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  • 1.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics.
    Advanced Monte Carlo Methods in Reactor Physics, Eigenvalue and Steady State Problems2007Licentiate thesis, comprehensive summary (Other scientific)
  • 2.
    Dufek, Jan
    Chalmers University of Technology, Applied Physics.
    Building the nodal nuclear data dependences in a many-dimensional state-variable space2011In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 38, no 7, p. 1569-1577Article in journal (Refereed)
    Abstract [en]

    We present new methods for building the polynomial-regression based nodal nuclear data models. Thedata models can reflect dependences on a large number of state variables, and they can consider varioushistory effects. Suitable multivariate polynomials that approximate the nodal data dependences are identifiedefficiently in an iterative manner. The history effects are analysed using a new sampling scheme forlattice calculations where the traditional base burnup and branch calculations are replaced by a largenumber of diverse burnup histories. The total number of lattice calculations is controlled so that the datamodels are built to a required accuracy.

  • 3.
    Dufek, Jan
    Chalmers University of Technology, Applied Physics.
    Complex models of nodal nuclear data2011In: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011), 2011Conference paper (Refereed)
    Abstract [en]

    During the core simulations, nuclear data are required at various nodal thermal-hydraulic and fuel burnup conditions. The nodal data are also partially affected by thermal-hydraulic and fuel burnup conditions in surrounding nodes as these change the neutron energy spectrum in the node. Therefore, the nodal data are functions of many parameters (state variables), and the more state variables are considered by the nodal data models the more accurate and flexible the models get. The existing table and polynomial regressionmodels, however, cannot reflect the data dependences on many state variables. As for the table models, the number of mesh points (and necessary lattice calculations) grows exponentially with the number of variables. As for the polynomial regression models, the number of possible multivariate polynomials exceeds the limits of existing selection algorithms that should identify a few dozens of the most important polynomials. Also, the standard scheme of lattice calculations is not convenient for modelling the data dependences on various burnup conditions since it performs only a single or few burnup calculations at fixed nominal conditions. We suggest a new efficient algorithm for selecting the most important multivariate polynomials for the polynomial regression models so that dependences on many state variables can be considered. We also present a new scheme for lattice calculations where a large number of burnup histories are accomplished at varied nodal conditions. The number of lattice calculations being performed and the number of polynomials being analysed are controlled and minimised while building the nodal data models of a required accuracy.

  • 4.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Development of New Monte Carlo Methods in Reactor Physics: Criticality, Non-Linear Steady-State and Burnup Problems2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The Monte Carlo method is, practically, the only approach capable of giving detail insight into complex neutron transport problems. In reactor physics, the method has been used mainly for determining the keff in criticality calculations. In the last decade, the continuously growing computer performance has allowed to apply the Monte Carlo method also on simple burnup simulations of nuclear systems. Nevertheless, due to its extensive computational demands the Monte Carlo method is still not used as commonly as deterministic methods.

    One of the reasons for the large computational demands of Monte Carlo criticality calculations is the necessity to carry out a number of inactive cycles to converge the fission source. This thesis presents a new concept of fission matrix based Monte Carlo criticality calculations where inactive cycles are not required. It is shown that the fission matrix is not sensitive to the errors in the fission source, and can be thus calculated by a Monte Carlo calculation without inactive cycles. All required results, including keff, are then derived via the final fission matrix. The confidence interval for the estimated keff can be conservatively derived from the variance in the fission matrix. This was confirmed by numerical test calculations of Whitesides's ``keff of the world problem'' model where other Monte Carlo methods fail to estimate the confidence interval correctly unless a large number of inactive cycles is simulated.

     

    Another problem is that the existing Monte Carlo criticality codes are not well shaped for parallel computations; they cannot fully utilise the processing power of modern multi-processor computers and computer clusters. This thesis presents a new parallel computing scheme for Monte Carlo criticality calculations based on the fission matrix. The fission matrix is combined over a number of independent parallel simulations, and the final results are derived by means of the fission matrix. This scheme allows for a practically ideal parallel scaling since no communication among the parallel simulations is required, and no inactive cycles need to be simulated.

     

    When the Monte Carlo criticality calculations are sufficiently fast, they will be more commonly applied on complex reactor physics problems, like non-linear steady-state calculations and fuel cycle calculations. This thesis develops an efficient method that introduces thermal-hydraulic and other feedbacks into the numerical model of a power reactor, allowing to carry out a non-linear Monte Carlo analysis of the reactor with steady-state core conditions. The thesis also shows that the major existing Monte Carlo burnup codes use unstable algorithms for coupling the neutronic and burnup calculations; therefore, they cannot be used for fuel cycle calculations. Nevertheless, stable coupling algorithms are known and can be implemented into the future Monte Carlo burnup codes.

     

  • 5.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI).
    Monte Carlo criticality calculations accelerated by a growing neutron population2016In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 94, p. 16-21Article in journal (Refereed)
    Abstract [en]

    We propose a fission source convergence acceleration method for Monte Carlo criticality simulation. As the efficiency of Monte Carlo criticality simulations is sensitive to the selected neutron population size, the method attempts to achieve the acceleration via on-the-fly control of the neutron population size. The neutron population size is gradually increased over successive criticality cycles so that the fission source bias amounts to a specific fraction of the total error in the cumulative fission source. An optimal setting then gives a reasonably small neutron population size, allowing for an efficient source iteration; at the same time the neutron population size is chosen large enough to ensure a sufficiently small source bias, such that does not limit accuracy of the simulation.

  • 6.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Anglart, Henryk
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Derivation of a stable coupling scheme for Monte Carlo burnup calculations with the thermal-hydraulic feedback2013In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 62, p. 260-263Article in journal (Refereed)
    Abstract [en]

    Numerically stable Monte Carlo burnup calculations of nuclear fuel cycles are now possible with the previously derived Stochastic Implicit Euler method based coupling scheme. In this paper, we show that this scheme can be easily extended to include the thermal-hydraulic feedback during the Monte Carlo burnup simulations, while preserving its unconditional stability property. At each time step, the implicit solution (for the end-of-step neutron flux, fuel nuclide densities and thermal-hydraulic conditions) is calculated iteratively by the stochastic approximation; the fuel nuclide densities and thermal-hydraulic conditions are iterated simultaneously. This coupling scheme is derived as stable in theory; i.e.; its stability is not conditioned by the choice of time steps.

  • 7.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Eduard Hoogenboom, J.
    Description of a stable scheme for steady-state coupled Monte Carlo-thermal-hydraulic calculations2014In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 68, p. 1-3Article in journal (Refereed)
    Abstract [en]

    We provide a detailed description of a numerically stable and efficient coupling scheme for steady-state Monte Carlo neutronic calculations with thermal-hydraulic feedback. While we have previously derived and published the stochastic approximation based method for coupling the Monte Carlo criticality and thermal-hydraulic calculations, its possible implementation has not been described in a step-by-step manner. As the simple description of the coupling scheme was repeatedly requested from us, we have decided to make it available via this note.

  • 8.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Gudowski, Waclaw
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    An efficient parallel computing scheme for Monte Carlo criticality calculations2009In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 36, no 8, p. 1276-1279Article in journal (Refereed)
    Abstract [en]

    The existing parallel computing schemes for Monte Carlo criticality calculations suffer from a low efficiency when applied on many processors. We suggest a new fission matrix based scheme for efficient parallel computing. The results are derived from the fission matrix that is combined from all parallel simulations. The scheme allows for a practically ideal parallel scaling as no communication among the parallel simulations is required, and inactive cycles are not needed. (C) 2009 Elsevier Ltd. All rights reserved.

  • 9.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Gudowski, Waclaw
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Fission matrix based Monte Carlo criticality calculations2009In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 36, no 8, p. 1270-1275Article in journal (Refereed)
    Abstract [en]

    We have described a fission matrix based method that allows to cancel the inactive cycles in Monte Carlo criticality calculations. The fission matrix must be sampled in the course of the Monte Carlo calculation using a space mesh with sufficiently small zones as it causes the fission matrix be insensitive to errors in the initial fission source. The k(eff) and other quantities can be derived by means of the final fission matrix. The confidence interval for the k(eff) estimate can be conservatively determined via the variance in the fission matrix.

  • 10.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Gudowski, Waclaw
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Parallelization of Monte Carlo Eigenvalue Callculations by the Stabilized Fission Matrix Method.Article in journal (Other academic)
  • 11.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Gudowski, Waclaw
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Stability and convergence problems of the Monte Carlo fission matrix acceleration methods2009In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 36, no 10, p. 1648-1651Article in journal (Refereed)
    Abstract [en]

    The Monte Carlo fission matrix acceleration methods aim at accelerating the convergence of the fission source in inactive cycles of Monte Carlo criticality calculations. In practice, however, these methods may corrupt the fission source, or slow down its convergence. These phenomena have not been completely understood so far. We demonstrate the convergence problems, and explain their reasons.

  • 12.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Gudowski, Waclaw
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Stochastic Approximation for Monte Carlo Calculation of Steady-State Conditions in Thermal Reactors2006In: Nuclear science and engineering, ISSN 0029-5639, E-ISSN 1943-748X, Vol. 152, p. 274-283Article in journal (Refereed)
    Abstract [en]

    A new adaptive stochastic approximation method for an efficient Monte Carlo calculation of steady-state conditions in thermal reactor cores is described The core conditions that we consider are spatial distributions of power, neutron flux, coolant density, and strongly absorbing fission products like Xe-135. These distributions relate to each other; thus, the steady-state conditions are described by a system of nonlinear equations. When a Monte Carlo method is used to evaluate the power or neutron flux, then the task turns to a nonlinear stochastic root-finding problem that is usually solved in the iterative manner by stochastic optimization methods. One of those methods is stochastic approximation where efficiency depends on a sequence of stepsize and sample size parameters. The stepsize generation is often based on the well-known Robbins-Monro algorithm; however, the efficient generation of the sample size (number of neutrons simulated at each iteration step) was not published yet. The proposed method controls both the stepsize and the sample size in an efficient way; according to the results, the method reaches the highest possible convergence rate.

  • 13.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Holst, Gustaf
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Correlation of errors in the Monte Carlo fission source and the fission matrix fundamental-mode eigenvector2016In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 94, p. 415-421Article in journal (Refereed)
    Abstract [en]

    Previous studies raised a question about the level of a possible correlation of errors in the cumulative Monte Carlo fission source and the fundamental-mode eigenvector of the fission matrix. A number of new methods tally the fission matrix during the actual Monte Carlo criticality calculation, and use its fundamental-mode eigenvector for various tasks. The methods assume the fission matrix eigenvector is a better representation of the fission source distribution than the actual Monte Carlo fission source, although the fission matrix and its eigenvectors do contain statistical and other errors. A recent study showed that the eigenvector could be used for an unbiased estimation of errors in the cumulative fission source if the errors in the eigenvector and the cumulative fission source were not correlated. Here we present new numerical study results that answer the question about the level of the possible error correlation. The results may be of importance to all methods that use the fission matrix. New numerical tests show that the error correlation is present at a level which strongly depends on properties of the spatial mesh used for tallying the fission matrix. The error correlation is relatively strong when the mesh is coarse, while the correlation weakens as the mesh gets finer. We suggest that the coarseness of the mesh is measured in terms of the value of the largest element in the tallied fission matrix as that way accounts for the mesh as well as system properties. In our test simulations, we observe only negligible error correlations when the value of the largest element in the fission matrix is about 0.1. Relatively strong error correlations appear when the value of the largest element in the fission matrix raises above about 0.5. We also study the effect of the error correlations on accuracy of the eigenvector-based error estimator. The numerical tests show that the eigenvector-based estimator consistently underestimates the errors in the cumulative fission source when a strong correlation is present between the errors in the fission matrix eigenvector and the cumulative fission source (i.e., when the mesh is too coarse). The error estimates are distributed around the real error value when the mesh is sufficiently fine.

  • 14.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Hoogenboom, Eduard
    Numerical Stability of Existing Monte Carlo Burnup Codes in Cycle Calculations of Critical Reactors2009In: Nuclear science and engineering, ISSN 0029-5639, E-ISSN 1943-748X, Vol. 162, no 3, p. 307-311Article in journal (Refereed)
    Abstract [en]

    We show that major existing Monte Carlo burnup codes are numerically unstable in cycle calculations of critical reactors; spatial oscillations of the neutron flux can be observed even when relatively small time steps are used. This is caused by using the explicit Euler or midpoint method that appear to be numerically unstable with the step sizes common in cycle calculations. More stable methods that are common in deterministic burnup calculations, like the modified Euler method, can easily be introduced into the Monte Carlo burnup codes.

  • 15.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Kotlyar, Dan
    Shwageraus, Eugene
    The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations2013In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 60, p. 295-300Article in journal (Refereed)
    Abstract [en]

    Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and bumup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail.

  • 16.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Kotlyar, Dan
    Shwageraus, Eugene
    Leppänen, Jaakko
    Numerical stability of the predictor-corrector method in Monte Carlo burnup calculations of critical reactors2013In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 56, p. 34-38Article in journal (Refereed)
    Abstract [en]

    Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor-corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems.

  • 17.
    Dufek, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Valtavirta, Ville
    Time step length versus efficiency of Monte Carlo burnup calculations2014In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 72, p. 409-412Article in journal (Refereed)
    Abstract [en]

    We demonstrate that efficiency of Monte Carlo burnup calculations can be largely affected by the selected time step length. This study employs the stochastic implicit Euler based coupling scheme for Monte Carlo burnup calculations that performs a number of inner iteration steps within each time step. In a series of calculations, we vary the time step length and the number of inner iteration steps; the results suggest that Monte Carlo burnup calculations get more efficient as the time step length is reduced. More time steps must be simulated as they get shorter; however, this is more than compensated by the decrease in computing cost per time step needed for achieving a certain accuracy.

  • 18. Hoogenboom, J. Eduard
    et al.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics. KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations2016In: SNA + MC 2013 - JOINT INTERNATIONAL CONFERENCE ON SUPERCOMPUTING IN NUCLEAR APPLICATIONS + MONTE CARLO / [ed] Caruge, D Calvin, C Diop, CM Malvagi, F Trama, JC, E D P SCIENCES , 2016, article id UNSP 03406Conference paper (Refereed)
    Abstract [en]

    This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.

  • 19. Isotalo, A. E.
    et al.
    Leppänen, J.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Preventing xenon oscillations in Monte Carlo burnup calculations by enforcing equilibrium xenon distribution2013In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 60, p. 78-85Article in journal (Refereed)
    Abstract [en]

    Existing Monte Carlo burnup codes suffer from instabilities caused by spatial xenon oscillations. These oscillations can be prevented by forcing equilibrium between the neutron flux and saturated xenon distribution. The equilibrium calculation can be integrated to Monte Carlo neutronics, which provides a simple and lightweight solution that can be used with any of the existing burnup calculation algorithms. The stabilizing effect of this approach, as well as its limitations are demonstrated using the reactor physics code Serpent.

  • 20.
    Mickus, Ignas
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.
    Optimal neutron population growth in accelerated Monte Carlo criticality calculations2018In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 117, p. 297-304Article in journal (Refereed)
    Abstract [en]

    We present a source convergence acceleration method for Monte Carlo criticality calculations. The method gradually increases the neutron population size over the successive inactive as well as active criticality cycles. This helps to iterate the fission source faster at the beginning of the simulation where the source may contain large errors coming from the initial cycle; and, as the neutron population size grows over the cycles, the bias in the source gets reduced. Unlike previously suggested acceleration methods that aim at optimisation of the neutron population size, the new method does not have any significant computing overhead, and moreover it can be easily implemented into existing Monte Carlo criticality codes. The effectiveness of the method is demonstrated on a number of PWR full-core criticality calculations using a modified SERPENT 2 code.

  • 21.
    Mickus, Ignas
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Tuttelberg, Kaur
    PERFORMANCE OF THE EXPLICIT EULER AND PREDICTOR-CORRECTOR-BASED COUPLING SCHEMES IN MONTE CARLO BURNUP CALCULATIONS OF FAST REACTORS2015In: Nuclear Technology, ISSN 0029-5450, E-ISSN 1943-7471, Vol. 191, no 2, p. 193-198Article in journal (Refereed)
    Abstract [en]

    We present a stability test of the explicit Euler and predictor-corrector based coupling schemes in Monte Carlo burnup calculations of the gas fast reactor fuel assembly. Previous studies have identified numerical instabilities of these coupling schemes in Monte Carlo burnup calculations of thermal-spectrum reactors due to spatial feedback induced neutron flux and nuclide density oscillations, where only sufficiently small time steps could guarantee acceptable precision. New results suggest that these instabilities are insignificant in fast-spectrum assembly burnup calculations, and the considered coupling schemes can therefore perform well in fast-spectrum reactor burnup calculations even with relatively large time steps. Note: Some figures in this technical note may be in color only in the electronic version.

  • 22.
    Olsen, Börge
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Fission source sampling in coupled Monte Carlo simulations2017In: Kerntechnik (1987), ISSN 0932-3902, E-ISSN 2195-8580, Vol. 82, no 2, p. 206-209Article in journal (Refereed)
    Abstract [en]

    We study fission source sampling methods suitable for the iterative way of solving coupled Monte Carlo neutronics problems. Specifically, we address the question as to how the initial Monte Carlo fission source should be optimally sampled at the beginning of each iteration step. We compare numerically two approaches of sampling the initial fission source; the tested techniques are derived from well-known methods for iterating the neutron flux in coupled simulations. The first technique samples the initial fission source using the source from the previous iteration step, while the other technique uses a combination of all previous steps for this purpose. We observe that the previous-step approach performs the best.

  • 23.
    Riber Marklund, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Development and comparison of spectral methods for passive acoustic anomaly detection in nuclear power plants2014In: Applied Acoustics, ISSN 0003-682X, E-ISSN 1872-910X, Vol. 83, p. 100-107Article in journal (Refereed)
    Abstract [en]

    We have developed spectral signal processing methods for passive acoustic anomaly detection in nuclear power plants. Furthermore, we compared the developed and existing methods by applying them to stationary sounds recorded in a controlled environment. Our new methods show significant improvement, in particular concerning robustness against false alarms. The results also demonstrate that clear detection of a given sound at a given signal-to-noise ratio is highly dependent on the distribution of characteristic frequency content in the spectrum in relation to the background noise and the spectral uncertainty. Since the frequency monitoring principle used here is quite rigid, we stress the need for research on more flexible methods, also taking into account differences between experiments and real reactor systems.

  • 24.
    Tuttelberg, Kaur
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Estimation of errors in the cumulative Monte Carlo fission source2014In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 72, p. 151-155Article in journal (Refereed)
    Abstract [en]

    We study the feasibility of estimating the error in the cumulative fission source in Monte Carlo criticality calculations by utilising the fundamental-mode eigenvector of the fission matrix. The cumulative fission source, representing the source combined over active cycles, contains errors of both statistical and systematic nature. Knowledge of the error in the cumulative fission source is crucial as it determines the accuracy of computed neutron flux and power distributions. While statistical errors are present in the eigenvector of the fission matrix, it appears that these are not (or they are only weakly) correlated to the errors in the cumulative fission source. This ensures the suggested methodology gives error estimates that are distributed around the real errors, which is also supported by results of our numerical test calculations.

  • 25.
    Tuttelberg, Kaur
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Technology.
    Neutron batch size optimisation methodology for Monte Carlo criticality calculations2015In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 75, p. 620-626Article in journal (Refereed)
    Abstract [en]

    We present a methodology that improves the efficiency of conventional power iteration based Monte Carlo criticality calculations by optimising the number of neutron histories simulated per criticality cycle (the so-called neutron batch size). The chosen neutron batch size affects both the rate of convergence (in computing time) and magnitude of bias in the fission source. Setting a small neutron batch size ensures a rapid simulation of criticality cycles, allowing the fission source to converge fast to its stationary state; however, at the same time, the small neutron batch size introduces a large systematic bias in the fission source. It follows that for a given allocated computing time, there is an optimal neutron batch size that balances these two effects. We approach this problem by studying the error in the cumulative fission source, i.e. the fission source combined over all simulated cycles, as all results are commonly combined over the simulated cycles. We have deduced a simplified formula for the error in the cumulative fission source, taking into account the neutron batch size, the dominance ratio of the system, the error in the initial fission source and the allocated computing time (in the form of the total number of simulated neutron histories). Knowing how the neutron batch size affects the error in the cumulative fission source allows us to find its optimal value. We demonstrate the benefits of the method on a number of numerical test calculations.

  • 26.
    Ålander, Alexandra
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Dufek, Jan
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Gudowski, Waclaw
    KTH, School of Engineering Sciences (SCI), Physics, Nuclear Power Safety.
    From once-through nuclear fuel cycle to accelerator-driven transmutation2006In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, ISSN 0168-9002, E-ISSN 1872-9576, Vol. 562, no 2, p. 630-633Article in journal (Refereed)
    Abstract [en]

    In this study simulation of different nuclear fuel cycle scenarios are performed. The reference scenario corresponds to a medium size nuclear power country, with 10 light water reactors (LWRs). The study addresses long-term, equilibrium fuel cycle scenarios, with and without plutonium recycling (MOX) in LWRs and transuranics (TRU) burning in accelerator-driven systems (ADS). However, also short-term phase-out scenarios, including TRU burning in ADS, are performed. The equilibrium simulation showed that four ADS units, each of 800 MWt, are sufficient to burn an amount of plutonium and americium corresponding to the build-up of those elements. The phase-out simulation of a country adopting an approach to reduce the spent nuclear fuel inventory, showed that complementary burning of TRU in three to four ADS units appear suitable. The fuel cycle simulations have been performed using the Nuclear Fuel Cycle Simulation (NFCSim) code [C.G. Bathke, E.A. Schneider, NFCSim User's Manual, Los Alamos National Laboratory Report LA-UR-04-8369, 2004.] and the Monteburns code [D.I. Poston, H.R. Trellue, User's Manual, Version 2.0 for Monteburns, Version 1.0, LA-UR-99-4999, 1999.].

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