Trajectory measurements and correlations in the final focus beam line at the KEK Accelerator Test Facility

The Accelerator Test Facility 2 (ATF2) commissioning group aims to demonstrate the feasibility of the beam delivery system of the next linear colliders (ILC and CLIC) as well as to define and to test the tuning methods. As the design vertical beam sizes of the linear colliders are about few nanometers, the stability of the trajectory as well as the control of the aberrations are very critical. ATF2 commissioning started in December 2008, and thanks to submicron resolution beam position monitors (BPMs), it has been possible to measure the beam position fluctuation along the final focus of ATF2 during the 2009 runs. The optics was not the nominal one yet, with a lower focusing to make the tuning easier. In this paper, a method to measure the noise of each BPM every pulse, in a model-independent way, will be presented. A method to reconstruct the trajectory's fluctuations is developed which uses the previously determined BPM resolution. As this reconstruction provides a measurement of the beam energy fluctuations, it was also possible to measure the horizontal and vertical dispersion function at each BPMs parasitically. The spatial and angular dispersions can be fitted from these measurements with uncertainties comparable with usual measurements.