A Novel Method and Error Analysis for Beam Optics Measurements and Corrections at the Large Hadron Collider

The Large Hadron Collider (LHC) is currently the world's largest particle accelerator with the highest center of mass energy in particle collision experiments. The control of the particle beam focusing is essential for the performance reach of such an accelerator. For the characterization of the focusing properties at the LHC, turn-by-turn beam position data is simultaneously recorded at numerous measurement devices (BPMs) along the accelerator, while an oscillation is excited on the beam. A novel analysis method for these measurements ($N$-BPM method) is developed here, which is based on a detailed analysis of systematic and statistical error sources and their correlations. It has been applied during the commissioning of the LHC for operation at an unprecedented energy of 6.5 TeV. In this process a stronger focusing than its design specifications has been achieved. This results in smaller transverse beam sizes at the collision points and allows for a higher rate of particle collisions. For the derivation of the focusing parameters at many synchrotron light sources, the change of the beam orbit is observed, which is induced by deliberate changes of magnetic fields (orbit response matrix). In contrast, the analysis of turn-by-turn beam position measurements is for many of these machines less precise due to the distance between two BPMs. The $N$-BPM method overcomes this limitation by allowing to include the measurement data from more BPMs in the analysis. It has been applied at the ALBA synchrotron light source and compared to the orbit response method. The significantly faster measurement with the $N$-BPM method is a considerable advantage in this case. Finally, an outlook is given to the challenges which lie ahead for the control of the beam focusing at the HL-LHC, which is a future major upgrade of the LHC.