K. Rothemund

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.

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.

Wake field calculation for the TTF-FEL bunch compressor section

The TTF free electron laser needs very short bunches to produce self-amplified spontaneous emission. This short bunch length is produced in a magnetic bunch compressor where the trajectories of particles with different energy have different path length in a way that the bunch is longitudinally compressed. As a parasitic effect the wake fields produced by the passing bunch will have the possibility to interact with the bunch itself and cause emittance growth. The high frequency behaviour of the beam pipe in the bunch compressor has to be analysed in order to identify trapped higher order modes (HOM) and to estimate beam distortion. Because of the complexity of the bunch compressor section direct eigenmode calculation is not possible due to lack of available computer power. A technique is presented which allows to compute eigenmodes of rf-structures by using scattering-parameters of subsections of the bunch compressor. This is done numerically based on the computer code MAFIA to model the different sections of the beam pipe.