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Description

Predictions of particle dynamics in the initial phase of an accelerator requires the full set of Maxwell's equations to be solved alongside the particle motion. The natural choice for a self-consistent simulation is the Particle-in-Cell (PIC) method.

The goal of this work is to provide reference solutions for some of our in-house codes. The modeling in these codes aims for performance improvements over the PIC method while making simplifying assumptions on the physics involved. In this work, a simplified model of an electrostatic electron gun is to be simulated using the Dassault Systèmes CST particle solver. The model will incorporate key features of a gun while reducing the computational cost compared to a real-case scenario. Simulation studies will determine the performance and scalability of the solver used. If time and the number of students permit, the comparison to the in-house codes will be done as well.

The students will gain significant knowledge about the usage of commercial simulation tools. Additionally, insights into the working principle of particle accelerators can be gained.

Anticipated milestones:

Gaining knowledge about the particle-in-cell method and it's usage in CST as well as some background on electron guns.

Creation of a simplified gun model.

Simulation runs determining particle dynamics, bunch parameters and solver performance.

(depending on time / # students: comparison to in-house codes in terms of performance, scalability and precision)

Prerequisites

Interest in learning commercial tools and the numerical schemes behind them, especially the CST studio suite. Interest in particle accelerators is beneficial. Feel free to pass by Jonas Christ for more details.

To improve the simulation of particle dynamics, we couple two types of solvers using a scattered field formulation to solve Maxwell's wave equations in the time domain. Herein, the total electric field E is decomposed into a prescribed incident field E_i and a scattered field E_s. The two are coupled by the PEC-boundary condition which the sum of the two fields (but not each individually) have to fulfill.

The aim of this thesis is to generalize the concept of a scattered field approach to non-perfectly conducting materials at the boundary. When using a single field formulation, one can use surface impedance boundary conditions (SIBC). We want to apply this concept also to the scattered field formulation and implement it into our current simulation code.

The student will gain a broad background in the modeling workflow: How to start from physical equations, how to transfer them to a discrete representation and how to finally implement an effective realization in an existing code framework.

Prerequisites: Strong interest in numerical methods for electromagnetic field computations (PDEs, FIT) and their application. Interest in working with C++.

Feel free to pass by Jonas Christ for more details.

Pyrit is a Finite Element Method Based numerical field simulation software written in Python to solve coupled systems of partial differential equations. Currently, the modular solver covers static and quasistatic electric and magnetic fields, stationary current problems, stationary, and transient heat conduction problems. The different modules can be coupled to analyze multiphysical engineering applications, such as e.g. foil windings, cable joints, and surge arresters. The software is under continuous development. Thus, developing further parts and maintaining existing parts of Pyrit are the main tasks.

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.

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.

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.

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.

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.

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.