REGAE (Relativistic Electron Gun for Atomic Exploration) at DESY in Hamburg is a linear accelerator for electron diffraction experiments. It is upgraded to allow for laser driven wake field accelerator experiments. The bunch length is around 10fs and the wakefield structure is about 100fs and the synchronization of the laser and the electron bunch needs to be in order of the bunch length. To achieve this, a RFbased scheme will be used, comparing the phase of a beam induced signal with the reference clock. To improve the performance for the operation with charges well below 1pC a beam arrival time cavity (BAC) at 3.025GHz is foreseen as a highly sensitive pickup. To provide the maximum energy to the measurement electronics, the cavity needs a high R/Qvalue and an optimized coupling. An over-coupled setting might be beneficial as it provides a higher signal-to-noise ratio for the first samples. In this paper the concept of the beam arrival time cavity, the influence of the dark current on the measurement and parameter studies and optimization of the cavity itself are presented.