# Presentation: 703386

## Study of Beam-Beam Limit in Hadron Colliders

- Yunhai Cai and Robert Warnock
- Beam Physics Department
- SLAC
- LARP collaboration meeting at SLAC
- October 18, 2007

## two new

| parameter | symbol | Early Separation | Large Piwinski Angle |
| --- | --- | --- | --- |
| transverse emittance |  [m] | 3.75 | 3.75 |
| protons per bunch | Nb [1011] | 1.7 | 4.9 |
| bunch spacing | t [ns] | 25 | 50 |
| beam current | I [A] | 0.86 | 1.22 |
| longitudinal profile |  | Gauss | Flat |
| rms bunch length | z [cm] | 7.55 | 11.8 |
| beta* at IP1&5 |  [m] | 0.08 | 0.25 |
| full crossing angle | c [rad] | 0 | 381 |
| Piwinski parameter | cz/(2*x*) | 0 | 2.0 |
| hourglass reduction  |  | 0.86 | 0.99 |
| peak luminosity | L [1034 cm-2s-1] | 15.5 | 10.7 |
| peak events per crossing |  | 294 | 403 |
| initial lumi lifetime | L [h] | 2.2 | 4.5 |
| effective luminosity 
(Tturnaround=10 h) | Leff [1034 cm-2s-1] | 2.4 | 2.5 |
|  | Trun,opt [h] | 6.6 | 9.5 |
| effective luminosity 
(Tturnaround=5 h) | Leff [1034 cm-2s-1] | 3.6 | 3.5 |
|  | Trun,opt [h] | 4.6 | 6.7 |
| e-c heat SEY=1.4(1.3) | P [W/m] | 1.04 (0.59) | 0.36 (0.1)  |
| SR heat load 4.6-20 K | PSR [W/m] | 0.25 | 0.36 |
| image current heat  | PIC [W/m] | 0.33 | 0.78 |
| gas-s. 100 h (10 h) b | Pgas [W/m] | 0.06 (0.56) | 0.09 (0.9) |
| extent luminous region | l [cm] | 3.7 | 5.3 |
| comment |  | D0 + crab (+ Q0) | wire comp. |

- upgrade
- scenarios

*compromises*
*between*
*# pile up*
*events** and*
*heat load*

*early separation (ES)*

*large Piwinski angle (LPA)*

**Zimmermann, 2007**

## Beam-Beam Effects in Hadron Machine

- Beam-Beam lifetime (T. Sen, A. Kabel )
- Parasitic collision
- Wire compensation (W. Fischer)
- Electron lens compensation (V. Shiltsev)
- Emittance growth due to beam-beam collisions
- Strong-weak, gives too small values
- Strong-strong
- Gives unreliable values due the numerical noise
- Predicts a beam-beam limit that is a factor of ten larger than in the electron machine

## Solve Poisson Equation with Reduced Region 

-  Assign potential on the reduced boundary:

-  Solve Poisson’s equation with
-   inhomogeneous boundary condition

- At the collision point:

- High resolution is achieved to
- compute the beam distribution
- at the core of the beam

- The solution is exact because
- of the uniqueness of the
- solution

## Crossing Experiments at PEP-II

- Simulation was carried out prior to the experiments to make sure there was enough sensitivity.
- ‘By-4’ bunch pattern to avoid parasitic collision (30 x- separation).
- The orbit bump used to change the angle. The knob was carefully calibrated against a pair of BPMs next to the IP.
- Luminosity feedbacks were on to align beams transversely after each change.
- Tune changes were necessary to compensate the optical errors introduced from the nonlinearity of the fringe field and magnets inside the bumps.

- geometric

## Slide 6

##  Improving Strong-Strong Codes

- Numerical noise in PIC codes
- Macro particle representation of density
- Discrete Poisson solver
- Vlasov-Poisson approach to eliminate the noise due to macro particles
- 1D code for microwave instabilities was proven very effective
- 2D beam-beam code was developed by Andrey Sobol. Ported
-     to computers at SLAC
- A new idea to solve Vlasov, with some advantages of PIC method (lower cost , while keeping low noise)
- Forward tracking (similar to macro particles)
- Smoothing by interpolation of data at quasi-random sites
- Probability conserving algorithm at data sites

## Goal and Plan

- Compare noise between PIC and Vlasov codes and quantify any improvements
- To understand emittance growth due to beam-beam in hadron machines at least in  relative terms within **two years**
- Benchmark the codes against experiments in Tevatron and RHIC, understand the emittance growth at 10% level within five years and compare to the result from LHC
- Resource:
- 2 FTE for two years possible extension to five years
- At least one new FTE (post-doctoral)
- Maybe a dedicated cluster later