Radio Frequency Quadrupole for Landau Damping in Accelerators: Analytical and numerical studies

It is proposed to use a radio frequency quadrupole (RFQ) to introduce a longitudinal spread of the betatron frequency for Landau damping of transverse beam instabilities in circular accelerators. The existing theory of stability diagrams for Landau damping is applied to the case of an RFQ. As an example, the required quadrupolar strength is calculated for stabilizing the Large Hadron Collider (LHC) beams at 7 TeV. It is shown that this strength can be provided by a superconducting RF device which is only a few meters long. Furthermore, the stabilizing effect of such a device is proven numerically by means of the PyHEADTAIL macroparticle tracking code for the case of a slow head-tail instability observed in the LHC at 3.5 TeV.