State of the art high energy accelerator facilities are using superconducting radio frequency (SRF) cavities made of niobium (Nb). The performance of bulk niobium SRF cavities has intrinsic limits, e.g., finite intrinsic rf-resistivity approximated by the BCS theory. This results in a limited quality factor Q0. Low critical magnetic field limits the achievable maximum accelerating field. The current research is therefore focused on new materials based on niobium like niobium tin alloys (e.g. Nb3Sn) or the niobium-nitrogen binary system (e.g. Nb-N dilution or specific NbN crystalline phases).

One method is to create the NbN δ-phase at the cavity surface. This phase is nucleated at temperatures of more than 1300°C. The ultra-high vacuum furnace at S-DALINAC is capable to do this nitration. In a first phase a recipe for the creation of the δ-phase will be investigated at small Nb samples. The validation of the success is done with the help of measurements done together with the ATFT group of TU Darmstadt.

The final recipe will be applied to 3-GHz single-cell test cavities. In a first step the quality factor of the virgin cavities will be determined in a vertical test cryostat. Afterwards the recipe found at the Nb samples will be applied to the cavities. Further measurements of the new quality factors will evaluate the results. The state of the cavities can be reset by, e.g., an electro-polishing (EP) treatment. Other recipes can then be tested at the single cell cavities for refining the nitration recipe. Depending on the procedure, a successful treatment method can also be applied to spare 20-cell cavities of the S-DALINAC. Their quality factors will then be measured in the vertical test cryostat, too.

**Betreuer/in**: Prof. Dr. Dr. h.c. mult. Norbert PietrallaThe SRF cavities used for the MESA main linac modules are TESLA/XFEL resonators treated with the standard XFEL recipe. This recipe comprises an initial hydrogen bakeout at 800o C, BCP, EP, HPR and a final 120o C bake. This procedure reliably led to high quality factors (>1010) and high usable gradients (>23.6 MV/m = XFEL-specification) on an industrial production scale within the XFEL project.

For future improvements of MESA’s beam energy and current after implementation of stage 1 the quality factor of the cavities needs to be increased when keeping the same cryogenic infrastructure. The project presented here will concentrate on improvements of the SRF properties of the HOM antennas. This is related with both future goals, the improvement of current and of energy. At increased accelerating gradient in cw operation the HOM antennas can quench due to thermal load or due to exceeding critical fields induced by the residual coupling to the monopole modes of the cavity. In addition, transverse modes induced by high beam current, occurring in ERL operation, can result in even higher amount of RF fields and thermal loads. Therefore, an improved cooling of the inner conductor of the HOM adsorbers is crucial for high current operation with high accelerating gradient. In addition, an alternative preparation of the HOM antenna using a nitrogen bakeout or a coating with a material of better superconducting properties (critical field, transition temperature) like e.g. Nb3Sn could be very helpful. Within this project, the proposed improvements will be investigated systematically.

**Betreuer/in**: JProf. Dr. Florian HugThe simulation of 3D electromagnetic fields in both SRF accelerator cavities and quadrupole resonators used for characterizing superconducting materials is standard and available in commercial and academic field solvers. Still challenging is attaining a sufficient accuracy for the eigenfrequencies of cavities with a high-quality factor and for the on-axis fields. TEMF@TU-Darmstadt disposes of an inhouse nonlinear eigenmode solver using 3D higher-order finite-elements (FEs).

Perfectly conducting surfaces can be modelled by homogeneous electric boundary conditions. Lossy surfaces with comparably small skin depths are modelled by surface impedance boundary conditions (SIBCs) which are easily implemented in frequency-domain solvers but need convolutions in time-domain solvers and cause eigenmode formulations to become nonlinear.

The objectives of the project are (a) to make multilayer SIBCs available within the 3D FE eigenmode solver (b) to study of the existing quadrupole resonators with respect to their sensitivity to inaccuracies in geometry and the resistance of the connection between sample holder and main cavity (c) to design an optimal measurement strategy, including error-controlled inverse problem solving and (d) to demonstrate the capabilities of improved surfaces in accelerator cavities.

**Betreuer/in**: Prof. Dr. Herbert De GersemA15 phase superconducting materials are potentially interesting for next generation accelerator cavities. The A15 intermetallic compounds, like Nb3Sn, V3Si or Nb3Ge have a significantly higher critical temperature than niobium. Nb3Sn is the most investigated after Nb as SRF cavity material. Nb3Sn is a very hard and brittle material, thus fabrication of bulk Nb3Sn cavities is not practical. With Nb3Sn theoretically fields up to 90 MV/m at 1.7 K are reachable, still the Nb3Sn coated cavities are quenching at around 18 MV/m. There is no fundamental physical reason for this performance gap. Again, advanced materials research could add to the improvement of this system.

Nb3Sn is either synthesized by a deposition of Sn on the Nb cavity or by a stoichiometric depositing of Nb and Sn followed by a diffusion process. An annealing process forms the Nb3Sn thin film, helps to further increase grain size, and improves its characteristics. Film thickness, and especially stoichiometry are essential to optimize the Nb3Sn material properties, in particular, under-stoichiometric layers may further improve their usage for SRF technology. A new modification to the sputtering process was made in the Advanced Thin Film Technology (ATFT) group to improve the stoichiometry of the layer. The superconducting resistance of the first sputtered Nb3Sn film has been measured resulting in a critical temperature of 16.4 K, which is already promising (literature value Tc = 18.3 K for Nb3Sn).

At the end of this PhD project the superconducting Nb3Sn phase will have been grown on different substrates including an optimization of the critical temperature and measurement of the Q-value. Possibilities to coat a cavity will be investigated and eventually a single-cell cavity will be coated and measured.

**Betreuer/in**: Prof. Dr. Lambert AlffThe main electron source used at the S-DALINAC is a thermionic gun operated at 250 kV in DC mode. The S-DALINAC is operated in cw mode at 3 GHz. This leads to a distance of 10 cm between the bunches and a time gap of 0.33 ns at the experiments. In twice-recirculating ERL mode the distance between adjacent bunches in the first recirculation beam line amounts to 167 ps, only, because the yet to be accelerated beam and the already decelerated beam are simultaneously present in this beam line. This makes the characterization of both beams difficult unless the entire bunch trains will be pulsed.

The implementation of a pulsed injector beamline (MHz region) will enhance both, the diagnostic systems of the accelerator and the experimental capabilities at the different setups. The pulsed injector beamline will be based on a pulsed quasi-electrostatic deflector]. A characterization of the pulsing will be done using a diagnostic beam line behind the prebuncher. It is enhanced accordingly within a project of this RTG. It will be part of this project to investigate the behavior of the low level radio frequency (LLRF) control system. It was designed for a continuous beam loading in the cavities. The pulsing of the beam might lead to the necessity to implement a feedforward system acting on the LLRF system if a certain bunch charge and thus beam loading is exceeded.

**Betreuer/in**: Prof. Dr. Dr. h.c. mult. Norbert PietrallaThe experiments in precision physics to be conducted at MESA are demanding for low energy spread of the order of 10-4 and high stability of the beam concerning mean energy and position. As the MESA accelerator will be operated in two operational modes, with a wide range of beam currents and thus at different synchronous phases a sound knowledge of the phase space at the exit of the injector linac MAMBO (MilliAMpere BOoster) is necessary to optimise the injection into the main linac MESA. Previous research showed that a low energy spread in the main linac can only be attained if the beam is injected at short bunch lengths rather than at low energy spread (see figure). Since at different beam currents defocussing due to space charge is different in strength it is necessary to match the phase space of MAMBO to MESA on a regular basis by adjusting the synchronous phases in the MAMBO RF-sections for longitudinal plane and the focussing elements of the transverse plains. To do so a diagnostics station capable of characterising the 6D phase space of MAMBO is necessary.

The goal of the project is to first develop and implement a diagnostics station to measure at least the longitudinal phase space of the injector. Then the phase space shall be characterised at different beam currents and different setup parameters of the chopper/buncher system together with the four MAMBO RF-sections to generate look-up tables for routine operations of the MESA facility. Those tables shall then be tested with different setups of the main linac to find optimum beam parameters at the experiments.

**Betreuer/in**: Dr. Robert HeineThe eigenfrequencies of a superconducting cavity heavily depend on its geometry. A deformation in micrometer range or an inhomogeneous rinsing may lead to a frequency shift of several kHz, thereby detuning the cavity. Despite the tuning procedure during commissioning and the use of tuning systems during operation, an accurate description of frequency detuning during design and operation of a superconducting cavity is of paramount importance. A second fact is related to the quality factor and the maximal electric field strength. There is a tendency to treat Nb-surfaces with nitrogen under controlled pressure and temperature in order to obtain Nb-N phases with which a higher electric field strength and/or a higher quality factor is achieved. The technique is not yet fully mature. Therefore, it is expected that inhomogeneous doping may lead to a performance drop. A similar concern applies to effects related to all kind of ageing processes (e.g. due to multipacting).

Both problems are related to uncertainties of the geometry or material distribution. Such uncertainties are commonly modelled by stochastic collocation finite-element methods. When, however, the number of uncertain parameters gets larger, dimension-adaptive polynomial chaos methods or low-rank tensor decompositions are indispensable to alleviate the curse of dimensionality of the stochastic problem. Such methods have been studied extensively during the last years at TEMF@TU-Darmstadt.

The objectives of this project are (a) to model smallest variations of the geometry in a consistent way (mesh morphing, see figure), (b) to model spatial uncertainties of the surface properties and (c) carry out uncertainty quantification according to the probabilities of the mentioned uncertainties. The outcome of the project will allow to define minimal requirements for a surface treatment of Nb cavities, guaranteeing a prescribed performance.

**Betreuer/in**: Prof. Dr. Herbert De GersemNiobium coated copper cavities could be a cost-effective alternative to bulk niobium SRF cavities. The so called Q-slope, a steep drop in the Q-factor with increasing electric field needs further attention from material scientists, as this performance-limiting factor has no fundamental physical reason. Better performing cavities can also be produced based on bulk Nb. The group of A. Grassellino (FNAL) pioneered the N-doping process for bulk niobium SRF cavities followed by the development of the N-infusion procedure. The scientific infrastructure of the Advanced Thin Film Technology (ATFT) group at the Institute of Materials Science (IMS) of TU Darmstadt is ideally suited for the growth and investigation of metallic systems, amongst them Nb films on Cu substrates. Various film deposition techniques, like sputtering and molecular beam epitaxy (MBE) can be utilised to find the coating with the best suited microstructure and composition, including advanced structures, like multilayer films with a diffusion barrier layer. Feedback from the locally available analytical characterization tools (x-ray diffraction – XRD, electron microscopy, secondary ion mass spectrometry – SIMS, X-ray photoelectron spectroscopy – XPS etc.) is indispensable in finding the optimal coating method and process parameters. Larger samples and finally cavities should be coated with the final goal of Q-factor measurement. The measurements will be done at the vertical test cryostat of the IKP at TU Darmstadt.

At the end of the PhD project a better-than-Nb cavity may be demonstrated. Either as a copper based niobium thin film cavity, or even better, a cavity coated with a material with higher critical temperature. The available special oven at IKP will be used for cavity coating. Bulk niobium samples have already been doped in that oven and analyzed with XRD (see figure). Similar doping procedures are planned on copper-based niobium samples.

**Betreuer/in**: Prof. Dr. Lambert Alff