Chromaticity Measurement based on Beam Transfer Function: Non-Linear Fits and Deep Learning

At the Large Hadron Collider (LHC), the stability of the beams is one of the most important characteristic that has to be ensured in order to not compromise the accelerator performances. The motion of high energetic particle beams in accelerators is influenced by their interactions with the accelerator environment through electromagnetic fields induced by the particle passages. Traveling with a speed close to the speed of light, the particles induce image charge and currents in the surroundings generating wakefields that act back on the beams. The chromaticity plays an important role in the developement of the beam instabilities, its control is crucial especially in view of the High-Luminosity upgrade (HL-LHC) that aims to increase the performance of the LHC, notably by doubling the beam intensity. The purpose of this project is to investigate and find the best class of algorithms that allows to extract the chromaticity from Beam Transfer Function (BTF) measurements. It is shown that neural networks outperform non-linear fitting method based on analytical expressions of the beam transfer functions. An accuracy below the unit could be achieved, even in the presence of strong wakefields.