Numerical analysis and experimental study of multi-field behaviour of fast ramping superconducting solenoids
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摘要: 北京大学拍瓦激光质子加速器针对肿瘤治疗需求，开发激光质子放疗系统，实现质子放射肿瘤治疗。其水平束流线和垂直束流线的公共收集段主要由三台超导螺线管(S1-S3)组成。在降温过程和励磁过程中螺线管内会产生较大的应力，此外超导螺线管采用快脉冲的方式运行，励磁过程中的交流损耗会对螺线管励磁速度和稳定运行有重要影响。以结构最复杂、中心场强为7.8 T、直径120 mm的螺线管S1为研究对象，使用COMSOL Multiphysics软件对超导螺线管进行了多场条件下的应力分析，同时对其由于快速变化的电流所产生的交流损耗进行了模拟计算。随后开展了相应的实验研究，获得了应变随温度变化，给出了电流、磁场、应变三者对应关系的变化曲线。在实验过程中，磁场和应变的测量值与电流的变化之间存在显著的正相关性，应变值小于线圈所受应力的最大限值，验证了超导螺线管设计的合理性。Abstract: The Peking University (petawatt) laser proton accelerator develops a laser proton radiotherapy system in response to the needs of proton radiation tumor treatment. The common collection section of its horizontal and vertical beam lines mainly consists of three superconducting solenoids (S1-S3). Large stresses are generated in the solenoids during the cooling down and excitation process, in addition, the superconducting solenoids are operated by fast ramping, and the AC loss in the process will have an important impact on the solenoid excitation speed and stable operation. In this paper, the highest field strength and the most complex structure of 7.8T-120 mm solenoid S1 is taken as the research object, and COMSOL Multiphysics software is used to carry out the stress analysis of superconducting solenoids under multi-field conditions, and at the same time, the simulation of the AC loss due to the rapid change of the current is carried out. Subsequently, corresponding experimental studies were carried out to obtain the variation curves of strain with temperature, correlations betweencurrent, magnetic field and strain correspondingly. According to the experiment data, there is a significant positive correlation between the measured values of magnetic field and strain and the change of current, which verifies the rationality of the superconducting solenoid design. It provides experience and reference for the subsequent design and development of similar superconducting magnets.
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图 5 二维径向、轴向电磁力密度分布
Figure 5. Electromagnetic force density distribution of 2D radial and axial
图 6 磁体对称面中心环向应力分布曲线
Figure 6. Hoop stress distribution curve at the center of the magnet symmetry plane
图 7 磁体对称面中心径向应力分布曲线
Figure 7. Radial stress distribution curve at the center of magnet symmetry plane
图 9 超导螺线管体积损耗密度分布
Figure 9. Volume loss density distribution of superconducting solenoids:
图 10 液氦浸泡冷却条件下总交流损耗引起的温升随时间的变化趋势
Figure 10. Trend of temperature rise due to total AC loss with time under liquid helium immersion cooling condition
图 13 磁场时变特性与磁体电-磁响应曲线
Figure 13. Temporal variation characteristics of the magnetic field and I-B response curve of the magnet
表 1 螺线管设计参数
Table 1. Solenoid design parameters
Coils Inner diameter/mm Inner diameter/mm Midplane/mm Length/mm Turns Iop/A Maximum magnetic
field of the coil/TC1 170.60 180.54 0.00 790.00 1744 176.98 7.82 C2 181.14 191.66 0.00 790.00 3678 176.98 7.34 C3 192.26 228.57 0.00 790.00 23520 176.98 6.3 C4a 377.00 422.36 384.33 21.34 750 −176.98 2.81 C4b 377.00 422.36 384.33 21.34 750 −176.98 2.81 
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表 2 线圈洛伦兹力
Table 2. Lorentz force in Solenoid
Coil Radial Lorentz force/kN Axial Lorentz force/kN C1a 295.5 −19.0 C1b 295.5 19.0 C2a 592.8 −44.9 C2b 592.8 44.9 C3a 1668.4 −336.1 C3b 1668.4 336.1 C4a 12.4 24.4 C4b 12.4 −24.4
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表 3 材料物性参数
Table 3. Physical parameters of materials
Material Young’s modulus (GPa) Poisson’s ratio Thermal expansion
coefficient (10−5 K−1)293K 4.2K 316L 193 210 0.282 1.004 Al6061-T6 70 79 0.33 1.45 Main coil C1 89 89 0.32 1.16 Main coil C2 90 90 0.32 1.24 Main coil C3 and shielding coils 82 82 0.32 1.28
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表 4 结构件涡流损耗
Table 4. Eddy current losses in structural components
Eddy current
loss (W)Total eddy current
loss (W)End plate 7.8 2.31 Skeletons 7.3 Binding 6.3
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表 5 各线圈交流损耗
Table 5. AC loss of each coil
Magnetic fields/T AC loss/W Total AC loss/W C1 7.8 0.61 2.31 C2 7.3 0.43 C3 6.3 1.17 C4a、C4b 2.8 0.10
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