Impedance reduction of the High-frequency Cavities in the CERN PS by Multi-harmonic Feedback

In the framework of the "LHC Injectors Upgrade" (LIU) project, the CERN Proton Synchrotron (PS) is being prepared as a pre-injector for the Large Hadron Collider at high luminosity (HL-LHC). RF systems at 20 MHz, 40 MHz and 80 MHz are required for longitudinal beam manipulations to provide 25 ns bunch spacing and short bunches at transfer to the Super Proton Synchrotron (SPS). Beam induced voltage in these cavities causes transient beam-loading and uncontrolled longitudinal emittance blow-up. To reduce the impedance beyond the reach of the wide-band feedback around the power amplifier, a new multi-harmonic feedback has been developed and commissioned. Based on narrow-band filters treating each revolution frequency harmonic separately, the feedback phase at these harmonics can be dynamically adapted during acceleration, taking into account the phase of the cavity transfer function. The beneficial effect on longitudinal beam quality of LHC-type beams is shown.