Simulation and Calibration of the ALICE TPC including innovative Space Charge Calculations

ALICE is one of the four main particle detectors located around the LHC accelerator at CERN. It is particularly designed to study the physics of the quark-gluon plasma by means of nucleus--nucleus collisions at center-of-mass energies up to 5.5 TeV per nucleon pair. A Time-Projection Chamber (TPC) was chosen to be its central-sub-detector due to its low mass properties and its capabilities to provide a robust and accurate Particle Identification even within ultra-high multiplicity environments (up to 8000 tracks per unit of eta). To achieve the required physics performance, the space point resolution of the TPC must be in the order of 0.2 mm. Due to its gigantic size of 5~m in diameter and 5~m in length, corrections for static as well as dynamic effects are indispensable in order to accomplish the design goal. The research presented covers all major issues relevant for the final calibration and therefore the enhancement of the TPC performance in terms of resolution. The main focus was to distinguish between the different effects which disturb the electron trajectory within the drift volume by means of quantifying the magnitude of their influences. The effects were parametrized in terms of physical parameters, as opposed to a multivariate fit, in order to minimize the residuals of the cluster positions. The different chapters of the present research work cover static imperfections, like magnetic and electric field inhom ogeneities due to mechanical imperfections, as well as dynamic variations of the drift properties due to pressure, temperature and gas composition variations which manifest themselves as gas density fluctuations. Furthermore, additional challenges were treated which will occur in future high multiplicity nucleus-nucleus collisions. These are the improvement of the two-track resolution as well as the quantification of additional dynamic field deviations due to space charges. Various simulation techniques were used to qualify and quantify the field imperfections due to mechanical deficiencies. Besides the localization and calibration of the field imperfections, the simulations led to optimized voltage settings which minimize the residuals. The different drift velocity v_d dependencies were parametrized to allow a quick estimation of the dynamic $v_d$ variations as a function of the measured ambient conditions. Besides that, the programmable signal shaping algorithm within the Front-End electronics was revised. This is expected to improve the two-track resolution in high multiplicity events. Moreover, novel analytical solutions were derived to allow a fast and precise prediction of additional dynamic field deviations due to ionic-charge pile up within the TPC gas volume. This analytic approach finally permits accurate simulations of additional systematic shifts along the electron trajectory due to any three dimensional space c harge distribution within the TPC. This innovative method is an essential part of the calibration algorithms which are being developed for the future Pb-Pb collisions at LHC.