Spherical harmonics method for neutron transport equation based on unstructured-meshes

Based on a new second-order neutron transport equation, self-adjoint angular flux (SAAF) equation, the spherical harmonics (PN) method for neutron transport equation on unstructured-meshes is derived. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variable, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on unstructured-meshes. A two-dimension transport calculation program is coded according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision results and avoid the ray effect very well.     

Much ado about nothing: response matrices for void regions

Weak form Galerkin approaches are examined for obtaining response matrices for void regions – that is regions where nothing is present. The need arises in spherical harmonics methods based on second-order forms of the neutron transport equation; the methods fail in voids because the cross-section appearing in the equation’s denominator then vanishes. The diffusion approximation, being the lowest-order spherical harmonic method, is first employed as a vehicle for examining response matrices derived from both primal and dual weak forms of the mixed-first-order and second-order transport equations. Those for which discretization results in singular matrix equations as the cross-section goes to zero are rejected. First-order- mixed formulations with modified natural boundary conditions are shown to lead to nonsingular response matrices for voids. The primal method is chosen as the better of the two candidates for generalization from the diffusion to the transport equations, and the transport formulation is presented.     

High power IGBT bridge application for the harmonic suppression on the load side of the power supply system of the Spanish Stellarator TJ-II

TJ-II is a medium size stellarator of the heliac-type, which is successfully in operation at CIEMAT in Madrid, since March 1998. This machine allows operation in a wide range of magnetic field configurations. This fusion device comprises seven inductively coupled coil systems, which produce the magnetic fields required for the confinement of the plasma. These coils are powered separately by 12-pulsed thyristor converters. The DC currents in the coils have a content of harmonics and sub-harmonics and these harmonics should be kept at very low level because of negative influence on the plasma confinement. The paper describes the design, calculations and tests of an active high power filter for the harmonic suppression.     

Magnetic probe diagnostics of nonlinear standing waves and bulk ohmic electron power absorption in capacitive discharges

It is recognized that standing wave effects appearing in large-area,very-high-frequency capacitively coupled plasma(CCP)reactors cause center-high plasma non-uniformity.Using a high-frequency magnetic probe,we present a direct experimental diagnostic of the nonlinear standing waves and bulk ohmic electron power absorption dynamics in low pressure CCP discharges for different driving frequencies of 13.56,30,and 60 MHz.The design,principle,calibration,and validation of the probe are described in detail.Spatial structures of the harmonics of the magnetic field,determined by the magnetic probe,were used to calculate the distributions of the harmonic current and the corresponding ohmic electron power deposition,providing insights into the behavior of nonlinear harmonics.At a low driving frequency,i.e.13.56 MHz,no remarkable nonlinear standing waves were identified and the bulk ohmic electron power absorption was observed to be negligible.The harmonic magnetic field/current was found to increase dramatically with the driving frequency,due to decreased sheath reactance and more remarkable nonlinear standing waves at a higher driving frequency,leading to the enhancements of the ohmic heating and the plasma density in the bulk,specifically at the electrode center.At a high driving frequency,i.e.60 MHz,the high-order harmonic current density and the corresponding ohmic electron power absorption exhibited a similar node structure,with the main peak on axis,and one or more minor peaks between the electrode center and the edge,contributing to the center-high profile of the plasma density.     

The spherical harmonics method for the multigroup transport equation in x−y geometry

A spherical harmonics equation in the form of a second-order differential equation is derived for the 2-D x−y geometry, including higher-order scattering within a group. Using this equation, a multigroup transport code for the spherical harmonics method of a general order of approximation is developed. Some numerical examples, including typical problems for the ray effect, are presented and compared with those obtained by the discrete-ordinates method. It is shown that the present method gives more accurate results than the discrete-ordinates method, although this spherical harmonics code requires more computer memory than the discrete-ordinates code.     

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry. Part I: Modeling and verification for time-independent solution

This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P_N) to solve the time-independent neutron transport equation in x–y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.     

Simulation and test results of low-order band harmonic filters to decrease resonance phenomenon in the KSTAR power system

The superconducting magnet power supply which supplies superconducting magnet coil (SC) with the power to generate plasma during a KSTAR experiment for nuclear fusion research is a nonlinear load. Characteristic harmonics are generally produced since it converts AC to DC using 6 or 12 pulsed operation. However, non-characteristic harmonics or inter-harmonics are generated according to output control characteristics. Also, 95% out of the power generated from superconducting magnet coil is reactive power. Therefore, harmonic and reactive power occurring during operation have some bad influences such as voltage drop, voltage distortion and decrease in power factor on the KSTAR power system, and reactive power compensator (RPC) & harmonic filter (HF) system which is able to compensate harmonic and reactive power at the same time was established and has been operated [1]. However, out of non-characteristic harmonics and inter-harmonics caused by output control characteristics of superconducting magnet power supply, the more compensation volume of the RPC & HF system increases, the more voltage distortion with harmonic expansion is caused by harmonics in a low-order band due to the parallel resonance in a low-order band between the KSTAR power system and the RPC & HF system. As a result, it has serious effect on the injection capacity restriction of the RPC & HF system, the unstable operation control of superconducting magnet coil, and the operation of main cooling facilities. This paper presents reasons of the resonance phenomenon of the KSTAR power system and suggests a design plan of additional facilities for stable operation of the KSTAR power system, and proves their effects through the simulation and test results.     

4B9A束线单色器的改进及在线调试

报导了北京同步辐射装置4B9A束线前期改造中单色器的改进安装调试情况,并对单色器出高的变化和实际光强进行了测量。结果表明：4B9A束线的前期改造已解决了单色器出高的变化问题,为衍射站和小角站的工作创造了条件。     

A non-conforming generalization of Raviart–Thomas elements to the spherical harmonic form of the even-parity neutron transport equation

The Raviart–Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or P_N) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements.     

Evaluation of external quality factor of the superconducting cavity using extrapolation method

The estimation of the external quality factor is important for designing coupling devices for the cavities. A new representation of the external quality factor calculations for single-cell cavity coupled to a coaxial transmission line is derived based on analytic analysis and numeric analysis with the help of 3D electromagnetic code, and verified with experimental measurements at room temperature. In logarithmic scale the results for the external quality factor were quasi-line, at over the limited range, and the simulated and measured data could be used and extrapolated to the superconducting case. For the unpolished 1.5 GHz 3rd harmonic superconducting cavity, the discrepancy between the evaluation value and measurement result is less than 25% within an acceptable deviation.     

High harmonic generation driven by two-color relativistic circularly polarized laser pulses at various frequency ratios

High harmonic generation(HHG) by two-color counter-rotating relativistic laser pulses with arbitrary frequency ratio is investigated through particle-in-cell simulations. It is shown that the dichromatic laser driver at various frequency ratios can effectively produce high-order harmonics with different spectral features. A general selection rule of this extended scheme can be obtained and the corresponding harmonic helicity can be identified through a simple analytical model based on a relativistic oscillating mirror. Thus, the results in this paper may offer new opportunities for arbitrary spectral control of generated harmonics, which is of significance for diverse potential applications in practice.     

A solution of the multigroup transport equation using a weighted residual technique

The paper is in two parts. First a solution of the multigroup diffusion equation using a weighted residual technique is described. The implementation enables high-order polynomial approximations to be made to the flux. Secondly the neutron transport equation is solved by expanding the flux in a series of unnormalized spherical harmonics, obtaining second-order diffusion-like equations for the coefficients in that series and applying the algorithm previously outlined.     

On-line reconstruction of in-core power distribution by harmonics expansion method

Fixed in-core detectors are most suitable in real-time response to in-core power distributions in pressurized water reactors (PWRs). In this paper, a harmonics expansion method is used to reconstruct the in-core power distribution of a PWR on-line. In this method, the in-core power distribution is expanded by the harmonics of one reference case. The expansion coefficients are calculated using signals provided by fixed in-core detectors. To conserve computing time and improve reconstruction precision, a harmonics data library containing the harmonics of different reference cases is constructed. Upon reconstruction of the in-core power distribution on-line, the two closest reference cases are searched from the harmonics data library to produce expanded harmonics by interpolation. The Unit 1 reactor of DayaBay Nuclear Power Plant (DayaBay NPP) in China is considered for verification. The maximum relative error between the measurement and reconstruction results is less than 5.5%, and the computing time is about 0.53 s for a single reconstruction, indicating that this method is suitable for the on-line monitoring of PWRs.     

锆铀合金中痕量硼的同位素稀释质谱法测定

本文介绍了用同位素稀释技术测定锆铀合金试样中痕量硼的方法。选用富集~(10)B为同位素稀释剂,用硫酸-硫酸铵溶样,使硼形成挥发的硼酸甲酯与基样分离,用热电离质谱仪进行硼的同位素比值测量。方法的检测下限为1.5ng(硼)。对于含硼量小于1.0μg/g(样)的锆铀合金试样,相对标准偏差小于±1.0%。     

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

We developed a cubic non-linear theory describing the dynamics of the multiharmonic spacecharge wave (SCW),with harmonics frequencies smaller than the two-stream instability critical frequency,with different relativistic electron beam (REB) parameters.The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation.This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect.Different REB parameters such as the input angle with respect to focusing magnetic field,the average relativistic factor value,difference of partial relativistic factors,and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels.We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers,with the main purpose of forming a powerful multiharmonic electromagnetic wave.     

非结构网格中子输运方程的球谐函数解法研究

从新的二阶自共扼角通量密度(SAAF：Self-Adjoint Angular Flux)中子输运方程出发．利用球谐函数对角度变量进行展开,导出了一组关于空间变量的偏微分方程组,中子通量密度的各个分量相互耦合,应用一定的迭代策略进行迭代求解。针对每一个方程,应用有限元方法对非结构网格进行离散求解。据此编写了二维球谐函数方法输运计算程序,对一系列基准题进行校算的数值结果表明,该方法具有较高的计算精度,克服了射线效应,并能用于非结构网格。     

同位素10B靶的制备

为准确测量¹⁰B(n，α)⁷Li和¹⁰B(n，t2α)的反应截面，需制备质量厚度为50～350 μg/cm²的¹⁰B靶。本文系统研究了同位素¹⁰B靶的制备工艺，确定了“压片-烧结-蒸发”三步法制备¹⁰B靶。研究了基片温度对¹⁰B膜生长过程、结构和膜基结合力的影响，测试和分析了¹⁰B靶的不均匀性。结果表明，利用间歇式静电聚焦微调电子轰击法制备同位素¹⁰B靶，蒸发速率应低于0.02 μg/(cm²·s)；灯丝平面与¹⁰B柱的最佳距离为10.5～11 mm；生长的¹⁰B膜随基片温度的升高而致密并逐步结晶，膜基结合力也更好，最佳基片温度约为300 ℃。对于尺寸为Ø80 mm同位素¹⁰B靶的制备，不均匀性可控制在10%以内。已经成功在Ta和Al基片上制备了厚度<350 μg/cm²的¹⁰B靶用于核物理实验测量。     

Characterization of solid particles sampled from condensates in boiling water reactor

The growth, activation and deposition of corrosion products are the primary sources of radiation buildup on the surface of out-of-core piping in nuclear power plants. The buildup of radiation can have negative effects on the performance of the facility and cause harm to staff during maintenance outages for refueling. This paper reports on the crystalline and amorphous structures of corrosion products sampled in the boiling water reactors in nuclear power plants of Kuo-Sheng and identified using an acid dissolving technique. X-ray diffraction, scanning electron microprobe and inductively coupled plasmaatomic emission spectroscopy were used to analyze the samples. The results indicate that the quantity of amorphous iron oxide at inlet of the condensate demineralizer in Unit 2 is higher than that in Unit 1. The proportion of crystalline to amorphous corrosion products can affect the efficiency of removal. Thus, these results can be used to explain the difference in removal efficiency of condensate demineralizers in different units. Moreover, the iron oxide structures with various properties were observed in different operational periods. It is probable that the higher proportion of amorphous structures with a smaller particle size would reduce efficiency in the removal of condensate demineralization in Unit 2.     

2D/1D耦合的堆芯实测功率分布快速重构研究

针对三代核电压水堆在线监测系统需要快速准确进行实测3D功率重构的需求,本文提出了一种2D/1D耦合的3D功率重构方法。首先采用耦合系数法对探测器层的功率进行了2D实测功率重构;其次针对每个组件,采用二次样条函数拟合方法进行了轴向1D实测功率重构,最后得到了全堆3D实测功率分布。该方法计算流程简单,占用内存少。针对华龙一号开展的4个典型例题的数值验证结果表明,该方法具备很高的精度,满足三代核电在线监测系统实测功率重构对精度和速度的要求。     

Laser-RF synchronization based on digital phase detector

Laser oscillator synchronization with RF reference signal is ultra-important for a modem light source based on the accelerator.For Tsinghua Thomson scattering X-ray source,we have synchronized the mode-locked laser oscillator to RF reference signal with 48.2 fs RMS relative jitter.Both fundamental and harmonic signals derived from photo diode detection are used for laser-RF synchronization in our scheme.The fundamental signal is for coarse laser-RF synchronization and multiple laser oscillator synchronization.The harmonic signal is for high precise phase locking.The digital phase detector is implemented in the synchronization scheme for less noise,replacing the mixing to DC phase detection scheme.The digital processing algorithm for synchronization is commonly used in low-level RF control field.In order to test the phase locking loop logic without damaging the real laser oscillator,a laser oscillator emulator was developed for phase locking.This paper will report the laser-RF synchronization scheme and its performance.The laser oscillator emulator system will also be introduced here.