Speaker
Description
Small momentum offsets in the LHC can generate significant optics distortions, particularly at low $\beta$*. The beam energy carries a relative uncertainty of approximately $10^{-3}$, which is insufficient for precise optics control. To better understand the impact of energy on the optics, two beam-based techniques have been explored. The first applies a global linear response matrix between BPM phase advances and $\Delta p/p$; while effective in simulation, this method is sensitive and does not reproduce the response observed in the machine. We introduce a new approach based on the principle of Deep Lie Map Networks (DLMN), which fits turn-by-turn BPM trajectories to a differentiable tracking model. Using the single-pass forward differentiation capability of MAD-NG, derivatives of the orbit with respect to $\Delta p/p$ are computed directly within the symplectic tracking engine. The results reveal arc-by-arc variations consistent with dipole-induced orbit distortions, providing insight into orbit behaviour around the ring. The measured response also agrees with that observed in the machine, demonstrating that the DLMN offers a promising new method for analysing the effect of energy on the optics of the LHC.
Funding Agency
CERN
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