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  • Open Access

Detuning related coupler kick variation of a superconducting nine-cell 1.3 GHz cavity

Thorsten Hellert and Martin Dohlus
Phys. Rev. Accel. Beams 21, 042001 – Published 2 April 2018
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Abstract
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  • INTRODUCTION
  • TESLA CAVITY
  • FIELD CALCULATIONS
  • DISCRETE COUPLER KICKS
  • NORMALIZED COUPLER KICK COEFFICIENTS
  • IMPLEMENTATION OF COUPLER KICKS IN…
  • EXPERIMENTAL VALIDATION OF DISCRETE…
  • EXPECTED COUPLER KICK VARIATIONS AT…
  • SUMMARY
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Superconducting TESLA-type cavities are widely used to accelerate electrons in long bunch trains, such as in high repetition rate free electron lasers. The TESLA cavity is equipped with two higher order mode couplers and a fundamental power coupler (FPC), which break the axial symmetry of the cavity. The passing electrons therefore experience axially asymmetrical coupler kicks, which depend on the transverse beam position at the couplers and the rf phase. The resulting emittance dilution has been studied in detail in the literature. However, the kick induced by the FPC depends explicitly on the ratio of the forward to the backward traveling waves at the coupler, which has received little attention. The intention of this paper is to present the concept of discrete coupler kicks with a novel approach of separating the field disturbances related to the standing wave and a reflection dependent part. Particular attention is directed to the role of the penetration depth of the FPC antenna, which determines the loaded quality factor of the cavity. The developed beam transport model is compared to dedicated experiments at FLASH and European XFEL. Both the observed transverse coupling and detuning related coupler kick variations are in good agreement with the model. Finally, the expected trajectory variations due to coupler kick variations at European XFEL are investigated and results of numerical studies are presented.

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    • Received 22 November 2017

    DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.042001

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Beam code development & simulation techniquesSuperconducting RF
    1. Physical Systems
    Particle accelerators
    Accelerators & Beams

    Authors & Affiliations

    Thorsten Hellert* and Martin Dohlus

    • DESY, Notkestrasse 85, 22603 Hamburg, Germany

    • *thorsten.hellert@desy.de

    Article Text

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    Issue

    Vol. 21, Iss. 4 — April 2018

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    Images

    • Figure 1
      Figure 1

      Tracking results for a particle which enters a TESLA cavity on axis with an initial beam energy of 120 MeV. Plotted are the longitudinal (top), vertical (mid) and horizontal (bottom) momentum as a function of the longitudinal coordinate z. The accelerating gradient is 24  MV/m. The significant change of transverse momenta at the coupler positions are related to coupler kicks. The sinusoidal variation inside the cavity is related to axially symmetrical rf focussing. Tracking is calculated for a purely forward traveling wave (black), a standing wave (red), and a backward wave (blue). Only the downstream horizontal coupler kick depends on the mode of cavity operation.

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    • Figure 2
      Figure 2

      Longitudinal cross section of a TESLA cavity. The beam direction is from left to right, thus the fundamental power coupler is located at the downstream end of the cavity.

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    • Figure 3
      Figure 3

      Geometry and orientation of the higher order mode (HOM, upstream, and downstream) and fundamental power coupler (FPC, downstream).

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    • Figure 4
      Figure 4

      Schematic drawing of the TTF-3 fundamental power coupler of the TESLA cavity. The waveguide (lower left end) connects the cavity with the rf power source and is at room temperature. A remote controlled stepper motor allows one to move the position of the coaxial antenna in the cavity beam pipe (right end).

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    • Figure 5
      Figure 5

      Schematic drawing of the third harmonic module at FLASH. Four cavities with alternate coupler orientation with respect to the beamline are installed in one cryomodule.

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    • Figure 6
      Figure 6

      Horizontal (top), vertical (mid), and longitudinal (bottom) voltage as experienced by an ultrarelativistic charged particle which traverses the cavity on axis.

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    • Figure 7
      Figure 7

      Real (upper plots) and imaginary part (lower plots) of the normalized complex kick factor for the upstream (left) and downstream coupler region (right) as a function of the transverse coordinates x and y. All vectors are scaled by the same amount in order to assure a quantitative comparison. The three colors in the right plots correspond to the cases of pure forward traveling wave (yellow) in the cavity, e.g., no backward wave and Γ=−1, standing-wave operation (red, Γ=0), and pure backward traveling wave (blue, Γ=1). Note that the kick induced by HOM couplers does not change for different Γ. The net effect of the FPC is primarily horizontal.

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    • Figure 8
      Figure 8

      Normalized complex kick coefficients [V0x,V0y,Vxx,Vxy] for the downstream coupler region as calculated via Eq. (16) with different field maps, reflecting different loaded quality factors QL. Plotted are the values related to the standing wave (left) and the reflection dependent part (right). The values are listed in Tables 2 and 3.

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    • Figure 9
      Figure 9

      Particle trajectory through a TESLA cavity as calculated by ASTRA (blue) and the linear beam dynamics model [red, cf. Eq. (22)]. Plotted are the horizontal (left) and vertical (right) positions (upper plots) and momenta (lower plots), respectively, as a function of the longitudinal coordinate z. The cavity is centered at z=0  m. The colored bars in the lower plots illustrate the different transfer matrices of the model. Beam initial and final energy is 10 MeV and 24 MeV, respectively.

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    • Figure 10
      Figure 10

      Comparison between the linear beam dynamics model [cf. Eq. (22)] and ASTRA for different initial beam energies E. Plotted are the rms differences [Δx,Δx′,Δy,Δy′]rms as evaluated for 104 particles at different rf amplitudes and phases.

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    • Figure 11
      Figure 11

      Schematic layout of the European XFEL (not to scale). The elements shown include 1.3 GHz (yellow) and 3.9 GHz (red) rf sections, undulators (green/red), main dipole magnets (blue), beam distribution systems (green), and beam dumps (black). The main accelerating sections (L1, L2, L3) contain 4, 12 and 84 eight-cavity cryomodules, respectively.

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    • Figure 12
      Figure 12

      Trajectory response measurement at European XFEL. The upper plots show the measured horizontal (left) and vertical (right) beam trajectories as excited by an horizontal steering magnet at s=86  m for various magnet strengths. The lower plots show the corresponding trajectory response as measured (red dots), and calculated both by the default optic server (black) and with the linear model including discrete coupler kicks [DCK, blue, cf. Eq. (22)]. The yellow rectangles in the lower row indicate the four L1 cryomodules.

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    • Figure 13
      Figure 13

      Schematic layout of the FLASH facility [43].

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    • Figure 14
      Figure 14

      Variation of the measured vector sum of the accelerating gradient δVVS (left) and the computed parameter ΔΓ (right) at ACC6 at FLASH while applying modulations with different frequencies on the forward power (from top to bottom: 20, 50, 100, and 300 kHz). The rf sampling time is 1  μs.

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    • Figure 15
      Figure 15

      Experimental observation of intrabunch train coupler kick variations at ACC6 at FLASH. Plotted are the differences between the reference trajectories and the particle trajectories while applying modulations with different frequencies on the forward power (from top to bottom: 20, 50, 100, and 300 kHz, cf. Fig. 14). The bunch spacing is 1  μs. The BPM readout differences (black) and the corresponding model evaluations (colored) are plotted for the horizontal (left) and vertical (right) plane at the exit of the module.

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    • Figure 16
      Figure 16

      Normalized rms intrabunch-train trajectory variation Δu˜rms downstream the European XFEL accelerator as a function of the maximum variation of the amplitude of the accelerating field ΔVmax (left) for the horizontal (blue) and vertical (red) plane. The different plot marks correspond to different maximum detuning Δfmax. The right plot shows the trajectory variation for zero amplitude variation as a function of Δfmax.

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