大功率端窗X射线管的束流优化【增强内容出版】
Wavelength dispersive X-ray fluorescence spectrometer (WDXRF) is widely applied in disparate fields such as metallurgy, building materials, and geological surveys. Its detection principle involves employing a primary X-ray beam to excite a fluorescent beam on the sample, which is then dispersed by a dispersive crystal based on wavelength. The intensities at different wavelengths are measured and a spectrum is generated to qualitatively and quantitatively analyze the elemental composition of the sample. During the test, certain degree of intensity is lost due to the dispersion of X-ray fluorescence by the dispersive crystal. Thus, a higher intensity of the primary X-ray beam is required, which is typically achieved by an X-ray tube with high-power as the excitation source. X-ray tubes with high power can be categorized into two types of side-window and end-window X-ray tubes based on their structural forms. For end-window X-ray tubes, since the window does not absorb backscattered electrons, the beryllium window is relatively thinner, which increases the transmissivity of longer wavelength radiation and facilitates the excitation of light elements. The power of an X-ray tube is determined by the tube voltage and current. Higher tube voltage produces X-rays with higher energy, while larger tube current increases the X-ray brightness. The power of an X-ray tube is influenced by factors such as the distribution of the electric field between the two electrodes inside the tube, cathode material, temperature, surface area, and shape. Currently, Malvern Panalytical is a representative company overseas that produces end-window X-ray tubes with high power, with 75 kV/4 kW being the main specification. In China, end-window X-ray tubes are mainly focused on low-power applications, and no products are available on the market for end-window X-ray tubes with high power. They are still in the design and testing phase, and there is still a gap in power control and target focal spot control compared with the advanced international level. Therefore, further simulation studies are needed for the relevant structures of end-window X-ray tubes with high power.
We develop methods to address the problem that the beam current and power of domestically produced end-window X-ray tubes with high power are below the design values. First, the structure of the end-window X-ray tube with high power is analyzed, and the structure is simplified based on the requirements of finite element calculations. The simplification method of the end-window X-ray tube with high power is as follows. 1) The unclosed filament is simplified into a closed ring structure. 2) The influence of the water-cooled structure inside the anode on the simulation results is not considered. 3) As the target and anode are at the same potential, both of them are modeled as a whole. 4) The ceramic column, the support structure of the filament, and the end-window structure of the X-ray tube are ignored. Then, the limiting factors for beam current emission in the end-window X-ray tube with high power are determined based on the thermionic emission theory and the theory of space charge limited emission. Two optimization schemes are proposed based on the analysis of simulation results. Finally, the feasibility of the optimization schemes is verified through simulation analysis and experiments.
In the theoretical simulation calculations, the electron beam trajectory, beam current, and target focal spot are computed for the two theoretical models (Tables 2 and 3). The results based on the thermionic emission theory show that a large number of electrons return to the filament surface due to insufficient initial energy to overcome the potential near the cathode, resulting in a beam current reaching the target material of only 32.65 mA. Considering the space charge effect, the beam current value obtained from the theory of space charge limited emission is 18.01 mA. The analysis of simulation results indicates that the potential distribution near the cathode has a significant influence on the beam current reaching the target material. Based on this analysis, we propose two optimization schemes. One scheme is changing the filament potential and increasing the potential gradient near the filament to improve the influence of space charge effects. The other is changing the filament position to increase the accelerating voltage near the filament, thereby better extracting the beam current (Figs. 4 and 5).
According to the simulation results, both schemes can improve the beam current of existing X-ray tubes with high power. An experimental platform is set up to validate the simulation results. The experimental setup consists of a vacuum pump unit, voltage source, current source, variable resistor, vacuum chamber, X-ray tube filament, and copper electrodes. The experiments confirm the applicability of the emission models adopted in our study to end-window X-ray tubes with high power, and the maximum beam current limited by temperature is obtained when the filament current is 12 A, with a value of 63.4 mA. The feasibility of the two optimization schemes is also verified.
1 引言
波长色散型X射线荧光光谱仪(WDXRF)广泛应用在冶金制造、建材制造、地质调查等领域[1-5]。其检测原理是:利用分光晶体,将原级X射线在样品上激发出的荧光光束按波长色散后,测定各波长位置的强度并绘制谱图,进而实现对样品组成元素的定性分析和定量分析。测试时,由于X射线荧光经分光晶体色散后会造成一定程度的强度损失,需要原级X射线有更高的强度,一般采用大功率X射线管作为激发源。大功率X射线管按照结构形式不同,分为侧窗和端窗两种[1]。对于端窗X射线管,由于窗口不吸收反向散射电子,铍窗的厚度相对更薄,因此可以提高对长波辐射的透射率,有利于对轻元素的激发[6]。X射线管的功率由管电压和管电流决定。管电压越高,产生的X射线能量越高;管电流越大,产生X射线的亮度越高。X射线管的功率与其内部两电极间的电场分布,阴极的材料、温度、表面积、形状等因素有关。目前,国外生产大功率端窗X射线管的代表性公司是Malvern Panalytical公司,设备性能一般以75 kV/4 kW为主。国内的端窗X射线管主要以小功率为主,对于大功率端窗X射线管,国内尚无产品上市,仍处于设计测试阶段,在管功率和靶面焦斑[7]的控制等方面与国外先进水平仍有差距。因此,需要对大功率端窗X射线管的相关结构开展进一步的仿真研究。
本文基于热电子发射理论[8]和空间电荷受限发射理论[9]分析端窗X射线管的发射性能,利用COMSOL Multiphysics软件进行静电场、粒子轨迹和束流仿真计算,研究现有X射线管结构尺寸、阴极电势等参数对束流的影响,并设计验证性实验,确定优化方案的合理性,为大功率端窗X射线管的结构设计提供参考。
2 大功率端窗X射线管的束流分析与计算
2.1 大功率端窗型X射线管结构分析
大功率端窗X射线管的结构如
本文中,为方便有限元计算,将不闭环的灯丝简化成圆环结构;不考虑阳极内部的水冷结构对仿真结果的影响,靶材和阳极为同电位,将两者看为一个整体进行建模;忽略灯丝柱和灯丝的支撑部分和端窗结构。简化后的几何模型如
表 1. 几何模型的关键初始参数
Table 1. Key initial parameters of geometric model
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2.2 电子在静电场中的运动分析
在不考虑空间电荷效应和相对论效应的情况下,阴极发射的电子只受电场力的作用。电子的运动方程遵循牛顿第二定律[11],表达式为
式中:m表示电子的质量;
2.3 发射束流限制因素的分析
热发射阴极的最大发射束流主要受温度限制和空间电荷效应限制,这两种限制分别对应了热电子发射理论和空间电荷受限发射理论。在热电子发射理论中,在不考虑空间电荷限制的条件下,阴极电子发射的电流密度
式中:A为Richard常数,采用钨灯丝时取120 A∙cm-2∙K-2,采用六硼化镧时取60 A∙cm-2∙K-2;T为灯丝工作温度,由不同材料的使用寿命决定,单位为K;φ为阴极的功函数;
式中:
利用COMSOL Multiphysics软件进行计算。静电场仿真计算的边界条件为:阳极和靶材电势
表 2. 热电子发射的结果
Table 2. Result of thermal electron emission
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当束流足够大时或电场足够小时,空间电荷效应将会是主要因素,并决定了最后发射束流的大小。此时所采用的发射模型是由一维Child定律推导出来的,一维Child定律[9]的束流密度
式中:U表示两极板间的电势差;d表示极距。在该发射模型[14]中,假定在阴极表面附近存在虚构的发射面,称为虚阴极。虚阴极与实际发射面的距离称为偏置距离
式中:
利用COMSOL Multiphysics软件的空间电荷受限发射(SCLE)模块进行束流计算,取阴极电压5 V,偏置距离d=0.2 mm,获得的电子束计算结果如
表 3. 空间电荷受限发射的结果
Table 3. Result of space charge limit emission
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3 大功率端窗X射线管的束流优化与仿真
如
3.1 灯丝电势对X射线管发射束流的影响
为了研究灯丝阴极电势变化对X射线管发射束流的影响,在5~-40 V区间上,计算了束流和传输概率。随着灯丝电势变化,电子到达靶材的能量没有发生明显的变化,计算结果均在83 keV左右。阴极的发射束流随着灯丝电压向负压增加而增大。但随着灯丝电压朝负压变化,灯丝附近的电势梯度变大,从虚阴极表面发射的电子初速度也会变大。而电子初速度的变大导致了束流传输概率的减少。但整体来说到达靶材的束流是增加的,束流计算结果如
图 4. 不同灯丝电压下束流计算结果
Fig. 4. Beam current calculation result for different filament voltages
3.2 电势分布对X射线管发射束流的影响
除了改变阴极电势,改变灯丝位置也可以达到改变灯丝附近电势的效果。主要研究结构参数hc对X射线管发射束流的影响。根据
图 5. 不同灯丝高度下束流计算结果
Fig. 5. Beam current calculation result for different filament heights
4 实验验证
4.1 实验设计
为了对仿真计算结果进行验证,搭建了实验平台。装置原理如
4.2 实验结果
不同灯丝电流下的束流测试结果如
在该实验中,得到了1000 V加速电压下的不同加热功率的束流。假设该加速电压下的束流大小为温度限制下发射束流,根据
加速电压的实验结果如
图 10. 在12 A下束流随加速电压的变化
Fig. 10. Relationship between beam current and voltage when filament current is 12 A
灯丝电势的实验结果如
5 结论
针对现有大功率端窗X射线管结构存在的功率较小的问题,讨论了热电子发射理论和空间电荷受限发射理论下的大功率端窗X射线管的发射束流限制因素,认为利用空间电荷受限理论的模型进行优化仿真计算更符合实际情况。据仿真结果分析,其主要原因是灯丝附近的电势分布不合理导致的。基于这个分析,提供了两种优化方案:一种改变灯丝电位,增大灯丝附近的电势梯度来改善空间电荷效应带来的影响;另一种通过改变灯丝位置来增大灯丝附近的加速电压,从而更好地引出束流。实验结果验证了所采用的发射模型对大功率端窗X射线管同样适用;得到了灯丝电流为12 A时的温度限制最大束流,其值为63.4 mA;同时验证了两种优化方案切实可行。由于钨灯丝的体积相对较大,灯丝电流施加到13 A时,灯丝的温度仍达不到2800 K,因此尚未在理论计算采用的工作温度下进行实验。在后续的研究中,考虑替换灯丝材料进行实验。
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Article Outline
王思霖, 刘俊标, 王大正, 王鹏飞, 韩立. 大功率端窗X射线管的束流优化[J]. 光学学报, 2023, 43(22): 2234001. Silin Wang, Junbiao Liu, Dazheng Wang, Pengfei Wang, Li Han. Optimization of Electron Beams for End-Window X-Ray Tubes with High Power[J]. Acta Optica Sinica, 2023, 43(22): 2234001.