Modeling and simulation of active plasma lenses for high brightness electron beams

In the last few decades, considerable effort has been devoted to the research aimed at the optimization of particle accelerators. Specifically, improving the efficiency and reducing the size of the high brightness electron machines can have a dramatic technological, scientific, and economic impact. Active plasma lenses are capable of fostering this process, given their compactness, high focusing strength (up to kT/m), and symmetry. However, experimental studies have shown that they are affected by aberrations, which may severely compromise the beam quality and enlarge the minimum spot attainable. In this thesis we discuss the working principle of active plasma lenses as well as their aberrations. We built a 2-D, axially symmetric numerical model that allows to study the hydrogen-filled capillary discharges typically used for focusing electron beams. We solved the model equations with a modified version of the open source, fluid dynamics code PLUTO. Specifically, we implemented an alternating direction implicit method to evolve the parabolic part of the problem with a semi-implicit approach. We compared the results of our simulations with measurements of the electron density inside the discharge plasma. We reproduced experimental results related to active plasma lensing of a high brightness electron beam. The results of the simulations were consistent with the measurements in both cases. We also explored the effect of capillary diameter variation on the lens aberrations, the results are discussed within the thesis.