Analysis of a method to measure the dodecapole component of the LHC triplet magnets with a wobbling closed bump

Due to finite manufacturing tolerances the triplet quadrupoles used in the interaction regions of LHC will have non-vanishing multipole errors which need to be measured and corrected in order to guarantee sufficient dynamic aperture at collision energy. Here we discuss a method to measure the unwanted multipole components by oscillating a closed orbit bump in the interaction region and observing the orbit at pickups outside the bump. The beam's response will contain very weak signals at harmonic frequencies of the sinusoidal excitation. Even though the amplitude of the harmonic signal will be below the resolution of the position monitor system, it can be made visible by adding noise to the original pickup data and subsequent careful filtering and averaging. We use a simple computer model to simulate the oscillating bump that generates pickup signals and then analyze those in a sophisticated signal processing chain in order to retrieve the magnitude of the unwanted multipole components.