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    Journals >High Power Laser and Particle Beams >Volume 35 >Issue 7 >Page 074001 > Article
    • High Power Laser and Particle Beams
    • Vol. 35, Issue 7, 074001 (2023)
    Simulation studies on the field flatness tuning of multi-cell superconducting radio-frequency cavities
    Yan Wang, Zhenyu Ma, Kai Xu, Qiang Chang, Zhigang Zhang, Chen Luo, Xuefang Huang, Xiang Zheng, Shenjie Zhao, and Yubin Zhao*
    Author Affiliations
  • Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China
    • show less
    DOI: 10.11884/HPLPB202335.220265 Cite this Article
    Yan Wang, Zhenyu Ma, Kai Xu, Qiang Chang, Zhigang Zhang, Chen Luo, Xuefang Huang, Xiang Zheng, Shenjie Zhao, Yubin Zhao. Simulation studies on the field flatness tuning of multi-cell superconducting radio-frequency cavities[J]. High Power Laser and Particle Beams, 2023, 35(7): 074001 Copy Citation Text show less
    The model of equivalent circuit for N-cell cavity with beam tubes
    Fig. 1. The model of equivalent circuit for N-cell cavity with beam tubes
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    The model of equivalent circuit for N-cell cavity operating in fundamental π-mode with ideal field flatness
    Fig. 2. The model of equivalent circuit for N-cell cavity operating in fundamental π-mode with ideal field flatness
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    Equivalent transformation of the models of equivalent circuit for end-cell and tube of N-cell cavity
    Fig. 3. Equivalent transformation of the models of equivalent circuit for end-cell and tube of N-cell cavity
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    Field flatness F variation with minor perturbation emid of cell capacity, given different A=B
    Fig. 4. Field flatness F variation with minor perturbation emid of cell capacity, given different A=B
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    Field flatness F variation with A, given B=0.5, for different minor perturbation of mid-cell emid不同中间腔胞微扰、B=0.5情况下，场平坦度随A的变化规律
    Fig. 5. Field flatness F variation with A, given B=0.5, for different minor perturbation of mid-cell emid不同中间腔胞微扰 、B=0.5情况下，场平坦度随A的变化规律
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    The geometry of a half-cell of an elliptical cavity
    Fig. 6. The geometry of a half-cell of an elliptical cavity
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    Structure diagram of 1.3 GHz 9-cell superconducting radio-frequency cavities without/with enhancement rings
    Fig. 7. Structure diagram of 1.3 GHz 9-cell superconducting radio-frequency cavities without/with enhancement rings
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    Types of cavity cellRe/mm Ri/mm A/mm B/mm a/mm b/mm L/mm
    Middle half-cellXFEL103.335.042.042.012.019.057.7
    TRIUMF103.335.042.042.012.019.057.7
    SHINE103.335.042.042.012.019.057.7
    Pick-up side half-cell XFEL103.339.042.042.09.012.856.7
    TRIUMF103.339.042.042.09.012.856.7
    SHINE103.339.042.042.09.012.856.7
    Coupler side half-cell XFEL103.339.040.3440.3410.013.555.7
    TRIUMF103.348.045.040.510.013.556.0
    SHINE103.355.048.936.79.012.858.1
    Table 1. Geometry parameters of three types of 1.3 GHz 9-cell cavities for main LINAC of XFEL, TRIUMF e-Linac, and for injector of SHINE as a candidate
    Tuning force/kN (squeezed)Types of cavity cellResonant frequency/MHz
    0-modeπ-mode
    0, undeformedMiddle half-cellXFEL1275.7481300
    TRIUMF1275.7481300
    SHINE1275.7481300
    Pick-up side half-cell with beam pipeXFEL1287.781300
    TRIUMF1287.781300
    SHINE1287.781300
    Coupler side half-cell with beam pipeXFEL1287.781300
    TRIUMF1288.1361300
    SHINE1288.8271300
    2, deformedMiddle half-cellXFEL1275.4681299.745
    TRIUMF1275.4681299.745
    SHINE1275.4681299.745
    Pick-up side half-cell with beam pipeXFEL1287.5441299.78
    TRIUMF1287.5441299.78
    SHINE1287.5441299.78
    Coupler side half-cell with beam pipeXFEL1287.5441299.78
    TRIUMF1287.9011299.781
    SHINE1288.6531299.836
    4, deformedMiddle half-cellXFEL1275.1551299.569
    TRIUMF1275.1551299.569
    SHINE1275.1551299.569
    Pick-up side half-cell with beam pipeXFEL1287.3281299.574
    TRIUMF1287.3281299.574
    SHINE1287.3281299.574
    Coupler side half-cell with beam pipeXFEL1287.3281299.574
    TRIUMF1287.6851299.574
    SHINE1288.4921299.68
    Table 2. Variation of resonant frequency due to different tuning force for XFEL, TRIUMF and SHINE 1.3 GHz 9-cell SRF cavities without enhancement rings
    Tuning force/kN (squeezed)emid/105eend1/105eend2/105
    0, undeformedXFEL000
    TRIUMF000
    SHINE000
    2, deformedXFEL4.8774.1494.149
    TRIUMF4.8774.1494.133
    SHINE4.8774.1493.062
    4, deformedXFEL10.3277.9467.946
    TRIUMF10.3277.9467.931
    SHINE10.3277.9465.894
    Table 3. Minor perturbations due to different tuning force for XFEL, TRIUMF and SHINE candidate 1.3 GHz 9-cell SRF cavities without enhancement rings
    Tuning force/kN (squeezed)F, (Field flatness)
    Theoretical calculation valueSimulation calculation value
    0, undeformedXFEL100%99.95%
    TRIUMF100%99.94%
    SHINE100%99.92%
    2, deformedXFEL98.79%97.7%
    TRIUMF98.74%97.6%
    SHINE95.35%93.9%
    4, deformedXFEL96.03%96.8%
    TRIUMF95.99%96.7%
    SHINE89.86%89.0%
    Table 4. Results comparison of field flatness between theoretical and simulation calculations for XFEL, TRIUMF and SHINE 1.3 GHz 9-cell SRF cavities without enhancement rings
    Tuning force/kN (squeezed)Types of cavity cellResonant frequency/MHz
    0-modeπ-mode
    0, undeformedMiddle half-cellXFEL1275.7481300
    TRIUMF1275.7481300
    SHINE1275.7481300
    Pick-up side half-cell with beam pipeXFEL1287.781300
    TRIUMF1287.781300
    SHINE1287.781300
    Coupler side half-cell with beam pipeXFEL1287.781300
    TRIUMF1288.1361300
    SHINE1288.8271300
    2, deformedMiddle half-cellXFEL1275.6031299.857
    TRIUMF1275.6031299.857
    SHINE1275.6031299.857
    Pick-up side half-cell with beam pipeXFEL1287.6311299.855
    TRIUMF1287.6311299.855
    SHINE1287.6311299.855
    Coupler side half-cell with beam pipeXFEL1287.6311299.855
    TRIUMF1287.9771299.848
    SHINE1288.6381299.865
    4, deformedMiddle half-cellXFEL1275.4491299.708
    TRIUMF1275.4491299.708
    SHINE1275.4491299.708
    Pick-up side half-cell with beam pipeXFEL1287.4681299.695
    TRIUMF1287.4681299.695
    SHINE1287.4681299.695
    Coupler side half-cell with beam pipeXFEL1287.4681299.695
    TRIUMF1287.8171299.688
    SHINE1288.4481299.733
    6, deformedMiddle half-cellXFEL1275.2991299.558
    TRIUMF1275.2991299.558
    SHINE1275.2991299.558
    Pick-up side half-cell with beam pipeXFEL1287.3061299.534
    TRIUMF1287.3061299.534
    SHINE1287.3061299.534
    Coupler side half-cell with beam pipeXFEL1287.3061299.534
    TRIUMF1287.6561299.529
    SHINE1288.2571299.600
    Table 5. Variation of resonant frequency due to different tuning force for XFEL, TRIUMF and SHINE 1.3 GHz 9-cell SRF cavities with enhancement rings
    Tuning force/kN (squeezed)emid/105eend1/105eend2/105
    0, undeformedXFEL000
    TRIUMF000
    SHINE000
    2, deformedXFEL2.5262.6202.620
    TRIUMF2.5262.6202.796
    SHINE2.5262.6203.326
    4, deformedXFEL5.2085.4855.485
    TRIUMF5.2085.4855.610
    SHINE5.2085.4856.668
    6, deformedXFEL7.8208.3338.333
    TRIUMF7.8208.3338.441
    SHINE7.8208.33310.028
    Table 6. Minor perturbations due to different tuning force for XFEL, TRIUMF and SHINE candidate 1.3 GHz 9-cell SRF cavities with enhancement rings
    Tuning force/kN (squeezed)F, (Field flatness)
    Theoretical calculation valueSimulation calculation value
    0, undeformedXFEL100%99.95%
    TRIUMF100%99.94%
    SHINE100%99.92%
    2, deformedXFEL99.84%99.16%
    TRIUMF99.27%98.77%
    SHINE97.35%98.48%
    4, deformedXFEL99.54%98.85%
    TRIUMF99.17%98.26%
    SHINE95.48%96.66%
    6, deformedXFEL99.14%98.32%
    TRIUMF98.85%97.56%
    SHINE93.44%94.27%
    Table 7. Results comparison of field flatness between theoretical and simulation calculations for XFEL, TRIUMF and SHINE candidate 1.3 GHz 9-cell SRF cavities with enhancement rings
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    Yan Wang, Zhenyu Ma, Kai Xu, Qiang Chang, Zhigang Zhang, Chen Luo, Xuefang Huang, Xiang Zheng, Shenjie Zhao, Yubin Zhao. Simulation studies on the field flatness tuning of multi-cell superconducting radio-frequency cavities[J]. High Power Laser and Particle Beams, 2023, 35(7): 074001
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