### Modeling and Simulation of Insulation Layers in Superconducting Magnets

2021

### Architecture Optimization in Physics-Informed Neural Networks

2021

### Optimization of a 320kV Cable Joint Specimen During Steady State Operation

2022

Bachelor thesis, Master thesis, HiWi Position

In the context of the green energy transition, efficient long-distance power transmission becomes increasingly important. The losses of extruded high voltage direct current (HVDC) systems are lower than those of high voltage alternating current systems and, hence, more and more HVDC systems are being deployed.

Cable joints connect cable segments, which are limited in length due to transport limitations. Cable joints are known to be the weakest part of HVDC systems as they are exposed to high internal field stresses. These stresses can be reduced by inserting a layer of so called field grading material (FGM), that features a strongly nonlinear conductivity. The FGM balances the electric field stress by becoming highly conductive in areas with high field strengths and, thus, shifting the voltage drop to less stressed areas. The aim of this work is to optimize the nonlinear conductivity of a 320kV HVDC cable joint specimen during steady state operation.

**Supervisor**: Maren Greta Ruppert-Schmidt, M.Sc.### Numerical Simulation of a Plasmonic Niobium Photocathode for SRF Gun Applications

2022

Bachelor thesis, Master thesis, HiWi Position

Currently available linear accelerators are operated in pulsed mode to prevent a thermal overload of the entire system. Upcoming planned CW operations are possible using SRF photoinjectors with either warm or cold photocathodes. The use of warm cathodes in an otherwise cold cavity, which initially appears advantageous, unfortunately leads to a variety of difficulties. On the other side, a cold photocathode cannot be made from the efficient semiconducting materials such that metals with intrinsically lower quantum efficiencies have to be applied instead. Nanostructured surfaces can be used to increase the effective quantum efficiency by surface plasmon resonance enhancement. Optimized nanostructures enable the efficient application of a given laser with a specified wavelength and allow a promising operating regime for future photoinjectors.

**Supervisor**: Dr.-Ing. Wolfgang Ackermann### Numerical Simulation of SRF Gun Coupler Kicks

2022

Bachelor thesis, Master thesis, HiWi Position

At DESY the currently available electron gun is based on a normal conductive copper cavity operated in pulsed mode. It will be replaced by a superconducting variant to enable also CW operation. The required electromagnetic field in the cavity is then excited by a dedicated input-coupler system originating from the well-known TESLA input power coupler. Additional HOM couplers are not considered in the current design phase but may be added if required. Due to the asymmetric coupling of the resonator fields to the external sources the extracted electron beam will observe a parasitic coupler kick which has to be minimized.

**Supervisor**: Dr.-Ing. Wolfgang Ackermann### Finite-Element Simulation of Eddy-Current Effects in Orbit Corrector Magnets

2022

Bachelor thesis, Master thesis, HiWi Position

The orbit corrector magnets of the PETRA IV will be excited at elevated frequencies. This causes eddy-current effects in the magnet’s yoke and in the beam pipe. The eddy currents may deteriorate the aperture field. Moreover, they cause losses, which need to be cooled away. Accurate predictions thereof are necessary already during early design stages. In this student project, 2D and 3D finite-element magnet models will be set up. Appropriate model parts for the laminated yoke parts, the windings and the thin beam pipe will be inserted. They should allow to accurately simulate the particular eddy-current effects in these parts. A parameter study of the eddy-current effects for different design choices will be carried out.

**Supervisor**: Prof. Dr.-Ing. Herbert De Gersem### Finite-Element Electric-Machine Simulations Accelerated by Cheap Surrogates

2022

Bachelor thesis, Master thesis, HiWi Position

The scientific question is whether a surrogate (low-fidelity) machine model can be employed to accelerate a computationally expensive (high-fidelity) finite-element machine simulation. The research hypothesis is that a well-constructed surrogate may perform better than a pure algebraic surrogate for standard machine types. It is expected that an established machine model can be trusted in a region which is substantially larger than a standard quadratic surrogate of the high-fidelity model. In order to preserve accuracy, the surrogate model will be adapted algebraically such that it locally has at least a linear consistency with the finite-elmeent model. This will be achieved by additive or multiplication defect corrections. In particular, an additive correction with quasi-second-order consistency will be set up using Broyden-Fletcher-Goldfarb-Shanno updates for the Hessian of the high- and low-fidelity models.

**Supervisor**: Prof. Dr.-Ing. Herbert De Gersem### Circuit simulation with a discontinous Galerkin based data-driven modified nodal analysis solver

2022

Master thesis, HiWi Position

An electrical circuit can be fully described through Kirchhoff's circuit laws and the employed lumped elements. Kirchhoff's circuit laws are directly derived from Maxwell's equations and thus considered to be exactly known. Contrarily, the behaviour of the lumped elements is at first only known through measurements. In conventional approaches, a model that fits best to the available measurement data must be derived. This is typically accomplished by means of empirical modeling approaches, which however cannot represent the elements' behaviour exactly, introduce epistemic uncertainties, and can be difficult to apply for sophisticated elements.

Data-driven solvers dispense with empirical models by solving the underlying problem directly on the measurement data instead.

Therefore, errors arising from the modelling process as well as epistemic uncertainties are avoided and the data-driven solutions can be considered as assumption-free.

The aim of this work is to develop a data-driven modified nodal analysis solver that employs a discontinuous Galerkin formulation to solve along the time scale.

**Supervisors**: Armin Galetzka , M.Sc., Dr.-Ing. Dimitrios Loukrezis### Adaptive Mesh Strategies for the Quasi-3D Method for Quench Simulation

2022

Bachelor thesis, Master thesis, HiWi Position

Superconducting coils are used for accelerator magnets to achieve very high magnetic fields. A major challenge is the quench phenomenon which is a sudden shift from superconductive to normal-conducting state. Such a quench can lead to heat losses and in the worst case to damages of the magnet.

Quenches not only impose physical, but also numerical challenges: While a magnet is about 10m long, quenches occur in the range of mm. To deal with this strong multi-scale problem, a special quasi-3D (Q3D) method is employed which utilizes hybrid basis functions.

The Q3D discretization is chosen at the beginning of the simulation to achieve an optimal representation of the steep temperature gradients of the quench. However, as the quench propagates, this initial discretization may turn inoptimal and lead to rising numerical errors. Therefore, adaptive mesh strategies and error estimators play an important role in the quench simulation and should be investigated in this work.

**Supervisor**: Laura D‘Angelo, M.Sc.### Simulation of the electromagnetic properties of accelerator cavities

2022

Master thesis

At DESY in Hamburg the particle accelerator PETRA will be equipped with new rf resonators for the acceleration of the particles. For this reason the electromagnetic properties of these cavities have to be investigated. The 3D electric and magnetic fields can be simulated with numeric tools. And these fields need to be evaluated by post processing to calculate the accelerating and deflecting effects on the charged particle beam.

**Supervisor**: Dr. phil. nat. Wolfgang F.O. Müller### Development of a Multirate Method for Adjoint Sensitivity Analysis in Nonlinear Networks

2022

Bachelor thesis, Master thesis, HiWi Position

In different fields of electrical engineering, such as power electronics or microwave engineering, the analysis of nonlinear electric networks is an important task.

As simulations for large scale nonlinear networks are numerically expensive, a structured approach for the analysis and optimization of such networks is advised.

In some applications, sensitivity analysis is used as an advanced approach to optimize given networks.

Sensitivity analysis is a study of how certain system parameters

influence the properties of a given quantity of interest (QoI).*p*The result is a very descriptive measure for the identification of relevent system parameters.

For networks with a large number of system parameters p, an adjoint sensitivity analysis shows advantages, as its computational cost is independent of the number of system parameters

.*p*Given the case, that the network contains largely scattered time scales, this analysis runs into issues if the sensitivity for the QoI has to be found at many points in time.

**Supervisor**: Julian Buschbaum, M.Sc.### Modeling and Simulation of Foil Windings

2022

Bachelor thesis, Master thesis, Projectseminar, HiWi Position

In many applications, foil windings are preferred over wire windings or Litz-wire windings because of their better thermal properties, higher fill factor, lower resistance and easier construction. Foil windings are used in inductors, magnet systems and transformers. Contemporary developments are focusing on increasing frequencies, lower weight and production cost and shorter time-to-market. Further research on foil windings is driven by applications such as, e.g., foil-winding transformers for DC-DC converters and foil windings used in filters or for wireless power transfer.

The skin effect which becomes increasingly important at higher frequencies, is counteracted by using thinner foils. For a skin depth below the foil’s thickness, the skin effect is assumed to be only relevant at the foil tips. There, however, high current densities may lead to hot spots, even when the tips are well cooled. Additionally, fringing flux impinging perpendicularly on the foils causes eddy currents, possibly leading to unacceptably high local losses.

**Supervisors**: Jonas Bundschuh, M.Sc., Dr.-Ing. Yvonne Späck-Leigsnering### Parareal Physics-Informed Neural Networks for Transient Electromagnetic Field Problems

2020

Bachelor thesis, Master thesis, Projectseminar, Type of work flexible, HiWi Position

Artificial Neural Networks (NNs) have provided transformative results in numerous and diverse engineering domains, e.g. image processing or pattern recognition. In recent years, NNs have also been utilized for solving Partial Differential Equations (PDEs). Therein, one of the most popular approaches are Physics-Informed Neural Networks (PINNs).

A major drawback of PINNs is the computational cost arising due to the use of large datasets and NNs with many degrees of freedom. As a remedy, a recent work has proposed a combination of the Parareal and PINN algorithms, resulting in a method referred as PPINN. The PPINN algorithm splits long-time problems into many independent short-time problems, supervised by an inexpensive and fast coarse-grained conjugatebgradient solver. The benefit of PPINN is that it decreases the computational cost of training a DNN by reducing the size of the training set and the number of d.o.f.s per network.

The task of the thesis is to implement the PPINN algorithm to a suitable, transient electromagnetics problem, a test case that has not appeared in the literature so far. A comparison against standard PINNs will complement this work.

**Supervisors**: Dr.-Ing. Dimitrios Loukrezis, Moritz von Tresckow, M.Sc.

### Modeling and Simulation of Insulation Layers in Superconducting Magnets

2021

### Architecture Optimization in Physics-Informed Neural Networks

2021