Crab Cavity at CERN SPS H J Kim
Crab Cavity at CERN SPS H. J. Kim and T. Sen Fermilab Nov. 2, 2010 LARP CM 15
Outline Introduction Stability analysis Simulation results Summary
Motivation (1) High luminosity in a collider increase beam current → beam instability/machine protection/collimation. increase # of bunches → parasitic collisions → crossing angle → luminosity degradation Nominal LHC RΦ: luminosity reduction factor, Φ: Piwinski angle
Motivation (2) Crab scheme reovers the geometric luminosity loss due to finite crossing angle without increasing bunch intensity. Crab cavity proposed by Palmer (1988). KEK-B's CC restores an effective head-on collision at IP. In CC, a particle gets a transverse deflection and collsion is effectively “head on”. “Head on” at IP
Motivation (3) CERN will persue crab crossing for LHC upgrade. 2020 shutdown – install CC SPS test with KEK-B crab cavities is proposed for deciding on a full crab-cavity implementation in LHC. “Following the success of KEKB, CERN must persue the use of crab cavaties for the LHC, since the potential luminosity is significant” by S. Myers (LHC-CC 09) KEK-B does not need CC after 2010 (Super. KEK-B) Using a weak-strong code BBSIMC, we investigate effects of crab cavity on emittance growth in the SPS.
Local scheme Two CC's per a beam Opitcs affected locally
Global scheme One CC per a beam Beam tilts all around the ring z-dependent horizontal(vertical) closed orbit large and are preferred
Crab Cavity at COLDEX location Longitudinal location: 4009 m betax, betay: 30, 77 m mux, muy: 15. 173, 15. 176 ηx, η'x : -0. 5, -0. 02 Crab Cavity Parameters: Length 5 m Voltage: 1. 5 MV Frequency: 509 MHz Wave Length: 60 cm Global Scheme Horizontal Crossing
Stability analysis model The characteristic polynomial of the matrix T is The stability conditions are
Stability boundary 26 Ge. V: Vcc = 0. 3 MV, qx=0. 13 ηx, η'x : -0. 5, -0. 02 Non-linearities not included.
Global crab scheme changes closed orbit
Large bunch length sigma_z = 1. 5 cm sigma_z = 12 cm fcc = 509 MHz, lambda_cc = 60 cm S-shaped bunch due to CC degrades luminosity.
Emittance growth (beam energy) CC + NL's No Crab Cavity Only crab cavity does not increase emittance, but CC + nonlinearties induce emittance growth. No non-linearity
Emittance growth (bunch length) Beam energy = 26 Ge. V Emittance growth depends on bunch length (momentum spread). Maximum emittance growth for large bunch length. Linear CC kick
Emittance growth (Crab voltage) Beam energy = 26 Ge. V Emittance growth depends on CC kicks. Nonlinear dependency upon CC kicks.
Emittance (dispersion)
Dynamic aperture (beam energy, bunch length, Vcc) DA depends on beam energy and CC kicks DA does not depend on bunch length.
Summary Linear stability model has been studied. Current SPS parameters are far away from unstable boundaries. Emittance growth and dynamic aperture studies for beam energy, bunch length(momentum spread), and crab cavity voltage. Dispersion function at CC location affects emittance growth. Need further study with CC: Allowable dispersion at CC location. Chromaticity/betatron tune/beam-beam collsion/crab cavity noise affect emittance?
- Slides: 18