On diffeologies from infinite dimensional geometry to PDE constrained optimization

We review how diffeologies complete the settings classically used from infinite dimensional geometry to partial differential equations, based on classical settings of functional analysis and with classical mapping spaces as key examples. As the classical examples of function spaces, we deal with manifolds of mappings in Sobolev classes (and describe the ILB setting), jet spaces and spaces of triangulations, that are key frameworks for the two fields of applications of diffeologies that we choose to highlight: evolution equations and integrable systems, and optimization problems constrained by partial differential equations

Scientific opportunies for bERLinPro 2020+, report with ideas and conclusions from bERLinProCamp 2019

The Energy Recovery Linac (ERL) paradigm offers the promise to generate intense electron beams of superior quality with extremely small six-dimensional phase space for many applications in the physical sciences, materials science, chemistry, health, information technology and security. Helmholtz-Zentrum Berlin started in 2010 an intensive R\&D programme to address the challenges related to the ERL as driver for future light sources by setting up the bERLinPro (Berlin ERL Project) ERL with 50 MeV beam energy and high average current. The project is close to reach its major milestone in 2020, acceleration and recovery of a high brightness electron beam. The goal of bERLinProCamp 2019 was to discuss scientific opportunities for bERLinPro 2020+. bERLinProCamp 2019 was held on Tue, 17.09.2019 at Helmholtz-Zentrum Berlin, Berlin, Germany. This paper summarizes the main themes and output of the workshop

Studies of harmonic generation in free electron lasers

Freie Elektronen Laser (FEL) erzeugen kohŠrente, hoch-intensive elektromagnetische Strahlung in einem WellenlŠngenbereich von Mikrowellen bis hinunter zu weichen Ršntgenstrahlen. Die Anwendungen von FELs sind vielfŠltig und finden sich unter anderem bei der Femtochemie, Strukturbiologie und Materialforschung. Dabei gehen die Anforderungen in Richtung immer kŸrzerer FEL-WellenlŠngen. Eine Methode zur Erzeugung von FEL-Strahlung mit extrem kurzen WellenlŠngen ist der High Gain Harmonic Generation (HGHG)-FEL. Er besteht aus zwei magnetischen Undulatoren, in denen ein hochenergetischer Elektronenstrahl mit einer externen Lichtquelle wechselwirkt und diese verstŠrkt. Gleichzeitig wird die WellenlŠnge des Lichts reduziert, sodass man durch eine Kaskade von mehreren HGHG-Stufen zu immer kŸrzeren AusgangswellenlŠngen gelangen kann. Benutzt man als externe Lichtquelle einen Laser, so lassen sich die Eigenschaften der Laserpulse (KohŠrenz, Pulsform und PulslŠnge) auf die FEL-Pulse Ÿbertragen. Die Bewegung der Elektronen im Feld des Undulators fŸhrt dabei auch zu Strahlung auf Harmonischen der FEL-Resonanzfrequenz. Die vorliegende Arbeit widmet sich den theoretischen Grundlagen, der numerischen Simulation und der Anwendung von harmonischer FEL-Strahlung. Ihre Eigenschaften werden anhand von verschiedenen Beispielen erlŠutert, unter anderem durch Simulationsrechnungen fŸr HGHG-FELs und andere FEL-Projekte und durch Messungen am FLASH FEL bei DESY Hamburg. Im Rahmen der Arbeit wird fŸr den BESSY Soft X-Ray FEL ein verbessertes Design erarbeitet, welches harmonische FEL-Strahlung nutzt, um den Aufbau des FELs zu vereinfachen und die Anzahl der HGHG-Stufen zu verringern.Free Electron Lasers (FELs) generate coherent, high-intensity radiation in a broad wavelength range from the microwave regime to soft X-ray. FEL applications are manifold and include experiments in femtochemistry, structural biology and material science. Efforts are directed towards even shorter FEL-wavelengths which can be achieved using the High Gain Harmonic Generation (HGHG)-FEL principle. An HGHG-FEL consists of two magnetic undulators in which a high-energy electron beam interacts with an external radiation source and amplifies the radiation beam. At the same time the radiation wavelength is converted to a shorter wavelength, and a cascade of multiple stages of HGHG can be used to reduce the output wavelength even further. If an external laser is used to seed the first HGHG-stage, the laser properties (coherence, pulse form and pulse duration) can be transferred to the FEL output pulses. During the FEL process, the specific electron trajectory in the undulator also leads to radiation at higher harmonics of the FEL resonance frequency. This thesis is dedicated to the theoretical background and numerical simulation of harmonic FEL radiation and its applications. Properties of harmonic radiation are discussed using the results of simulation studies of HGHG-FELs and other FEL-projects and analysing measurements of the FLASH FEL at DESY Hamburg. Finally a new design is proposed for the BESSY Soft X-Ray FEL that uses harmonic FEL radiation to simplify the FEL layout and to reduce the number of HGHG-stages

A semiderivative approach for shape optimization problems constrained by variational inequalities

Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive optimality conditions. Besides the non-smoothness there are complementary aspects due to the VIs as well as distributed, non-linear, non-convex and infinite-dimensional aspects due to the shapes which complicate to set up an optimality system and, thus, to develop efficient solution algorithms. In this paper, we consider the Hadamard semiderivative in order to formulate optimality conditions. In this context, we set up a Hadamard shape semiderivative approach and demonstrate its advantages over an proposed approach based on regulatizations

Start-to-end simulations for a seeded harmonic generation free electron laser

This paper shows how the MAX linac injector and transport system can be efficiently retuned to suit free electron laser (FEL) performance. In a collaboration between MAX-lab and BESSY, a seeded harmonic generation free electron laser is being constructed at MAX-lab. The setup uses the existing MAX-lab facility upgraded with a new low emittance photocathode gun, a Ti∶Sa 266 nm laser system used for both the gun and seeding and an FEL undulator system. To produce the high quality electron beam needed, it is shown how the magnet optics in an achromatic dogleg can be tuned to create an optimum bunch compression and how a good quality beam can be maintained through the beam transport and delivered to the FEL undulators. In extensive start-to-end simulations from the cathode of the gun to the generation of photons in the undulators, FEL performance and stability has been calculated using simulation tools like astra, elegant, and genesis. This has been done for both the third and fifth harmonic of the seed laser. The results from the calculation are 30 fs light pulses with a power of 11 MW at 88 nm and 1.4 MW at 53 nm