Experimental stabilization of transverse collective instabilities in the LHC with second order chromaticity

This paper discusses measurements on the stabilization of single bunches with second order chromaticity ($Q′′$) in the Large Hadron Collider (LHC) at CERN. $Q′′$ 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 $Q′′$ 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 $Q′′$ in a carefully prepared and well-understood accelerator environment. The agreement between measurements and pyheadtail tracking simulations shows that $Q′′$ 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.