wake fields

1
Impedance ( Beam-Beam)

• wake fields impedance
• longitudinal impedance
• transverse impedance
• beam-beam effects

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test particle traveling a distance z behind
driving particle experiences longitudinal and
transverse wake forces proportional to the
product of the two particles charges and depend
on the distance z , the transverse force is also
proportional to the offset of the drive particle
from the pipe center, x
3
transverse wake function
longitudinal wake function
longitudinal dipole wake function
Panofsky-Wenzel theorem
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longitudinal wake function starts at a finite
positive value which represents energy loss by
the test particle
transverse wake function starts at zero and for
small z grows with a linear slope negative
sign shows that it is defocusing close to the
source
both wake functions are zero ahead of the source
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Fourier transform of the wake function is the
impedance
usually the real part of the impedance is related
to instability growth (or damping) rates the
imaginary part shifts the mode frequencies
energy loss is due to the real part of Z0
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longitudinal effects
induced voltage
parasitic energy loss
Gaussian charge distribution
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transverse effects
deflection (tune shift, etc.)
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common types of impedance

• resistive wall W01/a, W11/a3
• low frequency impedance
• coupled-bunch single bunch
• hhigher-order modes modes in rf cavities
• narrow-band resonators
• drives coupled-bunch instabilities
• discontinuities in beam-pipe cross section
• broadband resonator
• single bunch

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• how to measure impedance effects
• detect variation of observable
• (tune, orbit,) with impedance-related
• parameter like
• bunch intensity
• bunch length
• chromaticity
• chamber aperture (e.g., collimator or
• insertion device)

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parasitic mode energy loss (real part of Z0)

• measurements
• coherent synchrotron tune vs. rf voltage for
• different bunch currents (LEP example)
• synchronous phase shift with current
• dispersive orbit vs. intensity local?
• orbit change with intensity in transport line
  local
• threshold of microwave instability (also ImZ0)
• instabilities during debunching w dependence!

imaginary part of longitudinal impedance

• measurements
• bunch lengthening/shortening with current
• quadrupole mode frequency (2Qs) vs. current
• shift of incoherent synchrotron tune vs.
  intensity

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LEP model
from localization of rf cavities (computed)
determined with 10-3 precision
voltage calibration
energy loss due to SR and impedance
synchrotron tune as a function of total rf
voltage in LEP at 60.6 GeV the two curves
are fits to the 640 mA and 10 mA data the
difference due to current-dependent parasitic
modes is clearly visible
(A.-S. Muller)
Qs vs Vrf for Different Beam Intensities
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Synchronous Phase Shift with Bunch Current
the rf component of the bunch signal filtered
from an intensity monitor is compared with rf
cavity voltage for different bunch intensities
by means of a vector voltmeter relative phase
and amplitude measured while the current
is decreased by a scraper
SLC Damping Ring 1985
this gives the energy loss for a given charge
bunch length dependence can be measured as
well other possibility phase distance of 2
bunches with unequal charge (K. Bane in SPEAR)
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Dispersive Orbit vs. Intensity
measure horizontal orbit change with
intensity due to energy loss at impedance
locations
the circumference also changes DC Dx Dx!?
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example horizontal orbit deviation vs. vertical
scraper aperture in ELETTRA
E. Karantzoulis et al., PRST-AB 6 (2003)
orbit deviation looks like dispersion!!?!
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example X orbit change in ANKA when Y collimator
is closed
example fitted momentum offset (energy
loss?) vs. collimator position
A.-S. Muller, F. Zimmermann, et al., 26.-27.
August 2003
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measurement of energy loss due to
longitudinal wake fields in the SLC collider
arcs, APAC98
data and fits for other bunch lengths
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CERN SPS (E. Shaphoshnikova)
detect unstable frequencies during
debunching identify different frequencies with
ring components (here effect of MKE kicker
magnets)
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SLC Damping Ring 1988
bunch lengthens due to inductive impedance and,
at higher current, microwave instability
energy spread stays constant up to microwave
threshold from where it steeply increases
synchronous phase shift was measured as well
bunch length was measured by using the RTL bunch
compressor as streak camera
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quadrupole mode frequency shift vs. intensity
CERN SPS (E. Shaphoshnikova)
20
incoherent synchrotron tune can be measured by
resonant depolarization on a synchrotron
sideband example is from ANKA (A.-S. Muller,
EPAC04)
change in ratio corresponds to change in bunch
length
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transverse impedance

• measurements of real part
• head-tail growth or damping rate vs.
  chromaticity,
• intensity, bunch length
• measurements of imaginary part
• betatron tune shift with intensity Im(Z1)
• orbit change with intensity (global or local
  bumps)
• local
• betatron phase advance with intensity local
• orbit response matrix at different intensities
  local

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Head-Tail Growth or Damping Rate
measure head-tail growth (or damping) rates for
different values of chromaticity, intensity and
bunch length
growth/damping rate proportional to impedance,
chromaticity, intensity and beta function
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1/t
LEP 45.63 GeV, damping rate 1/t vs. Ibunch for
different chromaticities A.-S. Muller
Q14
1/(100 turns)
horizontal damping partition number
Q2.7
1/tSR
Ib
(A.-S. Muller)
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Coherent Tune Shift
measure coherent vertical tune shift as a
function of intensity
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example tune shift vs. scraper-blade position in
ELETTRA
E. Karantzoulis et al., PRST-AB 6 (2003)
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Orbit Change Transverse Wake
measure orbit change as a function of
intensity and beam position (e.g., local bumps),
or, e.g., as a function of collimator gap, etc.
for large y the dependence becomes nonlinear
(Piwinski)
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example difference orbit in ANKA with collimator
closed and open red curve is a fit to the
optics model which gives the kick
A.-S. Muller, F. Zimmermann, et al., 26. August
2003
red curve is a fit, scraper is at s80.6 m,
bx20.7, by8.0 m, design Dx0 m, 0.5 GeV,
longitudinal curve, curve vs. collimator gap,
tune shift?
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example orbit deflection if either ANKA
collimator jaw is closed
A.-S. Muller, F. Zimmermann, et al., 26. August
2003
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example vertical orbit deviation vs. vertical
scraper aperture in ELETTRA
E. Karantzoulis et al., PRST-AB 6 (2003)
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examplenonlinear res.-wall geometric wake
deflection the collimator position is varied for
a constant gap size SLAC linac
sy1.35 mrad, sz1.3 mm, Nb4x1010, E33 GeV,
sx,y80 mm
K. Bane et al., PAC95 Dallas
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example same as previous slide, but deflection
plotted vs. distance from lower jaw revealing
1/(a-y0)2 dependence
K. Bane et al., PAC95 Dallas
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Current Dependent Phase Advance
Take 1000-turn data for different intensity
analysis of the current-dependent phase advance
should yield the impedance location and strength
effect of a single localized impedance
SPS
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impedance acts like current-dependent
quadrupole response matrix
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example localized SPS impedance from current
dependent phase advance
for impedance localization take data at variable
intensity (without changing quadrupoles) some
example data
26 GeV/c
14 GeV/c
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tune shift with intensity, average and spread
over all BPMs
in the following discard all data sets with
larger errors
36
typical slope with intensity at a few BPMs from
different regions of the SPS
at each BPM fit slope and offset to measured
phase vs. intensity (above the offset is already
subtracted)
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result of fitting phase vs. intensity at each BPM
offset vs BPM no. 0-tune at 14 GeV/c was quite
different from model
slope vs BPM no. impedance
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fit Df/DN (the 3rd fit!) by SVD technique with
weight and cut-off to the phase beating response
matrix trick to get defocusing impedance fit in
10 iterations, at each step increase weight of
wrong-sign DK by factor 10
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the final result large impedance at 4-7 locations
SPS regions with impedance identified at both
energies 119 (MKP), 301-307 (arc?), 417-422
(MKE), 507 (arc?)
extraction kickers
injection kickers
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Orbit Response Matrix
take LOCO orbit response data for different beam
intensities
example LOCO measurements at APS V. Sajaev,
PAC2003 Portland (2003)
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Beam-Beam Effects

• head-on and long-range beam-beam
• tune spread
• drop in beam lifetime, limit on luminosity
• beam sizes must be matched at IP
• sensitivity to tune modulation
• bunch-to-bunch orbit tune differences
• coherent and incoherent effects
• each tune splits into two or a larger
• number of coupled tunes
• various compensation techniques are
• under study, e.g.,
• Tevatron Electron Lens
• LHC Wire Compensation (Tests in SPS)

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head-on beam-beam collision
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long-range collisions on either side of IP
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beam-beam deflection vs. offset
head-on collision
long-range collision (30 of these for each
head-on!)
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LHC 4 primary IPs
and
30 long-range collisions per IP
120 in total
partial mitigation by alternating planes of
crossing at IP1 5 etc.
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Long-Range Beam-Beam Collisions

• perturb motion at large betatron amplitudes,
  where particles come close to opposing beam
• cause diffusive aperture (Irwin), high
  background, poor beam lifetime
• increasing problem for SPS, Tevatron, LHC,...
• that is for operation with larger of bunches

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experience from Tevatron Run-II
long-range beam-beam interactions in Run II at
the Tevatron are the dominant sources of beam
loss and lifetime limitations of anti-protons
(T. Sen, PAC2003)
LR collisions reduce the dynamic aperture by
about 3s to a value of 3-4s little correlation
between tune footprint and dynamic aperture
drop in ey for first 4 pbar bunches after
injection asymp- totic emittance is measure of
their dynamic aperture
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LHC tune footprint due to head-on
long-range collisions in IP1
IP5 (Courtesy H. Grote)
LR vertical crossing
head-on
LR horizontal crossing
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total LHC tune footprint for
regular and PACMAN bunch (Courtesy H. Grote)
LR collisions fold the footprint!
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Long-Range Beam-Beam Compensation for the LHC

• To correct all non-linear effects correction
  must be local.
• Layout 41 m upstream of D2, both sides of
  IP1/IP5

current-carrying wires
Phase difference between BBLRC average LR
collision is 2.6o
(Jean-Pierre Koutchouk)
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all 30 LR collisions around one IP occur at
nearly same betatron phase (spreadlt2o) one
current-carrying wire parallel to beam can
compensate their effect, field at large distance
is 1/r like the LR beam field distance
wire-beam average LR beam-beam
separation wire current x length Iw lw Nb nLR
e c
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simulated LHC tune footprint with w/o wire
correction

• .16s
• .005s
• .016s

Beam separation at IP
(Jean-Pierre Koutchouk, LHC Project Note 223,
2000)
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wire compensator prototype at CERN SPS
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summary

• basics on wake fields and impedance
• measurements of longitudinal impedance
• measurements of transverse impedance
• (new) beam-beam effects compensation

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all course material is posted on the web
site http// web.cern.ch/ab-abp-frankz-uspas04