Uniformity Control of Scanned Beam in 300 MeV Proton and Heavy Ion Accelerator Complex at SESRI

In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiation area is required for the extracted ion beams,which is crucial because it directly affects the experimental precision and therapeutic effect.Specifically,ultra-large-area and high-uniformity scanning are crucial requirements for spacecraft radiation effects assessment and serve as core specification for beamline terminal design.In the 300 MeV proton and heavy ion accelerator complex at the Space Environment Simulation and Research Infrastructure(SESRI),proton and heavy ion beams will be accelerated and ultimately delivered to three irradiation terminals.In order to achieve the required large irradiation area of 320 mm×320 mm,horizontal and vertical scanning magnets are used in the extraction beam line.However,considering the various requirements for beam species and energies,the tracking accuracy of power supplies(PSs),the eddy current effect of scanning magnets,and the fluctuation of ion bunch structure will reduce the irradiation uniformity.To mitigate these effects,a beam uniformity optimization method based on the measured beam distribution was proposed and applied in the accelerator complex at SESRI.In the experiment,the uniformity is successfully optimized from 75%to over 90%after five iterations of adjustment to the PS waveforms.In this paper,the method and experimental results were introduced.

Free vibration of non-uniform axially functionally graded beams using the asymptotic development method

The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.

Numerical Calculation of Dynamic Response for Multi-Span Non-Uniform Beam Subjected to Moving Mass with Friction

In order to simulate the coupling vibration of a vehicle or train moves on a multi-span continuous bridge with non-uniform cross sections, a moving mass model is used according to the Finite Element Method, the effect of the inertial force, Coriolis force and centrifugal force are considered by means of the additive matrices. For a non-uniform rectangular section beam with both linear and parabolic variable heights in a plane, the stiffness and mass matrices of the beam elements are presented. For a non-uniform box girder, Romberg numerical integral scheme is adopted, each coefficient of the stiffness matrix is obtained by means of a normal numerical computation. By applying these elements to calculate the non-uniform beam, the computational accuracy and efficiency are improved. The finite element method program is worked out and an entire dynamic response process of the beam with non-uniform cross sections subjected to a moving mass is simulated numerically, the results are compared to those previously published for some simple examples. For some complex multi-span bridges subjected to some moving vehicles with changeable velocity and friction, the computational results, which can be regarded as a reference for engineering design and scientific research, are also given simultaneously.

The Response of Viscously Damped Euler-Bernoulli Beam to Uniform Partially Distributed Moving Loads

The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and moving mass problem in order to determine the behaviour of the system under consideration. The analytical method in terms of series solution and numerical method were used for the governing equation. The effect of various beam observed that the response amplitude due to the moving force is greater than that due to moving mass. It was also found that the response amplitude of the moving force problem with non-initial stress increase as mass of the mass of the load M increases.

Transverse vibrations of arbitrary non-uniform beams

Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.

A New Non-uniform Beam Element and Its Application to Buckling Analysis for Framed Structures

The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.

On Uniform Decay of Solutions for Extensible Beam Equation with Strong Damping

This paper investigates the existence and uniform decay of global solutions to the initial and boundary value problem with clamped boundary conditions for a nonlinear beam equation with a strong damping.

Analytic Static Deflection Solutions of Uniform Cantilever Beams Resting on Nonlinear Elastic Rotational Boundary

In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force function is an analytic function,then the deflection function can be derived and expressed in Maclaurin series.A recurrence relation for the coefficients of the Maclaurin series is derived.It is shown that the proposed solution method is accurate and efficient.The solution method can be successfully applied to the uniform cantilever beam and non-linear elastic rotational boundary problem.

Non-Uniformity of Heavy-Ion Beam Irradiation on a Direct-Driven Pellet in Inertial Confinement Fusion

Heavy-ion-driven fusion （HIF） is a scheme to achieve inertial confinement fusion （ICF）. Investigation of the non-uniformity of heavy-ion beam （HIB） irradiation is one of the key issues for ICF driven by powerful heavy-ion beams. Ions in HIB impinge on the pellet surface and deposit their energy in a relatively deep and wide area. Therefore, the non-uniformity of HIB irradiation should be evaluated in the volume of the deposition area in the absorber layer. By using the OK1 code with some corrections, the non-uniformity of heavy-ion beam irradiation for the different ion beams on two kinds of targets were evaluated in 12-beam, 20-beam, 60-beam and 120-beam irradiation schemes. The root-mean-square （RMS） non-uniformity value becomes aRMS = 8.39% in an aluminum mono-layer pellet structure and aRMS = 6.53% in a lead-aluminum layer target for the 12-uranium-beam system. The RMS non-uniformity for the lead-aluminum layer target was lower than that for the mono-layer target. The RMS and peak-to-valley （PTV） non-uniformities are reduced with the increase in beam number, and low at the Bragg peak layer.

Evaluation of Single Field Uniform Dose (SFUD) Proton Pencil Beam Scanning (PBS) Planning Strategy for Lung Mobile Tumor Using a Digital Phantom

Purpose: To quantitatively evaluate four different Proton SFUD PBS initial planning strategies for lung mobile tumor. Methods and Materials: A virtual lung patient’s four-dimensional computed tomography (4DCT) was generated in this study. To avoid the uncertainties from target delineation and imaging artifacts, a sphere with diameter of 3 cm representing a rigid mobile target (GTV) was inserted into the right side of the lung. The target motion is set in superior-inferior (SI) direction from ?5 mm to 5 mm. Four SFUD planning strategies were used based on: 1) Maximum-In-tensity-Projection Image (MIP-CT);2) CT_average with ITV overridden to muscle density (CTavg_muscle);3) CT_average with ITV overridden to tumor density (CTavg_tumor);4) CT_average without any override density (CTavg_only). Dose distributions were recalculated on each individual phase and accumulated together to assess the “actual” treatment. To estimate the impact of proton range uncertainties, +/?3.5% CT calibration curve was applied to the 4DCT phase images. Results: Comparing initial plan to the dose accumulation: MIP-CT based GTV D98 degraded 2.42 Gy (60.10 Gy vs 57.68 Gy). Heart D1 increased 6.19 Gy (1.88 Gy vs 8.07 Gy);CTavg_tumor based GTV D98 degraded 0.34 Gy (60.07 Gy vs 59.73 Gy). Heart D1 increased 2.24 Gy (3.74 Gy vs 5.98 Gy);CTavg_muscle based initial GTV D98 degraded 0.31 Gy (60.4 Gy vs 60.19 Gy). Heart D1 increased 3.44 Gy (4.38 Gy vs 7.82 Gy);CTavg_only based Initial GTV D98 degraded 6.63 Gy (60.11 Gy vs 53.48 Gy). Heart D1 increased 0.30 Gy (2.69 Gy vs 2.96 Gy);in the presence of ±3.5% range uncertainties, CTavg_tumor based plan’s accumulated GTV D98 degraded to 57.99 Gy (+3.5%) 59.38 Gy (?3.5%), and CTavg_muscle based plan’s accumulated GTV D98 degraded to 59.37 Gy (+3.5%) 59.37 Gy (?3.5%). Conclusion: This study shows that CTavg_Tumor and CTavg_Muscle based planning strategies provide the most robust GTV coverage. However, clinicians need to be aware that the actual dose to OARs at distal end of target may increase. The study also indicates that the current SFUD PBS planning strategy might not be sufficient to compensate the CT calibration uncertainty.

背对式槽钢组合梁均布荷载下的弯曲应力研究

研究了均布荷载作用下的冷弯薄壁背对式组合梁的弯曲应力分布,基于梁的经典弯曲理论和约束扭转理论,在考虑翘曲作用的影响下推导了构件在均布荷载作用下的弯曲应力理论公式。并通过有限元软件ABAQUS分析算例,将算例的仿真值和理论解析值进行对比,验证了该理论公式的合理性。结果表明,弯曲应力在横截面上呈现线性梯度分布,以构件OT1.2-86-S75为例,当旋转约束k_(φ)取值分别为10、100、1000 N时,翼缘处的应力梯度分别为3.225、2.465、1.732 MPa/mm,即翼缘处的应力梯度随着旋转约束的减小而增大;沿纵向在相邻螺钉之间呈现连续抛物线式分布;若螺钉间距相等,弯曲应力最大值出现在跨中,弯曲应力极大值随着与支座距离减小逐渐递减。

基于平凸柱面镜的LIBS光束整形系统设计

为改善激光诱导击穿光谱(Laser-induced breakdown spectroscopy,LIBS)技术激光能量不均匀分布的问题,利用仿真软件对半径为12.5 mm的不同焦距型号的平凸柱面镜进行光路成像模拟,模拟显示满足激光器条件的最佳焦距为100 mm,在此基础上搭建基于LIBS光束的整形系统。实验表明,相比于无平凸柱面镜整形,样品中锶元素的焦斑光强均方差系数平均降低了41.91%,焦斑光强峰谷比系数平均降低了41.27%,而能量均匀度平均提高了17.23%,拟合决定系数由0.860提高到了0.914。结果显示,使用平凸柱面镜可提高光束能量的均匀性,验证了平凸柱面镜是激光光束整形的一种有效方法。

横向非均匀温度场作用的FGM夹层梁热屈曲分析

基于经典几何非线性梁理论,推导了受横向非均匀升温作用的FGM夹层梁热屈曲控制方程。对于端部夹紧边界条件梁,随着温度升高,梁发生分支屈曲,考虑到分支屈曲临界状态变形较小,将非线性边值问题退化成线性特征值问题,通过求线性特征值问题,得到了有量纲临界屈曲温度差解析解。另外,运用打靶法计算非线性边值问题,得到了热过屈曲平衡路径和平衡构型。利用算例探究层厚比、梯度指数、温度场级数项数目对FGM夹层梁热过屈曲平衡路径和平衡构型的影响。结果表明:当梯度层相对厚度和梯度指数增加时,FGM夹层梁临界屈曲温度差均增加。

孔隙度对具有不均匀横截面的功能分级多孔梁的自由振动和屈曲行为的影响

本文旨在研究孔隙度对具有不均匀横截面的功能分级多孔梁的自由振动和屈曲行为的影响。一般认为材料的性能沿厚度方向变化,而梁的横截面沿其长度方向分布不均匀。三种不同的孔隙度分布包括对称分布、非对称分布和均匀分布。利用经典的梁理论和Hamilton原理推导出了问题的控制方程,并用微分求积法推导出公式。通过已知方法和分析解法对所得结果进行了验证。通过网格独立性研究,确定了最优离散化设置。利用详细的参数化分析研究了不同力学参数,包括孔隙率系数、长径比和变化截面对基频和临界屈曲载荷的影响。结果表明,材料孔隙率的增加会导致梁的屈曲能力显著降低。然而,梁的自由振动行为完全取决于其孔隙度模式。此外,孔隙呈对称分布的梁其屈曲能力和基频性能最好。

双自由曲面光束整形系统的虚拟面迭代设计法

双自由曲面光束整形系统可在不改变光束相位分布的情况下实现光束空间光强分布的按需调控,然而其需要设置虚拟平面来进行双自由曲面面形的求解。研究发现,传统单一虚拟面法在应用于结构紧凑和扩束倍率较大的系统时,存在设计不精准、整形效果差等缺陷,为此,提出了一种基于虚拟面迭代策略的双自由曲面光束整形系统设计方法。基于不同参数的同轴透射式和离轴反射式光束整形系统的数值仿真研究结果,表明该方法可有效规避传统虚拟面法的局限性。以将束腰半径为5 mm的高斯光束整形为半径30 mm的准直平顶光束的透射式双自由曲面光束整形系统为例,虚拟面迭代法所设计的光束整形系统将光强分布均匀性和能量利用率相对于单一虚拟面法而言分别提升了2.93%和8.93%。

一种实现均匀线列阵恒定束宽的方法

当基阵接收信号为宽带时,若采用常规宽带波束形成,不同频率上波束图不同,频率越高,波束宽度越窄。当信号从波束主瓣内非主轴方向入射时,输出波形会发生失真,直接影响到后续的一系列功能,如系统估计波形、识别目标特性等。该问题的基本解决方法是,设计恒定束宽波束形成器,使基阵系统对不同频率的输入信号具有相似的波束图。研究了一种应用于均匀线列阵的恒定束宽控制方法——空间重采样法,仿真结果表明,在一定的带宽内,系统能够实现恒定束宽,证明了该方法的有效性。此外,仿真实现了空间重采样恒定束控算法在频域宽带波束形成系统中的应用。在频域宽带波束形成时,利用重叠保留法,解决了数据块之间相位不连续的问题。对于系统频带范围外的频点,采用置极小数处理的方法,抑制带外干扰,提高了结果的精确度。

A Note on Stability of Longitudinal Vibrations of an Inhomogeneous Beam

In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total energy of the system at any time t. By constructing suitable Lyapunov functional, it is established directly that the energy of this system decays exponentially.

基于非球面镜组的大口径激光匀化技术研究

为了优化对大口径激光探测组件灵敏度、角度参数等特性的测量能力,减小因高斯光束光强分布中间强、边缘弱的特点造成的测量值差异,基于小口径非球面镜组光束整形及高倍率扩束技术,设计了大口径均匀激光光束产生装置,提出了基于光强分布、非球面镜非球面度、光线光程差的综合优化整形方法。结果表明,设计的开普勒型非球面整形镜组非球面度小于20μm,工作束宽5 mm,输出平顶光束均匀性为92.8%;设计的40^(×)高质量扩束系统,与非球面镜组相匹配可实现2 m距离内150 mm口径均匀光束,可获得优于94.2%的Ф150 mm大口径均匀光束输出。该研究对激光测量与标定系统的工程化设计是有帮助的。