Abstract: In the ionisation of Rydberg hydrogen atoms near a metal surface, the electron will escape from the nucleus and arrive at the detector in a time sequence. This probability flux train relies on the initial electron wave packet irradiated by the laser pulse. For simplicity, the laser pulse is usually simplified to a delta function in energy domain, resulting in a sharp initial arrival time with an exponentially decaying tail at the detector. Actually and semiclassically, the initial outgoing wave should be modeled as an ensemble of trajectories propagating away from the atomic core in all directions with a range of launch times and a range of energies. In this case, each pulse in the pulse train is averaged out rather than a sharp profile. We examine how energy and time averaging of the electron wave packet affects the resolution of escaping electron pulses and study the energy dependence of the arrival time for each pulse in the ionisation train. An optimization condition for the laser pulse shape to generate narrow ionisation electron pulse in the train is obtained. The ionisation rates with various excitation energy are calculated also, which show the excitation to higher N Rydberg states will narrow the electron pulse as well.

Key words: Rydberg hydrogen, ionisation, trajectory