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Tuning of cyclotron resonant frequency and magnetic field of medical cyclotron

Wu Yong-Cun Yang Xing-Lin Shi Jin-Shui Zhao Liang-Chao He Xiao-Zhong

Tuning of cyclotron resonant frequency and magnetic field of medical cyclotron

Wu Yong-Cun, Yang Xing-Lin, Shi Jin-Shui, Zhao Liang-Chao, He Xiao-Zhong
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  • The high-frequency resonant cavity is affected by factors such as beam load, gravity and heat loss caused by cavity deformation during the actual operation of the medical cyclotron. The resonant frequency will shift to a certain extent, resulting in the high-frequency operation frequency varying with the resonant frequency of the resonator cavity. In order to meet the requirements for isochronous acceleration, the magnetic field strength should also be changed correspondingly when the high-frequency operation frequency changes, that is, the magnitude of the magnet current needs changing accordingly, so that the particle cyclotron frequency matches the high-frequency resonant frequency to overcome the sliding phase. Firstly, the static magnetic field model is established by finite element simulation software to simulate the average magnetic field of cyclotron under different magnet currents. Then the relationship between the magnetic field and the resonant frequency is theoretically analyzed. Finally, the relationship between the magnet current and the resonant frequency is obtained when the magnet current varies in a small interval. According to the optimal magnet current corresponding to different resonance frequencies, the automatic frequency tracking of magnet current is completed. In the case of ensuring the maximum carbon film beam, the optimal magnet current corresponding to different resonance frequencies is obtained, which makes the theory validated. According to the relationship, the magnet current is automatically adjusted, which overcomes the slip phase and ensures the stable output of the Faraday beam. The method enables the magnet current to be quickly and accurately find and track the cavity frequency, overcomes the slip phase caused by the frequency offset, and completes the stable output of the beam.
      Corresponding author: Wu Yong-Cun, yiranguwol@sina.cn
    [1]

    Gambhir S S, Czernin J, Schwimmer J 2001 J. Nucl. Med. 42 1S

    [2]

    Reske S N, Kotzerke J 2001 Eur. J. Nucl. Med. Mol. I. 28 1707

    [3]

    樊明武 2000 中国工程科学 2 9

    Fan M W 2000 Engineering 2 9

    [4]

    Bertrand S, Vaneycken I, Lahoutte T, Covens P, Caveliers V, Kral E, Geets J M, Nactergal B, Ghyoot M, Devillet F 2018 J. Nucl. Med. 59 2106

    [5]

    张锦明, 田嘉禾 2006 同位素 19 241

    Zhang J M, Tian J H 2006 Journal of Isotopes 19 241

    [6]

    赵籍九, 尹兆升 2006 粒子加速器技术 (北京: 高等教育出版社) 第236页

    Zhao J J, Yin Z S 2006 Particle Accelerator Technology (Beijing: Higher Education Press) p236 (in Chinese)

    [7]

    陈佳洱 1993 加速器物理基础 (北京: 原子能出版社) 第20, 21页

    Chen J E 1993 Basics of Accelerator Physics (Beijing: Atomic Energy Press) pp20, 21 (in Chinese)

    [8]

    赵凯, 牟宗信, 张家良 2014 物理学报 63 185208

    Zhao K, Mu Z X, Zhang J L 2014 Acta Phys. Sin. 63 185208

    [9]

    张天爵, 李振国, 储诚节 2010 科学通报 35 3351

    Zhang T J, Li Z G, Chu C J 2010 Science Bulletin 35 3351

    [10]

    雷钰 2012 硕士学位论文 (成都: 成都理工大学)

    Lei Yu 2012 M. S. Thesis (Chengdu: Chengdu University of Technology) (in Chinese)

    [11]

    答嘉曦, 洪越明, 董天临 2006 2005'全国微波毫米波会议论文集 (第三册) 中国 深圳, 2月27日−3月2日, 2006 pp64−67

    Da J X, Hong Y M, Dong T L 2006 2005' National Microwave and Millimeter Wave Conference Papers Collection (Vol.3) Shenzhen, China, February 27−March 2, 2006 pp64−67 (in Chinese)

    [12]

    答嘉曦 2006 硕士学位论文 (武汉: 华中科技大学)

    Da J X 2006 M. S. Thesis (Wuhan: Huazhong University of Science and Technology) (in Chinese)

    [13]

    刘毅 2008 硕士学位论文 (武汉: 华中科技大学)

    Liu Yi 2008 M. S. Thesis (Wuhan: Huazhong University of Science and Technology) (in Chinese)

    [14]

    田瑞霞, 王贤武, 金鹏 2014 强激光与粒子束 26 26105101

    Tian R X, Wang X W, Jin P 2014 High Power Laser and Particle Beam 26 26105101

    [15]

    郝焕锋 2014 博士学位论文 (北京: 中国科学院大学)

    Hao H F 2014 Ph.D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)

    [16]

    何小中, 杨国君, 龙继东 2014 核技术 37 10201

    He X Z, Yang G J, Long J D 2014 Nuclear Technol. 37 10201

    [17]

    Bhandari S, Lee G H, Klales A, Watanabe K, Taniguchi T, Heller E, Kim P, Westervelt R M 2016 Nano Lett. 16 1690

    [18]

    Xia W L, Wang Z, Lu Y R 2014 IEEE Trans. Nucl. Sci. 61 2345

    [19]

    李平, 黄娴, 文玉梅 2012 物理学报 61 137504

    Li P, Huang X, Wen YM 2012 Acta Phys. Sin. 61 137504

    [20]

    李毅, 王秋良 2016 Opera3D工程电磁场计算及多场耦合分析 (北京: 清华大学出版社) 第3页

    Li Y, Wang Q L 2016 Electromagnetic Field Calculation and Multi-field Coupling Analysis of Opera 3D Project (Beijing: Tsinghua University Press) p3

  • 图 1  高频相位随时间的变化

    Figure 1.  High frequency phase variation with time.

    图 2  高频腔压随时间的变化

    Figure 2.  High frequency cavity voltage variation with time.

    图 3  谐振频率随时间的变化

    Figure 3.  Resonant frequency variation with time.

    图 4  静磁场模型

    Figure 4.  Model of static magnetic field.

    图 5  后处理模型

    Figure 5.  Post-processing model.

    图 6  不同半径的平均磁场变化曲线

    Figure 6.  Average magnetic field curve at different radii.

    图 7  励磁电流与磁感应强度的关系

    Figure 7.  Relation between the excitation current and the magnetic induction intensity.

    图 8  励磁电流变化导致的相移

    Figure 8.  Phase shift caused by change of magnet current.

    图 9  谐振频率随励磁电流变化量的变化

    Figure 9.  Relation between resonant frequency and magnet current.

    图 10  谐振频率与励磁电流的对应关系

    Figure 10.  Corresponding relation between resonant frequency and magnet current.

    图 11  靶流随时间的变化

    Figure 11.  Variation of target beam current with time.

    图 12  输出能量的变化情况

    Figure 12.  Change of output energy

  • [1]

    Gambhir S S, Czernin J, Schwimmer J 2001 J. Nucl. Med. 42 1S

    [2]

    Reske S N, Kotzerke J 2001 Eur. J. Nucl. Med. Mol. I. 28 1707

    [3]

    樊明武 2000 中国工程科学 2 9

    Fan M W 2000 Engineering 2 9

    [4]

    Bertrand S, Vaneycken I, Lahoutte T, Covens P, Caveliers V, Kral E, Geets J M, Nactergal B, Ghyoot M, Devillet F 2018 J. Nucl. Med. 59 2106

    [5]

    张锦明, 田嘉禾 2006 同位素 19 241

    Zhang J M, Tian J H 2006 Journal of Isotopes 19 241

    [6]

    赵籍九, 尹兆升 2006 粒子加速器技术 (北京: 高等教育出版社) 第236页

    Zhao J J, Yin Z S 2006 Particle Accelerator Technology (Beijing: Higher Education Press) p236 (in Chinese)

    [7]

    陈佳洱 1993 加速器物理基础 (北京: 原子能出版社) 第20, 21页

    Chen J E 1993 Basics of Accelerator Physics (Beijing: Atomic Energy Press) pp20, 21 (in Chinese)

    [8]

    赵凯, 牟宗信, 张家良 2014 物理学报 63 185208

    Zhao K, Mu Z X, Zhang J L 2014 Acta Phys. Sin. 63 185208

    [9]

    张天爵, 李振国, 储诚节 2010 科学通报 35 3351

    Zhang T J, Li Z G, Chu C J 2010 Science Bulletin 35 3351

    [10]

    雷钰 2012 硕士学位论文 (成都: 成都理工大学)

    Lei Yu 2012 M. S. Thesis (Chengdu: Chengdu University of Technology) (in Chinese)

    [11]

    答嘉曦, 洪越明, 董天临 2006 2005'全国微波毫米波会议论文集 (第三册) 中国 深圳, 2月27日−3月2日, 2006 pp64−67

    Da J X, Hong Y M, Dong T L 2006 2005' National Microwave and Millimeter Wave Conference Papers Collection (Vol.3) Shenzhen, China, February 27−March 2, 2006 pp64−67 (in Chinese)

    [12]

    答嘉曦 2006 硕士学位论文 (武汉: 华中科技大学)

    Da J X 2006 M. S. Thesis (Wuhan: Huazhong University of Science and Technology) (in Chinese)

    [13]

    刘毅 2008 硕士学位论文 (武汉: 华中科技大学)

    Liu Yi 2008 M. S. Thesis (Wuhan: Huazhong University of Science and Technology) (in Chinese)

    [14]

    田瑞霞, 王贤武, 金鹏 2014 强激光与粒子束 26 26105101

    Tian R X, Wang X W, Jin P 2014 High Power Laser and Particle Beam 26 26105101

    [15]

    郝焕锋 2014 博士学位论文 (北京: 中国科学院大学)

    Hao H F 2014 Ph.D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)

    [16]

    何小中, 杨国君, 龙继东 2014 核技术 37 10201

    He X Z, Yang G J, Long J D 2014 Nuclear Technol. 37 10201

    [17]

    Bhandari S, Lee G H, Klales A, Watanabe K, Taniguchi T, Heller E, Kim P, Westervelt R M 2016 Nano Lett. 16 1690

    [18]

    Xia W L, Wang Z, Lu Y R 2014 IEEE Trans. Nucl. Sci. 61 2345

    [19]

    李平, 黄娴, 文玉梅 2012 物理学报 61 137504

    Li P, Huang X, Wen YM 2012 Acta Phys. Sin. 61 137504

    [20]

    李毅, 王秋良 2016 Opera3D工程电磁场计算及多场耦合分析 (北京: 清华大学出版社) 第3页

    Li Y, Wang Q L 2016 Electromagnetic Field Calculation and Multi-field Coupling Analysis of Opera 3D Project (Beijing: Tsinghua University Press) p3

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  • Received Date:  22 January 2019
  • Accepted Date:  18 March 2019
  • Available Online:  01 June 2019
  • Published Online:  20 June 2019

Tuning of cyclotron resonant frequency and magnetic field of medical cyclotron

    Corresponding author: Wu Yong-Cun, yiranguwol@sina.cn
  • Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China

Abstract: The high-frequency resonant cavity is affected by factors such as beam load, gravity and heat loss caused by cavity deformation during the actual operation of the medical cyclotron. The resonant frequency will shift to a certain extent, resulting in the high-frequency operation frequency varying with the resonant frequency of the resonator cavity. In order to meet the requirements for isochronous acceleration, the magnetic field strength should also be changed correspondingly when the high-frequency operation frequency changes, that is, the magnitude of the magnet current needs changing accordingly, so that the particle cyclotron frequency matches the high-frequency resonant frequency to overcome the sliding phase. Firstly, the static magnetic field model is established by finite element simulation software to simulate the average magnetic field of cyclotron under different magnet currents. Then the relationship between the magnetic field and the resonant frequency is theoretically analyzed. Finally, the relationship between the magnet current and the resonant frequency is obtained when the magnet current varies in a small interval. According to the optimal magnet current corresponding to different resonance frequencies, the automatic frequency tracking of magnet current is completed. In the case of ensuring the maximum carbon film beam, the optimal magnet current corresponding to different resonance frequencies is obtained, which makes the theory validated. According to the relationship, the magnet current is automatically adjusted, which overcomes the slip phase and ensures the stable output of the Faraday beam. The method enables the magnet current to be quickly and accurately find and track the cavity frequency, overcomes the slip phase caused by the frequency offset, and completes the stable output of the beam.

    • 正电子发射断层显像(positron emission tomography, PET)是一种先进的核医学影像技术. 在美国、欧洲和日本, 18F-FDG (氟代脱氧葡萄糖) PET已被纳入医疗保险范围[1,2], 其实现方法是将正电子核素标记到某种参与体内代谢的物质上, 形成放射性药物(也称显像剂、放射性示踪剂), 其具有很高的灵敏度和分辨率[3,4]. 然而只有PET是完不成成像工作的, 它需要配套回旋加速器. 在我国, 生产用于PET诊断的放射性同位素的回旋加速器几乎都是从国外进口的[5].

      回旋加速器正常工作时, 高频腔应处于谐振状态. 然而, 由于高频功率的大小、温度的升降、热损耗的差异、束流的强弱都是随时间而不停地变化的, 这导致腔体频率偏移, 不能有效地发挥加速器的性能[6,7]. 因此, 必须采取相应的措施来消除这些不确定因素带来的影响, 以保持高频谐振腔与高频功率源始终处于稳定的匹配状态[8].

      目前, 针对射频腔体会由于腔的热不稳定性产生微小形变, 从而导致谐振腔的固有谐振频率发生变化的问题, 张天爵等[9]、雷钰[10]、答嘉曦等[11,12]、刘毅[13]、田瑞霞等[14]、郝焕锋[15]以及美国通用电气公司(GE) MINItrace医用回旋加速器等都是通过控制器驱动频率微调马达, 带动微调电容片前后动作, 调整腔体的谐振频率, 使其固有谐振频率与高频功率源产生的信号频率一致.

      中国工程物理研究院流体物理研究所建造的紧凑型医用回旋加速器商业样机, 其引出能量为11 MeV, 引出束流为50 μA, 工作频率为72.12 MHz, 平均磁感应强度为1.18 T, 占空比可调节[16]. 其高频结构采用非对称的半波长腔, 高频腔用于产生高频加速电场, 高频腔主要设计参数有加速电压、频率、腔壁损耗功率、品质因数等, 回旋加速器没有为谐振腔设置自动稳频装置, 从结构上简化了腔体设计, 降低了成本. 针对回旋加速器运行过程中谐振腔频率会逐渐变化的问题, 高频系统采用高频功率源的频率实时与高频腔中加速电场的频率匹配的方案. 磁铁系统为带电粒子作回旋运动提供磁场, 同时实现粒子的聚焦[17]. 为了保证粒子的共振加速, 磁场需根据实际的高频运行频率进行调节, 即励磁电流需根据高频频率实时调节. 磁铁产生的轴向磁场须是等时性磁场, 使得被加速的离子在不同半径处的回旋频率相等, 最终在某一高频频率下得到共振加速.

      本文采用数值仿真、理论分析、实验研究等方法, 对回旋加速器谐振频移的问题使用新方法得以解决.

    2.   高频系统的控制
    • 为了实现高频功率源对谐振频率的寻找和跟踪, 在加速器启动之前, 应调节高频谐振腔处于合适的谐振频率点. 对于高频功率源工作频率与变化的腔体频率实时匹配的方法, 采用了锁相型自动频率控制(automatic frequency control, AFC)系统, 该系统高频腔的入射波信号与反射波信号之间的相位差$\Delta \varphi $是功率源输出频率f与高频腔谐振频率${f_0}$之差$\Delta f$的函数:

      其中, ${Q_{\rm{L}}}$是有载品质因数, $\omega $是谐振角频率. 驻波锁相型AFC系统通过检测$\Delta \varphi $来控制$\Delta f$, 使其频率一致, 即达到加速器正常工作的要求.

      在加速器运行过程中, 高频功率源不断改变信号源的输出频率并实时检测前向功率P1和反射功率P2的反馈信号, P1P2的比值大小直接反映频率的匹配情况, 当0.5P1 $ \leqslant$ P2 $\leqslant $ 0.8P1时, 视为严重失谐; 当P2 < 0.5P1, 视为轻度失谐; 当P2 > 0.8P1时, 判断为打火; 从而寻找高频谐振腔的谐振频率. 如果在加速器运行过程中谐振腔发生轻度失谐, 控制系统则会根据相位以寻找具有最小驻波比的频率[18]; 如果在加速器运行过程中谐振腔发生严重失谐, 则降低占空比至10%, 升高频率, 频率升高步长为(f1f0) × 0.1 (f1为当前频率, f0为初始频率), 若频率调节到f0时, 还处于严重失谐(相位变正常, 但反射未降低), 则将占空比降低为1%, 并重新启动扫描程序以确定频率; 如果在加速器运行过程中谐振腔发生打火, 那么高频功率源的控制模块将会切断高频功率源的输出, 一段时间之后, 高频功率源会以最终的工作频率再次运行. 图1图3分别为回旋加速器开机并连续工作2 h时高频相位、高频腔压、谐振频率的实时变化曲线.

      Figure 1.  High frequency phase variation with time.

      Figure 2.  High frequency cavity voltage variation with time.

      Figure 3.  Resonant frequency variation with time.

      图1可以看出, 在打靶的初始阶段, 由于占空比的迅速提升, 加速器内部分部件的温度发生显著变化, 导致高频谐振频率发生变化, 控制系统会自动调整高频信号源的频率以保证谐振关系[19], 此时相位也会发生变化, 而随着高频工作频率趋于稳定, 相位也稳定在208°左右. 从图2可以看出, 在占空比提升的初始阶段, 由于谐振频率发生偏移, 高频功率源工作频率还没稳定跟频, 而为了保证腔压, 需要强制提升激励电压, 待工作频率与谐振频率一致时, 激励电压还没下调, 因此出现短时间的波动, 之后腔压一直稳定在48 kV左右. 从图3可以看出, 当高频功率源开机, 占空比增加时, 谐振频率急剧下降, 约下降50 kHz、10 min后, 频率会基本稳定在72.52 MHz, 之后变化的范围约为10 kHz.

    3.   磁场计算
    • 对于电流产生静磁场, 导体磁场强度可直接由积分得到[20]:

      其中, H为磁场强度, J$\varOmega _J $域内的体分布电流, R为从源点到场点的矢径, $ \varOmega _J$表示分布区域.

      根据设计好的回旋加速器, 采用有限元软件, 建立静磁场的1/8模型, 如图4所示, 得到的后处理模型如图5所示.

      Figure 4.  Model of static magnetic field.

      计算得到不同半径的平均磁场变化曲线如图6, 励磁电流与磁感应强度的曲线见图7. 由图7可知, $\Delta I$$\Delta B$成正比, 当$\Delta I =$$ [\sum\limits_{i = 0}^n {({I_i} - {I_{i - 1}})} ]/n $= 1 A时, $\Delta B = [\sum\limits_{i = 0}^n {({B_i} - {B_{i - 1}})}]/n $ = 0.0025 T.

      Figure 5.  Post-processing model.

      Figure 6.  Average magnetic field curve at different radii.

      Figure 7.  Relation between the excitation current and the magnetic induction intensity.

      磁路中磁场强度的计算公式为

      所以由(3)和(4)式有

      其中, H为磁场强度(A/m), B为磁感应强度(T), μ为介质的绝对磁导率(H/m), Le为有效磁路长度(m), N为线圈数, I为励磁电流(A).

      由(5)式可得, 线圈圈数确定, 有效磁路长度确定, 则

      在励磁电流很小的变化范围内, $\dfrac{{\Delta I}}{I}$$\dfrac{{\Delta B}}{B}$呈近线性关系, 因此可得到

      计算得k = 2.3867.

      一个电荷量为q (C)、质量为m (kg)的粒子, 在恒定磁场以一定的速度v (m/s)在与磁场相垂直的平面上运动, 将受到磁场洛伦兹力的作用而做圆周运动, 圆周运动的曲率半径为r (m), 由下式可求得回旋加速器的回旋频率f (Hz):

      由(8)式可得, 粒子确定, 在频率小变化时, 则

      磁场发生变化必然引起相位的变化(°), 而磁感应强度B需要励磁电流I来体现. 由于由磁场引起的相移为

      那么,

      根据励磁电流得到束流的相移曲线如图8所示, 得到的谐振频率变化曲线如图9所示.

      Figure 8.  Phase shift caused by change of magnet current.

      Figure 9.  Relation between resonant frequency and magnet current.

      图8可以看出, 励磁电流增加0.5 A, 相移度数增大了37.8985°, 那么励磁电流增加0.01 A, 相移度数增大0.7580°; 励磁电流减少0.01 A, 相移度数减小0.7580°.

      图9可以看出, 励磁电流增加0.5 A, 谐振频率增加了76.429 kHz, 那么谐振频率每增大1.529 kHz, 励磁电流需要增大0.01 A; 谐振频率每减少1.529 kHz, 励磁电流需要减小0.01 A.

    4.   实验结果
    • 在高频功率源启动的初始阶段, 占空比提升, 谐振频率减小, 通过手动调节励磁电流, 以期得到最大碳膜束流. 通过30余次的可靠性打靶实验, 每次在保证最大束流的条件下, 记录不同谐振频率对应的励磁电流, 比较了每次的拟合曲线, 其斜率都是在1.55 kHz附近稍有浮动, 选取其中的一条实验结果, 得到的关系曲线如图10所示.

      Figure 10.  Corresponding relation between resonant frequency and magnet current.

      此前, 为了保证靶上束流的稳定性, 通过手动调节磁场大小. 整个打靶过程中, 虽然励磁电流的变化范围约只有0.3 A, 但是对束流的影响是巨大的, 如果不去调节, 可能只产生极小的束流, 甚至可能无法产生束流; 即使励磁电流的变化范围是0.02 A, 束流也会降低约10%; 而且在束流调节过程中, 经常性的调大或调小, 导致束流不够稳定. 基于此, 为了保证束流的足够稳定, 理论分析了励磁电流与谐振频率的关系, 设计了稳定靶流下关于励磁电流与谐振频率的实验, 并设计了励磁电流跟踪谐振频率变化的稳流算法, 在连续2 h的打靶实验中, 得到了如图11所示的靶流变化曲线.

      Figure 11.  Variation of target beam current with time.

      图10可以看出, 当励磁电流变化很小时, 励磁电流与高频谐振频率呈近线性关系: y = 0.1587x + 40.94, 吻合度R2 = 0.9686. 在此条件下, 励磁电流每变化0.01 A, 谐振频率变化0.001587 MHz (1.587 kHz), 与理论计算结果符合得很好, 验证了计算的正确性.

      图11中曲线在开始上升时, 靶流有一个下降, 这是由于占空比迅速上升, 虽然励磁电流能够实现对谐振频率的跟踪, 但是磁场响应偏慢. 在第1次到达目标束流值时, 靶流有小量的下降过程, 这是由于过快的占空比调整, 控制系统通过相位不断的调整谐振频率, 虽然励磁电流能够实现与谐振频率的匹配, 但是工作频率却并不是最佳频率, 此时最大偏差也不到稳态值的7%. 约7 min后, 腔压、相位、谐振频率、励磁电流、前向功率、反射功率等参数将稳定下来, 靶流能够很好地保持在24.2 μA左右, 误差值小于 ± 0.2 μA.

      高频功率源从开机到打靶结束, 谐振频率总变化约为50 kHz, 因此励磁电流最大约需调节0.33 A, 也就是说, 在加速器实际过程中进行磁场调节时, 能量从最大值11 MeV会减小为10.985 MeV, 减小量为0.015 MeV, 变化率为0.1379%. 显然, 这是可以忍受的, 基本保证了输出能量的稳定性, 保证了束流的稳定性, 输出能量的变化曲线如图12所示.

      Figure 12.  Change of output energy

    5.   结 论
    • 本文通过高频功率源工作频率与变化的腔体频率实时匹配的方法, 实现了加速器的稳定运行, 简化了加速器的腔体结构, 节约了医用回旋加速器的建造成本; 通过仿真模拟得到了励磁电流与磁场的匹配关系; 通过实验验证了理论计算的励磁电流变化对谐振频率影响的正确性; 通过改进自动控制算法, 使得励磁电流自动调节匹配高频功率源工作频率的方法实现了回旋加速器的自动出束、自动稳束.

     
    • 非常感谢回旋加速器研究组与其他参与者在问题讨论方面的帮助.

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