Experiments and Theory on Beam Stabilization with Second-Order Chromaticity

This study reports on an alternative method to generate transverse Landau damping to suppress coherent instabilities in circular accelerators. The incoherent betatron tune spread can be produced through detuning with longitudinal rather than transverse action. This approach is motivated by the high-brightness, low transverse emittance beams in future colliders where detuning with transverse amplitude will be less effective. Detuning with longitudinal action can be introduced with a radio frequency (rf) quadrupole, or similarly, using second-order chromaticity. The latter was enhanced in the Large Hadron Collider (LHC) at CERN and experimental results on single-bunch stabilization are briefly recapped. The observations are interpreted analytically by extending the Vlasov formalism to include nonlinear chromaticity. Finally, the newly developed theory is benchmarked against circulant matrix and particle tracking models.