Summary of Booster Dampers Systems Dave McGinnis December 7, 2010

Longitudinal Dampers Booster Cavities are transmission line structures. Higher order transmission line modes ~80 MHz Passive mode dampers connected to coupling flaps d-Q the modes

Longitudinal Dampers Active mode dampers are built for the following modes – 47, 48,49,50,51,52 Dampers are narrow band – Advantage: Narrow band can provide higher gain and better common mode rejection than wide band dampers Narrowband dampers are easier to phase for systems with large frequency swings – Disadvantage: Many channels for narrowband compared to one channel for wideband Narrow-band Dampers are IQ-filter channels – Initial in-phase mix at h=84 (~53MHz) to baseband – I-Q mix at mode 32, 33,34,35,36 (~22 MHz) – Phase to Energy derivate taken by a narrowband filtering with 2.5 kHz 2 pole filter 2.5 kHz ~ synchrotron frequency after transition Can be used after transition only – I-Q up-convert – In phase up-convert at 53 MHz – Kick applied with special 80 MHz longitudinal cavity with Q=10

Special Longitudinal Dampers Mode 1 and 2 – Driven by cavity de-tuning – Cavity bandwidth 600kHz – Narrowband filtering with 2.5 kHz 2 pole filter 2.5 kHz ~ synchrotron frequency after transition Can be used after transition only – I-Q systems with kick applied directly to cavity fan-out Longitudinal quadrupole damper – Large bunch-bucket shape mismatch at transition occurs because of large synchronous phase angle (> 40 degrees) – Causes large bunch length oscillation – bunch length detected from a peak detector – Derivative take with a 5kHz tunable filter – Correction signal applied to the cavity amplitude program AC radial position damper – Low level system does phase lock to Main injector with a divide-by-32 system. – The divide-by-32 system causes a mode 0 dipole oscillation – The signal is detected off the radial position detector and the derivative is take with an AC coupled high-pass filter. The correction is applied to the output phase-shifter drive. – This system will no longer be needed once the divide-by-32 phase lock is replaced

Transverse Dampers Large swing in chromaticity required at transition to combat effects of resistive wall Many versions of transverse dampers have been tried over the years. The sweeping frequency makes a broadband damper difficult – Small machine with sizeable cable delays – Frequency sweep peaks at 3 GHz /sec New transverse broadband damper system now under commissioning

New Broadband Transverse Damper System Similar to the Main Injector Damper systems Uses 1 meter long pickup and kickers Low pass the beam signal to remove the signal above 70MHz Digitize only the difference signal (no normalization) Digitize at 4x the bunch frequency (212 MHz) 3 turn FIR digital notch filter used to remove common mode and provide correct phase advance Open loop measurements are very difficult to perform but tests suggest an open loop gain of ~0dB Phasing done by dead reckoning using the Booster notch Damper used mostly after transition Coupling and large tune changes make damper phasing difficult Special vector signal analyzer software in progress to help with phasing.