NONLINEAR SEMIGROUP APPROACH TOTRANSPORT EQUATIONS WITH DELAYED NEUTRONS

This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.

Regulating the Nuclear Reactor through Changes of the Fraction of Delayed Neutrons: Theoretical Probabilities

In recent years а significant number of both theoretical and experimental works devoted to the influence of external electromagnetic fields and ionization on the probability of beta decays have been published. The present work investigates the feasibility of using this physical effect as the main mechanism for controlling the reactor. In this paper a system of equations is written and studied that allows one to describe the work of a nuclear reactor in the case where the probability of beta decay and, therefore, the fraction of delayed neu-trons is a function of time. It is shown that in the case of a constant fraction of delayed neutrons, the pro-posed system of equations is identical to the known system. As can be seen from analysis of a solution of the new system of equations for the proposed method of reactor control, acceleration by instantaneous neutrons is impossible even theoretically.

Application of Monte Carlo method to calculate the effective delayed neutron fraction in molten salt reactor

Delayed neutron loss is an important parameter in the safety analysis of molten salt reactors. In this study,to obtain the effective delayed neutron fraction under flow condition, a delayed neutron precursor transport was implemented in the Monte Carlo code MCNP. The moltensalt reactor experiment(MSRE) model was used to analyze the reliability of this method. The obtained flow losses of reactivity for 235 U and 233 U fuels in the MSRE are223 pcm and 100.8 pcm, respectively, which are in good agreement with the experimental values(212 pcm and100.5 pcm, respectively). Then, six groups of effective delayed neutron fractions in a small molten salt reactor were calculated under different mass flow rates. The flow loss of reactivity at full power operation is approximately105.6 pcm, which is significantly lower than that of the MSRE due to the longer residence time inside the active core. The sensitivity of the reactivity loss to other factors,such as the residence time inside or outside the core and flow distribution, was evaluated as well. As a conclusion,the sensitivity of the reactivity loss to the residence time inside the core is greater than to other parameters.

Flow field effect of delayed neutron precursors in liquid-fueled molten salt reactors

In molten salt reactors(MSRs),the liquid fuel salt circulates through the primary loop and a part of the delayed neutron precursors(DNPs)decays outside the reactor core.To model and analyze the flow field effect of DNPs in channel-type liquid-fueled MSRs,a three-dimensional space-time dynamics code,named ThorCORE3D,that couples neutronics,core thermalhydraulics,and a molten salt loop system was developed and validated with the Molten Salt Reactor Experiment(MSRE)benchmarks.The effects of external loop recirculation time,fuel flow rate,and core flow field distribution on the delayed neutron fraction loss of MSRE at steadystate were modeled and simulated using the ThorCORE3D code.Then,the flow field effect of the DNPs on the system responses of the MSRE in the reactivity insertion transient under different initial conditions was analyzed systematically for the channel-type liquid-fueled MSRs.The results indicate that the flow field condition has a significant effect on the steady-state delayed neutron fractions and will further affect the transient power and temperature responses of the reactor system.The analysis results for the effect of the DNP flow field can provide important references for the design optimization and safety analysis of liquid-fueled MSRs.

Measurement of k_(eff) by delayed neutron multiplication in subcritical systems

In this paper, we build on the concept of equivalent fundamental-mode source to propose using delayed neutrons as a neutron source in multiplication experiments to acquire the effective multiplication factor keffof subcritical systems, which is difficult to acquire directly from conventional neutron source multiplication method. We analyzed the difference between a fundamental-mode fission source and delayed neutron source,then adopted a factor to convert delayed neutron distribution to an equivalent fundamental-mode source distribution, and employed Monte Carlo code to acquire this factor.The delayed neutron multiplication measurement method was established for the first time, and corresponding experiments were conducted in subcritical systems. The multiplication of delayed neutrons was measured based on Chinese Fast Burst Reactor-Ⅱ(CFBR-Ⅱ) at subcritical states, and keffwas acquired from delayed neutron multiplication successfully(0.9921 and 0.9969, respectively).The relative difference between k_(eff)obtained by the new method and previous values acquired by the positive period method is less than 1% for these two studied cases.

The design and calculation of the delayed neutron detection system for PWR and CEFR

This paper discussed the importance of the delayed neutron detection system.We improved the delayed neutron detection station and delayed neutron detector,so the noise was greatly decreased and the detection efficiency was greatly increased.After the improvement the stability of the detector was enhanced and the false alarm was eliminated.We introduced the principle of the gas lift pump designed for the sodium cooled fast reactor.A calculation model of the failed fuel detection system of CEFR was proposed,and from the model a code using LabWindows/CVI was developed.The minimum broken area that could be detected by the delayed neutron detection system of CEFR was calculated and the delayed neutron detection signal in a few representative transient conditions during fuel failure happened was stimulated.

TIME INTERVAL APPROACH TO THE PULSED NEUTRON LOGGING METHOD

The time interval of neibouring neutrons emitted from a steady state neutron source can be treated as that from a time-dependent neutron source. In the rockspace, the neutron flux is given by the neutron diffusion equation and is composedof an infinite number of 'modes'. Each 'mode' is composed of two die-away curves.The delay action has been discussed and used to measure the time interval withonly one detector in the experimellt. Nuclear reactions with the time distributiondue to different types of radiations observed in the neutron well-logging methods arepresented with a view to getting the rock nuclear parameters from the time intervaltechnique.

Prediction of Neutronic and Kinetic Parameters of Ghana Research Reactor 1 (GHARR-1) after 19 Years of Operation Using Monte Carlo-N Particle (MCNP) Code

The Ghana Research Reactor-1 (GHARR-1) core was modified with an addition of a 9.0 mm layer of beryllium to the top shim tray to compensate for reactivity loss due to fuel depletion after 19 years of operation. Neutronic and kinetic parameters have been predicted using Monte Carlo N-Particle Code version 5 (MCNP5) to determine whether they were within acceptable operating margins. Excess reactivity, control rod worth, moderator reactivity coefficient, delayed neutron fraction and neutron generation time have been predicted as 3.86, 6.98, −0.1218 mk/°C, 8.17507 × 10−3 Δk/k, and 8.147 × 10−5 s respectively. These parameters compared favorably with those provided in the initial Safety Analysis Report.

Measurements of effective delayed neutron fraction in a fast neutron reactor using the perturbation method

A perturbation method is proposed to obtain the effective delayed neutron fraction βeff of a cylindrical highly enriched uranium reactor. Based on reactivity measurements with and without a sample at a specified position using the positive period technique, the reactor reactivity perturbation Ap of the sample in βeff units is measured. Simulations of the perturbation experiments are performed using the MCNP program. The PERT card is used to provide the difference dk of effective neutron multiplication factors with and without the sample inside the reactor. Based on the relationship between the effective multiplication factor and the reactivity, the equation βeff=dk/△ρ is derived. In this paper, the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated. The average βeff value of the reactor is given as 0.00645, and the standard uncertainty is 3.0%. Additionally, the perturbation experiments for fleer can be used to evaluate the reliabilities of the delayed neutron parameters. This work shows that the delayed neutron data of 235U and 23SU froin G.R. Keepin＇s publication are more reliable than those from ENDF-B6.0, ENDF-B7.0, JENDL3.3 and CENDL2.2.

Method for measuring promptγ-rays generated by D-T neutrons bombarding a depleted uranium spherical shell

The prompt T-ray spectrum from depleted uranium （DU） spherical shells induced by 14 MeV D-T neutrons is measured. Monte Carlo （MC） simulation gives the largest prompt 2/ flux with the optimal thickness of the DU spherical shells 3-5 cm and the optimal frequency of neutron pulse 1 MHz. The method of time of flight and pulse shape coincidence with energy （DC-TOF） is proposed, and the subtraction of the background y-rays discussed in detail. The electron recoil spectrum and time spectrum of the prompt γ-rays are obtained based on a 2＇＇ × 2＇＇ BC501A liquid scintillator detector. The energy spectrum and time spectrum of prompt γ-rays are obtained based on an iterative unfolding method that can remove the influence of γ-rays response matrix and pulsed neutron shape. The measured time spectrum and the calculated results are roughly consistent with each other. Experimental prompt γ-ray spectrum in the 0.4-3 MeV energy region agrees well with MC simulation based on the ENDF/BVI.5 library, and the discrepancies for the integral quantities ofγ-rays of energy 0.4-1 MeV and 1 3 MeV are 9.2% and 1.1%, respectively.

Spectrum behavior for the nonlinear fractional point reactor kinetics model

The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor's formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error(local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes.

Steady state investigation on neutronics of a molten salt reactor considering the flow effect of fuel salt

The Molten Salt Reactor （MSR）, one of the ‘Generation Ⅳ＇ concepts, is a liquid-fuel reactor, which is different from the conventional reactors using solid fissile materials due to the flow effect of fuel salt. The study on its neutronics considering the fuel salt flow, which is the base of the thermal-hydraulic calculation and safety analysis, must be done. In this paper, the theoretical model on neutronics under steady condition for a single-liquid-fueled MSR is conducted and calculated by numerical method. The neutronics model consists of two group neutron diffusion equations for fast and thermal neutron fluxes, and balance equations for six-group delayed neutron precursors considering the flow effect of fuel salt. The spatial discretization of the above models is based on the finite volume method, and the discretization equations are computed by the source iteration method. The distributions of neutron fluxes and the distributions of the delayed neutron precursors in the core are obtained. The numerical calculated results show that, the fuel salt flow has little effect on the distribution of fast and thermal neutron fluxes and the effective multiplication factor; however, it affects the distribution of the delayed neutron precursors significantly, especially the long-lived one. In addition, it could be found that the delayed neutron precursors influence the neutronics slightly under the steady condition.