Abstract
The horizontal and vertical betatron tunes of the Large Hadron Collider (LHC) mainly depend on the strength of the quadrupole magnets, but are also affected by the quadrupole component in the main dipoles. In case of systematic misalignments, the sextupole component from the main dipoles and sextupole corrector magnets also affect the tunes due to the feed down effect. During the first years of operation of the LHC, the tunes have been routinely measured and corrected through either a feedback or a feed forward system. In this paper, the evolution of the tunes during injection, ramp and flat top are reconstructed from the beam measurements and the settings of the tune feedback loop and of the feed forward corrections. This gives the obtained precision of the magnetic model of the machine with respect to quadrupole and sextupole components. Measurements at the injection plateau show an unexpected large decay whose origin is not understood. This data is discussed together with the time constants and the dependence on previous cycles. We present results of dedicated experiments that show that this effect does not originate from the decay of the main dipole component. During the ramp, the tunes drift by about 0.022. It is shown that this is related to the precision of tracking the quadrupole field in the machine and this effect is reduced to about 0.01 tune units during flat top.
Highlights
In a circular particle accelerator, particles oscillate around the nominal orbit due to the field of quadrupole magnets
The analysis of tune measurements collected during the two years of Run I of the Large Hadron Collider (LHC) have been presented and discussed in detail
Analysis of beam optics simulations together with beam-based measurements showed that the quadrupole strength should be the source of this decay
Summary
In a circular particle accelerator, particles oscillate around the nominal orbit due to the field of quadrupole magnets. The number of transverse oscillations of a particle in one revolution around the ring is defined as the betatron tune. In most colliders and storage rings this quantity has to be controlled within 10À3 tune units to avoid inducing beam losses due to resonances. In the LHC, this is achieved by measuring the tunes and correcting them through a feedback system that controls the tuning quadrupole families [1]. To estimate the precision of the Field Model of the LHC (FiDeL) [2,3,4], to assess whether improvements are possible or needed, and possibly to reduce the load on the feedback system by evaluating feed forward corrections
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