H.-W. Glock

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.

Time-Domain Field and Scattering Parameter Computation in Waveguide Structures by GPU-Accelerated Discontinuous-Galerkin Method

In this paper, we demonstrate the discontinuous Galerkin finite-element method (DG-FEM) used for the computation of electromagnetic fields in the interior of 3-D structures with open waveguide ports. This method is particularly applied to derive frequency-dependent scattering parameters. The method allows explicit formulations in time domain on unstructured meshes with high polynomial approximation order. Furthermore, it is well suited to be used in massively parallel organized computing environments. One necessary prerequisite for scattering parameter computations is the appropriate modeling of multimode broadband waveguide boundary conditions. Here we present a method of general applicability and its realization in the framework of DG-FEM. The entire procedure was implemented on low-cost graphic processing units. Two test examples are given, one of them of direct practical relevance in the field of particle accelerator design. The results are in excellent agreement with those of a commercially available frequency-domain finite-element method code.

An iterative algorithm to evaluate multimodal S-parameter-measurements

Scattering-(S-)parameters are well established quantities to characterize RF-components both in theory and for measurement purposes. In spite of this, there are very few approaches to measure S-parameters in waveguide environments with more than a single propagating mode. In this paper we present a method for this purpose using a conventional single mode network analyzer, coaxial-waveguide adaptors to be calibrated within the procedure and waveguides of adjustable length. The most important step is the extraction of the devices S-parameters aimed for from the ensemble of single mode measurements. This is done by an iterative algorithm described in this paper.

CSC - A procedure for coupled S-parameter calculations

Large rf-structures are sometimes too complex to be calculated entirely in single simulation runs. Usually, if the structure has open ports, the scattering properties - the so-called S-parameters - are of primary interest. As a matter of fact, they can be derived from scattering properties of parts of the entire structure, which are calculated in the procedure presented here in separate, less expensive simulations. A very compact representation of the underlying theory was found, which is presented in the paper. Furthermore, a Mathematica application called CSC based on this formulation is introduced. CSC calculates the scattering properties of an object, which are a combination of an arbitrary structure of segments with previously calculated S-parameters. To illustrate the use of CSC, three examples are shown: higher order mode (HOM) coupling properties of components of the TESLA Test Facility without and with accelerating cavities and the coupling of polarizations in chains of structures with slight deviations from circular cross sections.

Eigenmode calculation of complex RF-structures using S-parameters

This paper presents a technique to calculate eigenfrequencies and the corresponding field patterns of complex rf-structures or beam pipe sections in particle accelerators by subdividing the total section, calculating the distinct scattering parameters and then combining the results of the subsections. This allows a reduction in the effort of a single calculation step to a practical amount and the possibility to exploit the symmetry and multiplicity of some parts of the structure.

Periprosthetic Fields and Currents of an Electrostimulative Acetabular Revision System

Electrostimulative therapy has been used for more than 20 years to improve the healing of bone fractures. The objective is to adopt electrostimulative procedures to an acetabular cup revision system. One main issue is the optimization of the implants inherent electrical system using adjustable geometry and coil parameters to achieve an electric field distribution within the area of relevance with the appropriate strength and as homogeneous as possible. In the work described here the field distribution on the surface of the acetabular cup was determined by “finite-integration-theory” electromagnetic field simulations.

Calculation of Electromagnetic Eigenmodes in Complex Structures Using Coupled S-Parameter Calculation

Eigenmode calculations are usually carried out with dedicated solvers as e.g. [1]. If eigenmodes of large and complex structures have to be calculated, the application of these solvers is limited even on the most powerful workstations by the available computational resources in terms of memory and computation time. This paper will present a technique based on scattering parameters that allows to split the complete geometry into subsections which can be modeled individually. The broadband S-parameters of each section have to be calculated externally using appropriate solvers. Such runs are significantly smaller problems and may be performed in parallel on different machines. In the paper we present a description which is well suited to calculate the eigenfrequencies of an entire structure and the wave amplitudes needed to determine the internal fields once the S-parameter of the segments are known. This approach is of special advantage if the structure contains segments of identical shape, parts that can be described analytically or components of local complexity, which enforce enhanced grid resolution. Further it establish a mean for frequency selective eigenmode analysis, which is difficult for most eigenmode solvers. We illustrate the procedure with a test example that was calculated both with Coupled S-Parameter Calculation and a direct eigenmode solver. Results of the comparison are presented.

Calculation of HOMs in TESLA-cavities using the coupled S-parameter calculation method

The calculation of electromagnetic fields in accelerating structures is normally done by dedicated numerical solvers such as MAFIA. Even if components like cavities are of cylindrical symmetry, full 3D modelling is required in order to consider the effects of power- or HOM-couplers. This implies a numerical effort significantly higher than the separate treatment of parts with and without rotational symmetry. Therefore we have developed a method called coupled S-parameter calculation (CSC) which is based on a scattering parameter description. It uses S-parameters of the components found with field solving codes utilising any components symmetry or repetition of subsections. In the paper we present a parameter variations within a TESLA-9-cell-cavity with couplers and in a 4-cavity-chain in order to demonstrate the capabilities of CSC.

RF computations with the finite integration technique (FIT) and the coupled S-parameter calculation (CSC)

This paper starts with a very brief review of FIT on triangular grids. Next, it reports about some recent features in FIT to minimize the geometrical error while keeping the number of grid points as small as possible. Finally, a method is introduced to compute scattering properties and/or resonant fields in complex RF structures by combination of domain decomposition with any available CEM tool. We denote this method as coupled S-parameter calculation. Some examples are presented underlining the power of the methods described.

Coupled Calculation of Eigenmodes

In many technical applications the electromagnetic eigenmodes — frequency spectrum and field distributions - of rf-components are to be determined during the design process. There are numerous cases where the studied component is too complex to allow for a detailed enough simulation on usual servers. One way out of this situation is domain decomposition and parallelization of the field simulation. Yet, this demands for a parallelized solver. In our approach, we combine the use of commercial single processor-based software for the field simulation with a tool based on scattering parameter description. The studied component is decomposed in several sections. The scattering matrices of these sections are computed in time domain for instance with a FDTD field solver. A linear system is set up to compute the eigenfrequencies of the complete system and the field amplitudes at the internal ports common to a pair of sections. With the knowledge of these amplitudes the fields of the eigenmodes can be computed with help of a frequency domain field solver. This approach is denoted as Coupled S-Parameter Calculation (CSC). Some advantages of this procedure are the possibility of easy exploitation of symmetries in the studied components and the use of very different granularities in discretization of the single sections. This paper presents the method, its validation using a standard eigenmode solver and applications in the field of accelerator physics. Special attention is given to the eigenmodes of structures with slight deviations from rotational symmetry.