A New Formulation to the Point Kinetics Equations Considering the Time Variation of the Neutron Currents

The system of point kinetics equations describes the time behaviour of a nuclear reactor, assuming that, during the transient, the spatial form of the flux of neutrons varies very little. This system has been largely used in the analysis of transients, where the numerical solutions of the equations are limited by the stiffness problem that results from the different time scales of the instantaneous and delayed neutrons. Its derivation can be done directly from the neutron transport equation, from the neutron diffusion equation or through a heuristics procedure. All of them lead to the same functional form of the system of differential equations for point kinetics, but with different coefficients. However, the solution of the neutron transport equation is of little practical use as it requires the change of the existent core design systems, as used to calculate the design of the cores of nuclear reactors for different operating cycles. Several approximations can be made for the said derivation. One of them consists of disregarding the time derivative for neutron density in comparison with the remaining terms of the equation resulting from the P1 approximation of the transport equation. In this paper, we consider that the time derivative for neutron current density is not negligible in the P1 equation. Thus being, we obtained a new system of equations of point kinetics that we named as modified. The innovation of the method presented in the manuscript consists in adopting arising from the P1 equations, without neglecting the derivative of the current neutrons, to derive the modified point kinetics equations instead of adopting the Fick’s law which results in the classic point kinetics equations. The results of the comparison between the point kinetics equations, modified and classical, indicate that the time derivative for the neutron current density should not be disregarded in several of transient analysis situations.

Higher-order approximate solutions of fractional stochastic point kinetics equations in nuclear reactor dynamics

Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.

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.

Impact of photoneutrons on reactivity measurements for TMSR-SF1

The solid-fueled thorium molten salt reactor(TMSR-SF1) is a 10 MW_(th) test reactor design to be deployed in 5-10 years by the TMSR group.Its design combines coated particle fuel and molten FLiBe coolant for great intrinsic safety features and economic advantages.Due to a large amount of beryllium in the coolant salt,photoneutrons are produced by(y,n) reaction,hence the increasing fraction of effective delayed neutrons in the core by the photoneutrons originating from the long-lived fission products.Some of the delayed photoneutron groups are of long lifetime,so a direct effect is resulted in the transient process and reactivity measurement.To study the impact of photoneutrons for TMSR-SF1,the effective photoneutron fraction is estimated using k-ratio method and performed by the Monte Carlo code(MCNP5) with ENDF/B-Ⅶ cross sections.Based on the coupled neutronphoton point kinetics equations,influence of the photoneutrons is analyzed.The results show that the impact of photoneutrons is not negligible in reactivity measurement.Without considering photoneutrons in on-line reactivity measurement based on inverse point kinetics can result in overestimation of the positive reactivity and underestimation of the negative reactivity.The photoneutrons also lead to more waiting time for the doubling time measurement.Since the photoneutron precursors take extremely long time to achieve equilibrium,a "steady" power operation may not directly imply a "real" criticality.

Overrun phenomenon and neutron yield in Coulomb explosion of deuterated alkane clusters driven by intense laser field

By using a simplified Coulomb explosion model, the laser-driven Coulomb explosion processes of three deuterated alkane clusters, i.e., deuterated methane（CD4）N, ethane（C2D6）N and propane（C3D8）N clusters are simulated numerically.The overrun phenomenon that the deuterons overtake the carbon ions inside the expanding clusters, as well as the dependence of the energetic deuterons and fusion neutron yield on cluster size, is discussed in detail. Researches show that the average kinetic energy of deuterons and neutron yield generated in the Coulomb explosion of（C2D6）N cluster are higher than those of（CD4）N cluster with the same size, in qualitative agreement with the reported conclusions from the experiments of（C2 H6）N and（CH4）N clusters. It is indicated that（C2D6）N clusters are superior to（CD4）N clusters as a target for the laser-induced nuclear fusion reaction to achieve a higher neutron yield. In addition, by comparing the relevant data of（C3D8）N cluster with those of（C2D6）N cluster with the same size, it is theoretically concluded that（C3D8）N clusters with a larger competitive parameter might be a potential candidate for improving neutron generation. This will provide a theoretical basis for target selection in developing experimental schemes on laser-driven nuclear fusion in the future.

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.

An accurate solution of point kinetics equations of one-group delayed neutrons and an extraneous neutron source for step reactivity insertion

The continuous indication of the neutron density and its rate of change are important for the safe startup and operation of reactors. The best way to achieve this is to obtain analytical solutions of the neutron kinetics equations because none of the developed numerical methods can well satisfy the need for real-time or even super-time computation for the safe startup and operation of reactors in practice. In this paper, an accurate analytical solution of point kinetics equations with one-group delayed neutrons and an extraneous neutron source is proposed to calculate the change in neutron density, where the whole process from the subcritical stage to critical and supercritical stages is considered for step reactivity insertions. The accurate analytical solution can also be used as a benchmark of all numerical methods employed to solve stiff neutron kinetics equations.

非平衡态的中子增殖统一公式

导出了反应堆处于非平衡状态条件下的反应性阶跃变化时,反应堆从深度次临界到瞬发超临界整个区间通用的中子增殖统一的计算公式。通过对单组模型的修正,该公式还可以用于计算六组缓发中子的点堆中子动力学方程组。计算结果表明:利用修正后的单组解析方法计算阶跃反应性输入的中子密度响应问题,其计算结果与六组缓发中子的点堆中子动力学方程接近,精度满足工程计算要求。

用去耦合法解有温度反馈的点堆中子动力学方程

当引入大阶跃反应性时,应用去耦合法求解中子动力学方程,导出了新的反应堆功率响应表达式,可用于堆实际运行的功率区。

船用反应堆堆芯时空中子动力学仿真软件的研制

根据船用反应堆结构特点与运行方式,建立堆芯三维两群时空中子动力学仿真模型,研制了船用反应堆堆芯时空中子动力学仿真软件系统.利用软件系统进行堆芯物理计算,计算与验证结果表明,软件系统数学物理模型准确,可广泛应用于船用核动力装置模拟器的设计与研制.

输入小阶跃反应性有温度反馈时中子增殖公式

导出了输入小阶跃反应性、有温度反馈时的中子增殖表达式 。

临界反应堆阶跃正反应性输入时中子密度响应的近似修正解

通过修正单组缓发中子先驱核衰变常量A值，使点堆中子动力学方程单组缓发中子模型在正反应性阶跃输入时的数值计算结果趋近于六组缓发中子模型数值计算结果。在此基础上，用修正后的单组模型解析方法进行计算。结果表明：采用修正后的单组解析方法计算阶跃正反应性输入的中子密度响应，计算结果与六组的接近，满足工程计算精度要求，同时计算简便，避免了刚性问题，可以实现快速计算。

反应堆实际提棒的中子倍增公式

针对实际的反应堆启动过程中采用步选提棒的方式,并考虑单组缓发中子效应,以点堆中子动力学方程为基础,导出了反应堆启动的中子倍增公式,此公式的计算结果与用纯数值计算结果相同。

瞬发中子密度衰减法计算中子代时间

采用蒙特卡罗程序MCNP计算了西安脉冲堆中子代时间。使用MCNP程序模拟了反应堆瞬发中子通量密度衰减,基于忽略缓发中子项的点堆动力学方程计算出中子代时间。在微次临界下,研究了次临界度、源的分布、计数区域等对西安脉冲堆中子代时间计算结果的影响。计算分析表明:采用瞬发中子密度衰减法计算中子代时间时,微次临界度、源分布、计数区域等对计算结果影响都很小;误差产生的主要原因是忽略缓发中子项的点堆动力学方程并不能较好地反应瞬发中子通量密度的衰减规律。

点堆中子动力学方程的指数基函数法求解

给出了一个求解点堆中子动力学方程组的指数基函数法。该方法通过将点堆中子动力学方程组变成矩阵形式,利用指数函数为基函数的特点将其显式化,并根据初始条件求得各项系数,进而获得方程组的解。对阶跃、线性和正弦等不同反应性输入进行了计算。结果表明,指数基函数法过程简捷明了、易于编程,是一种计算速度较快、精度较高、适用性较强的求解点堆中子动力学方程的方法。

有温度反馈时中子动力学方程的新解法

当引入大阶跃反应性时 ,应用去耦合法求解中子动力学方程 ,导出了堆功率新的响应表达式 .与老的表达式相比 ,该表达式的应用范围更广 。

反应堆时空动力学方程的解法研究

利用分离变量法导出了均匀圆柱形反应堆时空中子动力学方程的近似解析解,它满足反应堆运行现场所需的计算速度和精度要求,对舰船反应堆安全运行有重要意义.

考虑单群缓发中子时中子增殖的统一公式

迄今为止,人们只分别导出了深度次临界、缓发临界附近和瞬发超临界的几个特定条件下的中子增殖公式,各公式都不具有通用性,使用很不便.文中导出了反应性阶跃变化时,只考虑单群缓发中子从深度次临界直到缓发超临界整个区间上的中子增殖统一公式.实例计算表明,该公式计算准确,实用性强,具有重要的理论意义与应用价值.

RELAP5堆芯功率计算模型的扩展

为了更好地将反应堆热工水力最佳估算程序RELAP5应用于分析控制棒控制的反应堆堆芯的功率瞬变过程,堆芯功率计算模块除保留原程序中使用的点堆中子动力学模型外,还必须向轴向一维中子动力学模型进行扩展。本文通过在现有轴向一维物理程序基础上进行改造和开发,实现了RELAP5程序与一维物理程序的耦合,并且通过例题验证了耦合的正确性。

用高阶泰勒多项式积分方法求解点堆中子动力学方程

在求解点堆中子动力学方程组中,对中子密度使用分段全隐式高阶泰勒多项式近似技术,给出一求解点堆中子动力学方程组的数值积分方法,并对该方法进行了修正优化。实例计算并与传统的三阶Hermite插值多项式法的比较表明:该方法能显著消除刚性方程组带来的数值计算不利因素,对给定的反应性输入能够取得较高精确度的数值结果,计算过程简洁,且计算速度快,通过对高阶泰勒多项式的修正,计算精度有了进一步提高,可适宜于反应堆中子动力学控制的设计分析和仿真计算。