Positron acceleration in a plasma column

The particle physics community has expressed significant interest in a 10 TeV-class electron-positron collider to advance our understanding of matter. However, the costs associated with such a collider usingconventional radio-frequency technology seem to be prohibitive. Thus,significant research and development is needed on the accelerator sideto reduce both construction and power consumption costs.Plasma-based accelerators, due to their extremely high acceleratinggradients, are a potential solution to reduce construction costs.Although significant progress has been made in plasma-based electronacceleration in recent years, positron acceleration still poses anotorious challenge and has been identified as a critical point in therealization of a plasma-based electron-positron collider. Additionally,plasma-based positron acceleration, while preserving the requiredhigh beam quality for a collider, is challenging even conceptually anddifficult to model with currently available simulation tools.Positron acceleration in a plasma column is a promising new conceptowing to its high accelerating gradient and the ability to preservepositron beam emittance, a fundamental requirement for a collider.In this scheme, a relativistic electron beam travels along the axis of aplasma column, driving a plasma wake in the blowout regime. Dueto the finite radius of the plasma, the restoring force acting on theplasma electrons is reduced and the plasma electrons return in a long,high-density electron filament to the axis some distance behind thedriver. This electron filament generates high-gradient accelerating andfocusing fields for positrons. However, questions regarding stabilityand beam quality remain.In this thesis, positron acceleration in a plasma column is put tothe test. Beyond proof of concept, the acceleration of high-qualitypositron beams and its resilience to realistic conditions, such as misalignmentis demonstrated. Realistic plasma profiles and temperatureeffects are also considered and found to be beneficial to the scheme.The results show that positron acceleration in a plasma column isindeed a viable concept for a possible collider application, althoughadditional research is needed to optimize efficiency. Furthermore, theGPU-accelerated, quasi-static Particle-in-Cell code HiPACE++ has beendeveloped. The new code allows for modeling plasma-based positronacceleration scenarios in full 3D with previously unattainable precisionwhile drastically reducing computational costs, enabling thestudies presented. An outlook for the next possible steps towards aplasma-based collider is given