Particle accelerators are used in a vast amount of elds in research and industry, everywhere where high energy particles are needed to probe materials, produce radiation for experiments or treatment of patients or simply to test the current understanding of Physics. They typically consist of a huge amount of dierent components, but most prominently of RFunits to accelerate and dipole and quadrupole magnets to deect and focus the particles. Though, as conventional particle accelerators, which achieve high energies, are huge and costly to built and operate, a cheap and compact particle accelerator option would be great to revolutionise several elds of research as it would grant access to high energy particles for nearly any laboratory. [3] One idea to solve this problem is the DLA (dielectric laser acceleration). This new type of accelerator design uses the electromagnetic elds of modern lasers in clever combination of dielectric materials to accelerate and focus the particles [4, 5, 6]. This masters thesis focused on optimisation of focusing structures for relativistic electrons in such dielectric laser accelerators within the ACHIP experiment. As accelerators not only need accelerating structures, but also focusing structures to keep the beam well collimated, the idea of this thesis was to model a laser based focusing structure, do electromagnetic simulations with it and use the discretised electromagnetic elds [7] to simulate the particles propagating through the simulation volume to track their path and deection. The design of the focusing structure was proposed by Joshua McNeur, a Postoctoral Researcher at the Chair of Laser Physics at the University of ErlangenNuremberg who conducted research on a similar design [8]. The construction of the design was done in Autodesk Inventor [9], a computer aided design application for 3D design. The electromagnetic simulations were performed with Lumerical FDTD Solutions [10], a nite dierence time domain solver for electromagnetic problems using the Maxwells equations, because sample les and some experience were already available. The particle tracking code was written from scratch during this thesis in Matlab [11], a numerical computing environment, using a discretised Lorentz force equation and the Boris algorithm for time propagation [7]. The main work of this thesis was about setting up the electromagnetic simulations and the particle tracker for ultrarelativistic electrons, as lower velocities would lead to further diculties in fabrication, to optimise said focusing structure to gure out the most appropriate design, featuring the highest deection, the best combined quadrupole like deection behaviour in both transversal directions as well as not too fragile setup for fabrication. Apart from the computational work, some time was also invested in fabrication possibilities and their limits, possible experiment setups to verify the computational results and theoretical description of the deection behaviour. The results of this work include several points. The deection at highest osets from the centre increased by up to a factor 60. The so called parallel eect, which shifts the deection curves independently of the oset depending on the laser phase the particle enters the structure at was strongly decreased. The behaviour of the structure at two dierent wavelengths to investigate scaling possibilities of parameters was investigated.Complications when using dierent refractive indices were described. A mathematical model to gure out the crucial aspects of the electric and magnetic elds was created. Also how deection in one direction contributes to deection in the other direction was investigated. Finally rst fabrication results and one possible experiment to verify the simulated results were elaborated.
