APS » Journals » Phys. Rev. ST Accel. Beams » Volume 11 » Issue 3

Phys. Rev. ST Accel. Beams 11, 032802 (2008)

Analytic approximation of the head-tail phase difference from continuous transverse excitation for measuring chromaticity

C. Y. Tan and V. H. Ranjbar
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  1. S. Fartoukh and J. Koutchouk, Technical Report, CERN LHC-B-ES-0004 rev 2.0, 2004.
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  9. C. Tan, Technical Report, Fermilab Technical Memo, TM-2155, 2001.
  10. These algebraic solutions have been verified with mathematica.
  11. C. Tan and V. Ranjbar, Technical Report, Fermilab Technical Memo, TM-2376, 2007.
  12. In general, this integral is 2-dimensional with σ(τB,δ,X), however, because of the initial condition that y(0)=y˙(0)=0, we have a sheet in the (τ,δ,X) space and not a volume.
  13. S. Fartoukh, Technical Report, CERN-LHC-PROJ. REP.-986, 2007.
  14. Uncoalesced beam in the Tevatron means that there are 30 bunches in adjacent buckets.
  15. Coalesced beam means that 7 bunches from the main injector are “coalesced” into 1 high current bunch and then injected into the Tevatron.
  16. Note that there is no 3D-BBQ electronics (which is used in the PLL tune tracker electronics at SPS and RHIC) in the setup so that there cannot be any arguments as to whether the phase difference effect is an artifact of the 3D-BBQ.
  17. V. Ranjbar and P. Ivanov, Technical Report, Fermilab PUB-07-448-AD, 2007.