On distortions of TPC coordinates: inhomogeneities of electric and magnetic field

After a general discussion of electron drift in a gas volume with electric and magnetic fields, distortions in the r and r phi coordinates arising from inhomogeneities of the electric and magnetic fields in the HARP TPC are calculated. Inhomogeneities of the electric field arise from i) positive ions released by cosmic rays, ii) positive ions released by interaction secondaries, iii) positive ions released by beam muons, iv) positive ions released from beam particles downstream of the inner field cage, and v) a high voltage misalignment between the outer and inner field cages. Also, distortions arising from the inhomogeneity of the magnetic field are calculated. These effects resolve the controversy on unphysical numbers of 'wrong-charge' TPC tracks. The bad news are that effects are too big to be neglected. The good news are that, with enough sweat and tears, they can be adequately corrected.