1. Beam-beam Effects in Hadron Colliders
Guo Yuanyuan

2. Outline Beam-beam effects in LHC
Beam-beam effects in RHIC and Tevatron
Next work

3. LHC layout Large Hadron Collider 8 arcs,8 straight sections
Two-in-one magnet design
IP2 and IP8:injection
IP6:beam dump region
IP4:RF
IP3 and IP7:collimators
4 Interaction Points
—IP5 and IP8:horizontal plane
—IP1 and IP2:vertical plane

4. Incoherent effects Single particle dynamics
—Non-linear dynamics
Linear beam-beam tune shift
Head-on:∆ 𝑄 𝐻𝑂 ≈−𝜉=− 𝑁 𝑏 𝑟 𝑝 4𝜋 𝜀 𝑛
Long-range: ∆ 𝑄 𝐿𝑅 ≈± 2𝑛 𝐿𝑅 𝑟 𝑝 𝑑 𝜎 2 𝜉
For nominal LHC: ∆ 𝑄 𝐿𝑅 ≈ ∆ 𝑄 𝐻𝑂

5. Incoherent effects Amplitude dependent tune spread
—experience from the SPS and Tevatron：0.01 for the overall beam-beam tune spread
—without crossing the dangerous resonance lines

6. Dynamic aperture with beam-beam effect
Significant reduction of dynamic aperture due to LR beam-beam; even small field errors lead to losses when beam-beam present.

7. LHC filling pattern
2808 bunches, every 25ns, about 30 parasitic interactions/IP

8. PACMAN effects
A bunch can meet a hole(at beginning and end of bunch train)
—miss some long-range interactions, PACMAN bunches, Only about half of the bunches are regular
—they see fewer unwanted interactions in total
—different integrated beam-beam effect
expect bunch-to-bunch variation of orbit, tune and chromaticity

9. Bunch-to-bunch orbit variation
horizontal orbit variation at IP1
HH crossing
VH crossing

10. Bunch-to-bunch tune chromaticity variation
alternating crossing—>efficiently compensate the effects of the long-rang interactions

11. Coherent beam-beam effects
one bunch and one head-on collision with equal intensity
more bunch and more IPs
p-mode is shift by ~1.22x, outside the incoherent tune spread ~x
No Landau damping possible

12. Coherent beam-beam effects
Intensity ratio 0.55
p-mode Landau damped
Landau damping can be restored by symmetry breaking
–different intensities
–different tunes
–broken symmetry for multiple interaction regions

13. Introduction of RHIC
RHIC consists of two super- conducting rings which intersect at 6 locations along its 3.8 Km circumference.
Two beams collide head-on at IP6 and IP8. They are vertically separated at other non-collisional IPs.
RHIC collides heavy ions and polarized protons. The total maximum beam-beam parameters and for p-p collision.

14. Beam lifetime and transverse emittance
During RHIC p-p runs, beam losses at store are dominated by the beam-beam interactions.
—With collision at store, a fast beam loss was observed in the first 1-2 hours, followed by a slow loss in the rest store.
—Emittances are reduced shortly after collision, then they slowly increase in the rest of store. The reduced emittances in the beginning of store are also related to the fast beam loss.

15. Beam-beam effects in Tevatron
RUN II: p-pbar, single ring,36+36
Long-range effects was important during injection and ramp:
—Orbit variation in the trains
—Tune variation in the trains
The total measured HO tune shift went beyond 0.02

16. next work Choice of filling pattern(constraint of injection and dump)
Simulation
—tune spread
—orbit effects due to long-range interaction
—choice of working point
Synchrobetatron resonances
Beam-beam limit
…….

17. Thanks for your attention!