Eigenmode compendium of the third harmonic module of the European X-ray Free Electron Laser

Abstract

Chains of superconducting radio-frequency resonators are key components of modern particle accelerators such as the European XFEL, which is currently under construction in the north of Germany. In addition to the accelerating mode of the resonators, their beam excited higher order modes are of special interest, because they can harm the beam quality. In contrast to the accelerating mode, these modes are in general not confined within single resonators of the cavity string. For instance, eigenmodes can be localized between adjacent cavities or can be distributed along the entire chain of cavities. Therefore, the full chain has to be considered for a reasonable investigation of its resonant spectra. Accounting for such complex structures is computationally challenging and is therefore often avoided. In this article, the challenge is faced by using the so-called state-space concatenation approach, which is a combination of domain decomposition and model-order reduction. The technique allows for a reduction of the number of degrees of freedom by a factor of ≈ 1.471 × 10 −4. The method is employed to generate a compendium of eigenmodes in the chain of third harmonic cavities for the European XFEL. The results are discussed in detail and are compared with experimental measurements. The compendium serves as a reference for experiments (inter alia for diagnostics based on higher order modes) at the third harmonic cavity string of the European XFEL, it allows for qualitative understanding of resonant effects appearing in chains of cavities, and it is meant to be a proof of principle of the state-space concatenation approach to handle very long and complex radio-frequency structures. To the authors' knowledge, it is the first time that a modal compendium of a structure with the given complexity is generated. The article presents geometrical details of the chain, defines quantities relevant to superconducting radio-frequency cavities, and describes the employed computational approach.

Resonant excitation of high order modes in the 3.9 GHz cavity of the Linac Coherent Light Source

“…In spite of its simplicity, which greatly saves eigenmode computation time, the single resonator model lacks accuracy, since the HOM parameters depend on a combination of boundary conditions. Recently, new results have been published for the chain of XFEL 3.9 GHz cavities with matched boundary conditions on the coupler ports [12,13]. The authors use chains of four and eight cavities connected together, which gives a precise evaluation of HOM properties for propagating modes.…”

Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation

“…The parallel finite-element simulation suite ACE3P (Advanced Computational Electromagnetic 3D Parallel) [32], developed at the SLAC National Accelerator Laboratory, exploits both the power of HPC on state-of-the-art supercomputers and the accuracy of high-order finite elements for discretizing the partial difference equations that model the physical systems. ACE3P contains multiphysics modeling capabilities for integrated electromagnetic, thermal, and mechanical characteristics, and has been applied to a wide range of accelerator projects [18,13].…”