Search

GRE@T-PIONEeR - GRaduate Education Alliance for Teaching the PhysIcs and safety Of NuclEar Reactors - is a project funded by the Euratom – Horizon 2020 Framework Programme which aims at developing and providing specialised and advanced courses in computational and experimental reactor physics at the graduate level (MSc and PhD levels) and post-graduate level, as well as the staff members working in the nuclear industry. One of the work packages of GRE@T-PIONEeR is devoted to developing a specific course on the nuclear data pipeline processes and to present the role of nuclear data to play in calculations of innovative reactor systems. This course covers all steps in the nuclear data life cycle, starting from the measurements to their validation and final use in nuclear reactor calculations. Beyond the technical contents of the courses being developed, the paper describes the use of innovative pedagogical methods and active learning techniques, such as flipped classes, aimed at promoting student learning.

Presentation of the GRE@T-PIONEeR project , updates and activities, with a focus on work package 2 on Nuclear Data.

International audience; The knowledge of higher-order harmonics beyond the fundamental mode is important and useful in the prediction of the spatial behaviour of nuclear reactors. Previous works have evidenced that the information on higher-order modes is of great relevance in the interpretation, by means of perturbation techniques (Gandini, 1978), of flux tilts in large cores. In order to assess the performance of the methods that are available to evaluate such modes in nuclear systems, simple configurations that allow for an analytical solution are analysed, and the iteration processes of filtered power, of sub-space iteration and of implicitly restarted Arnoldi methods are compared and discussed. The drawbacks of the filtered power method are highlighted. The implicitly restarted Arnoldi and the sub-space iteration methods are then applied to two benchmarks, the C5G7 and the more realistic UAM configurations, in order to draw some practical indications on their performances. The analysis of the results for all the different configurations considered allow highlighting the better computational performance of the implicitly restarted Arnoldi method as compared to the sub-space iteration method. © 2019 Elsevier Ltd

The study of the steady-state solutions of neutron transport equation requires the introduction of appropriate eigenvalues: this can be done in various different ways by changing each of the operators in the transport equation; such modifications can be physically viewed as a variation of the corresponding macroscopic cross sections only, so making the different (generalized) eigenvalue problems non-equivalent. In this paper the eigenvalue problem associated to the time-dependent problem (α eigenvalue), also in the presence of delayed emissions is evaluated. The properties of associated spectra can give different insight into the physics of the problem.

In this work, we present the results of a preliminary uncertainty quantification and sensitivity analysis study of the Molten Salt Fast Reactor (MSFR) behavior at steady-state performed by applying a non-intrusive Polynomial Chaos Expansion (PCE) approach. An in-house high-fidelity multi-physics simulation tool is used as reactor reference model. Considering several thermal-hydraulics and neutronics parameters as stochastic inputs, with a limited number of samples we build a PCE meta-model able to reproduce he reactor response in terms of effective multiplication factor, maximum, minimum, and average salt temperatures, and complete salt temperature distribution. The probability density functions of the responses are constructed and analyzed, highlighting strengths and issues of the current MSFR design. The sensitivity study highlights the relative importance of each input parameter, thus providing useful indications for future research efforts. The analysis on the whole temperature field shows that the heat exchanger can be a critical component, so its design requires particular care.

A 2-D noise model is implemented in the deterministic reactor code APOLLO3® to simulate a periodic oscillation of a structural component. The Two/Three Dimensional Transport (TDT) solver, using the Method of Characteristics, is adopted for the calculation of the case studies, constituted by a moving detector and control-rod bundle. The periodic movement is built by properly linking the geometries corresponding to the temporal positions. The calculation is entirely performed in the real time domain, without resorting to the traditional frequency approach. A specifically defined dynamic eigenvalue is used to renormalize in average the reactivity over a period. The algorithm is accelerated by the DP N synthetic method. For each cell of the domain, the time values of fission rates are analysed to determine the noise extent. Moreover we propose a systematic approach to the definition of the macroscopic cross sections to be used in dynamical calculations starting from library data. As an aside of our work we have found that even in static calculation this approach can produce significant changes.

The FRENETIC code is being developed at Politecnico di Torino in the frame of the international effort for the deployment of lead fast reactors technology. FRENETIC is a multiphysics computational tool solving the neutronics and thermal-hydraulics equation at the full-core level, aiming at performing steady-state and time-dependent simulations in different conditions. In the present work, the validation activity of FRENETIC is carried forward by performing a benchmark against a reference computational model for the ALFRED design implemented in Serpent. Different core configurations in FRENETIC and different temperature distributions are considered, performing consistent comparisons between the two codes. All the results obtained show an extremely good agreement between the two models, implying that the ALFRED core can be well characterized by the FRENETIC code. The present study sets the basis for the future application of the code to simulate safety-relevant transients with FRENETIC.

The Fast REactor NEutronics/Thermal-hydraulICs (FRENETIC) code has been developed during the last years at Politecnico di Torino, implementing a full-core coupled neutronic/thermal-hydraulics model for steady-state and transient analysis of liquid-metal cooled fast breeder reactor (LMFBR). In the framework of the validation activities for the code, an analysis of the sodium-cooled reactor EBR-II, previously carried out in the frame of a IAEA Coordinated Research Project, is performed with FRENETIC including the most recent physics models. In particular, photon transport and heat deposition are taken into account, a feature which has been proved in previous studies to be relevant to the correct study of the EBR-II core. To this purpose, a set of nuclear data for photons has been generated by means of the Monte Carlo code Serpent-2, and it is demonstrated that the code is able to take into account the photon heat deposition in the EBR-II.

The solution of the linear transport equation used for the study of neutral particle fields requires the imposition of appropriate boundary conditions. The choice of the conditions to impose for an infinite medium is not straightforward. The question has been given different formulations in the literature with various justifications based on some physical reasoning. Some aspects of the question are here analysed, from both the mathematical and the physical point of view. It is concluded that the inspiring golden rule should be the establishment of conditions that do not require any reference to the properties of the specific medium being considered for their justification., 4 pages, 9 references

Plasma disruptions are rapid and dramatic off-normal operation events, lasting only a few milliseconds, which can damage the tokamak in-vessel structures. Shattered Pellet Injection (SPI) can be employed to mitigate these transients. This technique consists of injecting impurities to enhance the isotropic radiation emission, thus reducing the peak heat load onto the Plasma Facing Components (PFCs). In this work, we employ the CHERAB code to assess the radiative heat load on the EU-DEMO in-vessel structures following a disruption mitigated via SPI with 0.5 GJ of radiated energy. The effect of different penetration depths of shattered pellets varying in the range 0.2–3.5 m is parametrically studied. The computed peak radiative load in the case of deep deposition of the impurities ( ∼ 5.6 · 102 MW/m2) is around 18 times smaller than in the case of shallow penetration ( ∼ 1.0 · 104 MW/m2). Instead, a figure for an intermediate penetration would be ∼ 1.5 · 103 MW/m2.

A new approach to assess the risk associated with jetfire and poolfire accidents on an offshore oil facility using cellular automata is presented. This model simulates many accident scenarios, and the related evacuation processes, adopting a Monte Carlo approach in order to evaluate an average consequence and then a more realistic value of the risk associated with these accidents. The results of this new method are discussed and compared with the results obtained from a traditional approach over a real case study. The comparison shows that this new approach supplies lower risk-related results, still being conservative; besides, it can supply further information useful in the design phase.

International audience; The Molten Salt Fast Reactor (MSFR) with its liquid circulating fuel and its fast neutron spectrum calls for a new safety approach and adaptation of the analysis tools. In the frame of the Horizon2020 program SAMOFAR (Safety Assessment of the Molten Salt Fast Reactor), a safety approach suitable for Molten Salt Reactors has been developed and is now applied to the MSFR. For this purpose, the Lines of Defence (LoD) method is selected to drive the design consistently with the Defence in Depth principle. This paper presents the main characteristics of the method, along with some practical guidelines to apply it to the specific case of the MSFR; moreover, some initiating events are analyzed through the implementation of the LoD tool. The outcomes of this analysis drive the design evolution.

Kinetics experiments are carried out in subcritical systems in order to estimate the subcriticality level. The reactivity is reconstructed from neutron flux measurements obtained by local neutron detectors. In this paper a method to reconstruct the prompt time constant for a subcritical system using flux measurements following a source pulse is presented. While the prompt time constant is by itself a significant characterization of the subcriticality level, it can also be used to reconstruct the system reactivity. The approach is based on Prony’s analysis, which is a standard method for non-linear minimization problems when only exponentials or sinusoids are involved. The problems connected to the presence of experimental errors are overcome by properly modifying the technique. The effects of experimental uncertainties and detector positioning is analyzed.

The Molten Salt Fast Reactor (MSFR) with its liquid circulating fuel and its fast neutron spectrum calls for a new safety approach including technological neutral methodologies and analysis tools adapted to early design phases. In the frame of the Horizon2020 program SAMOFAR (Safety Assessment of the Molten Salt Fast Reactor) a safety approach suitable for Molten Salt Reactors is being developed and applied to the MSFR. After a description of the MSFR reference design, this paper focuses on the identification of the Postulated Initiating Events (PIEs), which is a core part of the global assessment methodology. To fulfil this task, the Functional Failure Mode and Effect Analysis (FFMEA) and the Master Logic Diagram (MLD) are selected and employed separately in order to be as exhaustive as possible in the identification of the initiating events of the system. Finally, an extract of the list of PIEs, selected as the most representative events resulting from the implementation of both methods, is presented to illustrate the methodology and some of the outcomes of the methods are compared in order to highlight symbioses and differences between the MLD and the FFMEA.

This paper describes the neutronic benchmarks and the results obtained by the various participants of the FP7 project EVOL and the ROSATOM project MARS. The aim of the benchmarks was two-fold: first to verify and validate each of the code packages of the project partners, adapted for liquid-fueled reactors, and second to check the dependence of the core characteristics to nuclear data set for application on a molten salt fast reactor (MSFR). The MSFR operates with the thorium fuel cycle and can be started with 233U-enriched U and/or TRU elements as initial fissile load. All three compositions were covered by the present benchmark. The calculations have confirmed that the MSFR has very favorable characteristics not present in other Gen4 fast reactors, like strong negative temperature and void reactivity coefficients, a low-fissile inventory, a reduced long-lived waste production and its burning capacities of nuclear waste produced in currently operational reactors.

Neutron transport adjoint calculations are useful in many reactor physics applications. Among various applications, the adjoint flux can be used in perturbation theory to prevent large calculations and computational costs when estimating a small reactivity insertion into the system. Furthermore, they can serve as validation tests for numerical schemes, since both direct and adjoint calculations for a given system should lead to the same eigenvalue, although using two different physicomathematical formulations of the transport model. The synchronized implementation of the method of characteristic (MOC) for neutron transport in forward and adjoint approaches is accomplished in this work. The result is validated using the C5G7 benchmark with comparisons of the multiplication factor and pin power values. Differences between forward and adjoint multiplication factors in the results are achieved in the order of 1.0E-6. Meanwhile, the difference between the multiplication factor and the C5G7 benchmark is in order of 1.0E-5, using an S16 level symmetric angular discretization and a track spacing of 0.01 cm.

The paper shows the application of the most recent sensitivity techniques implemented in Serpent-2 in order to propagate the uncertainty from the nuclear data to the macroscopic, homogenised cross sections of the ALFRED reactor, which is then simulated with the multi-physics code FRENETIC. The main results are encouraging and define a possible methodology to propagate the nuclear data uncertainties to the main macroscopic parameters computed with FRENETIC, in order to perform thorough safety analyses for the ALFRED reactor.

The ability to accurately model the dynamic behaviour of the neutron distribution in a nuclear system is a fundamental aspect of reactor design and safety assessment. Due to the heavy computational burden associated to the direct time inversion of the full model, the quasi-static method has become a standard approach to the numerical solution of the nuclear reactor dynamic equations on the full phase space. The present paper is opened by an introductory critical review of the basics of the quasi-static scheme for the general neutron kinetic problem. Afterwards, the implementation of the quasi-static method in the context of a three-dimensional nodal diffusion theory model in hexagonal- z geometry is described, including some peculiar aspects of the adjoint nodal equations and the explicit formulation of the quasi-static nodal equations. The presentation includes the discussion of different formulations of the quasi-static technique. The results presented illustrate the features of the various formulations, highlighting the corresponding advantages and drawbacks. An adaptive procedure for the selection of the time interval between shape recalculations is also presented, showing its usefulness in practical applications.

The reactivity monitoring in subcritical accelerator-driven systems is a key aspect for the development of this technology. In this work, an inverse method for the determination of the system reactivity from the analysis of flux and power signals, based on the point kinetic approach, is applied to source-driven systems. The features of the algorithm specific to the application to subcritical assemblies are identified, and the sensitivity to the integral parameters characterizing the system is discussed. The technique is applied to different transient situations, simulated by neutronic codes adopting point kinetics and multigroup diffusion, and its accuracy in the presence of localized spatial and spectral phenomena is assessed. Different approaches for the reduction of the uncertainties introduced by the experimental noise are proposed and compared.

The analytical approach to the neutron kinetics of a reflected multiplying system constitutes a challenging problem in mathematical physics and provides useful results for a full physical understanding of the multiplication process in non-homogeneous media, opening the possibility to establish reliable benchmarks. In this work, the basic mathematical features of the neutron diffusion operator in a reflected configuration are investigated. The completeness of the eigenstates is discussed and proven. The case of the infinite reflector is taken into consideration, highlighting its peculiarities that lead to the appearance of a continuum spectrum. The limitation of the critical eigenfunctions is also discussed. The analysis is carried out at first disregarding the presence of delayed emissions. The work is then extended to include also in the model the presence of delayed neutron precursors.

International audience; Solving the adjoint linear transport equation by Monte Carlo methods can be convenient forapplications emerging in radiation shielding, where the detector is typically small (in terms of probabilityof detecting a signal). In this work we compare a few stochastic models that can be used in order toformally solve the adjoint transport equation by simulating artificial particles called adjunctons thesemodels dier in the form of adjuncton cross sections, scattering laws and multiplicities. In view of testingthe accuracy and the performances of these schemes, we have selected some benchmark configurations forcontinuous-energy transport in infinite media, where reference solutions can be established. The role ofpopulation control techniques, such as Russian roulette and splitting, is also carefully examined

Heat transfer phenomena involving internally heated fluid flows are of particular interest in several industrial applications, in chemical plants as in the nuclear field. This topic is relevant for the development of the Molten Salt Reactors (MSRs) since it involves the safety characteristics of the liquid molten salt fuel. In the literature, there is a lack of systematic studies on the heat transfer mechanism and correlations for flows in ducts featuring an internal heat source, apart from some analytical studies performed in Fiorina et al., "Thermal-hydraulics of internally heated molten salts and application to the MSFR", Journal of physics, Conference series 501 (2014)., In this work, the Nusselt number is computed multiplying the traditional Nu for internal flows times a corrective factor to account for the internal heat source. As a main outcome of this work, it is possible to obtain a CFD-based improved estimate of the corrective factor correlation for turbulent flow regime with respect to the work by Fiorina. The numerical CFD analysis is performed with the open source code OpenFOAM., Despite its simplicity, the method is general and applicable for any geometrical and thermal situations.

We develop a fully analytical study of the spectrum of the neutron diffusion operator both for spatially homogeneous and reflected reactors in a multi-group energy model. We illustrate and discuss the results of the analysis of the time spectrum of the diffusion operator, to highlight some general properties of the neutronic evolution in a multiplying system. Various new results are presented, particularly regarding the possible existence of complex time eigenvalues, the appearance of a continuum part of the spectrum and the orthogonality properties of the eigenfunctions in the case of an infinite reflector.

The current studies on the development of the EU DEMO breeding blanket include among the options the use of liquid Lithium-Lead (17Li-83Pb) as tritium breeder (and multiplier), with different coolants. As the tritium is steadily produced in the blanket during the reactor operation, suitably efficient strategies for the Tritium Extraction System (TES) from the breeder must be developed, allowing a closed fuel cycle in situ and avoiding tritium accumulation in the machine. The Permeator Against Vacuum (PAV) appears to be one of the most promising solutions to achieve this goal. In this paper, the performance of a PAV system is studied by means of different models describing the transport of tritium in the liquid PbLi and in the metallic membrane separating it from the vacuum. The comparison of the results for different membrane materials and size of the device, for a given target efficiency, allows to optimize the PAV design, also taking into account corrosion issues. The approximations and limitati...

A recently developed method for the continuous reactivity monitoring in nuclear reactors and in subcritical source-driven systems is applied for the interpretation of flux measurements carried out in the KUCA facility. The scope of the work is to validate the method using real experimental data. The method is based on general mathematical properties of the differential equations constituting the point kinetic model. Several pulsed experiments performed in different system configurations and using different source target materials are analysed. The results are compared with the classic area ratio method. A good agreement is obtained when the space-energy transient following the source shut-down dies out and when the system sets on a point-like evolution. The results prove the suitability of the proposed method for application to the reactivity monitoring of source-driven systems.

The spectral element method can be used to deal with the spatial operators of neutron transport problems with high efficiency, as shown recently in the framework of the second-order A N transport approximation. The results highlight interesting computational features and show the appeal of the scheme for reactor physics applications. In this paper we investigate the numerical performance of the method in detail. In order to carry out an accurate monitoring of the error behavior to levels close to numerical round-off, we use benchmark problems with known analytical solutions, or with manufactured solutions. Manufactured solutions can easily be obtained for source-injected problems, by tailoring the external neutron source and the boundary conditions to a pre-established analytical solution for a given system. The results presented prove the effectiveness of the method and the high level of accuracy that can be attained.

The problem of the effect of fissile lumps spatially appearing in a random fashion inside a fluid fuel reactor is addressed. The effect on static reactivity is evaluated by means of first-order perturbation theory. The analysis is carried out in diffusion theory with the presence of delayed neutron emissions, taking into account the fuel motion that introduces a distortion of the space distribution of the delayed neutron precursors. The method is applied to a one-dimensional configuration to investigate the general features of the random process. Afterwards, a more realistic two-dimensional cylindrical geometry is considered. The estimation of the mean value and standard deviation of the reactivity inserted is performed by Monte Carlo simulations and a deterministic quadrature approach, to compare the methods in terms of computational effort and accuracy of the results. The reconstruction of the probability density function of the reactivity is also performed by polynomial chaos expansion. The results presented show that random reactivity effects constitute an important issue in the assessment of these innovative molten salt systems.

Within European Partitioning & Transmutation research programs, infrastructures specifically dedicated to the study of funda- mental reactor physics and engineering parameters of future fast-neutron-based reactors are very important, being some of these features not available in present zero-power prototypes. This presentation will illustrate the conceptual design of an ADS with high safety standards, but ample flexibility for measurements. The design assumes as base option the 70 MeV, 0.75 mA proton cyclotron facility planned to be constructed at the INFN National Laboratory in Legnaro, Italy and a Beryllium target, with Helium gas as core coolant. Safety is guaranteed by limiting the thermal power to 200 kW, with a neutron multiplication coefficient around 0.94, loading the core with fuel containing Uranium enriched at 20% and a solid-lead diffuser. The small decay heat can be passively removed by thermal radiation from the vessel. Such a system could be used to study, among others, some specific aspects of neutron diffusion in lead, beam-core coupling, target cooling and could serve as a training facility.

A new multi-physics simulation tool – FRENETIC (Fast REactor NEutronics/Thermal-hydraulICs) – is presented for the quasi-3D analysis of a lead-cooled fast reactor core with the hexagonal fuel element configuration, as currently proposed within the framework of the European project LEADER. The tool implements coupled neutronic (NE) and thermal-hydraulic (TH) models. In the NE module, a 2D + 1D full-core multi-group diffusion solver has been developed based on a coarse-mesh nodal scheme and adapted to cope with the hexagonal geometry. In the TH module, the hexagonal elements, described by 1D (axial) transient advection and conduction in the coolant coupled to conduction in the fuel pins, are thermally coupled to each other in the transverse directions to obtain the full-core evolution of the distribution of the TH variables. The NE and TH modules are coupled at each TH time step by transferring to the TH module the distribution of the power source computed by the NE module, which is the driver of the TH evolution; alternately, the temperature distribution computed by the TH module is input to the NE module, in order to update the cross sections. The code is benchmarked against pure TH and pure NE analytical solutions and the results of a coupled NE/TH pseudo-transient (criticality search) are also presented. The convergence of the numerical solution is demonstrated both in space and time by computational simulations.

Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2 N −1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems.

The adjoint equation was introduced in the early days of neutron transport and its solution, the neutron importance, has ben used for several applications in neutronics. The work presents at first a critical review of the adjoint neutron transport equation. Afterwards, the adjont model is constructed for a reference physical situation, for which an analytical approach is viable, i.e. an infinite homogeneous scattering medium. This problem leads to an equation that is the adjoint of the slowing-down equation that is well-known in nuclear reactor physics. A general closed-form analytical solution to such adjoint equation is obtained by a procedure that can be used also to derive the classical Placzek functions. This solution constitutes a benchmark for any statistical or numerical approach to the adjoint equation. A sampling technique to evaluate the adjoint flux for the transport equation is then proposed and physically interpreted as a transport model for pseudo-particles. This can be done by introducing appropriate kernels describing the transfer of the pseudo-particles in phase space. This technique allows estimating the importance function by a standard Monte Carlo approach. The sampling scheme is validated by comparison with the analytical results previously obtained., 21 pages, 6 figures, 31 references

The CR-39 detectors are widely used as passive radon dosimeters, as well as in physics laboratories or for industrial applications. For what concerns radon monitoring, the calibration curve which is usually adopted corresponds to a linear relation between the actual etched track density and the track density counted by an automatic acquisition system. This linear calibration provides very accurate radon exposure assessments in a restricted range of etched track density, however it neglects the effect of the tracks overlapping that becomes as relevant as the track density increases. In the present work the mathematical expression of the area covered by a set of uniformly distributed tracks is deduced. This result allows then to infer the probability that the system acquires the right track density, providing a general calibration curve for a solid state radon track detector. The process of track production and reading routine is also simulated adopting a Monte Carlo approach, showing that the obtained results are in agreement with the function proposed as calibration curve. Moreover, a linear dependence between the track average area and the rate parameter of the calibration curve has been observed. Finally a semi-empirical correlation based on the previous results is proposed.

The present work addresses the problem of the determination of the eigenvalue spectrum of the multigroup diffusion equation for nuclear reactor physics applications. The analytical determination of the multiplication eigenvalues is presented for the material homogeneous configuration case. The characteristics of the time eigenvalue spectrum is further considered and illustrated, highlighting the possibility of the appearance of complex eigenvalues and discussing their physical significance. Various results are presented for different material compositions and energy group structure. Some comparisons to reference results, obtained with highly detailed Monte Carlo evaluations, are also carried out. Such comparisons evidence the limits of the diffusive approach and of the energy group discretization.

This study introduces a new formulation of kinetic parameters for accelerator driven systems and it is structured into two parts. The first part is dedicated to the classic definition of the kinetic parameters and compares different calculation methodologies. The second part considers a new definition of the kinetic parameters for subcritical assemblies, with particular emphasis on the delayed neutron fraction and the prompt neutron lifetime. This new definition takes into account neutrons from the external neutron source and (n, xn) reactions, which increase the fraction of prompt neutrons. The developed theoretical framework has been applied by Monte Carlo and deterministic calculations to the YALINA Thermal subcritical assembly located in Belarus. This facility can be driven by californium, deuterium–deuterium (D–D), or deuterium–tritium (D–T) external neutron sources. For the D–T neutron source, (n, xn) reactions must be taken into account in order to produce accurate results because the average energy of D–T source neutrons is 14.1 MeV, a value which is much higher than the threshold energy of the (n, 2n) cross section of uranium isotopes.

The determination of the subcriticality level constitutes an important issue in the assessment of the accelerator-driven system technology. For this purpose, the interpretation of flux measurements requires a lumped-parameter model employed in an inverse fashion. This papers addresses the drawbacks of point kinetics in performing such a task. In particular, the problem of the generation of integral parameters is considered, in connection with the use of a shape function and of a projection weight tailored to the neutron flux detector. Furthermore, the question of the generation of the effective source is analysed, and some proposals to modify the time dependence of such a function to account for the time delay at the flux detector are presented and discussed.

Integral parameters can give useful information on the physical properties of a multiplying system. However, various theoretical problems are encountered when trying to introduce them in a consistent way for source-driven systems. Many questions also arise for their experimental estimation. After some general considerations, the paper presents comparisons of numerical results obtained in different approaches and by the application of inverse methods to localized neutron flux signal detections. Results presented refer to the Yalina Booster experimental facility, which constitutes an excellent challenging test for the models and methods, being a neutronically, spatially and spectrally decoupled system. Some considerations on the usefulness of such parameters for kinetic analyses and to qualify the system characteristics are also included in the paper, analyzing both highly and loosely coupled configurations.

The spatially asymptotic theory is a useful approach to the neutron transport model for nuclear reactor physics applications. For steady-state problems the transport equation is taken in an infinite medium and it is treated by the Fourier transform. A formal solution is thus obtained for any assumption on the order of anisotropy, leading to the B"N formulation. In the case of isotropic emissions the Green function of the problem can be given an explicit expression by the inverse Fourier transformation, leading to the solution that can also be obtained by Case method. The analysis of the kernel of the solution in the Fourier space can give important physical information on the transport phenomenon. Lower order models can be derived by giving an approximate formulation to the exact kernel, and thus somewhat allowing a distortion of the rigorous physical transport features. A study of the eigenvalues of various models can give an important insight on the physical limits of approximations introduced. Within the asymptotic approach an optimization strategy allows to evaluate diffusion theory parameters for realistic system calculations. A discussion on the performance yielded by various definitions is carried out by comparisons of the numerical results for a two-dimensional system. The results presented evidence the impossibility to have a general formulation of diffusion parameters capable to perform satisfactorily in all physical situations.

This work is a revisitation of the rigorous analytical method to obtain the solution of the neutron space-time kinetic problem in diffusion theory for spatially non-homogeneous systems. The results obtained for simple plane geometry configurations may well serve for benchmarking numerical codes. The general problem for a multilayer reactor is considered and the analytical procedure for the solution by means of the Laplace transform and the identification of eigenvalues and spatial eigenfunctions are presented. The theory is applied to a symmetrically reflected slab reactor, with a detailed presentation of some mathematical features, such as the reality of the eigenvalues and the concept of orthogonality of the eigenfunctions. Afterwards, various transients are simulated and the study of the error associated to series truncation is carried out.

This work is devoted to the derivation of alternative formulations of the one-velocity neutron transport equation. The Peierl's integral form of the transport equation is considered as the starting point. Using a generalization of the mathematical procedure applied to derive the A N approximation, two formulations are obtained, both second-order differential in time and space, which can be considered as alternative forms of the A ∞ model. Some features and physical interpretations are investigated for the special case of plane geometry.

The quasi-static method is a standard tool for the space–time solution of neutron transport problems in multiplying media. Its basic principle lies in a factorization of the angular flux into the product of two functions, ‘amplitude’ and ‘shape’, where the amplitude depends only on time (and contains the major part of the time-dependence) while the shape function depends on all variables, time included. The shape equation is solved on a long time-scale, while the amplitude is determined on a short time-scale. The factorization is made unique by proper normalization conditions for the shape function. Most implementations replace the basic equation (transport or diffusion) by the set of coupled amplitude and shape equations derived from the factorization, the so-called ‘Improved Quasi-static Method’ (IQM). In this paper we describe an alternate approach already known for some time we have called ‘Predictor–Corrector Quasi-static Method’ (PCQM). We discuss its efficiency for both solid- and liquid-fuel systems dynamics.

The study of the neutronic response to a localized pulsed source requires accurate models, due to the strong spatial effects coming into play associated with the wavefront propagation. Furthermore, usually neutron sources inject particles at high energy and, consequently, important spectral effects may come into play. In previous works, the propagation phenomenon has been investigated for idealized configurations in exact transport (Dulla et al., Annals of Nuclear Energy C 33:932–940, 2006), restricting the analysis to one-group problems. Furthermore, the numerical effects associated with the application of discrete ordinate and spherical harmonics methods have been analyzed (Dulla and Ravetto, Transactions of the American Nuclear Society C 90:278–280, 2004; Annals of Nuclear Energy C 35:656–664, 2008), illustrating the appearance of time-dependent ray effects.