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

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

Run II Initial Separator Arrangement 3 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 Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

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 Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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 decay @ 150)  Remove unused C0 Lambertsons (the tightest aperture restriction) and cover F0 Lambertsons with foil to reduce impedance Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

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

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. Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

Losses @ 150 GeV vs Chromaticity 10 Losses @ 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 @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

12 Pbar Efficiency @ 150 GeV Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

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

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

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

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 functions @ 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 @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

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

Beam-Beam Chromaticity: Measurements vs. Calculations 20 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 Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

“Scallops” in Pbar Emittance 21 “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 @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

Diffusion due to 12th Order Resonances: a Puzzle 23 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) Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

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

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

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

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

Evolution of BB Tuneshifts 29 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 @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

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. Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

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 Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

Dedicated Experiment on Colliding Beams Stability 34 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 Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

Bunch-by-Bunch Tune Monitor 35 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. Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011

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

37 Lessons Learned  Head-on tuneshifts as high as 0.025 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) Beam-beam @ Tevatron - Y. Alexahin ICE meeting 02/16/2011