theoretical physical models without the use of a fitting procedure. The theoretical approach is deemed sufficient because measurements are often limited in scope, have higher uncertainty or don't exist [3]. Even so, evaluations of only 24 materials are made available in the ENDF/B-VIII.0 library [4], where the latest 14 contributions were produced by only three institutions [5]. As with any measured, calculated or estimated quantity, knowledge of the quantity is near meaningless, unless its uncertainty is assessed. Results of such assessments are commonly represented using covariance matrices, whose elements represent uncertainties and correlations between different energy regions of the energy-discretized density of states or scattering cross section. However, while there exist nuclear data libraries, which tabulate covariance data for higher energy neutron cross sections, resonance data and other nuclear data, no such database exists for thermal cross sections. Furthermore, the most commonly used nuclear data format ENDF-6, does not even permit storing covariance data for thermal neutron scattering [6]. Methodology exists for propagation of nuclear data uncertainties through the neutron transport equation to uncertainty in calculated physical parameters of a nuclear reactor [7] such as multiplication factor, neutron flux energy spectrum, reaction rates, etc. Due to the lack of covariance data these uncertainty propagation methods have not been implemented to propagate uncertainties due to thermal cross sections, even though such data can have significant impact on the uncertainty of calculated physical parameters [8].

Objective

The objective of the proposed research is to generate thermal neutron scattering cross sections and corresponding covariance data in a rigorous manner that is from first principles, by employing state-of-the-art atomistic simulations, which rely on density functional theory in combination with lattice or molecular dynamics calculations. The main focus of the research will be given to the study of uncertainties in thermal scattering laws (TSL), namely to the determination of sources of uncertainty, their quantification and generation of associated covariance data, with the aim of developing a rigorous approach for covariance and cross section data generation. In order to be able to proceed with the uncertainty analysis, which is omitted in most existing studies, TSL evaluations will be produced for materials that have not yet been studied in a similar fashion. This includes materials such as UZrHx which serves as nuclear fuel in the most common type of research reactors, i.e. TRIGA reactors and is candidate fuel for future light water reactors [9], Teflon ((C2F4)n), which can be used as a moderator. Materials that have already been investigated in this manner, for example UO2 [10, 11], Lucite (C5O2H8)n [12], polyethylene [12] and others will be re-evaluated in a consistent manner with the aim of validating or improving existing data. Uncertainty and correlations in TSL have recently been investigated by the NEA WPEC subgroup 42 [13] which has been established to review existing methodologies in TSL and thermal neutron covariance data generation but has failed to present a definitive framework for dealing with thermal neutron scattering cross section covariances. On those grounds and because no standardized format for representing and storing thermal neutron scattering covariance data exists, a new format will be developed and proposed for inclusion in new editions of nuclear data libraries. Furthermore, with the help of neutron transport simulation codes, research will also focus on the study of propagation of uncertainties in thermal neutron scattering data to uncertainties in system response parameters, such as the effective neutron multiplication factor, reactor kinetic parameters, neutron induced fission reaction rates, etc. To this end a brute force approach, based on the Total Monte Carlo (TMC) method [14, 15], will first be undertaken, with the intention of later developing a smarter, less resource demanding Reduced Order Total Monte Carlo method (ROTMC). The method will implement variance reduction measures, based on a sensitivity analysis of the input parameters. The impact of the newly generated uncertainty information on uncertainties of reactor physical parameters will be assessed by means of simulating benchmark experiments from the ICSBEP handbook [16]. Lastly, with the use of improved TSL, which will be generated in the course of the project, effort will be made to reproduce the positive isothermal reactivity coefficient of a typical TRIGA reactor, which has been measured experimentally [17], but has never been reproduced in any stochastic neutron transport calculations, due to inadequate thermal neutron scattering data. The generated thermal neutron scattering cross sections could potentially impact development of new research directions in other areas of physics and chemistry, for example in the study of protein structure by thermal neutron scattering at high intensity neutron sources, such as high flux reactors or spallation sources.

- State-of-the-art in the proposed field of research

Firstly, new TSL will be generated for materials, which have not yet been investigated in this manner and data will be made available for inclusion in the upcoming ENDF/B and JEFF libraries. TSL will also be generated for already evaluated materials, and evaluations produced by other institutions will be validated against ours. In the beginning, priority will be given to the study of TSL of uranium-zirconium hydride UZrHx, which serves as moderator in the most common type of research reactor, the TRIGA reactor, which is also located at JSI. Critical experiments performed at the JSI TRIGA reactor serve as benchmark criticality safety experiments for UZrHx fuel. In addition new experiments, studying isothermal temperature reactivity coefficient, could be performed for experimental validation of temperature dependence of generated TSL for H in UZrHx. Secondly, thermal neutron scattering covariance data will be generated using both approaches outlined above and the impact of new data and newly obtained uncertainties on reactor physical parameters will be studied by means of comparison with benchmark calculations Completely new data will be produced for reactor physics applications which will provide scientists all over the world with uncertainty information that was, until recently, regularly neglected. Thirdly, a format for storage of thermal neutron scattering covariance data will be developed, which will solve some of the current problems, especially the problem of the size of data files representing thermal neutron scattering cross section covariance matrices. A few approaches will be considered, namely first order matrix propagation of uncertainty, uneven energy and momentum transfer grids and others. Evaluations of performance will be done, and the best performing format will be proposed for inclusion in the upcoming revisions of nuclear data library Finally, a Reduced Order Total Monte Carlo method will be developed to allow for faster, smarter, and less CPU demanding calculation of uncertainty propagation from the TSL to reactor physical parameters.

Relevance and potential impact of the results expected from the proposed research project The results will contribute to complement studies reported in this field with the aim of proposing new easy-to-use methods to ascertain impacts of TSL. This will lead to better knowledge of safety margins, better knowledge of reliability of nuclear data, as well as more reliable calculations of physical parameters of nuclear reactors. The highest impact is expected on application of improved nuclear data on modelling of hydride fuel reactors featuring several advantages over existing UO2 fuelled reactors, such as 50 % higher power density, 40 % lower electricity production costs, increased safety due to larger and faster (prompt) negative feedback effects (prompt negative temperature reactivity coefficient) [9]. As Hydrogen bound in a crystal lattice is an essential feature of hydride fuelled power reactors, accurate modelling of reactor behaviour is directly limited by the quality of thermal neutron scattering nuclear data. In addition generation of TSL will allow studies of nuclear criticality safety at ultracold conditions, i.e. criticality of materials having a temperature below 100 K.

REFERENCES: 1. Turchin V. F. Slow Neutrons. Israel Program for Scientific Translations, 1965. 2. Squires G. L. Introduction to the Theory of Thermal Neutron Scattering. Cambridge University Press, 1978. 3. Holmes J. C. et al. Nuclear science and engineering, 184(1):84-113, 2016. 4. Brown D. A. et al. Nuclear Data Sheets, 148:1-142, 2018. 5. Hawari, A., Noguere, G. SG42 Meeting Summary [Internet]. Twenty-Eight Meeting of the NEA WPEC, Paris France, May 15-29, 2017 [cited 26 September 2018]. Available from: https://www.oecd-nea.org/science/wpec/meeting2017/sg_meetings/WPEC-REP-SG42-A.Hawari.pdf. 6. Trkov, A. et al. Report: BNL-90365-2009 Rev. 1, Brookhaven National Laboratory, 2010. 7. Rochman, D. et al. Journal of the Korean Physical Society, 95(2):1236-1241, 2011. 8. Snoj, L. et al. Annals of Nuclear Energy, 42:71-79, 2012. 9. Greenspan, E. et al. Nuclear Engineering and Design, 239(8):1374-1405, 2009. 10. Pang, J. et al. Physical Review Letters, 110(15), 2013. 11. Pang, J. et al. Physical Review B, 89(11), 2014. 12. Hawari, A. I. et al. Thermal Neutron Scattering Law Data Evaluations for Nuclear Technology Applications. M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Jeju, Korea, April 16-20, 2017. 13. WPEC Subgroup 42 homepage, https://www.oecd-nea.org/science/wpec/sg42/. 14. Rochman, D., Koning, A. J. Nuclear Science and Engineering, 172:287-299, 2012. 15. Holmes, J. C. Monte Carlo Calculation of Thermal Neutron Inelastic Scattering Cross Section Uncertainties by Sampling Perturbed Phonon Spectra. North Carolina State University, 2014. 16. International Handbook of Evaluated Reactor Physics Benchmark Experiments. OECD/Nuclear Energy Agency, 2017. 17. Žagar, T., Ravnik, M. Kerntechnik, 70(4):223-229, 2005. 18. Sinitsa, V., https://www-nds.iaea.org/grucon/.

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### Faze projekta in opis njihove realizacije

Firstly, new TSL will be generated for materials, which have not yet been investigated in this manner and data will be made available for inclusion in the upcoming ENDF/B and JEFF libraries. TSL will also be generated for already evaluated materials, and evaluations produced by other institutions will be validated against ours. In the beginning, priority will be given to the study of TSL of uranium-zirconium hydride UZrHx, which serves as moderator in the most common type of research reactor, the TRIGA reactor, which is also located at JSI. Critical experiments performed at the JSI TRIGA reactor serve as benchmark criticality safety experiments for UZrHx fuel. In addition new experiments, studying isothermal temperature reactivity coefficient, could be performed for experimental validation of temperature dependence of generated TSL for H in UZrHx. Secondly, thermal neutron scattering covariance data will be generated using both approaches outlined above and the impact of new data and newly obtained uncertainties on reactor physical parameters will be studied by means of comparison with benchmark calculations Completely new data will be produced for reactor physics applications which will provide scientists all over the world with uncertainty information that was, until recently, regularly neglected. Thirdly, a format for storage of thermal neutron scattering covariance data will be developed, which will solve some of the current problems, especially the problem of the size of data files representing thermal neutron scattering cross section covariance matrices. A few approaches will be considered, namely first order matrix propagation of uncertainty, uneven energy and momentum transfer grids and others. Evaluations of performance will be done, and the best performing format will be proposed for inclusion in the upcoming revisions of nuclear data library Finally, a Reduced Order Total Monte Carlo method will be developed to allow for faster, smarter, and less CPU demanding calculation of uncertainty propagation from the TSL to reactor physical parameters.