Software alignment of the LHCb inner tracker sensors [Elektronische Ressource] / put forward by Florin Maciuc

Dissertationsubmitted to theCombined Faculties for the Natural Sciences and for Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural SciencesPut forward byDiplom-Physiker Florin MACIUCBorn in: Craiova, RomaniaOral examination: 20.04.2009Software Alignmentof the LHCb Inner Tracker SensorsReferees: Prof. Dr. Werner HofmannProf. Dr. Stephanie Hansmann-MenzemerThis thesis is dedicated to my wonderful parents and my entire family.Abstract2This work uses the Millepede linear alignment method, which is essentially a minimization algo-rithm, to determine simultaneously between 76 and 476 alignment parameters and several million trackparameters. For the case of non-linear alignment models, Millepede is embedded in a Newton-Raphsoniterative procedure. If needed a more robust approach is provided by adding quasi-Newton steps which2minimize the approximate model function. The alignment apparatus is applied to locally align theLHCb’s Inner Tracker sensors in an a priori xed system of coordinate. An analytic measurement modelwas derived as function of track parameters and alignment parameters, for the two cases: null and non-null magnetic eld. The alignment problem is equivalent to solving a linear system of equations, andusually a matrix inversion is required. In general, as consequence of global degrees of freedom or poorlyconstrained modes, the alignment matrix is singular or near-singular.