Summary of Booster Dampers Systems

1. Summary of Booster Dampers Systems Dave McGinnis December 7, 2010

2. 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

3. 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

4. Special Longitudinal Dampers • Mode 1 and 2 • Driven by cavity de-tuning • Cavity bandwidth < 50kHz and revolution frequency > 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

5. 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

6. 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.