Laser-driven plasma wakefield accelerators provide accelerating electric fields orders of magnitude higher compared to conventional accelerators. Towards the generation of quasi-monoenergetic, multi-gigaelectronvolt electron beams, a precise control in the femtosecond time scale of the injection of electrons is needed. In this diploma thesis a new computational method to study external injection of electrons in laser-wakefield accelerators was derived. By loading a relativistic, charged particle bunch with arbitrary distribution in energy, space and time new ways to study the properties of wakefield accelerated electrons are possible. Furthermore, the proposed scheme was implemented together with an advanced field solver to suppress numerical Cherenkov noise in the open source Particle-in-Cell code PIConGPU as they are critical to reduce numerical uncertainties in relativistic simulations. Powered with modern compute hardware (GPUs) it is now possible to reach a new quality of predictive simulations, running repeated simulations in a few hours compared to weeks as with today's legacy codes. New parallel algorithms to study the evolution of the acceleration process have been implemented such as the in-situ calculation of a two-dimensional phase space distribution. Providing live feedback from simulations introduces a paradigm change towards interactive numerical studies and dramatically reduces the amount of data for post-processing. Finally, numerical studies have been carried out benefiting from the new methods and implementations such as an extended down-ramp triggered self-injection scenario suitable for the reproducible generation of tunable electron bunches.

Diploma thesis for the german degree "Diplom-Physiker".