Energy loss spectra of Arq+(q=0-12) ions in grazing incidence on single-crystal copper surface
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Abstract: By performing a Monte Carlo simulation, energy spectra as a function of surface structure for slow highly charged Arq+ ions in grazing incidence on a single-crystal copper surface were studied. Four possible mechanisms were taken into account in energy loss calculation. The energy loss spectrum consisting of two peak structure with an obvious small peak at higher energy loss side was found for Ar atoms grazing along low-index direction. The channeling effect observed in the energy loss of Arq+ ions grazing from surface was discussed. The calculated energy loss spectra agree reasonably well with those of experiment.
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Key words:
- Monte Carlo /
- energy loss /
- highly charged ion /
- grazing incidence
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对于第三代同步辐射光源电子储存环来说,对获取高亮度X射线同步辐射光的迫切需求促使设计者尽可能地降低发射度。最近,世界多个国家和地区的加速器领域专家开始讨论并设计具有极低束流发射度、更高亮度和更高横向相干性的储存环。由于其束流水平自然发射度接近X射线的衍射极限,因此被称为衍射极限储存环(DLSR)。国内,中国科学院高能物理研究所正在进行超低发射度的衍射极限环,即高能光源(HEPS)的预研工作。
束流发射度是判断储存环性能的重要参数之一,可通过测量光源点束流横向截面尺寸后结合该点Twiss参数计算得到。DLSR的束流发射度在0.01~0.3 nm·rad范围内,束流尺寸在μm量级。运用传统的方法对如此小的束流尺寸进行测量极具挑战性。可见光成像法[1]受到可见光波段(约400 nm)衍射的限制,空间分辨率极限为数十μm;可见光双缝干涉法[2]具有更高的分辨率,可通过增大狭缝间距的方法提高分辨率,但受到同步光垂直自然张角的限制;X射线波段的小孔成像法[3]由于结构简单、实用性高的特点被广泛应用,其最佳分辨率的计算需对衍射极限(孔过小)及几何弥散(孔过大)进行平衡,适合测量大于10 μm的光斑;X射线菲涅尔波带片成像法[4]及复合折射透镜法[5]的分辨率可达μm量级,但需要使用单色器消除色差,光通量较低,很难实现实时测量;而基于Kirkpatrick-Baez(KB)镜的成像方法,由于采用掠反射聚焦方式而不存在色差,无需单色器,因此光通量高,信噪比高,同时具备分辨率高的特点,成为我们在DLSR束流截面成像的研究方向。
上海光源(SSRF)是我国第一台三代同步辐射光源,其水平束流发射度设计值为3.9 nm·rad,是目前国内发射度最低的光源。在光源建设初期,已经搭建有X射线小孔成像系统(X-pinhole)[6]及可见光空间干涉系统[7]来测量束流横向截面尺寸。为了开展衍射极限储存环束流截面尺寸测量的预研工作,我们在SSRF原X-pinhole系统基础上设计并搭建了KB镜成像系统,借助SSRF条件开展研究,实现了与X-pinhole系统可切换并用。本文详细介绍了KB镜系统的设计、像差与点扩散函数计算及在线调试结果等。
1. 系统设计
上海光源以第一单元第二块弯铁的0.8°线作为引出光源点,建立了专用的X射线电子束流诊断线站[8],该光源点的束流尺寸σ值约为78 μm(水平)与20 μm(垂直)。引出前端区使用厚度1 mm、直径2 mm的铝作为引出窗隔离真空,使用前端开孔的锥型吸收块,吸收0.8°线外的X射线。铝窗口距离弯铁光源点为5.69 m,引出同步辐射光的张角为0.35 mrad。原X-pinhole系统的针孔放置在距铝窗口0.5 m处,KB镜真空室放置在X-pinhole系统的针孔后。
1.1 Kirkpatrick-Baez镜系统
1948年,Kirkpatrick与Baez二人首次提出KB聚焦反射镜[9],它由两面相互垂直放置的球面镜分别对水平和垂直方向的X射线进行聚焦。KB镜系统典型的优势是没有色差,无需单色器,相互垂直放置也起到消除像散的作用。由于两面镜子相互独立,非耦合式,且具有相同的聚焦模式,所以两成像关系相互影响很小。KB镜子午方向的聚焦方程为
1p+1q=1f=2Rsinθ (1) 式中:p与q分别是物距和像距;f为焦距;R为镜面曲率半径;θ为掠入射角度。
如果KB聚焦镜的两块镜子都是柱面,弧矢方向没有聚焦能力,两镜子各自独立在入射平面内对光束聚焦;如果两块镜子中有一块是球面镜或两块都是球面镜,需考虑弧矢方向的聚焦对第二块镜子子午聚焦的影响。
1.2 上海光源KB镜系统设计
上海光源KB镜束测成像系统的设计简图如图 1所示。两面KB镜垂直放置,均为内凹的圆柱面型,分别聚焦水平及垂直方向的X射线,详细参数见表 1。镜体被姿态调节机构固定,均放置在独立的超高真空室内,以防止镜面在X射线照射下被氧化。为了隔离低频震动,KB镜经由超高真空调节机构固定在一块518 mm×712 mm×857 mm的大理石基座上。两面KB镜均可远控调节姿态,包括切入、切出光路,倾斜角度(pitch)调整等。垂直聚焦镜(VFM)距离光源点7.36 m,距离像点8.08 m,放大率为1.1倍;水平聚焦镜(HFM)距离光源点7.72 m,距离像点7.72 m,放大率为1倍。在KB镜真空室前,放置有水平及垂直两个入射狭缝,分别确定入射至系统内X射线的水平及垂直角度为122 μrad×117 μrad。狭缝前的Cu衰减片用于衰减入射光子通量,同时保护镜面免受长时间、高热负载运行。
表 1 KB镜参数Table 1. Design parameters of KB mirrorsmirror VFM HFM shape cylindrical cylindrical radius of curvature/km 2.57 2.57 grazing angle/mrad 3 3 substrate silicon silicon coating Rh Rh acceptance angle/μrad 122 117 size L×W×H 320 mm×40 mm×40 mm 320 mm×40 mm×40 mm clear aperture L×W 300 mm×10 mm 300 mm×10 mm roughness RMS/nm < 0.2 < 0.2 slope error RMS/μrad < 0.3 < 0.3 distance to source/m 7.36 7.72 distance to image/m 8.08 7.72 magnification 1.1 1 heat load hitting 1.083 W@absorbed 0.832 W hitting 0.251 W@absorbed 0.058 W 两面KB镜均为Thales SESO加工,基底材料为Si,表面镀铑厚度50 nm,曲率半径为2.57 km。两镜的子午方向面型误差要求优于0.3 μrad,弧矢方向面型误差优于5 μrad。两镜的掠入射角度均为3 mrad,因此高能的硬X射线会被第一面反射镜所吸收。考虑到铝窗口及入射狭缝对X射线的吸收,在300 mA束流流强下,计算得到入射至第一面镜的热负载为1.083 W。其中0.832 W会被吸收需要水冷带走,0.251 W被反射至第二面反射镜。图 2为经过系统的同步辐射光谱,包括被铝窗口及狭缝衰减后的光谱,范围为12~60 keV,峰值处的光子能量约为26 keV;经过VFM镜及HFM镜后,峰值处光子能量约为20.5 keV。
1.3 图像采集系统
KB镜系统的像斑被X射线相机采集,该相机距弯铁光源点15.44 m,由YAG:Ce(400 μm)闪烁体、微距镜头(Componon 2.8/50,Schneider-Kreuznach)及CCD相机(AVT Guppy F-080B,像素单元尺寸4.65 μm)组成。闪烁体将X射线转换为峰值波长为530 nm的可见光,闪烁体上的光斑被微距镜头成像至IEEE 1394接口的CCD相机上。镜头的放大率为2倍,因此X射线相机的有效像素为4.65 μm/2=2.325 μm。系统的数据采集处理软件在Windows平台上采用LabVIEW图形化编程语言进行开发,通过Shared Memory IOC core技术来实现EPICS的数据接口,完成LabVIEW应用程序和控制系统之间的数据交换。
2. 像差及点扩散函数
2.1 像差
由于反射式聚焦结构的设计,使得KB镜系统无色差。根据Jean Susini的分析[10],引起KB镜成像像斑尺寸变大的主要像差为三阶球差、一阶慧差及三阶慧差。仅从几何学上来考虑,像斑尺寸可以表示为
F=316L2θp1−M2M+SM+S(M+1)L4p (2) 式中:F为像斑尺寸(FWHM);L为光线照射在镜面上的长度;M=q/p为放大率;S为光源点尺寸。公式右侧第一项为三阶球差;第二项为光源点尺寸经过放大后的像斑尺寸;第三项中包含一阶慧差及三阶慧差项。
当M≈1,即物距与像距相等时,物点与像点处于罗兰圆上,第一项球差为零,成像系统无球差,此时慧差成为导致像斑展宽的主要像差。经过计算,慧差所引起的像斑展宽小于光源点尺寸(FWHM)的2%,可以忽略。因此,下节中在计算系统点扩散函数所引起的像斑展宽时未将像差因素包含进去。
2.2 点扩散函数(PSF)
KB镜成像质量的优劣主要取决于系统的点扩散函数(PSF)。X射线相机所采集的图像为光源点横向截面与整个系统PSF的卷积,包括如下几项:KB镜衍射的PSF,X射线相机的PSF,KB镜面型精度所引起的像展宽。我们无法直接测量系统的点扩散函数,因此我们假设光源及各项PSF均为高斯分布,通过计算各项的RMS值来评估系统的PSF。CCD采集到的像斑RMS值Σ可表示为
Σ2=(σM)2+S2diff +S2slope +S2camera =(σM)2+S2sys (3) 式中:σ是弯转磁铁光源点束流尺寸的RMS值;M是KB镜的放大倍率;Sdiff是KB镜孔径引起的衍射;Sslope是KB镜面型精度引起像展宽的RMS值;Scamera是X射线相机RMS空间分辨率;Ssys是整个系统的有效RMS点扩散函数。
由于HFM镜和VFM镜在放大倍率和入射孔径上有较小差别,在此我们仅讨论VFM镜,其目标测量尺寸S≈20 μm,放大率M=1.1。
衍射极限Sdiff以FWHM表示的公式为
SFWHMdiff =0.88λ2NA (4) NA=OA2q (5) OA=pθ⊥ (6) θ⊥=E0E(λ3λc)1/2 (7) 式中:NA为数值孔径,表示成像系统收集光的能力;λ为X射线的波长,取光谱峰值20.5 keV,即0.06 nm;p=7.36 m,为物距;q=8.08 m为像距;OA为X射线投射至VFM镜的光学孔径,由于我们的VFM镜尺寸足够大,20.5 keV能量的X射线完全投射至VFM镜内,因此计算OA时可采用X射线的垂直张角θ⊥乘以物距p;E0=0.51 MeV,为电子的静止能量;E=3.5 GeV,为SSRF储存环电子能量;λc=0.326 nm,为SSRF弯铁光源的特征波长。计算得到以FWHM表示的衍射极限SdiffFWHM=1.6 μm,以RMS表示的衍射极限为SdiffRMS=SdiffFWHM/2.35=0.68 μm。
当X射线被KB镜表面反射至像面时,KB镜的面型影响将被放大。我们用公式Sslope=2σslopeq来计算KB镜面型误差引起像面展宽的RMS值,其中σslope=0.3 μrad,q=8.08 m,可得Sslope=4.8 μm。
目前,KB镜系统与X-pinhole系统共用一台X射线相机,根据之前的测量结果,其空间分辨率Scamera=10 μm。因此,计算得到系统的RMS点扩散函数Ssys=11.1 μm。当图像采集端获取到像斑截面时,经过高斯拟合,可得到RMS值Σ,再根据式(3)进行反卷积计算,可进一步将测量精度提高以逼近真实值S。可以看出,X射线相机的空间分辨率在系统的PSF中占主导因素,我们下一步将对其进行升级更新,采用20倍的高倍物镜及像素单元尺寸更小的CCD相机,来获得空间分辨率约1.5 μm的X射线相机。
3. 实验结果
上海光源对用户供光时运行在恒流注入(Top-up)模式下,流强稳定在260 mA。在恒流注入模式下,经过对KB镜姿态的反复调节优化,在X射线相机上采集到了成像光斑,如图 3所示。经过高斯拟合,采集到的光斑水平及垂直尺寸(RMS)分别为76.7 μm和24.8 μm。图 4为KB镜系统在线运行1 h的历史数据,水平尺寸及垂直尺寸的标准差分别为0.083 μm和0.1 μm,小于束流尺寸的0.4%,可以看出工作在硬X射线波段的KB镜成像系统非常稳定。由式(3)计算真实尺寸为75.9 μm和20.2 μm。KB镜光源点的Twiss参数理论值如表 2所示。束流发射度εi将由计算得到的束流尺寸σi(i=x,y分别对应束流截面水平、垂直尺寸)及相关的Twiss参数βi、色散函数ηi、能散σe由以下公式获得
表 2 光源点理论参数Table 2. Theoretical electron parameters of source pointβx/m βy/m ηx/m ηy/m σe 0.794 0 12.65 0.048 7 0 0.985 3×10-3 σ2i=βiεi+(ηiσe)2 (8) 得到当前状态下束流的水平发射度为4.36 nm·rad,垂直发射度为32.3 pm·rad。
4. 结论
本文对上海光源KB镜束流截面成像系统的系统设计、像差及点扩散函数计算、在线调试结果等进行了详细介绍。目前,系统已经完成了调试,可以对束流截面进行实时成像,精确测量水平及垂直方向束斑尺寸,监测两个方向束斑尺寸的动态变化。在恒流注入模式下,得到水平及垂直尺寸分别为75.9 μm和20.2 μm,系统测量标准差小于束流尺寸的0.4%。原X射线相机的分辨率较低,是当前影响系统空间分辨率的主导因素,更换高分辨率相机是系统进一步优化的方向。
致谢: 感谢中国科学院上海应用物理研究所束测组、物理组、机械组、真空组、运行组的帮助。 -
Figure 1. Energy loss spectra for 12 keV Ar scattering from single-crystal copper surface under an incidence angle of θin=2.2°
The azimuthal orientation of the target surface was chosen by azimuthal angles
Full circles: experimental results of Ref. [18]. Curves: the present calculations fitted by Gaussian functions
(Dotted curve: elastic energy loss; dashed curves: inelastic energy loss; solid curves: summation of energy loss, i.e., total energy loss) -
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