Sensitivities of neutron transport modes with Monte Carlo Methods
Despite being the reference neutron transport method, Monte Carlo used to be limited in its capacity to calculate sensitivities (relative change in output associated with a change in input, such as a cross-section), or adjoint-based outputs, such as kinetics parameters (effective delayed neutron fractions, etc.). This has completely changed with the very fast development of perturbation methods and generalization in most of the codes in the last decade . This field is still growing and few researchers have focused on the question of the statistical convergence of those new objects when compared to the large bibliography that exists for other parameters, such as eigenvalues, in particular for problems with high dominance ratios, i.e. when the second eigenvalue is very close from the first one, the inverse of keff. Another very active field of research related to Monte Carlo is its use for the calculation of higher modes than the first eigenvalue or for other modes types. Many applications are based on the use of the modes of different formalisms, which are often “matrix filled” formalisms, i.e. formalisms that use matrices built from Monte Carlo tallies such as “Fission Matrices”. Kinetics calculations are historically based on spectral analysis and can now rely on Monte Carlo associated parameters for which sensitivities are also available .
The convergence of local variables such as local fluxes in Monte Carlo may be much slower than global ones, e.g. keff. The convergence of their sensitivities with the number of histories simulated is not well known and their actual convergence may be doubtful as it depends on « new » parameters of the Monte Carlo method used for the calculations of sensitivities such as the number of « latent » generations . We expect that the convergence speed of the sensitivities of the modes would be faster, if they could be calculated.
The objective of this project is to work on the combination of the two dynamic fields discussed above and extend the sensitivity capacities of Serpent2  for the calculation of the sensitivities of modes to different perturbations, such as nuclide densities or nuclear data, and to study the convergence speed of those new output parameters.
This PhD is part of the joint “NEEDS” project called SUDEC (Sensitivity Uncertainty comparison for Depletion Calculations) in which CNRS, CEA and IRSN work together to study the propagation of uncertainty in fuel burn-up calculations. Those fuel burn-up calculations rely on the calculation of reaction rates that can be considered as local variables that could be projected on an adequate mode base. The student will then contribute to the project by developing a key component of it and will benefit from the collective work and competencies of the partners.
Tools discovery. Convergence tests of sensitivities of existing Serpent 2 outputs.
Preliminary set up of innovative mode calculation sensitivities.
Development and tests of the performance of the sensitivities of the modes.
Research and set up of reduced models of coupling, with TH and/or depletion.
End of developments.
In depths studies with the tools developed.
Manuscript and defence preparations.
Adrien Bidaud has 20 years of experience in the field of nuclear data uncertainty and sensitivities. Besides this research and the associated teaching activities, he also teaches and develops interdisciplinary research projects in long term energy prospective with energy economists. He is the co-chair of the Energy and Nuclear Engineering program of the Engineering school PHELMA of Grenoble Institute of Technology.
Laboratoire de Physique Subatomique et Cosmologie (http://lpsc.in2p3.fr)
The aim of the research at LPSC is to improve our knowledge about the most elementary particles and about the forces that govern their interactions. It helps to broaden our understanding of the universe, its structure and its evolution. These activities require the development of sophisticated, state-of-the-art instrumentation, a strong theoretical research activity as well as strong modelling competencies that support the experiments during the preparatory stages and during the data analysis.
The research also affects our everyday lives; for example, it enables to come up with innovative solutions in the field of nuclear power or cancer treatment and to train a new generation of researchers, teachers and engineers.
Candidates interested in teaching activities may be offered to contribute to the nuclear engineering curriculum of Grenoble Institute of Technologie (school PHELMA) and Université Grenoble Alpes, which include for instance electronics, mathematics, signal processing, nuclear instrumentation lab sessions, numerical methods, numerical methods projects etc.
 “Review of Early 21st-Century Monte Carlo Perturbation and Sensitivity Techniques for k- Eigenvalue Radiation Transport Calculations”, Brian Kiedrowski, Nuclear Science and Engineering, 2017, 185:3, 426-444, https://doi.org/10.1080/00295639.2017.1283153
 “Perturbation and sensitivity calculations for time eigenvalues using the Generalized Iterated Fission Probability, Alexis Jinaphanh, Andrea Zoia,
2019, Annals of Nuclear Energy, 133, 678-687, https://doi.org/10.1016/j.anucene.2019.06.062
 « Sensitivity Analysis and Its Convergence Through Monte Carlo Calculations for the UAM GEN-III Benchmark: Application to Power Distributions », Pamela Lopez and Adrien Bidaud, Proceedings of the Conference: Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Raleigh, North Carolina, USA, April 2021
 “A collision history-based approach to sensitivity/perturbation calculations in the continuous energy Monte Carlo code SERPENT”, Manuele Aufiero et al., Annals of Nuclear Energy, 2015, https://doi.org/10.1016/j.anucene.2015.05.008.
Key-words: Neutronics, Nuclear Data sensitivity, Uncertainty analysis, Monte Carlo, Perturbation Theory.
Profile: Candidates must have a background in Reactor Physics, with a demonstrated knowledge of Neutron Transport. Some experience in Monte Carlo codes would be an asset.
LPSC – Groupe Physique des Réacteurs
Téléphone : 0476284045 email : firstname.lastname@example.org
THE PHD SHALL START IN: FALL 2022 – TO APPLY, CONTACT PROF. BIDAUD As Soon As Possible
Studying in Grenoble