An analytical approach to space charge distortions for time projection chambers

In a time projection chamber (TPC), the possible ion feedback and also the primary ionization of high multiplicity events result in accumulation of ionic charges inside the gas volume (space charge). This charge introduces electrical field distortions and modifies the cluster trajectory along the drift path, affecting the tracking performance of the detector. In order to calculate the track distortions due to an arbitrary space charge distribution in the TPC, novel representations of the Greenʹs function for a TPC geometry were worked out. This analytical approach finally permits accurate predictions of track distortions due to an arbitrary space charge distribution by solving the Langevin equation.