The interaction of ions with solids is of considerable interest for many fields in industry, medicine and science. However, the underlying relaxation dynamics of the solid atoms due to the ion-solid interaction is not fully understood. A direct experimental access to the underlying dynamics via conventional pump-probe techniques appears in principle feasible. Most of the currently used pump-probe experiments utilize an ultrashort laser pulse for the excitation (pump), which is combined with a time-delayed laser-based analysis (probe). In order to provide the time resolved observation of the relaxation dynamics using established ultrafast pump-probe techniques, it is necessary to pinpoint the projectile impact with sufficient, i. e. with a time resolution of a picosecond or below. However, the generation of these ion(s) was long deemed impossible. The possibility to generate (sub)-picosecond ionpulses with energies in the keV-range is explored in this thesis by numerical simulations. Simultaneously the working group of Prof. Wucher is working on the experimental realization of such an ion source. The concept provides femtosecond ionization of rare gas atoms entrained in a supersonic jet. Jet and laser beam intersect each other at orthogonal angles, the resulting photoions are accelerated in the direction perpendicular to both beams and the photoions impinge in a temporally compressed manner onto the target electrode. The bunching configuration consists of three electrodes at different potentials, which are tuned to provide first order flight time focusing conditions at the position of the target electrode. The exact setup of the ultrashort pulse source heavily relies on the ability to predict the resulting ion pulse shape by numerical simulations. This way, for an operating ion source producing (sub)-ps ion pulses, the exact influence of various experimental parameter on the ion flight time –distribution can be studied. Due to the complexity of the underlying equations, a realistic study of this influence on the ions is not possible with analytical techniques. Within our concept, the expected challenges in the experimental realization will be the initial velocity distribution of the generated ions, which is therefore crucial to understand. The ion trajectories were calculated in electric fields modelling the experimental buncher setup. The spatial distribution of the ions, resulting from the photoionization process, was calculated using standard-photoionization theory. The ion velocity distribution was modelled by making use of experimental as well as theoretical data. Numerical simulations were performed ensuring the necessary accuracy in the calculations of both the electric fields as well as the integration of the iontrajectories in these fields. From the simulations presented in this thesis one can conclude that the generation of (sub)-picosecond ion pulses with energies in the keV range is possible. Ion pulses with less than 1 ion are mainly limited in their temporal resolution due to their velocity distribution. Additionally ion pulses with more than 1 ion experience a flighttime dispersion, due to their coulomb-interaction, so called space charge. A central finding of this thesis is that space charge effects can be reduced by adjusting the electric fields in the buncher