HeadTail Chromaticity measurement methods

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Head-Tail Chromaticity measurement methods

• Vahid Ranjbar and C.Y. Tan

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Motivation

• We are interested in investigating
  non-destructive methods to measure chromaticity
  in the LHC
• In particular the head-tail phase difference
  approach using BBQ to detect head and tail phases.

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Longitudinal Beam Dynamics
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Chromaticity Measurement Using Head-Tail Phase
Shift   In the presence of non-zero chromaticity
the betatron frequency is perturbed by the
equation of motion per particle becomes Which
when integrated over a guassian ? distribution
gives1
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The result of this simple model predicts a beam
envelope which recoheres every half synchrotron
period.
And a phase which recoheres every full
synchrotron period reaching a maximum phase
difference every half synchrotron period. Thus
from the phase difference between two locations
in a bunch the chromaticity can be calculated
using
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Set-up
flipped polarity
We attached the BBQ to the E0 stripline with one
o f the diodes flipped to sample the negative
peak. The output of the BBQ was then sampled by a
fast digital oscilloscope at 25MHz
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The BBQ peak detects. Because of the over-lap in
the doublet positive and negative peak detector
should effectively sample different parts of the
bunch. However the peak location in the bunch may
experience some jitter which should be correlated
with closed orbit offset, kick amplitude and
rms bunch length.
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Chromaticity 5.04 units by C100 5.2
Chromaticity 3.66 units by C100 5.86
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Chromaticity 4.6 (if picking peak 6.5) by C100
6.65
Chrom 7.24 by C100 7.83
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Chrom 9.5 by C100 8.98
Peak chromaticity 4.4 units occurs 60 turns
later than It should. By C100 4.29
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Peak chromaticity 3.05 units occurs 60 turns
later than It should. By C100 4.23
Peak chromaticity 3.4 units occurs 60 turns
later than It should. By C100 3.4
Peak chromaticity 3.4 units occurs 60 turns
later than It should. By C100 3.4
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Xamp1 mm
Xamp10 mm
At Xamp1 mm /- .5 nsecs change in sigma
translates into change of 1 nsecs
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Future Plans and Conclusions

• Based on our understanding jitter in delta tau is
  driven by size of the closed orbit offset,
  amplitude of the kick and the bunch length
• We should be able to control jitter driven by
  amplitudes by just giving the beam a much smaller
  kick.
• The bunch length jitter however is a more
  difficult problem.( we should be able to extract
  bunch length information and adjust our
  chromaticity calculation based on this on the
  fly)
• I suggest we continue test this and other methods
  when time is available in Tevatron, SPS and
  possibly RHIC.