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Study of Beam-Beam Limit in Hadron Colliders

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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

upgrade

scenarios

large Piwinski angle (LPA)

early separation (ES)

compromises

between

# pile up

events and

heat load

Zimmermann, 2007

- 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

High resolution is achieved to

compute the beam distribution

at the core of the beam

At the collision point:

The solution is exact because

of the uniqueness of the

solution

- Assign potential on the reduced boundary:

- Solve Poisson’s equation with
- inhomogeneous boundary condition

geometric

- Simulation was carried out prior to the experiments to make sure there was enough sensitivity.
- ‘By-4’ bunch pattern to avoid parasitic collision (30 sx- 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.

- 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

- 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