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The present study develops a new method for calculating reactivity by using the Gauss-Legendre quadrature to numerically solve the inverse point kinetic equation. This quadrature can use different nodes and weights from Legendre polynomials with different orders. The results show good accuracy for polynomial higher orders with small time steps. The discretization obtained with the Gauss-Legendre quadrature allows expressing the reactivity calculation in the form of linear convolutions for integral dependence. The differential is approximated with a special quadrature by taking advantage of the behavior of the Lagrange polynomials. Results can be improved, but increases computational cost. It is concluded that the method developed here can be implemented in a reactivity digital meter that measures neutron populations as input signals for a nuclear reactor. [ABSTRACT FROM AUTHOR]

In this article, we propose a methodology based on cubature Kalman filtering (CKF) for simultaneous estimation of two important variables of nuclear reactors, viz. the neutron flux and the total core reactivity, from signals of delayed response self-powered neutron detectors (SPNDs). Moreover, by using the linearity of our model, the Rao-Blackwellized CKF (RBCKF) algorithm is developed for our estimation problem, which offers benefits in terms of smaller computational load in comparison to standard CKF. Furthermore, a scheme which is termed as adaptive-RBCKF (A-RBCKF) has been designed for adaptation of process noise covariance. A comparative study of the two state estimators, that is, RBCKF and A-RBCKF, through simulations under different transient scenarios demonstrates the efficacy of A-RBCKF over RBCKF. [ABSTRACT FROM AUTHOR]

Methods of calculating the nuclear reactor reactivity from the measured time-dependence of the neutron flux are discussed. It is noted that the corresponding problems for the direct and inverse equations of point kinetics in the approximation of a prompt-jump change of neutron flux are not equivalent, which is expressed in that the reactivity values in these problems do not coincide with one another. The reasons for the nonequivalence and ways of its elimination are investigated. New equations of inverse point kinetics without this deficiency are proposed. It is shown that the proposed equations give the correct reactivity immediately after the onset of a perturbation in the reactor and not asymptotically as in the case of the conventional equations. [ABSTRACT FROM AUTHOR]

Devices for measuring (calculating) the reactivity of a nuclear reactor using information from ionization chambers must be checked periodically, just as any other measuring apparatus. This is associated with the fact that under the influence of external factors (temperature, humidity, pressure, vibrations, control regimes) the working characteristics of such apparatus, just as any technical object, change in the course of operation and in time the apparatus becomes unserviceable. In order to determine the serviceability of the checked working reactivity meters, it is necessary to have a standard signal and, correspondingly, a standard apparatus. The present article proposes an approach to solving this problem on the basis of the equivalent model method. [ABSTRACT FROM AUTHOR]

Abstract Feasibility of subcriticality monitoring with a digital reactivity meter based on inverse kinetics method has been investigated at the lead-based zero power reactor VENUS-II. A series of control rod drop experiments have been carried out in this work. The subcriticality before and after the rod drop were estimated considering the effect of external neutron source. The control rod worth was also extracted from the rod drop experiments. The measurement results exhibited obvious spatial dependence induced by the control rod insertion, and they could be corrected by correction factors calculated with MCNP code. The corrected values of control rod worth were found to be consistent with the reference ones predetermined at critical condition. Moreover, this method could also provide real time subcriticality without any correction when the detectors were placed at appropriate positions at slightly subcritical state. Based on these measurements, it has been proved that the digital reactivity meter could be a useful tool for continuous reactivity monitoring in the operation of ADS in future. [ABSTRACT FROM AUTHOR]

An attempt is made to improve our confidence in current adjustment techniques based on the Generalized Linear Least-Squares (GLLS) method. Instead of involving all considered experiments simultaneously, the adjustment is made progressively by considering at a time small groups of correlated and well documented experiments which have been performed preferably in the same configuration. Nonlinearity is accounted for implying that the required sensitivity coefficients are recalculated within an iterative procedure. The individual experiments may refer to spectral indices, reaction rate traverses, as well as local reactivity effects in fast-spectrum systems. It is shown that specific Progressing Incremental nuclear data Adjustment (PIA) techniques developed in compliance with ideas of Palmiotti and Salvatores, which specifically make use of preprocessed a priori cross-sections and variance/covariance data in 33 neutron groups as a basis for analyzes in the framework of the deterministic code system ERANOS (Edition 2.2-N), allow to a large extent separating effects and also providing automatic criteria for the inclusion or exclusion of experiments from the adjustment. Other important results are that (1) global parameters such as effective multiplication factors may be considered but only marginally in the adjustment and (2) only the adjustment of those cross-sections resulting independent of the PIA sequence may be considered as a basis for reliable adjustments, provided that nonlinearity is accounted for. [ABSTRACT FROM AUTHOR]

The new model of the Point Reactor Kinetics (PRK) equations developed based on the Telegraph approximation of the neutron transport equation, is solved for several cases of time varying Reactivities insertions and Temperature feedback while comparing it to that of the diffusion PRK model in an infinite Thermal Homogenous Nuclear Reactor. Diffusion PRK is based on the Neutron Diffusion Equation which is a parabolic differential equation and hence it assumes an infinite velocity of propagation, while neutrons propagate with a finite velocity. By the introduction of the hyperbolic type Telegraph equation which is a more accurate representation of the neutron transport than the diffusion equation and in which neutrons propagate with a finite velocity, one could overcome this paradox that contradicts causality. The new model introduces a new parameter called the relaxation time ( τ ), which is not present in the diffusion approximation, and affects the neutron density calculations. Both Ramp insertions of reactivity and Sinusoidal insertions of reactivity were studied, as well as the effect of The Adiabatic Temperature feedback. The general phenomena in the solution of the new model is a Relaxation in the time response of the solution. It is found that the Telegraph model with its extra second order time derivative, will give observable different values than that of the diffusion even when we used small ( τ ) especially for the cases at which the neutron density changes rapidly. [ABSTRACT FROM AUTHOR]

• The boric acid concentration is accurately measured by using sodium fluorescein for the first time as the indicator based on the LIF. • The mixing behavior of boric acid under the action of turbulent flow in a T-tube were established. • CFD method was proposed to calculate the specific parameters of boric acid transport in the primary circuit. 10B has a large neutron absorption cross section and is commonly used as a neutron poison in the light water reactor (LWR) to adjust the reactivity of nuclear reactors. In this paper, for the first time, a new planar laser-induced fluorescence (PLIF) method with sodium fluorescein as the tracer is used to measure the concentration field of boric acid. In this paper, the injection process is abstracted as a T-tube. The accuracy of LIF is verified by wire mesh sensor. The CFD method is used to simulate the mixing process to come up with proper parameters to consider the influence of turbulence on the flow. The branch velocity of T-tube has a great influence on the diffusion process. The mixing process in the pipeline is mainly driven by turbulence of the side jet. Boric acid is evenly mixed in the pipe within 8 ∼ 10 times of the pipe diameter. [ABSTRACT FROM AUTHOR]

Due to the gamma radiation, the noise of the electronic system, and the environmental radiation, a significant background exists in the electrical current during the measurement of reactivity through the external detectors, resulting in a significant error of the reactivity, especially at a low-power level. Based on an analysis of the inverse kinetics equation which contains the background term, the impact of the background current to the measured reactivity is analyzed, and a method is introduced which calculates the reactivity in an iterative way. The calculation results are compared with the theoretical value and those obtained by other methods. The iterative method is of sufficient precision and has the advantages in efficiency and convenience. It can be applied in the dynamic control rod worth calibration or used independently in the measurement of reactivity in NPPs. [ABSTRACT FROM AUTHOR]

The extended Kalman filtering (EKF) technique has been utilized in the estimation of reactivity which is a significantly important parameter to indicate the status of the nuclear reactor. In this paper, the performances of two EKF schemes using different Jacobian matrices are compared. Numerical simulations are used for the validation and comparison of these two EKF schemes, and the results show that the Jacobian matrix obtained directly from the discrete-time state model performs better than the one which is the discretization form of the Jacobian matrix obtained from the continuous-time state model. [ABSTRACT FROM AUTHOR]

Highlights: [•] We have identified areas where nuclear safety and security share similarities as well areas where these two differ. [•] Application of concepts, criteria, and operational practices used for safety, to nuclear security, enhances protection. [•] Integration of safety and security measures such that implementation of one does not compromise the other. [•] To improve the synergy, awareness of the intersection between nuclear safety and security should be increased. [Copyright &y& Elsevier]

Highlights: [•] Tier 1 and Tier 2 in MCNPX-C90 underestimate the effect of depletion upon reactivity. [•] Calculations using Tier 3 are twice as expensive as those using Tier 2. [•] Results of MCNPX-C90 with Tier 3 and TRIPOLI-4 coupled to MENDEL using the CSADA temporal scheme are very similar. [•] TRIPOLI-4 has advantage over MCNPX (2.6.0) because takes half the time when using CSADA. [•] The low order depletion solver in TRIPOLI-4/MENDEL yields satisfactory results for GFR. [Copyright &y& Elsevier]

Highlights: [•] A thirty-fourth order model is used to simulate the dynamics of a research reactor. [•] We consider delayed neutrons fraction as a function of time. [•] Variable fuel and temperature reactivity coefficients are used. [•] WIMS, BORGES and CITVAP codes are used for initial condition calculations. [•] Results are in agreement with experimental data rather than common codes. [ABSTRACT FROM AUTHOR]

Abstract: A comparative safety assessment of both HEU and the proposed LEU1 & LEU2 cores having UAl x –Al, U3O8–Al and U3Si2–Al fuels respectively in a typical MTR system has been carried out using the PARET code. Super prompt-critical transients initiated with the insertion of single as well as double ramps at low power start-up have been studied in this work. The results for the standard HEU core with single reactivity ramps up to $2.2/0.5 s show excellent agreement with the already published data. According to these simulations, for large time gap values ( = 1 s) between double ramps, the first peak power dominates for all three cores and each system remains safe up to $2.2/0.5 s ramp rates. However, for closely spaced double ramps ( = 0.1 s), for both HEU and the LEU2 cores, the simulations indicate clad melting for $2.4/0.5 s ramp rates. The peak power, fuel centerline & clad surface temperature values remain within safe limits for single as well as for double reactivity ramps up to $2.2/0.5 s for all three cores. [Copyright &y& Elsevier]

Abstract: In this work, kinetic parameters of Tehran research reactor (TRR) mixed cores have been calculated. The mixed core configurations are made by replacement of the low enriched uranium control fuel elements with highly enriched uranium control fuel elements in the reference core. The MTR_PC package, a nuclear reactor analysis tool, is used to perform the analysis. Simulations were carried out to compute effective delayed neutron fraction and prompt neutron lifetime. Calculation of kinetic parameters is necessary for reactivity and power excursion transient analysis. The results of this research show that effective delayed neutron fraction decreases and prompt neutron lifetime increases with the fuels burn-up. Also, by increasing the number of highly enriched uranium control fuel elements in the reference core, the prompt neutron lifetime increases, but effective delayed neutron fraction does not show any considerable change. [Copyright &y& Elsevier]

Abstract: We develop an approximation method based on the Euler–Maclaurin formula for numerically solving the integral of the inverse point kinetic equation for nuclear reactor power. Due to its greater precision, this method requires fewer history points than other methods based on the nuclear power history. The approximation is validated with different forms of the nuclear power and with different time step calculations. Results suggest that this method, though easier to implement, has a better precision and lower computational costs than other methods that require the nuclear power history. [Copyright &y& Elsevier]

Abstract: The concepts of static and dynamic reactivity are discussed and the practical differences between them are noted. Special emphasis is given to the use of these concepts in defining uncertainties in reactivity calculations due to uncertainties in cross sections. Currently, in order to define uncertainty, it is the static reactivity that is used. But we show that this may give a non-conservative result compared with the dynamic method. For example, we show that while a static calculation of reactivity involving uncertainty may give a mean value of reactivity which is less than zero, the corresponding dynamic method can yield a value for the time constant which is greater than zero. As the time constant is the physical parameter of interest then the static method must be used with caution. [Copyright &y& Elsevier]

Abstract: A point reactor kinetics code, coupled with thermal hydraulics of plate type fuel, is developed in order to carry out the reactivity initiated transient analysis of a reactor. Point kinetics equations are solved by matrix algebra, which involves piecewise constant approximation (PCA) i.e. the time dependent functions-reactivity and neutron source terms are assumed to be constant within an interval of time. This code is able to simulate various kinds of reactivity insertion like step, ramp, sinusoidal etc. for transient analysis. Effect of reactivity feedback is included into the code. Solution of kinetics equations gives neutronic power and it is then fed into a thermal hydraulic code where thermal energy conservation equations are solved by finite difference method along with Crank–Nicolson technique to find out the fuel, clad and coolant temperatures during transients. Results of the code corroborate well with the benchmark results. [Copyright &y& Elsevier]

Abstract: EUREKA-2/RR code has been used for the analyses of reactivity insertion accident (RIA) and loss of flow accident (LOFA) of 3MW TRIGA Mark-II research reactor of Bangladesh. Transient characteristics of different parameters such as core power, fuel temperature, clad temperature, departure from nucleate boiling ratio (DNBR) due to the different form and magnitude of reactivity insertion has been focused. It is found from the analysis that the magnitude of insertion reactivity and the reactor operating power during this insertion impose a total effect on the core safety. Also, transient effects on reactor were studied for 15% loss of flow of the primary coolant. Provided the scram system is available, the reactor is found to shutdown safely in both cases. From these two studies in series, it is seen that EUREKA-2/RR is well suited for the analyses of reactor safety parameters with good approximations. [Copyright &y& Elsevier]

Abstract: The self-shielding factors for the upper reflector of the Miniature Neutron Source Reactors (MNSRs) are evaluated in this paper. Unlike nuclear fuels the values of these factors for the reflector in MNSRs are greater than unity. Different modes are used to fill the upper reflector in the shim tray, namely: the In-Out Radial Cumulative (IORC) mode, the In-Out Radial Singular (IORS) mode, the Out-In radial Cumulative (OIRC) mode, the Out-In Radial Singular (OIRS) mode, the Axial Singular Mode (ASM), and the Axial Cumulative Mode (ACM). The volumetric reactivity of the upper reflector in MNSRs is best utilized in average in the OIRC filling mode (0.003877mk/cm3), while it reaches a maximum with the ACM of 0.01607 mk/cm3. The presence of the upper reflector does not compromise the safety of MNSRs. [Copyright &y& Elsevier]

Abstract: The feedback reactivity coefficients which account for variation in fuel and moderator temperatures as well as the void coefficient have been calculated using the WIMS-D/4 and CITATION codes for the Syrian MNSR research reactor. The cross sections of all the reactor components at different temperatures were generated using the WIMSD4 code. These group constants were used then in the CITATION code to calculate the multiplication factor and the neutron spectrum at different water and fuel temperatures using 69 energy groups. Only one parameter was changed where all other parameters were kept constant. The calculated feedback coefficients were compared with the measured ones. Good agreements between the measured and calculated feedback reactivity coefficients were obtained. [Copyright &y& Elsevier]

Abstract: The PARET/ANL code has been adapted by the IAEA for testing transient behaviour in research reactors since it provides a coupled thermal hydrodynamic and point kinetics capability for estimating thermal hydraulic margins. A two-channel power peaking profile of the Ghana Research Reactor-1 (GHARR-1) has been developed for the PARET/ANL (Version 7.3; 2007) using the Monte Carlo N-Particle code (MCNP) to determine the thermal hydraulic data for reactivity insertion transients in the range of 2.0×10−3 Δk/k to 5.5×10−3 Δk/k. Peak clad and coolant temperatures ranged from 59.18°C to 112.36°C and 42.95°C to 79.42°C respectively. Calculated safety margins (DNBR) satisfied the MNSR thermal hydraulic design criteria for which no boiling occurs in the reactor core. The generated thermal hydraulic data demonstrated a high inherent safety feature of GHARR-1 for which the high negative reactivity feedback of the moderator limits power excursion and consequently the escalation of the clad temperature. [Copyright &y& Elsevier]

Abstract: The main goals in nuclear fuel lattice design are: (1) minimizing the rod power peaking factor (PPF) in order that the power level distribution is the most uniform; (2) obtaining a prescribed target value for the multiplication factor (k) at the end of the irradiation in order that the fuel lattice reaches the desired reactivity; and (3) obtaining a prescribed target value for the k at the beginning of the irradiation in order that the reactivity excess is neither a high value (to ease the maneuvering of the control systems) nor a low value (to avoid the penalization of the high cost of the burnable poison content). In this work a simple algorithm to design the burnable poison bearing nuclear fuel lattice is presented. This algorithm is based on a reactor physics analysis. The algorithm is focused on finding the radial distribution of the fuel rods having different fissile and burnable poison contents in order to obtain: (1) an adequate minimum PPF; (2) a prescribed target value of the k at the end of the irradiation; and (3) a prescribed target value of the k at the beginning of the irradiation. This algorithm is based on the factorization of the fissile and burnable poison contents of each fuel rod and on the application of the first-order perturbation theory. The performance of the algorithm is demonstrated with the design of a fuel lattice composed of uranium dioxide (UO2) and gadolinium dioxide (Gd2O3) for boiling water reactors (BWR). This algorithm has been accomplished using HELIOS calculation codes. The results show that this simple algorithm is very efficient and precise. [Copyright &y& Elsevier]

Abstract: The IPR-R1 TRIGA is a research nuclear reactor managed and located at the Nuclear Technology Development Center (CDTN) a research institute of the Brazilian Nuclear Energy Commission (CNEN). It is mainly used to radioisotopes production, scientific experiments, training of nuclear engineers for research and nuclear power plant reactor operation, experiments with materials and minerals and neutron activation analysis. In this work, criticality calculation and reactivity changes are presented and discussed using two modelings of the IPR-R1 TRIGA in the MCNP5 code. The first model (Model 1) analyzes the criticality over the reactor. On the other hand, the second model (Model 2) includes the possibility of radial and axial neutron flux evaluation with different operation conditions. The calculated results are compared with experimental data in different situations. For the two models, the standard deviation and relative error presented values of around 4.9×10−4. Both models present good agreement with respect to the experimental data. The goal is to validate the models that could be used to determine the neutron flux profiles to optimize the irradiation conditions, as well as to study reactivity insertion experiments and also to evaluate the fuel composition. [Copyright &y& Elsevier]

Abstract: The reactivity feedback coefficients at end-of-life of a material test reactor fuelled with low enriched uranium fuel were calculated. The reactor used for the study was the IAEA’s 10MW benchmark reactor. Simulations were carried out to calculate the different reactivity feedback coefficients including Doppler feedback coefficient, reactivity coefficient for change of water temperature and reactivity coefficient for change of water density. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It was observed that the magnitude of all the reactivity feedback coefficients increased at end of life of the reactor by almost 2–5%. [Copyright &y& Elsevier]

Abstract: In this paper a preconceptual neutronics design study for a SUstainable Proliferation-resistance Enhanced Refined Secure Transportable Autonomous Reactor (SUPERSTAR) demonstrator is presented. The main goal of achieving the highest realistic power level limited by natural circulation and transportability, while providing energy security and proliferation resistance thanks to a long core lifetime design has been satisfactorily attained. A preliminary core configuration has been developed meeting the foremost requirements of limiting the reactivity swing over the core lifetime to about 1$ and flattening the radial power profiles, as demanded by the choice of wrapper-less (i.e. without flow ducts) fuel assemblies and by the stringent technological constraints imposed by the requirement of short-term deployment. Reactivity coefficients and kinetic parameters have been evaluated for the reference beginning-of-life, middle-of-life and end-of-life core configurations. Furthermore, the results of thermal-hydraulic analyses of the primary loop have confirmed that the system can be effectively cooled by natural circulation heat transport, all the technological constraints being respected even when incorporating peaking factors. [Copyright &y& Elsevier]

Abstract: The Prototype Fast Breeder Reactor (PFBR) which is under construction at Kalpakkam, India, is a 500MWe sodium cooled pool type reactor. The core of the PFBR consists of 1758 free standing subassemblies supported on the grid plate. The entire core is divided into 15 different flow zones and the flow rate required through each zone is calculated based on the fission heat generation. The coolant sodium flows from the bottom of the subassembly to top and the design of the subassembly for each flow zone is quite complex. There are 181 fuel subassemblies in PFBR core with 217 fuel pins in each subassembly, vertically held in the form of bundle within a hexagonal wrapper tube. The pins are separated by spacer wires wound around the pins helically. Analytical prediction of subassembly pressure drop, vibration and determination of inception of cavitation for this complex geometry is very difficult. So experiments were conducted extensively to get a more accurate evaluation of the design and for its qualification for the use in PFBR, which is designed for 40 years of operation. Pressure drop and cavitation experiments were carried out in water on full scale (1:1) subassemblies of all flow zones. The overall pressure drop of the subassembly determines the ratings of the pump. Cavitation of the pressure drop devices lead to erosion damage of fuelpins and may also result in reactivity fluctuation due to sodium-void effect. So it is essential to confirm that the subassembly is not cavitating in the operating regime of the reactor. Subassembly can vibrate in cantilever mode due to the turbulence in the flow and can result in reactivity fluctuation, reactor control problem and can even lead to the failure of the fuel pins. So vibration measurements were carried out in water on the maximum rated subassembly. This paper discusses various experiments carried out on PFBR subassembly, the similarity criteria followed, instrumentation, results and conclusion. [Copyright &y& Elsevier]

Abstract: The Atominstitute (ATI) of Vienna University of Technology (VUT) operates a TRIGA Mark II research reactor since March 1962. Its initial criticality was achieved on 7th March 1962 when 57th Fuel Element (FE) was loaded to the core. This paper describes the development of the MCNP model of the TRIGA reactor and its validation through three different experiments i.e. initial criticality, reactivity distribution and a thermal flux mapping experiment in the reactor core. All these experiments were performed on the initial core configuration. The MCNP model includes all necessary core components i.e. FE, Graphite Element GE, neutron Source Element (SE), Central IRradiation channel (CIR) etc. Outside the core, this model simulates the annular grooved graphite reflector, the thermal and thermalizing column, four beam tubes and the reactor water tank up to 100cm in radial and +60 and −60cm in axial direction. Each grid position at its exact location is modeled. This model employs the ENDF/B-VI data library except for the Sm-isotopes which are taken from JEFF 3.1 because ENDF/B-VI lacks samarium (Sm) cross sections. For the first experiment, the model predicts an effective multiplication factor (κ eff) of 1.00183 with an estimated standard deviation 0.00031 which is very close to the experimental value 1.00114. The second experiment measures the reactivity values of four FE and one GE. In comparison to the MCNP results, the percent difference ranges from 4 to 22. The third experiment verifies the model at a local level with the radial and axial thermal flux density distribution in the core. Though the trends are similar, the MCNP model overestimates the radial thermal flux density in the core and underestimates these results at the core periphery. [Copyright &y& Elsevier]

Abstract: Taylor’s series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor’s series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor’s series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations. [Copyright &y& Elsevier]

Abstract: This paper presents about conceptual designs of Advanced Recycling Reactor (ARR) focusing on enhancement in transuranics (TRU) burning and americium (Am) transmutation. The design has been conducted in the context of the Global Nuclear Energy Partnership (GNEP) seeking to close nuclear fuel cycle in ways that reduce proliferation risks, reduce the nuclear waste in the US and further improve global energy security. This study strives to enhance the TRU burning and the Am transmutation, assuming the development of related technologies in this study, while the ARR based on mature technologies was designed in the previous study. It has followed that the provided TRU burning core is designed to burn TRU at 28kg/TWthh, by adding moderator pins of B4C (Enriched B-11) and the Am transmutation core will be able to transmute Am at 34kg/TWthh, by locating Am blanket of AmN around the TRU burning core. It indicates that these concepts improve TRU burning by 40–50% than the previous core and can transmute Am effectively, keeping the void reactivity acceptable. [Copyright &y& Elsevier]

Abstract: The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010. [ABSTRACT FROM AUTHOR]

Abstract: Rossi-Alpha (βeff /Λ) for critical reactor measured experimentally by noise analysis technique at PARR-1 core at 35.26 full power days burn up. In noise analysis technique the inherent reactivity fluctuations are taken as input to reactor system and the neutron density population fluctuations are considered as output of the reactor system. The auto power spectral density of the linear channel is taken and used to find out the break frequency by non-linear least square fitting method, which leads to βeff /Λ =161.45s−1. Calculations were performed with the help of computer codes WIMSD/4 and CITATION. The calculated βeff /Λ =161.07s−1 at 35.26 full power days burn up. The measured and calculated values for Rossi-Alpha are in good agreement within 0.235% of error. [ABSTRACT FROM AUTHOR]

Abstract: In block-type high temperature gas-cooled reactors (HTGRs), insertion depth of control rods (CRs) into a core should be retained shallow to keep fuel temperature below 1495°C through a burnup period, and hence excess reactivity should be reduced through a different method. Loading burnable poisons (BPs) into the core is considered as a method to resolve this problem as in case of light water reactors (LWRs). Effectiveness of BPs on reactivity control in LWRs has been validated by experimental data, however, this has not been done yet for HTGRs, because there was not enough burnup characteristics data for HTGRs required for the validation. The High Temperature Engineering Test Reactor (HTTR) is a block-type HTGRs and it adopts rod-type BPs to control reactivity. The HTTR has been operated up to middle burnup, and thereby the experimental data was expected to show effect of the BPs on the reactivity control. Hence, in order to validate effectiveness of rod-type BPs on reactivity control in the HTTR, we investigated on the HTTR results whether the BPs have functioned as designed. As a result, the CRs insertion depth has been retained shallow within allowable range, and then effectiveness of rod-type BPs on reactivity control in the HTTR was validated. [ABSTRACT FROM AUTHOR]

Abstract: The Nigerian Research Reactor-1 (NIRR-1) falls in the category of Miniature Neutron Source Reactors (MNSR) using a fuel of 90% HEU. It is therefore desirable to convert it from this enrichment to LEU (less than 20%) in conformity with the new global trend of making research reactor fuel as unattractive as possible to groups that may be interested in using such highly enriched cores for non-peaceful purposes. In this work, we have developed a computational scheme based on WIMS and CITATION that would theoretically achieve this objective as easily as possible. The scheme systematically reduces the enrichment from 90% (or any other initial values) to less than 20% in steps of 5% or any desired percentage variation. Two fuel types (UAl4 and UO2) are considered in here, while maintaining the size and geometry of the core as well as the excess reactivity (between 3.5 and 4mk). Our results show that the U-235 loading increases sharply as enrichment decreases. It has also been noticed that at 5% enrichment the fuel loading for both types is 2505g. However, at 90% enrichment, the loading drops sharply to 998g for UAl4 fuel and 946g for UO2 fuel. Below the enrichment of 5%, the operation of NIRR-1 with both fuel types can be considered unrealistic as this requires structural adjustment which the work tries to maintain constant. [Copyright &y& Elsevier]

Abstract: Point reactor kinetics equations with one group of delayed neutrons are solved analytically to determine the neutron population as a function of time for any ramp reactivity insertion in the presence of external neutron source using prompt jump approximation. With the time dependent neutron population the other important kinetic parameters such as the reactor period also can be derived. Analytical solutions are available in the literatures for any ramp reactivity insertion into a critical reactor without considering the source term. Analytical solutions available in the literature by considering the source term also to study sub-critical reactor kinetics. But such a solutions either uses constant source approximation which under predicts the solution, or the available solution is not useful for all kind of sub-critical reactivity and external ramp reactivity insertion combination due to the computer precision incompatibility. In the present work, analyses are carried out to determine the reactivity boundary to which the existing results can converge to a true solution, beyond where the precision incompatibility arises. A new series solution is recommended in the region where existing solution converges to false solution due to precision incompatibility. [Copyright &y& Elsevier]

Abstract: New analytical solution for solving the point reactor kinetics equations with multi-group of delayed neutrons is presented. This solution is based on the roots of inhour equation, eigenvalues of the coefficient matrix. The inhour equation presents in new sample formula. The analytical solution represents the exact analytical solution for the point kinetics equations of multi-group of delayed neutrons with constant reactivity. Also, it represents the accurate solution for solving the point kinetics equations of multi-group of delayed neutrons with ramp and temperature feedback reactivities. This method are applied to different types of reactivity and compared to the traditional methods. [Copyright &y& Elsevier]

Abstract: The effects of using different clad materials on the uncontrolled reactivity insertion transients of a material test research reactor were studied. For this purpose, the aluminium clad of an MTR was replaced separately with stainless steel-316 and zircaloy–4. Simulations were carried out to determine the reactor performance under reactivity insertion transients with totally failed control rods. Ramp reactivities of 0.25$/0.5s and 1.35$/0.5s were inserted with reactor operating at full power level of 10MW. Nuclear reactor analysis code PARET was employed to carry out these calculations. It was observed that when reactivity insertion was 0.25$/0.5s, all the reactors stabilised at new power levels. The SS cladded fuel attained the minimum power level of 17.72MW, followed by Zr-4 cladded with 23.62MW while it was maximum at 24.31MW for Al cladded fuel. When reactivity insertion was 1.35$/0.5s, the feedback reactivities were unable to control the reactor which resulted in the bulk boiling of the coolant; the Al cladded was the first to reach ONB while SS cladded was the last. [Copyright &y& Elsevier]

Abstract: While withdrawing control rods to extrapolate to critical state during physical startup of reactor, even if reactivity added is equal to 1/3 of the extrapolation value, there exists the possibility that the reactor reaches supercriticality accidentally. Therefore, continuous indication of neutron density level and its change rate is required at all times for the startup safety. The reactor safety requires the development of a method to monitor criticality. In this paper, an accurate analytical solution for point kinetics equations with one-group delayed neutron and extraneous neutron source is introduced to calculate the change of neutron density, which considers that the reactor does not reach steady state before a new reactivity is added. A comparison with the traditional methods indicates the superiority and validity of the developed analytical solution. The results can be used to monitor physical startup of reactor in real time for critical extrapolation. [Copyright &y& Elsevier]

Abstract: The current study emphasizes an aspect related to the assessment of a model embedded in a computer code. The study concerns more particularly the point neutron kinetics model of the RELAP5/Mod3 code which is worldwide used. The model is assessed against positive reactivity insertion transient taking into account calculations involving thermal-hydraulic feedback as well as transients with no feedback effects. It was concluded that the RELAP5 point kinetics model provides unphysical power evolution trends due most probably to a bug during the programming process. [Copyright &y& Elsevier]

Abstract: Point reactor kinetics equations are solved numerically using one group of delayed neutrons and with fuel burn-up and temperature feedback included. To calculate the fraction of one-group delayed neutrons, a group of differential equations are solved by an implicit time method. Using point reactor kinetics equations, changes in mean neutrons density, temperature, and reactivity are calculated in different times during the reactor operation. The variation of reactivity, temperature, and maximum power with time are compared with the predictions by other methods. [Copyright &y& Elsevier]

Abstract: New experiments for the inversion point of the isothermal reactivity coefficient of the IPEN/MB-01 research reactor facility have been successfully conducted. The experiments considered the removal of 12 central fuel rods. These positions of the core were filled either by stainless steel rods or by water. The purpose of the experiments was to give more physical insight of the reactivity coefficient behavior of the IPEN/MB-01 reactor. Particularly, it was shown that in these conditions, when compared to the previous work, the inversion point moves to higher temperatures which are in a very much agreement to the model proposed in the previous work. TORT, a SN 3-D transport code, is employed for the analysis of this set of new experiments. The analyses were performed in a companion NJOY, AMPX-II and TORT systems considering the data libraries ENDF/B-VI.8, ENDF/B-VII.0 and a third case which considers all nuclides from ENDF/B-VI.8 but 235U which was taken from the work of Haicheng-Wu. The theoretical analysis reveals that the best result for the calculated and experimental comparison was found when the 235U data which was taken from the work of Haicheng-Wu. However, all libraries considered in this work meets the desired accuracy (−1.0 pcm/°C) for the determination of this integral parameter for thermal reactors fuelled with slightly enriched uranium. [Copyright &y& Elsevier]

Abstract: The integro-differential equation of the point kinetics of nuclear reactor was solved by approximating the neutron density with piecewise polynomial and exponential functions. The developed numerical algorithms are simple and easy to implement. Three sets of applications were used: constant, sinusoidal and ramp reactivity. [Copyright &y& Elsevier]

Abstract: This paper compares two ex-core control options of the gas-cooled Submersion Subcritical Safe Space (S^4) reactor with a fast neutrons energy spectrum: (a) rotating BeO drums with 120° thin segments of enriched B4C in the BeO radial reflector; and (b) sliding segments in the BeO radial reflector. Investigated are the effects on the beginning-of-life (BOL) excess reactivity, reactivity depletion rate and operation life, and the spatial neutron flux distributions and fission power profiles in the core. Also investigated is the effect of reducing the thickness of the enriched B4C segments in the control drums on the BOL excess reactivity, when one or two of the 6 drums are stuck in the shutdown position. Reducing the thickness of the B4C segments from 0.5mm to 0.238mm, with one drums stuck in the shutdown position, increases BOL cold and hot-clean excess reactivity from +$1.71 and +$0.47 to +$2.38 and +$0.89, respectively. These reactivity values are almost identical to those of the reactor with one of the six reflector segments stuck open in the shutdown position. Results also showed that the control options made little difference in the reactor performance. The power peaking in the reactor core with sliding reflector segments is slightly lower and the spatial power profiles are relatively flatter. The operation life of the reactor with a sliding reflector segments control, when operating at a nominal thermal power of 471kW, is only 22 full power days longer than with rotating drums control. [Copyright &y& Elsevier]

The fast power and void reactivity coefficients are applied to characterize the RBMK-1500 reactor exploitation at the Ignalina NPP. These reactivity coefficients are estimated during measurements at the Ignalina NPP. The paper deals with the modelling of the fast power and void reactivity coefficient measurements (transient processes). The simulation of these transients was performed using the TITAN database of the reactor core and QUABOX / CUBBOX-HYCA software. The fast power and void reactivity coefficients for chosen RBMK-1500 reactor core states were evaluated. The modelling results were compared with the measurement data. [ABSTRACT FROM AUTHOR]

Abstract  The method of inverse solution of the equation of point kinetics is often used for measuring reactivity. The conventional formulations of this method give an approach based on interval estimates of the parameters in the equation; this makes it possible to take into account more adequately and methodologically correctly the a priori existing information and measurements of the neutron flux. Aside from reactivity, the method makes it possible to refine the parameters in the kinetic equation, which are associated with the source, delayed-neutron yield, and prompt-neutron lifetime. An approximate method of determining the covariation matrix of a more accurate estimate for the case of a small error in the a priori data and measurements is proposed. [ABSTRACT FROM AUTHOR]

In late 1993 and early 1994, tests in France and Japan showed that cladding damage in fuel rods with burnups above 50 GWd/ton occurs at much lower energies than in unirradiated fuel rods when exposed to large power pulses. During the last decade, significant additional test results have become available to permit an interim assessment of potential cladding failure in reactivity-initiated accidents (RIAs) in reactors with fuel burnups above 40 GWd/ton, which is generally regarded as high-burnup fuel. These data are summarized, and systematic biases due to atypical test conditions are identified. The magnitude of biases in the fuel enthalpy for failure are estimated to range from -19 to +27 cal/g for the cases analyzed. With these adjustments, a lower bound of the enthalpies for experimentally observed cladding failure is compared with potential enthalpies in pressurized water reactors and boiling water reactors. Based on available information on control rod worths, it is concluded that current operating reactors in the United States are not likely to experience cladding failure during the worst postulated RIAs. [ABSTRACT FROM AUTHOR]

Abstract: In recent years great interest has been displayed, worldwide, for Accelerator Driven Sub-critical reactors (ADS) to incinerate the minor actinides generated by existing energy-producing reactors. In sub-critical systems, the effective neutron multiplication factor is lower than 1.0 and the neutrons otherwise required to maintain the chain reaction can be put to other uses, in particular, the destruction of nuclear wastes such as minor actinides (MA). One of the major advantages of such ADS systems is that it can be operated with very high MA content without jeopardizing the overall safety due to a small effective delayed neutron fraction, a small Doppler temperature coefficient and possibly also a large void coefficient depending on the chosen coolant. This enhanced safety, however, requires at all time a sufficient sub-criticality margin. Reliable reactivity monitoring techniques are hence required to achieve this goal. The MUSE-4 program is a series of low power experiments carried out at the CEA-Cadarache MASURCA facility to investigate the various methods leading to the measurement of the reactivity level and associated kinetic parameters such as the effective delayed neutron fraction. The aim of this paper is to present the results obtained with a method which directly gives the ratio, for a sub-critical assembly, between the reactivity ρ and the effective delayed neutron fraction β eff. By combining these results to those obtained with the k p-method for the prompt neutron multiplication coefficient, we have access to the parameters which govern the prompt and the slow kinetics of a sub-critical assembly. These parameters can be obtained without reference to any calibration measurement in critical configuration. It opens the way to the control of larger sub-critical demonstrators that are operating with fuels which cannot be used in critical reactor, and, thanks to sub-criticality, which are characterized by a deterministic safety. [Copyright &y& Elsevier]

We examined the molecular mechanisms underlying the formation of the thalamocortical pathway in the cerebral neocortex of normal and reeler mutant mice. During normal development of the mouse neocortex, thalamic axons immunoreactive for the neural cell adhesion molecule L1 rarely invaded the cortical plate and ran centered in the subplate which is immunoreactive for neurocan, a brain-specific chondroitin sulfate proteoglycan. On the other hand, in homozygous reeler mutant mice, thalamic axons took an aberrant course to run obliquely through the cortical plate. Injection of bromodeoxyuridine at embryonic day 11 specifically labeled subplate neurons in normal mice, whilst in the reeler neocortex it labeled cells scattered in the cortical plate as well as in the superficial layer (superplate). Neurocan immunoreactivity was associated with the bromodeoxyuridine-positive cells in the superplate, as well as being present in oblique bands within the cortical plate, along which L1-bearing thalamic axons preferentially ran. The present results support our previous hypothesis proposed for normal rats that a heterophilic molecular interaction between L1 and neurocan is involved in determining the thalamocortical pathway within the neocortical anlage [T. Fukuda et al. (1997) Journal of Comparative Neurology, 382, 141–152]. [ABSTRACT FROM AUTHOR]