Measurements, ideas, curiosities

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Measurements, ideas, curiosities

• beam diagnostics and fundamental limitations to
  the performance of high-intensity accelerators

Complement to the lecture on Collective Effects
Beam Measurements
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Transverse head-tail modes at the CERN PS (E.
Metral, 1999, 20 revolutions superimposed)
Time (20 ns/div)
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Fast vertical single-bunch instability with
protons at the PS near transition in 2000
(Courtesy E. Metral)
?, ?R, ?V signals
Tail unstable
Head stable
700 MHz
Time (10 ns/div)
? Instability suppressed by increasing the
longitudinal emittance
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Fast vertical single-bunch instability with
protons at injection in the CERN SPS (E. Metral,
2003)

• Instability suppressed by increasing the
  chromaticity

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LONGITUDINAL HIGH INTENSITY EFFECTSExperiment
with a CERN PS proton beam in 1999
? Longitudinal Schottky scan spectrogram during
debunching
200 ms
Low-intensity beam
High-intensity beam
Courtesy R. Garoby
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Longitudinal Solitons in RHIC

• Wall Current Monitor data for a proton bunch
  freshly injected into RHIC (left) and for the
  same bunch after 17 minutes (right)
• Injection is at g 25.9, i.e. above transition
  gt 23.8
• These oscillations should be Landau damped
• When nonlinear effects are included, long lived,
  stable coherent oscillations become possible for
  low-intensity beams
• Long-lived beam holes have been observed below
  transition in the CERN PS Booster

Longitudinal phase space distribution obtained by
a self-consistent solution of the Vlasov equation
Longitudinal Solitons in RHIC, M. Blaskiewicz,
J.M. Brennan, P. Cameron, W. Fischer, J. Wei, A.
Luque, H. Schamel, PAC03
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• Vertical growth rate of head-tail modes in the
  LHC as a function of chromaticity at injection
  energy, for 3000 bunches of nominal intensity

At injection head-tail modes with growth rates up
to about 4 sec-1 are stabilized by lattice
nonlinearities (assuming an amplitude detuning of
0.002 at 6 sigma). The rigid mode m0 has to be
stabilized by the transverse feedback.
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Beam Echo Measurements at CERN

• An echo is formed by the interference of two
  consecutive RF pulses with slightly different
  frequencies. Each RF excitation induces a well
  defined pattern of particle energy along the
  machine circumference, rapidly destroyed by the
  revolution frequency spread. However, the long
  lasting memory of the proton beam allows the
  re-appearance of an ordered structure long after
  the initial excitations.
• The timing of the echo response depends on the
  frequency of the kicks and their separation the
  longer the separation, the later the echo in the
  SPS we have observed echo delays up to two
  minutes (i.e., more than 5 millions turns).
• The picture shows the superposition of 22 echo
  measurements with different time separations
  between the two RF-kicks, ranging from 5 to 220
  ms. The vertical axis shows the absolute value of
  the echo amplitude on a linear scale and the
  horizontal axis shows the time measured from the
  first RF-kick. The horizontal scale is 50 s. The
  solid line shows the analytical estimate for the
  echo envelope assuming a diffusion coefficient of
  10-13 s-1 in order to observe such a small
  diffusion with the Schottky signal, one would
  have to wait more than one day.

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Collective Effects web links references
http//ab-abp-rlc.web.cern.ch/ab-abp-rlc/ (web
site of the RD and LHC Collective Effects team
at CERN) Physics of Collective Beam
Instabilities in High Energy Accelerators,
A. Chao, (Wiley, 1993) Impedances and Wakes in
High-Energy Particle Accelerators, B.W. Zotter
and S. Kheifets, (World Scientific,
1998) Longitudinal holes in debunched particle
beams in storage rings, perpetuated by
space-charge forces, S. Koscielniak, S. Hancock,
and M. Lindroos, Phys. Rev. ST Accel. Beams 4,
044201 (2001) Beam dynamics studies for uniform
(hollow) bunches or super-bunches in the LHC
beambeam effects, electron cloud, longitudinal
dynamics, and intra-beam scattering, F.
Ruggiero, G. Rumolo, F. Zimmermann, Y.
Papaphilippou, CERN LHC Project Report 627
(2002) Intrabeam Scattering with
Non-Ultrarelativistic Corrections and Vertical
Dispersion for MAD-X, F. Zimmermann,
CERN-AB-2006-002 (2006)