The LHC is currently operating with a proton energy of 4 TeV and à functions at the ATLAS and CMS interaction points of 0.6 m. This is close to the design value at 7 TeV (à ¼ 0:55 m) and represented a challenge for various aspects of the machine operation. In particular, a huge effort was put into the optics commissioning and an unprecedented peak beating of around 7% was achieved in a high energy hadron collider.

Since 2015 the LHC has been operating at 6.5 TeV. In 2016 the β-functions at the interaction points of ATLAS and CMS were squeezed to 0.4 m. This is below the design β Ã ¼ 0.55 m at 7 TeV, and has been instrumental to surpass the design luminosity of 10 34 cm −2 s −1. Achieving a lower than nominal β Ã has been possible thanks to the extraordinary performance of the LHC, in which the control of the optics has played a fundamental role. Even though the β-beating for the virgin machine was above 100%, corrections reduced the rms β-beating below 1% at the two main experiments and below 2% rms around the ring. This guarantees a safe operation as well as providing equal amount of luminosity for the two experiments. In this article we describe the recent improvements to the measurement, correction algorithms and technical equipment which allowed this unprecedented control of the optics for a high-energy hadron collider.

Recently, resonance driving terms were successfully measured in the CERN SPS and the BNL RHIC from the Fourier spectrum of beam position monitor (BPM) data. Based on these measurements a new analysis has been derived to extract truly local observables from BPM data. These local observables are called local resonance terms since they share some similarities with the global resonance terms. In this paper we derive these local terms analytically and present experimental measurements of sextupolar global and local resonance terms in RHIC. Nondestructive measurements of these terms using ac dipoles are also presented.

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A novel scheme for the focusing of high-energy leptons in future linear colliders was proposed in 2001 [P. Raimondi and A. Seryi, Phys. Rev. Lett. 86, 3779 (2001)]. This scheme has many advantageous properties over previously studied focusing schemes, including being significantly shorter for a given energy and having a significantly better energy bandwidth. Experimental results from the ATF2 accelerator at KEK are presented that validate the operating principle of such a scheme by demonstrating the demagnification of a 1.3 GeV electron beam down to below 65 nm in height using an energy-scaled version of the compact focusing optics designed for the ILC collider.