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低能量强流高电荷态离子加速器装置（Low Energy intense-highly-charged ion Accelerator Facility, LEAF）由中国科学院近代物理研究所提出并建设，用于材料辐照性能、高电荷原子物理、低能核天体物理等方面的研究，同时作为强流重离子加速器装置（High Intensity heavy-ion Accelerator Facility, HIAF）的前期预研装置[1-3]。LEAF主要由45 GHz电子回旋共振(Electron Cyclotron Resonance, ECR)离子源、300 kV高压平台、低能束流传输线、81.25 MHz射频四极(Radio Frequency Quadrupole, RFQ)加速器、中能束流传输线及多个实验终端组成[4-6]。
RFQ是LEAF的关键设备，负责实现对离子的加速、聚焦和聚束。LEAF RFQ[7]由六段腔组成，总长6 m，采用八角空腔结构，四翼型极头将腔内空间近似分为四个象限，三维结构图如图1所示。加速离子荷质比从1/7到1，包含从质子到铀离子的全部离子束，RFQ运行频率为81.25 MHz，可将上述各类离子从14 keV/u加速至0.5 MeV/u。作为连续波运行的高功率射频腔，高的真空度可以降低微打火放电现象，是RFQ加速器稳定运行的关键[8-9]。为保障LEAF RFQ连续稳定运行，设计真空度定为10−6 Pa。由于四翼型极头的存在，导致腔体内流导较小，给目标超高真空及真空均匀性的实现增添了困难。对于此类型RFQ的真空系统，已有的经验是采用真空管道将腔体四个象限连通，以实现泵组对四个象限空间同时抽气，如美国APT/LEDA(Accelerator Production of Tritium/Low Energy Demonstration Accelerator)装置、FRIB(The Facility for Rare Isotope Beams)装置以及中国CSNS (China Spallation Neutron Source)装置的RFQ真空系统[10-12]。本文中为满足紧凑布局要求，并考虑尽量缩短抽气管道，摒弃了上述环绕式抽气管道布局，选择在腔室③、④象限处配备二级分子泵组，实现了相对均匀的超高真空环境，满足LEAF RFQ运行要求。
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LEAF RFQ系统气载Q可归纳为三部分[13]
（1）系统真空材料表面出气量Q1，为材料出气率与系统表面积的乘积。LEAF RFQ采用无氧铜真空材料，出气率按照7.98×10−9 Pa·L·s−1·cm−2计算，系统表面积约
304426 cm2，则Q1约为2.43×10−3 Pa·L/s。（2）系统漏气及渗透量Q2，在超高真空系统中通常为总气载的5%-10%，这里保守取为Q2=10%Q。
（3）放入系统的其它元器件出气量Q3，这里主要是真空规管出气，取Q3=10%Q1。
综合三部分气源，LEAF RFQ系统总出气量Q约为2.97×10−3 Pa·L·s−1。
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依据10−6 Pa的设计真空度，真空室所需有效总抽速St由式(1)确定，约
2970 L/s。式中，St是所需有效总抽速，Q是系统总出气量，P是设计真空度。按照配备8台分子泵设计，则单台分子泵对真空室的有效抽速S需达到371.25 L/s。考虑泵口与真空室之间连接管对分子泵抽速的衰减作用，单台分子泵所需抽速Sp由式(2)确定
式中，Sp是单台分子泵抽速，S是单台分子泵对真空室的有效抽速，U是分子泵口与真空室之间连接管的流导。连接管内径d=150 mm，管长l=180 mm，流导U按分子流短管计算，如式(3)[13]
式中，
$ \alpha $ 为克劳辛系数，由连接管的相对长度(l/d)确定[13]，取为0.4711 ；R为摩尔气体常数；T为气体温度；M为气体摩尔质量；A0为连接管的入口面积。对于室温空气，流导U为965.7 L/s。根据式(2)可得Sp=603.11 L/s，实际选用设计真空度下标定抽速为600 L/s的分子泵。 -
LEAF RFQ真空系统整体布局如图2所示，选择采用二级分子泵方案。一级分子泵与RFQ腔体连接，首尾两段腔体分别配备2台600 L/s分子泵，布置于腔体第③、④象限处；中间四段各配备1台600 L/s分子泵，布置于腔体第④象限处。选用由1台分子泵和2台机械泵组成的分子泵机组作为前级，与一级分子泵串联。采用分子泵串联的方法可增大系统对氢气的压缩比[14]，有效提高极限真空[15]。真空测量系统选择在RFQ腔体安装电阻真空计和冷阴极电离真空计各1套，在前级管道安装电阻真空计1套。
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VAKTRAK[16- 17]是斯坦福大学直线加速器中心Volker Ziemann开发，用于求解气体分子流状态下压强分布的软件。该软件使用传输矩阵模型表述气体分子传输过程，通过求解压强微分方程获得系统压强分布。VAKTRAK具有对计算机硬件要求低、可即时获得真空压强分布的特点，是设计加速器真空系统的基础软件之一。对几何结构简单的真空系统，使用VAKTRAK的模拟计算简洁而有效。
针对LEAF RFQ真空系统，根据分子泵口位置将系统划分成长度分别为0.5，1，1，1，1，1，0.5 m的七段，分别给出每段的长度、流导、抽速及出气量等参数，如表1所示。此处流导为RFQ腔室的流导，考虑四翼型极头结构，计算流导时将RFQ腔室等效视为并联的四个等边三角形管道，0.5 m腔体段流导为
9788 L/s，1 m腔体段流导为4894 L/s。依据表1所示的输入参数，VAKTRAK计算LEAF RFQ真空压强分布结果如图3所示。整段RFQ系统稳态真空度在9.20×10−7 −1.02×10−6 Pa范围内波动，均值9.70×10−7 Pa。
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MOLFLOW+[18-20]是欧洲核子研究中心（European Organization for Nuclear Research, CERN）开发的一款采用蒙特卡洛方法计算超高真空系统压强分布及流导的软件。超高真空下，气体分子的平均自由程远超真空室的特征长度，因此MOLFLOW+软件忽略分子间的碰撞，只考虑分子与壁面的相互作用。MOLFLOW+可以对任意复杂几何结构进行真空压强分布模拟。
根据LEAF RFQ系统的实际几何尺寸，建立三维模型并导入MOLFLOW+软件，系统被划分成784个平面。给定每个平面的出气率、抽速、反射能力和温度等属性，软件可通过蒙特卡洛方法模拟追踪每个气体分子的运动轨迹，从而获得各个平面的压强分布。综合1.1节所述三部分气载，除泵口外的其余平面出气率等效为9.75×10−9 Pa·L·s−1·cm−2，8个泵口面设定为抽速600 L/s的吸附面。
MOLFLOW+对LEAF RFQ真空系统建模计算的界面及束流中心面的压强分布曲线如图4所示。模拟计算结果显示LEAF RFQ系统真空度在1.1×10−6−1.7×10−6 Pa范围内波动，均值1.4×10−6 Pa，高于VAKTRAK模拟结果。分析两软件结果存在较大差异的原因为：VAKTRAK软件无法直接考虑腔室内部四翼型结构，而是将腔室简化视为等流导的圆管进行计算，流导等效过程中的误差导致了真空压强结果的差异。
为验证LEAF RFQ腔体内部真空度的均匀性，分别在腔室四个象限中心平行于端面取一计算面，如图1（右）中蓝色线所示，计算了四个象限内的真空压强分布，计算结果如图5所示。结果显示，象限①和②由于远离泵口，压强最高，约1.8×10−6 Pa；象限④配备6台分子泵，压强最低，约7×10−7 Pa。RFQ腔室内整体压强差小于半个量级，真空均匀度满足要求。
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LEAF装置于2018年完成安装调试，由于LEAF RFQ的高真空度，在高功率射频锻炼期间，仅耗时44 h即达到了设计功率，同年正式开始供束，目前平稳高效运行。LEAF RFQ现场图及腔体真空读数如图6所示，RFQ腔体稳态真空测量值在1.4×10−6 Pa左右，满足腔体稳定运行、加速器供束及实验要求。
LEAF RFQ真空实际测量值与两种软件的模拟计算结果相近，误差小于半个量级，MOLFLOW+的结果相对更准确。
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采用二级分子泵方案实现了LEAF RFQ加速器的超高真空系统设计，分别使用VAKTRAK和MOLFLOW+软件模拟计算了设计方案下的真空分布。运行测试结果显示实际真空度在1.4×10−6 Pa左右，VAKTRAK和MOLFLOW+模拟结果误差在半个量级以内。本文工作为HIAF装置真空系统设计积累了可靠经验。
低能强流高电荷态离子加速器RFQ真空系统设计
Design of RFQ Vacuum System for Low Energy Intense-Highly-Charged Ion Accelerator Facility
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摘要: 81.25 MHz射频四极加速器(RFQ)是低能量强流高电荷态离子加速器装置（LEAF）的关键设备，为保障RFQ加速器的稳定运行和高质量出束，要求RFQ腔体达到10−6 Pa的超高真空环境。本文采用二级分子泵方案完成了LEAF RFQ的真空系统设计，详细介绍了真空系统设计及设备选型流程，并使用VAKTRAK和MOLFLOW+软件分别对设计方案进行了模拟计算。目前，LEAF RFQ平稳高效运行，实际测量真空度在1.4×10−6 Pa左右，满足供束和实验的要求。本工作验证了VAKTRAK和MOLFLOW+计算结果的可靠性，为强流重离子加速器装置（HIAF）真空系统设计积累了经验。Abstract: The 81.25 MHz radio frequency quadrupole (RFQ) accelerator is the key equipment of low energy intense-highly-charged ion accelerator facility (LEAF). In order to ensure the RFQ can achieve a stable operation and high-quality beam supply, the RFQ cavity vacuum is required to reach an ultra-high vacuum of about 10−6 Pa. In this paper, the design of the vacuum system of LEAF RFQ is completed by the two-stage molecular pump scheme, and the process of vacuum system design and equipment selection are introduced in detail. In addition, VAKTRAK and MOLFLOW+ were used to simulate the vacuum distribution under the design scheme. At present, LEAF RFQ operates stably and efficiently, and the measured vacuum is about 1.4×10−6 Pa, which meets the requirements of beam supply and experiments. This work verifies the reliability of VAKTRAK and MOLFLOW+ results and accumulates experience for vacuum system design of high intensity heavy-ion accelerator facility (HIAF).
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Key words:
- LEAF /
- RFQ /
- Vacuum system /
- VAKTRAK /
- MOLFLOW+ .
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图 3 LEAF RFQ真空压强分布(VAKTRAK软件)
Figure 3. LEAF RFQ vacuum pressure distribution (calculated by VAKTRAK)
图 4 MOLFLOW+对LEAF RFQ真空系统建模计算的界面及束流中心面的压强分布曲线
Figure 4. MOLFLOW+ interface for LEAF RFQ vacuum system modeling calculation and pressure distribution curve of beam center surface
图 5 LEAF RFQ腔室四个象限内的真空压强分布对比
Figure 5. Comparison of vacuum pressure distribution in the four quadrants of LEAF RFQ cavity
图 6 LEAF RFQ现场图及真空读数图（图中单位为mbar）
Figure 6. LEAF RFQ field photo and vacuum gauge reading interface photo (the unit in this photo is mbar)
表 1 VAKTRAK软件计算LEAF RFQ真空压强分布的输入参数
Table 1. VAKTRAK input parameters for calculating LEAF RFQ vacuum pressure distribution
编号 元件
代码长度
/m流导
/(L/s)有效抽速
/(L/s)出气量
/(Pa L/s)备注 1 5 0.5 9788 0 2.39×10−4 “RFQ腔体1” 2 2 0 0 742.86 0 “分子泵1+2” 3 5 1 4894 0 4.78×10−4 “RFQ腔体2” 4 2 0 0 371.43 0 “分子泵3” 5 5 1 4894 0 4.78×10−4 “RFQ腔体3” 6 2 0 0 371.43 0 “分子泵4” 7 5 1 4894 0 4.78×10−4 “RFQ腔体4” 8 2 0 0 371.43 0 “分子泵5” 9 5 1 4894 0 4.78×10−4 “RFQ腔体5” 10 2 0 0 371.43 0 “分子泵6” 11 5 1 4894 0 4.78×10−4 “RFQ腔体6” 12 2 0 0 742.86 0 “分子泵7+8” 13 5 0.5 9788 0 2.39×10−4 “RFQ腔体7” 
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