  Nowadays the development of novel particle accelerators is a hot topic for
both experimental and theoretical sciences. In the CERN-AWAKE experiment
electrons are accelerated in a cold rubidium plasma, generated by a short,
intense laser pulse. We describe the corresponding photoionisation process with
ab initio quantum mechanical calculations. In this paper we primarily
investigate how the frequency chirping of the applied laser pulse influences
the photoionisation. Secondarily we also study how the results of the numerical
simulations depend on the shape of the envelope of the laser pulse. Based on
our results, we give a recommendation to fine-tune the physical parameters of
the applied laser pulse in order to improve the homogeneity of the rubidium
plasma.
