During the first funding period of this RTG the S-DALINAC was operated successfully as a once-recirculating energy recovery linac (ERL), becoming the first running ERL in Germany in August 2017. The lattice of the S-DALINAC also offers the possibility to operate in twice-recirculating ERL mode. For this multi-turn ERL operation a test phase has already started.

The operation in multi-turn ERL mode is a challenging endeavor. It is absolutely necessary to perform complex beam dynamics simulations. Especially the effect of phase slippage, describing a mismatch of the real beam velocity to the target beam velocity, has to be taken into account very carefully. The simulation of the energy-gain distribution used during the first test phase shows a high momentum deviation at the end of the second deceleration due to the effect of phase slippage. Not only the central momentum of the decelerated beam has to be controlled properly by the phase settings of the cavities. The momentum spread is an important parameter as well. It has to stay below certain thresholds to ensure that the beam fits into the acceptance of the machine. Also most applications of the ERL mode will profit from a low momentum spread. Different settings following a non-isochronous arc scheme combined with an off-crest acceleration / deceleration will be investigated.

**Betreuer/in**: Prof. Dr. Dr. h.c. mult. Norbert PietrallaAllowing for high beam energies with relatively short linac sections, multi-turn ERLs are cost effective and have smaller footprints. However, they are also more prone to instabilities, such as CSR and space-charge driven micro-bunching, Beam Break-Up (BBU) and ion trapping. Multi-pass BBU caused by Higher Order Modes (HOMs) in cavities is one of the main limitations to the beam current of multi-turn ERLs. Additionally, current limitation can also be caused due to the lack of thermal load capacity of HOM antennas in cw mode. This applies, for example, to the two-turn ERL facility MESA.

Beside the improvement of cavities, a storage ring fed by an ERL or a linac could be a solution. It meets the requirements of experiments which demand high brightness beams with higher current. Operated in pulsed mode, the ERL or linac could fill the ring but avoid strong BBU. This is possible because the HOMs add up from bunch passage to bunch passage. Gaps in the bunch train can damp them significantly. Of course, the beam has to circulate just a few turns in the ring, far less than the damping time, in order to maintain the superior beam quality. This requires continuous bunch train injection and extraction much like the schemes used for stretcher rings.

The goal of this project is a feasibility study investigating the merit of a stretcher-like ring at MESA facility.

The concept of beam coupling impedance describes the electromagnetic interaction of the beam with their accelerator chamber. In synchrotron accelerators, beam-coupling impedances can lead to transverse beam instabilities and/or to beam induced heating. The calculation in the general case of arbitrary geometries, eventually, including resistive walls and dispersive materials is only possible by numerical simulations. So far, there is no appropriate numerical method for the calculation of low frequency coupling impedances in 3D geometry and for arbitrary particle beam trajectories.

In this project, we propose a novel numerical approach for the calculation of impedances directly in the frequency domain. The method is based on a high order finite element approach employing a special hybrid mesh discretization that allows to resolve properly the beam current and cavity geometry. In order to describe the electromagnetic fields above the cutoff frequency, the method requires the development of appropriate boundary conditions for the incident particle fields at the in- and outgoing beam pipes. Furthermore, since the typical cavity structures considered are electrically large, the development of fast multigrid type solvers and domain decomposition techniques is required. Finally, a generalized scattering matrix technique for large accelerator components that allows to concatenate coupling impedances from smaller cavity structures will be developed and implemented in the simulation tool. The simulations using this approach aim primarily at the investigation of accelerator structures of the European X-FEL, such as corrugated plate dechirpers and bunch compressors that could so far not be properly be described by numerical simulations.

**Betreuer/in**: Dr. Erion GjonajA further miniaturization and integration of magnets for beam matching and beam transport necessitates 3D finite-element simulation, parameter studies and optimization steps. Thereby, fringing-field effects (related to the relatively short components), cross-talk effects (disturbances from one to the other function) and manufacturing tolerances (resulting in relatively larger effects for smaller devices) need to be considered already during early design stages. The possibility of high-temperature superconducting magnets (HTS) will be evaluated, which on its turns requires a large simulation effort. Both iron-dominated as well as coil-dominated magnets are considered. With a random-field approach, spatial variations and ageing effects in iron properties and in the superconductor will be embedded in the field models. Uncertainty quantification will be carried out to study the impact of manufacturing tolerances on the overall performance of the system. The simulations will spend special care to quantifying the interferences between the combined functionalities.

The techniques developed in this project will be applied to the existing magnet systems in the S DALINAC in order to further optimize its beam dynamics, especially for capturing and guiding the beam in energy-recovery operation. Thereby, capturing the beam and interaction with a target are considered as particular challenges. The project will consider a large range of scenarios including epistemic uncertainties using the developed simulation tools.

**Betreuer/in**: Prof. Dr. Herbert De GersemOne of the operation modes of the MESA accelerator will be a twice recirculating ERL mode with four passes of the beam in each cavity. The energy recovery operation shall accelerate a beam current of 1 mA in its starting phase; later in stage 2 a current upgrade to 10 mA shall take place. MESA will use four TESLA/XFEL-type SRF cavities for acceleration. Because of their high quality factors, HOMs in SRF cavities can strongly influence the beam and may lead to BBU by transversely deflecting the bunches until particles get lost. This effect can be observed in single pass linacs but is much stronger in recirculating setups like ERLs.

Therefore, detailed studies on the beam dynamical behavior of the MESA modules have been carried out in the first funding period of the GRK 2128. Simulation results so far indicate that MESA stage 2 is not limited by the HOMs as the threshold current of 13.4 mA exceeds the 10 mA design value (see figure). Nevertheless, quenching of the HOM antennas could be an issue if HOM loads induced by high current would heat the HOM damping antennas too much. For that reason, a cooling concept for the antennas has been developed. Investigating the behavior of the MESA modules at high beam current would be the next step forward.

Research goals of the proposed project will be the cw application of TESLA/XFEL cavities at very high beam currents including investigations on HOM antenna heating, BBU in ERL operation and improvement of LLRF systems for high current operation.

**Betreuer/in**: JProf. Dr. Florian HugThe maximum beam current that can be accelerated in an energy recovery linac (ERL) can be severely limited by the transverse multi-pass beam breakup instability (BBU). In this project, we plan to accurately predict and increase the beam intensity limits in MESA due to the BBU. The predictions will rely on particle tracking including the kicks caused by high-order dipole (HOM) modes in the SRF cavities. The simulation will employ as much as possible existing tools, like the tracking tool elegant. However, we also plan to implement simplified simulation models as well as analytical models, also for validation purposes. The HOMs and the resulting momentum kicks will be obtained from CST simulations for the MESA cavities. Manufacturing tolerances and possible randomization effects will be taken into account. The aim of this project is the identification of suitable counter-measures for MESA parameters. Options to be studied are, for example, chromaticity and BNS damping. Chromaticity usually only plays a minor role in ERLs. In order to enhance the chromatic tune spread external sextupoles have to be installed together with RF cavities for the generation and removal of an energy chirp. BNS damping would require a RF quadrupole in order to generate a tune spread along the bunches. We plan to include both stabilization measures in our simulation models and quantify their effect on the BBU in MESA. Besides the described passive counter-measures we also plan to include models for microbunching instabilities and an active transverse feedback system into our models. This project should deliver the specifications for such a system in MESA.

**Betreuer/in**: Prof. Dr. Oliver Boine-Frankenheim