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High Power Laser and Particle Beams, Volume. 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
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    AbstractGet PDF(in Chinese)
    Figures&Tables (14)
    Equations (17)
    References (10)
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    Figures & Tables(14)
    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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    • 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

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      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

      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 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

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      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)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 3. Minor perturbations due to different tuning force for XFEL, TRIUMF and SHINE candidate 1.3 GHz 9-cell SRF cavities without enhancement rings

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      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)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 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

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      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)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 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

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      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)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 6. Minor perturbations due to different tuning force for XFEL, TRIUMF and SHINE candidate 1.3 GHz 9-cell SRF cavities with enhancement rings

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      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)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 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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      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

      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%
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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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    Paper Information

    Category: Particle Beams and Accelerator Technology

    Received: Aug. 26, 2022

    Accepted: Jan. 11, 2023

    Published Online: Jul. 24, 2023

    The Author Email: Zhao Yubin (zhaoyubin@zjlab.org.cn)

    DOI:10.11884/HPLPB202335.220265

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology