Loss of Transverse Landau Damping by Diffusion in High-Energy Hadron Colliders

Circular hadron colliders rely on Landau damping to stabilize the beams. Landau damping depends strongly on the bunch distribution, which is often assumed to be Gaussian in the transverse planes. In this paper, we introduce and explain an instability mechanism observed in the LHC, where Landau damping is eventually lost due to a diffusion that modifies the transverse bunch distribution. The mechanism is caused by a wide-spectrum noise that excites the transverse motion of the beam, which consequently produces wakefields that drive a narrow-spectrum diffusion. It is shown that this diffusion efficiently lowers the stability diagram at the frequency of the least stable coherent mode, leading to a loss of Landau damping after a latency. A semi-analytical model agrees with measurements in dedicated latency experiments performed in the LHC. This instability mechanism explains the need for a stability margin in octupole current in the LHC, relative to the amount needed to stabilize a Gaussian beam. We detail the impact of this mechanism and possible mitigations for the LHC and HL-LHC.