In this work, effective electric permittivity and magnetic permeability of metallic-dielectric mixtures are extracted from electromagnetic full 3D simulation data in the microwave range. The numerical method used here is the finite integration technique with periodic boundary conditions. Simulated mixtures have periodic extend in directions perpendicular to the direction of the plane wave. Thus, it is sufficient to analyze a unit element in order to extract the effective electric and magnetic properties. Using this procedure, the behavior of fine copper powders irradiated by microwaves at a frequency of 2.45 GHz is simulated. Then, the relation between particle size and the mixture's effective properties is studied. By introducing a thin copper oxide or conductive layer it is possible to emulate the effective properties of metallic powder compacts in the early stage of sintering. Thus, this work contributes to improving the insight into the mechanisms of microwave absorption in powders of conductive materials in contrast to non-absorption in bulk metals.

No 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.

Superconducting radio frequency cavities used for accelerating charged particle beams are commonly used in accelerator facilities around the world. The design and optimization of modern superconducting RF cavities requires intensive numerical simulations. Vast number of operational parameters must be calculated to ensure appropriate functioning of the accelerating structures. In this study, we primarily focus on estimation and behavior of higher order modes in superconducting RF cavities connected in chains. To calculate large RF models the state-space concatenation scheme, an efficient hybrid method, is employed.