TPC track distortions III: fiat lux

We present a comprehensive overview and final summary of all four types of static track distortions seen in the HARP TPC, in terms of physical origins, mathematical modelling, and correction algorithms. 'Static'™ distortions are defined as not depending on the event time within the 400 ms long accelerator spill. Calculated static distortions are compared with measurements from cosmic-muon tracks. We characterize track distortions by the r phi residuals of cluster positions with respect to the transverse projection of a helical trajectory constrained by hits in the RPC overlap regions. This method provides a fixed TPC-external reference system (by contrast to the co-moving coordinate system associated with a fit) which solely permits to identify individually, and measure quantitatively, the static TPC track distortions arising from (i) the inhomogeneity of the solenoidal magnetic field, (ii) the inhomogeneity of the electric field from the high-voltage mismatch between the inner and outer TPC field cages, (iii) the anode-wire durchgriff, and (iv) a homogenous ion-charge density in the drift volume. Five voltage levels are identified which were set incorrectly during data taking with the HARP TPC, and unfortunately conspired toward large static and dynamic track distortions. The observed time development of static distortions after a 83mKr calibration lends decisive support to our conclusions on static TPC distortions.