Advanced Landau damping with radio-frequency quadrupoles or nonlinear chromaticity

Landau damping is a powerful mechanism to suppress impedance-driven coherent instabilities in circular accelerators. In the transverse planes it is usually introduced by means of magnetic octupoles. We will discuss a method to generate the required incoherent betatron frequency spread through detuning with the longitudinal rather than the transverse amplitudes. The approach is motivated mainly by the high-brightness, low transverse emittance beams in future colliders where detuning with the transverse amplitudes from magnetic octupoles becomes significantly less effective. Two equivalent methods are under study: a radio-frequency quadrupole cavity and the nonlinear chromaticity. The underlying beam dynamics mechanisms are explained based on a recently extended Vlasov theory and relevant results are discussed for dierent longitudinal beam distributions under specific approximations. Finally, the analytical studies are benchmarked against numerical simulations employing a circulant matrix and a macroparticle tracking model.