The microwave properties of a number of polymers common in industry are investigated. A cylindrical resonator in the TM012 mode is used. The cavity perturbation method and detailed COMSOL simulations ...are applied for extracting the complex permittivity as a function of temperature. The results are useful for the design of plastic processing tools by heating with electromagnetic fields. The intrinsic parameters of absorption are derived based on two exponential decays: polarization and Arrhenius dependence of the decay times on temperature.
Vacuum chambers of particle accelerators are typically equipped with radio-frequency couplers. The couplers are employed to excite modes for particle acceleration, to extract the energy of ...higher-order modes, or for diagnostic purposes. From a network theory perspective, these couplers represent terminal ports by which means the structure can exchange energy with its exterior. Usually, these ports are terminated with fixed impedances corresponding to the characteristic impedances of the coaxial lines attached to them. In this paper, we investigate the influence of the termination conditions of vacuum chambers on beam coupling impedances. For this purpose, we introduce a novel approach that allows us to determine beam coupling impedances for arbitrary port terminations. A full-wave Maxwell solver is employed to determine a generalized scattering matrix of the vacuum chamber and its couplers terminated with prespecified reference impedances. Often, these impedances are chosen to be the characteristic line impedances of the waveguides so that coupler ports are free of reflection. Using the generalized scattering matrix, the beam coupling impedances can be readily determined by means of a computationally inexpensive postprocessing step that takes into account arbitrary impedance loads at the coupler ports. Thus, the influence of various port terminations on the beam coupling impedances can be conveniently examined. This is relevant to improve older structures that were designed when no sophisticated design tools were available or to improve the operation of existing structures for a purpose they were initially not designed for. Using the proposed approach, we investigate the 33-cell 200 MHz traveling-wave accelerating structures of the SPS at CERN. It is shown that port termination conditions do have an important influence on the beam coupling impedance and, therefore, must be taken into account in beam stability considerations.
We determine Faraday rotations and measure the optical reflection and transmission from magneto-optical Cd1−xMnxTe crystals with various stoichiometric ratios. For wavelengths between 675 and ...1025 nm, we derive Verdet constants, optical loss coefficients, and the complex indices of reflection that are relevant measures to find suitable stoichiometric ratios of Cd1−xMnxTe for the realization of miniaturized optical isolators. By reflection and transmission measurements, we determine the stoichiometric ratios of several different Cd1−xMnxTe crystals and discuss the observed dependence of the optical properties on the stoichiometric ratio with respect to their use in optical isolators. Finally, we show the relevant figure of merit, i.e., the ratio of Verdet constants and optical loss coefficients for Cd1−xMnxTe crystals with Mn contents ranging from x = 0.14 to x = 0.50.
In the context of the Large Hadron Collider (LHC) injector upgrade, components with high contribution to the beam coupling impedance of the injector chain have to be identified and optimized to ...ensure the delivery of high-intensity proton beams to the LHC. The Super Proton Synchrotron (SPS) is the last accelerator in the LHC injector chain. In the existing design, the longitudinal beam coupling impedance of the SPS cavities limits the increase of the beam intensity in the SPS ring. Since the 200 MHz traveling wave cavities are one of the main contributors to the overall beam coupling budget of the SPS machine, different types of higher-order mode (HOM) couplers are used in the long 33-cell and 44-cell cavities for the damping of various HOMs. The location of the HOM couplers in the cavity, as well as their shape, affects the damping of HOMs. Finding a suitable arrangement of the HOM couplers requires solving a discrete optimization problem. The repetitive calculation of the beam coupling impedance by the conventional time-domain wakefield solvers in the optimization is hindered by the large size of the SPS cavities. The generalized coupledS-parameter method is a domain decomposition method for the calculation of theSparameters and beam coupling impedance of large structures. In this paper, this method is employed to calculate the beam coupling impedance of the SPS cavities. Then, an optimization method is proposed to find an optimal arrangement of the HOM couplers in the cavities. The article presents the geometrical details of the SPS cavities, a short description of the generalized coupledS-parameter method, and a discrete optimization method applied to the SPS cavities.
In this article, a decomposition approach for the computation of beam coupling impedances is proposed. This approach can account for the mutual electromagnetic coupling in long accelerator structures ...consisting of several consecutive segments. The method is based on the description of the individual segments using a multimodal network matrix formulation in which the charged particle beam is considered as an additional port. Then, the generalized multimodal network matrices of all segments are combined to a multimodal network matrix of the complete structure. The beam coupling impedance as well as the scattering parameters of the full structure are recovered as particular matrix elements in this multimodal network matrix. The new method generalizes CoupledS-Parameter Calculation (CSC) introduced in earlier work such that charged particle beams are considered. Consequently, the introduced scheme is referred to as CSC. Application examples for realistic accelerator components such as the simulation of a full TESLA 1.3 GHz-cavity of the European XFEL are provided. These simulations demonstrate the high accuracy and numerical performance of the proposed method.
Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite ...element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.
•Eigenpair derivatives can be used to approximate the eigenpair of a perturbed system.•An algorithm is developed to approximate the eigenpairs of a perturbed structure.•First-order numerical approximation of eigenfrequency equals Slater's theorem.
This article presents a comparison between measured and simulated scattering parameters in a wide frequency interval for the third harmonic accelerating module ACC39 in the linear accelerator FLASH, ...located at DESY in Hamburg/Germany. ACC39 is a cryomodule housing four superconducting 3.9 GHz accelerating cavities. Due to the special shape of the cavities (in particular its end cells and the beam pipes) in ACC39, the electromagnetic field in the module is, in many frequency ranges, coupled from one cavity to the next. Therefore, the scattering parameters are determined by the entire string and not solely by the individual cavities. This makes the determination of the scattering properties demanding. As far as the authors can determine, this paper shows for the first time a direct comparison between state-of-the-art simulations and measurements of rf properties of long, complex, and asymmetric structures over a wide frequency band. Taking into account the complexity of the system and various geometrical unknowns, the agreement between experimental measurements and simulations is remarkably good for several distinct measurements, although a variety of effects (e.g. cavity deviations from the ideal shape or interactions with not modeled parts of the structure) is not considered in the computer simulation. After a short introduction, the paper provides detailed descriptions of simulations and experimental measurements performed at the module. In this context, the estimation of the cable properties is discussed as well. As a central part of the article, the comparison between measured and simulated transmission spectra and quality factors is presented. This study represents one of the first detailed comparisons between simulations and measurements for a coupled accelerator cavity system.
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.
We determine Faraday rotations and measure the optical reflection and transmission from magneto-optical Cd1−xMnxTe crystals with various stoichiometric ratios. For wavelengths between 675 and ...1025 nm, we derive Verdet constants, optical loss coefficients, and the complex indices of reflection that are relevant measures to find suitable stoichiometric ratios of Cd1−xMnxTe for the realization of miniaturized optical isolators. By reflection and transmission measurements, we determine the stoichiometric ratios of several different Cd1−xMnxTe crystals and discuss the observed dependence of the optical properties on the stoichiometric ratio with respect to their use in optical isolators. Finally, we show the relevant figure of merit, i.e., the ratio of Verdet constants and optical loss coefficients for Cd1−xMnxTe crystals with Mn contents ranging from x = 0.14 to x = 0.50.
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