• A. Noda, M. Nakao, H. Souda, H. Tongu
  Kyoto University/ICR, Kyoto
• A.V. Smirnov
  JINR, Dubna
• T. Shirai
  NIRS, Chiba-shi
• K. Jimbo
  Kyoto University/IAE, Kyoto
• M. Grieser
  MPI-K, Heidelberg

Funding: The present work was supported by Advanced Compact Accelerator Development program by MEXT of Japanese Government. Support from Global COE, The Next Generation of Physics, is also greatly appreciated.

Laser cooling for bunched Mg ion beam with the kinetic energy of 40 keV has been applied with S-LSR at ICR, Kyoto University. Up to now, clear peaking of equilibrium momentum spread after laser cooling has been observed at such a synchrotron tune as resonates with the horizontal betatron tune, which is considered to be due to heat transfer from the horizontal degree of freedom to the longitudinal one. In order to demonstrate transverse cooling by observation of reduction of the horizontal beam size, spontaneous emission from laser induced excited state of the Mg ion, has been observed with the use of CCD camera. Some reduction of horizontal beam size has been observed with a certain synchrotron tune, a little bit smaller compared with the fractional part of the horizontal tune.

• V. Zhabitsky
  JINR, Dubna

The stability of an ion beam in synchrotrons with digital filters in the feedback loop of a transverse damper is treated. Solving the characteristic equation allows to calculate the achievable damping rates as a function of instability growth rate, feedback gain and parameters of the signal processing. A transverse feedback system (TFS) is required in synchrotrons to stabilize the high intensity ion beams against transverse instabilities and to damp the beam injection errors. The TFS damper kicker (DK) corrects the transverse momentum of a bunch in proportion to its displacement from the closed orbit at the location of the beam position monitor (BPM). The digital signal processing unit in the feedback loop between BPM and DK ensures a condition to achieve optimal damping. Transverse Feedback Systems commonly use digital FIR (finite impulse response) and IIR (infinite impulse response) filters for the signal processing. A notch filter is required to remove the closed orbit content of the signal and correct for the imperfect electric centre of the BPM. Further processing is required to adjust for the betatron phase advance between the beam pick-up (BPM) and the damper kicker (DK). Damping rates of the feedback systems with digital notch, Hilbert and all-pass filters are analysed in comparison with those in an ideal feedback system.