In the past, transverse coherent instabilities have been observed at the Hadron-Electron Ring Accelerator (HERA) proton ring that were instigated by the presence of linear coupling. Linear coupling can also potentially explain some transverse instabilities that were observed in the Large Hadron Collider (LHC) in both run I and run II, however a detailed description of the destabilizing mechanism of linear coupling was not known at the time. A study into the effect of linear coupling on transverse beam stability was carried out, and a new mechanism that could incite transverse instabilities by causing a loss of Landau damping has been found. The study includes time domain simulations with PYHEADTAIL and frequency domain computations based on analytical approaches, and was then verified by measurements with a single proton bunch in the LHC.

This paper discusses measurements on the stabilization of single bunches with second order chromaticity (Q 00) in the Large Hadron Collider (LHC) at CERN. Q 00 introduces an incoherent betatron tune spread which can produce Landau damping of transverse instabilities. Although the resulting stabilizing effect is similar to that provided by Landau octupoles, the underlying beam dynamics are different. Since the tune spread from Q 00 is based on the longitudinal rather than the transverse action of the particles, it will not be affected by the smaller transverse emittance beams of future machines, such as the High Luminosity LHC or the Future Circular Collider, and may hence provide more efficient Landau damping than magnetic octupoles. This study serves as a proof-of-principle experiment to demonstrate Landau damping from detuning with longitudinal action by means of Q 00 in a carefully prepared and well-understood accelerator environment. The agreement between measurements and PyHEADTAIL tracking simulations shows that Q 00 indeed contributes to the beam stability, that the numerical model of the LHC is accurate, and that the involved beam dynamics mechanisms are understood from both the single-and multiparticle effects points of view. The results also serve as a first experimental validation of the recently proposed radio frequency quadrupole for Landau damping.

The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up a new energy frontier for exploration in 2010, it has gathered a global user community working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will undergo a major upgrade in the 2020s. This will increase its rate of collisions by a factor of five beyond the original design value and the integrated luminosity by a factor ten. The new configuration, known as High Luminosity LHC (HL-LHC), will rely on a number of key innovations that push accelerator technology beyond its present limits. Among these are cutting-edge 11 − 12 T superconducting magnets, including Nb 3 Sn-based magnets never used in accelerators before, compact superconducting cavities for longitudinal beam rotation, new technology and physical processes for beam collimation. The dynamics of the HL-LHC beams will be also particularly challenging and this aspect is the main focus of this paper.

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