1. Experience with Beam-Beam Effects at the Tevatron
Y. Alexahin (Fermilab APC)
Incoherent injection/acceleration/squeeze
Incoherent collisions
- emittance initiate collisions
- lifetime in colliding beams
Beam-beam compensation
Observations of coherent beam-beam modes
Instabilities & Coherent Effects group meeting CERN, 02/16/2011

2. Tevatron Run II Parameters2
Tevatron Run II Parameters
Circumference km
6.28
Beam energy
GeV
980 * cm 28
Proton bunch length
~ 50
Tunes, hor / ver /
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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

3. Run II Initial Separator Arrangement3
Run II Initial Separator Arrangement D0
CDF
(B0)
B17H
C49H
D11H
D48H
A49H
C17V
B11H
C49V
A49V
A17V
B11V
D11V
@ injection/acceleration/squeeze only 2 separators – B17H and C17V were used
@ collisions separators formed closed 3-bumps between IPs in each plane
@ step 13 of the squeeze (out of 17 initially) the transition from injection to collision helix took place
Tevatron - Y. Alexahin ICE meeting 02/16/2011

4. Typical Early Run II “Comfort Plot”4
Typical Early Run II “Comfort Plot”
Tevatron - Y. Alexahin ICE meeting 02/16/2011

5. 5
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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

6. Long Laundry List 6  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 150)
 Remove unused C0 Lambertsons (the tightest aperture restriction) and cover F0 Lambertsons with foil to reduce impedance
Tevatron - Y. Alexahin ICE meeting 02/16/2011

7. Figure of Merit for Beam Separation7
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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

8. “Radial” Beam Separation8
“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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

9. Squeeze Sequence 13 9 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.
Tevatron - Y. Alexahin ICE meeting 02/16/2011

10. Losses @ 150 GeV vs Chromaticity10
150 GeV vs Chromaticity
(data mining by V. Shiltsev)
With introduction of octupoles in Jan the chromaticity for protons and pbars was lowered to 3/0.
Tevatron - Y. Alexahin ICE meeting 02/16/2011

11. Effect of Octupoles on Pbar Losses @ 150 GeV11
Effect of Octupoles on Pbar 150 GeV
Tevatron - Y. Alexahin ICE meeting 02/16/2011

12. 12
Pbar 150 GeV
Tevatron - Y. Alexahin ICE meeting 02/16/2011

13. Effect of Octupoles on Proton Losses @ Pbar Injection13
Effect of Octupoles on Proton Pbar Injection
Tevatron - Y. Alexahin ICE meeting 02/16/2011

14. Particle Losses at Different Stages14
Particle Losses at Different Stages
Tevatron - Y. Alexahin ICE meeting 02/16/2011

15. More Comforting “Comfort Plot”15
More Comforting “Comfort Plot”
Tevatron - Y. Alexahin ICE meeting 02/16/2011

16. Incoherent BB Effects @ Collisions16
Incoherent BB 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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

17. 2
Nearest Parasitic IPs 17
(d)
(u) 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
D12
 1.162
-0.586
11.1
Beam separation and optics 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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

18. Beam-Beam Pbar Tuneshifts18
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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

19. Beam-Beam Chromaticity: Theory19
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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

20. Beam-Beam Chromaticity: Measurements vs. Calculations20
Beam-Beam Chromaticity: Measurements vs. Calculations
bunch #
chromaticty
Antiproton chromaticity measured with 1.7GHz Schottky monitor (store 3678, 07/28/04).
Bare lattice chromaticity:
Cx=10.5, Cy=11.5 on the pbar helix
Cx=12.5, Cy=10.5 on the proton helix
bunch #
LR chromaticty
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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

21. “Scallops” in Pbar Emittance21
“Scallops” in Pbar Emittance
hN ( mm mrad)
vN ( mm mrad)
Pbar emittance growth over first 10’ of HEP (store /29/04)
- clearly the work of the 5th order resonances
Tevatron - Y. Alexahin ICE meeting 02/16/2011

22. Diffusion due to Beam-Beam Resonances: Theory22
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)
Tevatron - Y. Alexahin ICE meeting 02/16/2011

23. Diffusion due to 12th Order Resonances: a Puzzle23
Diffusion due to 12th Order Resonances: a Puzzle ax
4x+8y
12y
6x+6y
2x+10y ay
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)
Tevatron - Y. Alexahin ICE meeting 02/16/2011

24. Pbar & Luminosity Losses vs. Separation24
Pbar & Luminosity Losses vs. Separation
Pbar NL losses at the beginning of 35 stores (March–April 2005) at indicated values of the helix size.
Tevatron - Y. Alexahin ICE meeting 02/16/2011

25. What Was Attempted to Reduce Pbar Blowup & Losses25
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 collisions – abandoned
New working point (close to 2/3 or 1/2) – abandoned
Tevatron - Y. Alexahin ICE meeting 02/16/2011

26. Run II Initial Separator Arrangement26
Run II Initial Separator Arrangement
CDF
(B0)
B11V
B17H
B11H
A49V
C17V
A49H
A17V
C49H
C49V D0
D11H
D11V
D48H
Tevatron - Y. Alexahin ICE meeting 02/16/2011

27. Run II Final Separator Arrangement27
Run II Final Separator Arrangement
CDF
(B0)
B11V
B17H
B11H
B48V
A49V
C17V
A49H
A17V
C49H
A17H
C49V D0
D11H
D11V
D17V
D48H
Tevatron - Y. Alexahin ICE meeting 02/16/2011

28. Collision Helix Upgrade28
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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

29. Evolution of BB Tuneshifts29
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).
Tevatron - Y. Alexahin ICE meeting 02/16/2011

30. Effect of 2nd Order Chromaticity Compensation30
Effect of 2nd Order Chromaticity Compensation
Presently beam-beam effects in collision impose ~5% tax on integrated luminosity
Tevatron - Y. Alexahin ICE meeting 02/16/2011

31. 31
BBC with TELs
TEL1 increases the horizontal tune for p-bunch #13 which is normally too low  close to 12th order.
TEL2 operated on all p-bunches (not only the last bunches in trains, #12*k) raising the vertical tune.
Both TEL1 and TEL2 improve proton lifetime significantly better than just lattice tune change – nonlinear resonance compensation?
I don’t 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.
Tevatron - Y. Alexahin ICE meeting 02/16/2011

32. Coherent Oscillations: Run Ib Observations32
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.
Tevatron - Y. Alexahin ICE meeting 02/16/2011

33. 33
36x36 Spectra in Collision
At initiate collisions nice quasi- and  mode excited (there is large difference in lattice tunes and intensities: Na=2232e9, Np=7855e9) but are quickly damped at nominal chromaticity
Tevatron - Y. Alexahin ICE meeting 02/16/2011

34. Dedicated Experiment on Colliding Beams Stability34
Dedicated Experiment on Colliding Beams Stability
End-of-store study (Np=21011, Na=21010 ) on 04/21/05:
vertical chromaticity lowered from 10.5 to 2.5 units
chromaticity lowered from 7 to 1.5 units -> 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
Tevatron - Y. Alexahin ICE meeting 02/16/2011

35. Bunch-by-Bunch Tune Monitor35
Bunch-by-Bunch Tune Monitor
A. Valishev et al., EPAC’08
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.
Tevatron - Y. Alexahin ICE meeting 02/16/2011

36. 3x3 Beam-Beam Modes with TEL2 off/on36
3x3 Beam-Beam Modes with TEL2 off/on
Tevatron - Y. Alexahin ICE meeting 02/16/2011

37. 37
Lessons Learned
 Head-on tuneshifts as high as can be tolerated in hadron colliders
 Separation > 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)
Tevatron - Y. Alexahin ICE meeting 02/16/2011