少鹏夏

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brade gomez

Universidad de Buenos Aires

Rudi Zagst

Technische Universität München

Marc Atlan

Goldsmiths, University of London

Sappi Eric

Henan University

Itsaso Apezteguia Extramiana

Universidad autonoma de barcelona

JULIO CESAR SOSA ALVA

Nadzeya Yakimchyk

Alex Edmans

University of Pennsylvania

Hardy Hulley

University of Technology Sydney

Rene Garcia

Université de Montréal

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Papers by 少鹏夏

Analysis of producing 238Pu as a byproduct in an MSFR

Annals of Nuclear Energy, 2021

We present a novel approach to depicting asset-pricing dynamics by characterizing shock exposures... more We present a novel approach to depicting asset-pricing dynamics by characterizing shock exposures and prices for alternative investment horizons. We quantify the shock exposures in terms of elasticities that measure the impact of a current shock on future cash flow growth. The elasticities are designed to accommodate nonlinearities in the stochastic evolution modeled as a Markov process. Stochastic growth in the underlying macroeconomy and stochastic discounting in the representation of asset values are central ingredients in our investigation. We provide elasticity calculations in a series of examples featuring consumption externalities, recursive utility, and jump risk.

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Solving variable-coefficient burnup equations by exponential Rosenbrock methods

Annals of Nuclear Energy, 2021

Abstract Burnup calculation is an essential topic in reactor physics analysis, which is based on ... more Abstract Burnup calculation is an essential topic in reactor physics analysis, which is based on the neutronic-depletion coupling calculation. High order neutronic-depletion coupling methods have been demonstrated much superior to the traditional coupling methods in terms of accuracy, but introduce the variable-coefficient burnup equations. The straightforward and general method for solving variable-coefficient burnup equations is to discretize the burnup step into several substeps and then approximate variable-coefficient equations by a sequence of constant-coefficient ones. However, substep sizes must be rather small to obtain satisfactory accuracy, which causes numerous computational cost. In this work, a class of one-step methods called exponential Rosenbrock methods is proposed to solve variable-coefficient burnup equations. The major part of the implementation of exponential Rosenbrock methods is computing the matrix exponentials and related φ functions, so the matrix exponential methods for constant-coefficient burnup equations can be applied to exponential Rosenbrock methods directly. Moreover, each exponential Rosenbrock method has a corresponding embedded error estimator for adaptive time-stepping. A 4th-order exponential Rosenbrock method called EXPRB43 is used in this work, and two EXPRB43-based predictor–corrector coupling methods called EXPRB43-CE/LI and EXPRB43-LE/QI are further established by replacing the time step discretization method used in the conventional CE/LI and LE/QI with EXPRB43. To investigate the correctness and performance of EXPRB43 for solving variable-coefficient burnup equations, three artificial test Cases are first constructed by combining three different time-dependent fluxes and a specific cross-section library. The numerical results show EXPRB43 can improve the computational efficiency by 2 to 3 orders of magnitude compared to the straightforward method, and this novel method could easily obtain more accurate and reliable solutions by using an adaptive stepsize controller. Then, a test case for depleting a 2D UO2-Gd fuel pin is investigated to further demonstrate the performance of EXPRB43 in realistic neutronic-depletion coupling problems. By comparing to the conventional CE/LI and LE/QI, EXPRB43-based coupling methods can obtain slightly more accurate solutions especially for several important fission products, such as 155Gd, 157Gd, 135Xe and 149Sm. Although the overall computational errors dominated by the errors of polynomial approximation of the time dependent burnup matrix cover up the improvement of EXPRB43 to the naive substep method, EXPRB43-based coupling methods can be alternative to the conventional ones.

Solving Burnup Equations by Numerical Inversion of the Laplace Transform Using Padé Rational Approximation

Nuclear Science and Engineering, 2020

Abstract Burnup calculations play a very important role in nuclear reactor design and analysis, a... more Abstract Burnup calculations play a very important role in nuclear reactor design and analysis, and solving burnup equations is an essential topic in burnup calculations. In the last decade, several high-accuracy methods, mainly including the Chebyshev rational approximation method (CRAM), the quadrature-based rational approximation method, the Laguerre polynomial approximation method, and the mini-max polynomial approximation method, have been proposed to solve the burnup equations. Although these methods have been demonstrated to be quite successful in the burnup calculations, limitations still exist in some cases, one of which is that the accuracy becomes compromised when treating the time-dependent polynomial external feed rate. In this work, a new method called the Padé rational approximation method (PRAM) is proposed. Without directly approximating the matrix exponential, this new method is derived by using the Padé rational function to approximate the scalar exponential function in the formula of the inverse Laplace transform of burnup equations. Several test cases are carried out to verify the proposed new method. The high accuracy of the PRAM is validated by comparing the numerical results with the high-precision reference solutions. Against CRAM, PRAM is significantly superior in handling the burnup equations with time-dependent polynomial external feed rates and is much more efficient in improving the accuracy by using substeps, which demonstrates that PRAM is the attractive method for burnup calculations.

Dynamic analysis for a 2 MW liquid-fueled molten salt reactor

Progress in Nuclear Energy, 2020

Abstract In a liquid-fueled molten salt reactor (MSR), the fuel salt acts as both fuel and coolan... more Abstract In a liquid-fueled molten salt reactor (MSR), the fuel salt acts as both fuel and coolant, and the fission energy is released into the fuel salt immediately. The delayed neutron precursors drift through the graphite channels in the core and the primary loop during operation. Therefore, the dynamics for a MSR is characterized by the strong interplay between the neutronics and thermal hydraulics, which is significantly different from that of a solid-fueled reactor, such as PWR. In this study, a dynamic analysis for a graphite moderated, fluoride based, liquid-fueled molten salt reactor with a power of 2 MWth (TMSR-LF) is carried out based on a coupled neutronics/thermal hydraulics code named TMSR-2D. The steady-state characteristics including the distributions of flow field, temperature and neutron fluxes, and effective delayed neutron fraction under different fuel flow rates, transients perturbed by fuel pump start-up and coast-down, overcooling and overheating of inlet fuel and reactivity insertion are simulated and analyzed. The numerical results indicate that the dynamic behavior of TMSR-LF is acceptable in the aspect of reactor safety. Furthermore, the dynamic analysis offers valuable information for future construction and operation of this experimental reactor.

Influence of 7Li enrichment on Th-U fuel breeding performance for molten salt reactors under different neutron spectra

Progress in Nuclear Energy, 2020

Abstract To obtain an outstanding neutron economy and Th-U (Thorium-Uranium) breeding performance... more Abstract To obtain an outstanding neutron economy and Th-U (Thorium-Uranium) breeding performance, a quite high 7Li enrichment up to 99.995% is generally required for the designs of molten salt reactors with FLiBe carrier salt. While such high 7Li enrichment would undoubtedly bring great technical challenges and high costs to the molten salt preparation. Meanwhile, the 6Li neutron absorption cross section differs greatly under different neutron spectra, which would probably mean the choice of 7Li enrichment can be different for the molten salt reactors with different neutron spectra. With the aim to provide an appropriate reference for the choice of 7Li enrichment in the engineering design of molten salt reactors, key parameters (including 233U inventory, neutron spectrum, temperature coefficient, 7Li enrichment, 7Li and 6Li neutron absorption rate, breeding ratio, relative 233U production and doubling time) and their time evolution are systematically explored based on the in-house developed code MSR-RS. The results show that 99.99% and 99.95% in 7Li enrichment introduce limited influence on Th-U breeding performance for a thermal and fast reactor respectively, and their temperature coefficient are negative. By trading off the cost and technologies required for enriching 7Li, the above two 7Li enrichment are therefore recommended.

Radiotoxicity of minor actinides in thermal, epithermal and fast TMSRs with very high burnup

Annals of Nuclear Energy, 2020

A liquid-fueled molten salt reactor (MSR) can be flexibly designed as a thermal, epithermal or fa... more A liquid-fueled molten salt reactor (MSR) can be flexibly designed as a thermal, epithermal or fast system. Meanwhile, available online fuel reprocessing can inherently interconnect the closed fuel cycle with the reactor, which would have a substantial impact on the MA production as well as nuclear waste management of a MSR. In this work, three thorium-based MSRs (thermal, epithermal and fast spectra) are chosen for analysis. The results indicate that the mass equilibrium time of a nuclide strongly depends on the vanishing coefficient of its dominant precursor nuclides and of itself. Owing to the low generation rate of MA caused by small vanishing coefficient, the fast TMSR shows a lower radiotoxicity over the thermal and epithermal TMSRs for a short operation time. Nevertheless, this advantage gradually losses as the operation time further progresses and so that the MA inventory in the fast reactor can also achieve equilibrium state.

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The Laplace transform method for solving the burnup equation with external feed

Annals of Nuclear Energy, 2019

Burnup calculation is an essential topic in reactor physics analysis. And in some advanced reacto... more Burnup calculation is an essential topic in reactor physics analysis. And in some advanced reactors, the fuel material is continously fed into the reactor core, so that external feed must be introduced into the burnup calculations. In this work, the Laplace transform method for solving the burnup equation with external feed is presented. Based on the Laplace transform method, the Quadrature-based Rational Approximation Method (QRAM) and the Chebyshev Rational Approximation Method (CRAM) have been extended to handle the burnup equation with either constant or time-dependent external feed term. Several numerical test cases are carried out to demonstrate the correctness and high-performance of the proposed method.

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Transition toward thorium fuel cycle in a molten salt reactor by using plutonium

Nuclear Science and Techniques, 2017

The molten salt reactor (MSR), as one of the Generation IV advanced nuclear systems, has attracte... more The molten salt reactor (MSR), as one of the Generation IV advanced nuclear systems, has attracted a worldwide interest due to its excellent performances in safety, economics, sustainability, and proliferation resistance. The aim of this work is to provide and evaluate possible solutions to fissile 233 U production and further the fuel transition to thorium fuel cycle in a thermal MSR by using plutonium partitioned from light water reactors spent fuel. By using an in-house developed tool, a breeding and burning (B&B) scenario is first introduced and analyzed from the aspects of the evolution of main nuclides, net 233 U production, spectrum shift, and temperature feedback coefficient. It can be concluded that such a Th/Pu to Th= 233 U transition can be accomplished by employing a relatively fast fuel reprocessing with a cycle time less than 60 days. At the equilibrium state, the reactor can achieve a conversion ratio of about 0.996 for the 60-day reprocessing period (RP) case and about 1.047 for the 10-day RP case. The results also show that it is difficult to accomplish such a fuel transition with limited reprocessing (RP is 180 days), and the reactor operates as a converter and burns the plutonium with the help of thorium. Meanwhile, a prebreeding and burning (PB&B) scenario is also analyzed briefly with respect to the net 233 U production and evolution of main nuclides. One can find that it is more efficient to produce 233 U under this scenario, resulting in a double time varying from about 1.96 years for the 10-day RP case to about 6.15 years for the 180-day RP case.

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Possible scenarios for the transition to thorium fuel cycle in molten salt reactor by using enriched uranium

Progress in Nuclear Energy, 2017

Molten Salt Reactor (MSR) with Th-233 U fuel cycle attracts more and more attention with its exce... more Molten Salt Reactor (MSR) with Th-233 U fuel cycle attracts more and more attention with its excellent performance such as desirable breeding capacity, low waste production and high inherent safety. Considering the fact that there is no available 233 U in the nature, it is necessary to analyze the fuel transition from enriched 235 U/Th to 233 U/Th and then give a flexible transition scenario for a graphitemoderated MSR. By employing an in-house developed tool which is based on SCALE6.1, two scenarios, a Breeding and Burning (B&B) scenario and a Pre-breeding scenario, are studied. The evolution of the inventories of main nuclides, net 233 U production and isothermal temperature coefficient are presented and discussed in the B&B scenario. It is found that the fuel transition can be achieved smoothly by using enriched uranium with greater than 40% concentration of 235 U. The fuel transition can still be accomplished with 20% enriched uranium but takes a long double time of about 79 years. Meanwhile, we perform an analysis of the Pre-breeding scenario and conclude that it is efficient to produce 233 U and the double time ranges from 2.07 years for the 10-day reprocessing to 10.7 years for the 180-day reprocessing. A comparison of these two scenarios is conducted, which indicates that the B&B scenario is more favorable than the Pre-breeding scenario from the aspect of resource utilization efficiency. Finally, a combined three-stage program for developing Th-based MSRs is proposed.

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Development of a Molten Salt Reactor specific depletion code MODEC

Annals of Nuclear Energy, 2019

Molten Salt Reactor (MSR) has the characteristics of on-line reprocessing and continuously refuel... more Molten Salt Reactor (MSR) has the characteristics of on-line reprocessing and continuously refueling, which bring significant differences from traditional reactors in burnup calculations. To handle its specific burnup characteristics, a Molten Salt Reactor specific depletion code-MODEC has been newly developed. MODEC implements two depletion algorithms to solve the basic burnup equations: the transmutation trajectory analysis (TTA) and the Chebyshev rational approximation method (CRAM). To simulate the on-line reprocessing, the fictive decay constant method is applied. And three different methods are implemented in MODEC to solve the nonhomogeneous burnup equations in the continuously refueling problems. Moreover, it can trace in real time the evolution of the in-stockpile nuclides which is extracted by on-line reprocessing. MODEC has three calculating modes for decay, constant flux and constant power calculations. By comparing with ORIGEN-S, the validity of performance of MODEC in conventional burnup calculations, burnup calculations with on-line reprocessing and burnup calculations with continuously refueling is proved. And a comparison of the three methods of solving nonhomogeneous burnup equations is presented and discussed. Additionally, a detailed analysis of error sources in ORIGEN-S is applied and an unpublished error source is found. Finally, a specific Monte Carlo burnup procedure for actual MSR burnup calculations is developed by coupling KENO-VI with MODEC, and the burnup benchmark of Molten Salt Fast Reactor (MSFR) is calculated to validate the specific Monte Carlo burnup procedure.

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Analysis of producing 238Pu as a byproduct in an MSFR

Annals of Nuclear Energy, 2021

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Solving variable-coefficient burnup equations by exponential Rosenbrock methods

Annals of Nuclear Energy, 2021