Thomas Flisgen

Compact Time-Domain Models of Complex RF Structures Based on the Real Eigenmodes of Segments

Wideband modeling of complex loss-free isotropic RF structures is a challenging task in electrical engineering. This paper presents a new formalism to create compact wideband equivalent models of complex RF structures. In a first step, the complex structure is partitioned into segments. On the basis of the segments eigenmodes with either vanishing tangential electric or magnetic fields on the boundary and a correction term, systems of ordinary differential equations (ODEs) are derived. In consequence, real eigenvalue problems need to be solved for each segment in addition to the actual field distribution in the segment, which only needs to be computed for a small number of discrete frequency samples for the correction term. Linking the established ODE systems of the segments with a suitable concatenation scheme leads to an ODE system for the entire structure. This system allows the computation of complex structure responses because of transient port excitation and the determination of transient 3-D fields in the structure. As a side product, the frequency-domain transfer function of the complex structure is available. Besides the theoretical derivations, two validation examples for the time-domain scheme are presented. These examples show that the method provides a good approximation of the transient processes in the structures under consideration.

A study of beam position diagnostics using beam-excited dipole modes in third harmonic superconducting accelerating cavities at a free-electron laser.

We investigate the feasibility of beam position diagnostics using higher order mode (HOM) signals excited by an electron beam in the third harmonic 3.9 GHz superconducting accelerating cavities at FLASH. After careful theoretical and experimental assessment of the HOM spectrum, three modal choices have been narrowed down to fulfill different diagnostics requirements. These are localized dipole beam-pipe modes, trapped cavity modes from the fifth dipole band, and propagating modes from the first two dipole bands. These modes are treated with various data analysis techniques: modal identification, direct linear regression (DLR), and singular value decomposition (SVD). Promising options for beam diagnostics are found from all three modal choices. This constitutes the first prediction, subsequently confirmed by experiments, of trapped HOMs in third harmonic cavities, and also the first direct comparison of DLR and SVD in the analysis of HOM-based beam diagnostics.

Comparison of techniques for uncertainty quantification of superconducting radio frequency cavities

This study examines the influence of uncertainty in the geometry parameters on the properties of superconducting cavities considering the 1.3 GHz TESLA mid-cell cavity. Monte Carlo simulation as well as uni-variate and multi-variate generalized Polynomial Chaos expansions are applied to estimate these stochastic properties. These stochastic methods are compared based on their computational efficiency and suitability for the uncertainty quantification in the given computational model. For this purpose, crucial geometry parameters are identified and used to reduce the random model parameter space. A central result comprises that the generalised Polynomial Chaos approach is highly applicable for the quantification of uncertainty in single-cell cavities.

Efficient Computation of the Neural Activation During Deep Brain Stimulation for Dispersive Electrical Properties of Brain Tissue

Deep brain stimulation (DBS) is a widely employed neurosurgical method to treat symptoms of neurodegenerative disorders. Computational modeling of DBS can help to gain insight into the mechanisms of its action. Among these models, the estimation of the volume of tissue activated (VTA) comprises a method to predict the extent of beneficial stimulation and unwanted side effects. This method requires the computation of the time-dependent extracellular potential in the proximity of the stimulation electrode, which is, in general, computationally expensive due to the dispersive electrical properties of brain tissue. We present an adaptive scheme based on two interpolation methods, which approximates the transfer function of the extracellular potential distribution in the frequency domain. The results suggest that the proposed method is able to substantially reduce the computational expense for the computation of the extracellular field distribution and VTA compared with the standard approach.

Time-Domain Absorbing Boundary Terminations for Waveguide Ports Based on State-Space Models

Absorbing boundary conditions for waveguide ports in time domain are important elements of transient approaches to treat RF structures. A successful way to implement these termination conditions is the decomposition of the transient fields in the absorbing plane in terms of modal field patterns. The absorbing condition is then accomplished by transferring the wave impedances (or admittances) of the modes to time domain, which leads to convolution operations involving Bessel functions and integrals of Bessel functions. This paper presents a new alternative approach: the convolution operations are approximated by appropriate state-space models whose system responses can be conveniently computed by standard integration schemes. These schemes are indispensable for transient simulations anyhow. Sufficiently far away from the cutoff frequency, a wideband match is achieved.

HOM Power Levels in the BESSY VSR Cold String

The BESSY VSR upgrade of the BESSY II light source represents a novel approach to simultaneously store long and short bunches in the storage ring. This challenging goal requires installation of four new SRF cavities (2x1.5GHz and 2x1.75GHz) in one module for installation in a single straight. These cavities are equipped with strong waveguide HOM dampers necessary for stable operation. The expected HOM power and spectrum has been analyzed for the complete cold string. The cold string is a combination of various elements such as SRF cavities, bellows with and without shielding, warm HOM beam-pipe absorbers and UHV pumping domes. The presented study is performed for various BESSY VSR bunch filling patterns with 300 mA beam current. The contribution of each component to the total HOM power is presented. INTRODUCTION The BESSY Variable pulse length Storage Ring (VSR) project [1, 2] is a future upgrade of the 3rd generation BESSY II light source. The key feature of the project is the simultaneous storage of long (ca. 15ps) and short (ca. 1.7ps) electron bunches under “standard” user optics. This challenging goal requires installation of SRF higher harmonic cavities of the fundamental 500MHz at two different frequencies. Therefore four new SRF cavities (2x1.5GHz and 2x1.75GHz) are designed [3, 4]. These cavities will operate in CW mode at high gradients of 20MV/m. The combination of these factors with a high beam current (Ib=300 mA) make the cavity design a challenging goal, since stable operation must be ensured. Thus special attention was paid to the damping of HOMs excited by the beam that may otherwise lead to coupled bunch instabilities. The HOM power levels for different cavity arrangements in the SRF module are presented. A dedicated spectral weighting technique for calculation of RF power propagation due to the HOMs excited by the circulating beam in SRF cavities is used [5, 6]. The method makes use of wakefield simulations using the CST software [7] and an external post-processing of the port signals. Calculations were performed for different bunch filling patterns of the BESSY VSR project. The propagated HOM RF power is obtained by spectral weighting of port signals (calculated with a single bunch excitation) with the bunch train spectrum. In this manner the resonances of the cold string component excited by the periodic bunch pattern will be detected. The evaluation procedure is used for the calculation of the expected HOM powers (broadband) to be absorbed in the RF loads and of the efficiency of HOM dampers in terms of power flow balance between FPC, HOM waveguides and beampipes. The HOM power levels for complete cold string with warm elements outside the SRF module are presented as well. THE BESSY-VSR FILLING PATTERN The realisation of the BESSY VSR project implies installation of a single superconducting module with four cavities in one of the straight sections of the existing BESSY II ring (Fig.1). The module integration is a challenging engineering task because of strict space limitations of the ring-straight to ~4.5m. The complete module design is currently in the development stage. Figure 1: Schematic view of BESSY VSR cavities in ring straight. The nominal BESSY VSR filling pattern of the 240m circumference ring is shown in Figure 2 where the short and long bunches will be stored simultaneously. In total 400 RF buckets with 2ns bunch spacing are available. Figure 2: BESSY VSR filling pattern including short (blue) and long (red) bunches. Two type of bunch filling patterns are considered, so-called “extended” shown in Figure 2 and “baseline” with omission of 150 short-pulse, low-charge bunches. The repetition rates of 500MHz and 250MHz are defined by the bunch spacing in each pattern, respectively. In the estimated HOM power levels given in this paper we present results for “baseline” pattern as the highest contributor. Note that in case of single bunch operation the bunch repetition rate will be 1.25MHz, defined by ring circumference of 240m corresponding to 800ns revolution time. ____________________________________________ † email address andranik.tsakanian@helmholtz-berlin.de 9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW Publishing ISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-WEPML048

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

Abstract 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.

Erratum: Eigenmode Compendium of the Third Harmonic Module of the European X-ray Free Electron Laser [Phys. Rev. Accel. Beams 20 , 042002 (2017)]

We regret the oversight of not acknowledging the significant amount of work by several colleagues in the field (see [1–4] and references therein). In particular, we would like to highlight the work performed at the Istituto Nazionale di Fisica Nucleare (INFN) for the realization of the third harmonic system of the European XFEL. We are also grateful to W.-D. Möller and E. Vogel from DESY and H. Edwards and T. Khabiboulline from FNAL for facilitating rapid access to the technical drawings of the FLASH third harmonic module ACC39. Based on drawings of the FLASHmodule and articles on the module for the European XFEL such as [5], the CADmodel of the third harmonic cavity string, which is available via [6], was assembled. Furthermore, wewould like to thank the colleagues from INFN and DESY, in particular P. Pierini, E. Vogel and the XFEL operation team for supporting and facilitating our measurements at the third harmonic module during the busy injector commissioning period. We also would like to express our appreciation to J. Chen from INFN for sharing his experience in measured and simulated rf properties of the third harmonic cavities, especially for the modes with field energy strongly localized at the region of the first cell, the main coupler and the nearby beam pipe (see modes with the indices 105 to 112 in the compendium [7]).

Analysis of higher order modes in large superconducting radio frequency accelerating structures

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.