Luminosity Tuning at the Large Hadron Collider

By measuring and adjusting the β-functions at the interaction point (IP) the luminosity is being optimized. In LEP (Large Electron Positron Collider) this was done with the two closest doublet magnets. This approach is not applicable for the LHC (Large Hadron Collider) and RHIC (Relativistic Heavy Ion Collider) due to the asymmetric lattice. In addition in the LHC both beams share a common beam pipe through the inner triplet magnets (in these region changes of the magnetic field act on both beams). To control and adjust the β-functions without perturbation of other optics functions, quadrupole groups situated on both sides further away from the IP have to be used where the two beams are already separated. The quadrupoles are excited in specific linear combinations, forming the so-called "tuning knobs" for the IP β functions. For a specific correction this knob is scaled by a common multiplier. The different methods which were used to compute such knobs are discussed: (1) matching in MAD, (2) inversion and conditioning of the response matrix by singular value decomposition, and (3) conditioning the response matrix by multidimensional minimization using an adapted Moore Penrose method. For each accelerator, LHC and RHIC, a set of knobs was calculated and the performance compared. In addition the knobs for RHIC were successfully applied to accelerator. Simultaneously this approach allows us theoretically to measure the beam sizes of both colliding beams at the IP, based on the tuneability provided by the knobs. This possibility was investigated. The standard method for LEP to measure the IP β-functions was adapted and advanced to the asymmetric LHC lattice. First of all I would like to thank my wife Eva and two sons, Maxi and Martin, for their love, support and understating during these years of my thesis. The confidence and patience they spent me to face the sometimes difficult time. I would like to thank my university supervisor Univ. Prof. Dr. Bernhard Schnizer of the Institute fuer Theoretische Physik, TU-Graz, who encouraged me, despite of all circumstances, to start and carry out this thesis, for his help and faith. My CERN supervisor Dr. Frank Zimmermann, of the AB Department, Accelerator and Beam Physics group, for his guidance of this thesis, and the confidence in me and my ideas. With their assistance, patience and many fruitful discussions they made this time a great experience. I would also like to thank other members, especially Andre Verdier and Daniel Schulte, who always had time to discuss sometimes crazy ideas. This work would not have been possible without the help of the many members of this group. CERN CERN, from the French "Conseil Europèen pour la Recherche Nuclaire" is one of the world's largest scientific research facilities. It is located at the border between France and Switzerland close to the city of Geneva. In English referred to as the European Organization for Nuclear Research, it was founded in 1953. The motivation for establishing this laboratory was to drive the nuclear research to smaller dimensions to win a deeper insight into matter. Starting with the Proton Synchrotron (PS) Complex, demands to increase the energy of the accelerated particle led to expansion of the facility. Figure 1.1 shows a sketch of the now existing or currently being constructed accelerators. The machine built after the PS is the SPS (Super Proton Synchrotron). It provided the energy to discover the weak force particles W + , W − , Z 0 earning Carlo Rubbia and Simon Van de Meer the Nobel prize 1984 for their discovery. To push the frontier of energy higher and to obtain more precise data the particle accelerator LEP (Large Electron Positron collider) was built. LHC To step one step higher on the energy ladder, currently the LHC (Large Hadron Collider) is constructed. Using two proton beams, it will provide a top center of mass energy of 2 × 7 TeV (Tera electron Volts = 10 12 eV) to the high energy physics community. It is currently being installed in the tunnel that earlier hosted the LEP collider. This tunnel and the adaptations are depicted in Fig.1.2. Contrary to LEP the LHC is based on superconducting magnets which are needed to provide the field strengths for guiding and focusing a beam at this energy level. The LHC will collide the two beams in four interaction points (IPs) which host four different experiments with their detectors (ATLAS, CMS, ALICE, LHC-B), and a fifth experiment (TOTEM) installed close to LHC-B. Figure 1.3: Acceleration chain of the installation located at Brookhaven National Laboratory. The Relativistic Heavy Ion Collider is the final stage of this chain. In RHIC gold ions and spin polarized protons are brought into collision.