Instabilities%20

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Experience with Beam-Beam Effects at the Tevatron
Y. Alexahin (Fermilab APC)

• Incoherent beam-beam _at_ injection/acceleration/sq
  ueeze
• Incoherent beam-beam _at_ collisions
• - emittance blowup _at_ initiate collisions
• - lifetime in colliding beams
• Beam-beam compensation
• Observations of coherent beam-beam modes

Instabilities Coherent Effects group meeting
CERN, 02/16/2011
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Tevatron Run II Parameters
Circumference km 6.28
Beam energy GeV 980
? cm 28
Proton bunch length cm 50
Tunes, hor / ver   20.585 / 20.575
Bunches / beam   36
Protons / bunch   2.7?1011
Pbars / bunch   0.9?1011
Normalized emittance proton / pbar ??mm?mrad 18 / 9
Total beam-beam tuneshift, proton / pbar   0.017 / 0.027
36 bunches in each beam are grouped in 3 trains
by 12 bunches. Each bunch experience head-on
collisions at 2 detectors (B0, D0) and 70 LR
interactions
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Run II Initial Separator Arrangement
_at_ injection/acceleration/squeeze only 2
separators B17H and C17V were used _at_
collisions separators formed closed 3-bumps
between IPs in each plane _at_ step 13 of the
squeeze (out of 17 initially) the transition from
injection to collision helix took place
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Typical Early Run II Comfort Plot
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Early Run II Debacle
Impact of beam-beam effect on peak luminosity (V.
Shiltsev) (design total proton intensity 1013
10000e9) Record Run I average initial lumi 27e30
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Long Laundry List
? Increase beam separation - use more
separators (including new ones) ? Reduce
chromaticity - Landau damping octupoles to
stabilize coherent oscillations - transverse
feedback (helped at some point but was
abandoned) - feed-down octupoles to lower
pbar chromaticity even more ? Reduce beam
emittance - eliminate mismatch between the
machines - e-cooling in RR - helped
immensely ? Optimize beam cogging (determines
IP azimuthal positions) ? Better control tunes
chromaticity (compensation of the drift caused by
the persistent current decay _at_ 150) ? Remove
unused C0 Lambertsons (the tightest aperture
restriction) and cover F0 Lambertsons with foil
to reduce impedance
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Figure of Merit for Beam Separation
Separation in respective (betatron) sigmas
or separation in maximal sigmas?

• both can be quite misleading, but Sr was found
  to better reflect the helix properties.
• Still, it was necessary to calculate beam-beam
  tuneshifts and RDTs to make a choice.
• ) using full sigmas (with dispersion
  contribution) does not make more sense

Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Radial Beam Separation
- radial separation (reference
emittance 15? mm?mrad)
- Jan 2002 helix 2005 helix
5-star helix had to be reduced due to aperture
restrictions and was finally replaced with design
using 7 separators
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Squeeze Sequence 13
Beam intensities through the squeeze left -
store 1074 (03/13/02), right store 3101
(12/17/03). Note higher proton intensity in store
3101, 8.5?1012, compared to 6?1012 in store 1074.
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Losses _at_ 150 GeV vs Chromaticity
(data mining by V. Shiltsev)
With introduction of octupoles in Jan. 2005 the
chromaticity for protons and pbars was lowered to
3/0.
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Effect of Octupoles on Pbar Losses _at_ 150 GeV
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Pbar Efficiency _at_ 150 GeV
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Effect of Octupoles on Proton Losses _at_ Pbar
Injection
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Particle Losses at Different Stages
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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More Comforting Comfort Plot
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Incoherent BB Effects _at_ Collisions

• Manifestations
• Pbar (and sometimes proton) emittance blowup at
  the start of HEP
• Proton and (to lesser degree) pbar non-luminous
  losses
• Problems
• Not enough room for pbar tunes between 5th and
  12th order resonances
• Large BB-induced split in chromaticity Chpbar -
  Chproton 7
• Large emittance ratio ?proton/?pbar (good for
  pbars, not for protons)
• Insufficient separation at the nearest parasitics

Calculated tune distribution of protons (orange)
and pbars (blue) in collision and measured with
1.7GHz Schottky bunch-by-bunch pbar tunes
(yellow) in store 3867, 07/28/2004 Both
calculations and measurements (!) ignore coupling
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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2
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Nearest Parasitic IPs
IP dx mm (pbar-prot) dy mm (pbar-prot) ?x m ?y m
A48 -0.599 1.142 152.5 11.5
B12 -1.365 -0.6 11.2 151.2
C48 -0.545 -1.114 150.0 11.5
D12  1.162 -0.586 11.1 152.5
Beam separation and optics functions _at_ nearest
parasitics (ideal optics)
upstream PIPs not seen by 1st proton and last
pbar bunches in trains downstream PIPs not
seen by last proton and 1st pbar bunches in
trains
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Beam-Beam Pbar Tuneshifts
1.7 GHz Schottky 07/27/2004
Qh
Qv
PACMAN bunches have much lower tunes do not
see 5th order Tunes go down with time due to
proton emittance growth (mostly by
IBS) Calculations satisfactorily reproduce
measurements
Analytics
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Beam-Beam Chromaticity Theory

• Comes from
• head-on interactions owing to ?-function
  modulation

measured chromatic functions were initially up to
600 (A.Valishev)

• long-range interactions owing mainly to
  modulation of the beam separation dx,y

Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Beam-Beam Chromaticity Measurements vs.
Calculations
Antiproton chromaticity measured with 1.7GHz
Schottky monitor (store 3678, 07/28/04). Bare
lattice chromaticity Cx10.5, Cy11.5 on the
pbar helix Cx12.5, Cy10.5 on the proton helix
Calculated long-range contribution for
antiprotons with small betatron amplitudes

• The bb-chromaticity is huge and difficult to
  compensate since it
• varies from bunch to bunch
• depends on betatron amplitudes

Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Scallops in Pbar Emittance
??hN (? mm mrad)
??vN (? mm mrad)
Pbar emittance growth over first 10 of HEP
(store 3456 04/29/04) - clearly the work of the
5th order resonances
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Diffusion due to Beam-Beam Resonances Theory
bunch 11
bunch 12
ay (sigmas)
ay (sigmas)
ax (sigmas)
ax (sigmas)
Analytically calculated 5th order resonance
widths in the plane of betatron amplitudes
(magenta - 5Qx, red - 5Qy) for on-momentum pbars
at Qx.577, Qy.582 At synchrotron amplitude ?p
?2?p 1.3e-4 the synchrotron satellites overlap
? dynamical chaos for bunch 11 (but not for
bunch 12)
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Diffusion due to 12th Order Resonances a Puzzle
Observations indicate a strong effect of the 12th
order resonances on the lifetime and even on pbar
emittance. But calculations (left) show that they
are too weak to produce dynamical chaos.
Amplitude beat on 12th order resonances and their
synchrotron satellites at Qx.585, Qy.575
Possible explanation cooperative effect of
resonances and external noise (multiplicative
diffusion enhancement - D.Neuffer, A.Riddiford,
A.Ruggiero, 1980) The mechanism - loss of phase
correlation between subsequent crossings of a
resonance in the course of synchrotron
oscillations - was first discussed by P. Sturrock
while at CERN in 1958
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Pbar Luminosity Losses vs. Separation
Pbar NL losses at the beginning of 35 stores
(MarchApril 2005) at indicated values of the
helix size.
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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What Was Attempted to Reduce Pbar Blowup Losses

• Increased beam separation with new separators
  making 4-bumps instead of 3-bumps
• Reduced pbar emittance (e-cooling in RR,
  matching)
• Compensation of pbar BB tuneshift decrease
  during a store with feeddowns
• Damping of LB quad motion to reduce orbit
  response
• Orbit feedback (essential!)
• Lower chromaticity (possible due to reduced
  impedance)
• Landau damping octupoles _at_ collisions
  abandoned
• New working point (close to 2/3 or 1/2)
  abandoned

Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Run II Initial Separator Arrangement
CDF (B0)
B17H
B11V
B11H
C17V
A49V
A49H
C49H
A17V
C49V
D0
D11H
D11V
D48H
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Run II Final Separator Arrangement
CDF (B0)
B17H
B11V
B48V
B11H
C17V
A49V
A49H
C49H
A17V
C49V
A17H
D0
D11H
D11V
D17V
D48H
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Collision Helix Upgrade
?35cm optics (design) 12 separators 13
separators (D17V)
?28cm optics (fit) 13 separators 15 separators
(A17H B48V ) - more than 10 increase in
separation at the nearest parasitics
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Evolution of BB Tuneshifts
After the commissioning of e-cooling in RR the
problem with the proton lifetime became dominant.
The cures implemented - pbar jacking to
increase emittance, - correction of chromatic
beta-beat (A.Valishev) beneficial by itself,
but also reducing 2nd order chromaticty (and
therefore the total tunespread).
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Effect of 2nd Order Chromaticity Compensation
One more measure significantly improved proton
lifetime equalization of pbar bunch-by-bunch
intensity. Presently beam-beam effects in
collision impose 5 tax on integrated luminosity
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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BBC with TELs
TEL2 operated on all p-bunches (not only the last
bunches in trains, 12k) raising the vertical
tune.
TEL1 increases the horizontal tune for p-bunch
13 which is normally too low ? close to 12th
order.

• Both TEL1 and TEL2 improve proton lifetime
  significantly better than just lattice tune
  change nonlinear resonance compensation?
• I dont think so, there is much simpler and
  effective mechanism beta-beat. It happened so
  that TELs reduce ?-functions at IPs making the
  ration of proton/pbar sizes smaller.
• No study of the beta-beat due to TELs performed.

Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Coherent Oscillations Run Ib Observations
From V. Bharadwaj et al. Fermilab-TM-1970 (1996)
At collisions, the chromaticities are quite
small and may even be slightly negative. (They
are probably between about -5 and 5 units in both
planes.) This seems to be a requirement for good
particle and luminosity lifetimes. It has also
been observed that when the beams are colliding
they can tolerate chromaticities that would make
a single beam unstable.
- Nobody of the Tevatron people could recollect
working with negative chromaticities nor were
able to find any evidence in logbooks.
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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36x36 Spectra in Collision
At initiate collisions nice quasi-? and ? mode
excited (there is large difference in lattice
tunes and intensities Na2232e9, Np7855e9) but
are quickly damped at nominal chromaticity
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Dedicated Experiment on Colliding Beams Stability

• End-of-store study (Np2?1011, Na2?1010 ) on
  04/21/05
• vertical chromaticity lowered from 10.5 to 2.5
  units
• chromaticity lowered from 7 to 1.5 units -gt
  beams went unstable
• Tev quenched due to pbar losses

1.7 GHz Schottky spectra in the proton (left) and
antiproton (right) beams before the onset of
instability (blue) and just before the quench
(red) (data provided by A. Jansson)

• Beam-beam tunespread failed to provide Landau
  damping
• Pbars had a factor of 4 larger amplitude, very
  much in line with the rigid-bunch model
  predictions

Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Bunch-by-Bunch Tune Monitor
A. Valishev et al., EPAC08
Clearly all bunches participate in coherent
motion (but with different amplitude). Some
tickling was applied to protons. Strong pbar
line at 0.563 is a puzzle too low to be
related to main bunches which experience head-on
collisions, may be a mini-bunch is caught
somewhere in between.
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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3x3 Beam-Beam Modes with TEL2 off/on
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011
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Lessons Learned
? Head-on tuneshifts as high as 0.025 can be
tolerated in hadron colliders ? Separation gt 6
sigma, for a short time as low as 3 sigma ? Low
chromaticity (?4) is essential for good
lifetime ? Multiple crossing of even weak
high-order resonances (12th in the Tevatron case)
can affect particles in the beam core (the
mechanism first discussed by P. Sturrock in 1958
while at CERN) ? There can be a non-trivial
interplay between beam-beam and lattice
nonlinearities (as testified by detrimental
effect of octupoles in collision) ? Beam-beam
tunespread may be insufficient for colliding beam
stability contrary to Run I indications and
simplified theoretical predictions ? Beneficial
effect of electron lense exceeded expectations
(but the reason is not completely understood)
Beam-beam _at_ Tevatron - Y. Alexahin
ICE meeting 02/16/2011