Local correction of quadrupole errors at LHC interaction regions using action and phase jump analysis on turn-by-turn beam position data

This article shows that the effect of all quadrupole errors present in an interaction region with low β* can be modeled by an equivalent magnetic kick, which can be estimated from action and phase jumps found on beam position data. This equivalent kick is used to find the strengths that certain normal and skew quadrupoles located on the IR must have to make an effective correction in that region. Additionally, averaging techniques to reduce noise on beam position data, which allows precise estimates of equivalent kicks, are presented and mathematically justified. The complete procedure is tested with simulated data obtained from madx and 2015-LHC experimental data. The analyses performed in the experimental data indicate that the strengths of the IR skew quadrupole correctors and normal quadrupole correctors can be estimated within a 10% uncertainty. Finally, the effect of IR corrections in the β* is studied, and a correction scheme that returns this parameter to its designed value is proposed.