Study of Fast Ions in CESR M. Billing & G. Codner April 26, 2007 Study of Fast Ions in CESR

Motivation: Fast Ion Instability? - 45 bunch train - Electrons - 14ns spacing - 1.2e10/bunch Qh 0.6 kHz full scale Instability? Linear theory predicts 100 turn growth rate for 45th bunch Vertical beam size Qv 0.5 kHz full scale April 26, 2007 Study of Fast Ions in CESR

Study of Fast Ions in CESR Basic Plan Store electron beam 40-45 bunches in 1 train 14 nsec spacing between bunches Use bunch-by-bunch feedback (H, V & L) for stabilization Fill to a total current below an instability threshold Take Grow-Damp measurements Briefly turn off vertical feedback (automatically turns on when instability amplitude grows to preset value) Measure the positions of each bunch for 1K turns Analysis Reconstruct the multi-bunch spectrum from FFT’s of all of the bunches Compare with linear model for the Fast Ion Instability April 26, 2007 Study of Fast Ions in CESR

Linear Model of Fast Ion Instability* Assumptions Beam-ion force is linear (small amplitude motion < y) Ignore Landau damping Model treats ion frequency as a constant Within bunch-train ions are not over-focused Number of neutral gas ions is large wrt number of ions Ions are generated by ionization from beam and synchrotron radiation Neutralization of ions from electrons from the vacuum chamber walls was ignored Predicts a Fast Ion Vertical Instability Growth along train (s): amplitude ~ Amplitude growth turn-to-turn * Raubenhiemer et al, Phys Rev E, Vol 52, #5, p 5487 April 26, 2007 Study of Fast Ions in CESR

Ion Oscillation Frequency In Drift or Horizontal Bend Nb - particles/b; Lsep - distance between bunches; x,y - beam sizes; A - atomic mass of ion f i ~ 1 / (A y)1/2 Model for CESR Assume H2+ (A = 2) ions Every 1 cm (in drift or bend) calculate the ion frequency Histogram to find frequency distribution of ions April 26, 2007 Study of Fast Ions in CESR

Study of Fast Ions in CESR Plan for Measurements Two vertical beam sizes 140 m 330 m Two current distributions Uniform train of 40 bunches (1.3 mA/b) Instability threshold ~ 54 mA total current Case modeled by Raubenhiemer, et al Expect to see an amplitude growth along the train 15 higher current bunches (3 mA/b) & 25-30 (1.3 mA/b) First 15 bunches - initiate beam-ion motion Subsequent bunches - act like a longer time current probe - expect to get a narrower resolution for the ion frequencies April 26, 2007 Study of Fast Ions in CESR

Ion Frequency Resolution Calculated resolution for finite number of bunches (Essentially is an interference pattern in frequency) For 15 bunches with the same amplitude oscillation: Width of main spectral peak HWHM = 2 MHz ~ 1/Nbunches Number of lobes = Nbunches - 1 Measured spectrum is convolved with this resolution April 26, 2007 Study of Fast Ions in CESR

Predicted Ion Spectrum in CESR Small vertical size - 140 m 5.7 MHz April 26, 2007 Study of Fast Ions in CESR

Predicted Ion Spectrum in CESR Larger vertical size - 330 m 3.3 MHz April 26, 2007 Study of Fast Ions in CESR

Vertical Betatron Dipole Motion for Three of the Bunches in the Train Conditions 40 bunches: 1.36 mA/b v = 140 m 1024 turns Conclusions: Amplitude of motion grows down the train Amplitude grows “exponentially” in time Motion exceeds linear range Bunch 2 Bunch 36 20 mm Bunch 41 April 26, 2007 Study of Fast Ions in CESR

Construction of Multi-bunch Spectrum from Individual Bunch Spectra FFT each bunch’s motion Obtain Vn(') amplitude and (') phase for ' in the range [0,  0] for all Nb bunches where  0 = 2  frev Construct multi-bunch spectrum where Vtotal is the complex spectrum Tbb is the time between bunches mod(x, x’) is the modulus function April 26, 2007 Study of Fast Ions in CESR

Multi-bunch Spectrum of Vertical Betatron Dipole Modes Conditions 40 bunches: 1.36 mA/b v = 140 m 30 dB 0 - 71.4 MHz April 26, 2007 Study of Fast Ions in CESR

Multi-bunch Spectrum of Vertical Betatron Dipole Modes Conditions 40 bunches: 1.36 mA/b v = 140 m Trigger at 1/5 the preceding threshold level as a test Spectral peak shifts upward April 26, 2007 Study of Fast Ions in CESR

Multi-bunch Spectrum of Vertical Betatron Dipole Modes Conditions 40 bunches: 1.3 mA/b v = 330 m April 26, 2007 Study of Fast Ions in CESR

Multi-bunch Spectrum of Vertical Betatron Dipole Modes Conditions 15 bunches: 3 mA/b & 25 bunches: 1.1 mA/b v = 330 m April 26, 2007 Study of Fast Ions in CESR

Multi-bunch Spectrum of Vertical Betatron Dipole Modes Conditions 15 bunches: 3 mA/b & 25 bunches: 1.1 mA/b v = 130 m April 26, 2007 Study of Fast Ions in CESR

Multi-bunch Spectrum of Vertical Betatron Dipole Modes Conditions (Repeated measurements) 15 bunches: 3 mA/b & 30 bunches: 1.1 mA/b v = 140 m Lower ion frequencies due to larger amplitude motion? April 26, 2007 Study of Fast Ions in CESR

Study of Fast Ions in CESR Conclusions Observations See general shape of computed ion frequency distribution Ion frequencies appear to be higher than those for H2+ -> suggests H+ (H2 consistent with CESR vacuum) Large amplitude oscillations shift frequencies down See dependence of 1 / y1/2 Oscillation amplitude grows along the train Future measurements Explore smaller amplitude oscillation regime Compare with positron trains (to separate wakefield effects) April 26, 2007 Study of Fast Ions in CESR