Large Hadron Collider momentum calibration and accuracy

As a result of the excellent quality of the Large Hadron Collider (LHC) experimental detectors and the accurate calibration of the luminosity at the LHC, uncertainties on the LHC beam energy may contribute significantly to the measurement errors on certain observables unless the relative uncertainty is well below 1%. Direct measurements of the beam energy using the revolution frequency difference of proton and lead beams combined with the magnetic model errors are used to provide the energy uncertainty of the LHC beams. Above injection energy the relative uncertainty on the beam energy is determined to be $\pm 0.1\%$. The energy values as reconstructed and distributed online to the LHC experiments do not require any correction above injection energy. At injection a correction of $+0.31\mathrm{GeV}/\mathrm{c}$ must be applied to the online energy values.

Figure 1

LHC dipole cross-section (top) and detail of one quarter of the coil (bottom).

Figure 2

A magnet given by a Helmholtz like coil (top) and a sector coil (bottom).

Figure 3

Comparison between integrated dipole fields measured with single stretched wire and with a rotating coil for 11 LHC dipoles (courtesy of L. Bottura and M. Buzio). The dashed lines correspond to deviations of $\pm 0.1\%$.

Figure 4

Transfer function of the LHC main dipole magnets as a function of the circuit current.

Figure 5

Evolution of the bare machine tunes (before any correction) along the cycle from injection to $6.5\mathrm{TeV}/\mathrm{c}$ at constant optics.

Figure 6

Predicted (blue line) and observed (red point) tidal energy variations of the LHC ring in November 2016 during long consecutive fills at $4\mathrm{TeV}/\mathrm{c}$ spanning almost an entire week. The outliers that can be observed around midday November 13th are radial oscillations of the ring induced by the surface waves from a magnitude 7.8 Earthquake in New-Zealand.

Figure 7

rf frequency changes required to center the beam in the BPMs at $4\mathrm{TeV}/\mathrm{c}$ along the 2012 LHC run. The full range corresponds to a circumference change of 2 mm.

Figure 8

Expected central rf frequency difference between proton and ${\mathrm{Pb}}^{82+}$ beams as a function of the beam momentum at the LHC.

Figure 9

Evolution of the proton and lead ion rf frequencies during an energy ramp to $4\mathrm{TeV}/\mathrm{c}$. The frequencies are locked together at $4\mathrm{TeV}/\mathrm{c}$ (around time 960).

Figure 10

Beam position change for the protons in ring 1 (top) and lead ions in ring 2 (bottom) between start and end of the rf manipulations at $4\mathrm{TeV}/\mathrm{c}$. For both plots the horizontal axis represents the BPM index, while the vertical axis is the horizontal (radial) beam position measured at each BPM in mm. The position shift is modulated by the horizontal dispersion $D_{x,i}$ at each BPM.

Figure 11

Principle of the cancellation of systematic errors on the radial position by inversion of the protons and lead ions in the two rings.

Figure 12

Time dependence of the frequency difference $\mathrm{\Delta }{f}_{\text{rf}}$ of protons and lead ions at $4\mathrm{TeV}/\mathrm{c}$ as a function of the LHC fill number in 2013. For the figure on the left, the frequency is reconstructed after the rf cogging (method B), for the figure on the right before rf cogging (method A). The red dotted line is the frequency difference corresponding to an energy of $4\mathrm{TeV}/\mathrm{c}$.

Figure 13

Time dependence of the frequency difference $\mathrm{\Delta }{f}_{\text{rf}}$ of protons and lead ions at $6.5\mathrm{TeV}/\mathrm{c}$ as a function of the LHC fill number in 2016. For the figure on the left, the frequency is reconstructed after the rf cogging (method B), for the figure on the right before rf cogging (method A). The red dotted line is the frequency difference corresponding to an energy of $6.5\mathrm{TeV}/\mathrm{c}$.

Figure 14

Time dependence of the frequency difference $\mathrm{\Delta }{f}_{\text{rf}}$ of protons and lead ions as a function of the LHC fill number in 2013 (left) and 2016 (right). The red dotted line is the frequency difference corresponding to an energy of $450.0\mathrm{GeV}/\mathrm{c}$.