Expected and measured behaviour of the tune in the LHC operation at 3.5 TeV

The tune of the Large Hadron Collider (LHC) mainly depends on the strength of the quadrupole magnets. It is also affected by the b2 component in the main dipoles. In case of systematic misalignments, the b3 component due to the main dipoles and the sextupolar correctors also affect the tune due to the feed down effect. The magnetic model of the machine, based on a fit of magnetic measurements, has an intrinsic precision which can be estimated in a few units (one part over 10000). During the first years of operation of the LHC, the tune has been routinely measured and corrected through a feedback system. In this paper, we reconstruct from the beam measurements and the settings of the feedback loop, the evolution of the tune during injection and ramp. This gives the obtained precision of the magnetic model of the machine with respect to quadrupolar and sextupolar components. At the injection plateau there is an unexpected large decay whose origin is not understood: we present the data, with the time constants and the dependence on the previous cycles. Dedicated experiments aimed at excluding that this decay comes from a decay of the main dipole component were done. During the ramp the tune drifts by about 0.05: this precision is related to the precision in tracking the quadrupolar field in the machine.