Beam-beam simulations

M.E. Biagini, P. RaimondiLNF/INFN, SLAC

2nd Workshop on SuperB, Frascati 16th March 2006

Outline

• Round or flat?• 4 beams scheme• 2 beams scheme with asymmetric

energies• Conclusions

BB simulations

• Evolution of the SuperB layout is a consequence of the beam-beam studies

• Both luminosity and beam blow-up are the parameters to “watch”

• Optimization of beam parameters must include Damping Ring optimization and Final Focus design

Round or Flat ?• An extensive campaign of beam-beam

simulations has been carried out to find the best beam parameters set

• GuineaPig code by D. Schulte (CERN) has been used (same as ILC studies)

• Round and Flat beams have been considered

• Optimization of beam parameters performed with Mathematica + GuineaPig (see next talk by E. Paoloni)

4 Beams Scheme

• Option of colliding 4 beams in a “charge compensation” scheme considered

• GuineaPig modified to allow 4 beams (many thanks to D. Schulte !!!)

• 4 identical beams (energy, beam sizes, current) simulated

• Parameters from optimization studies

e- Gun

2GeVe+ DR

IP

5 GeV e+ & 3.5GeV e- SC Linac

e- Dump

0.5GeV SC Linac

7GeV e+

4 GeV e-

e-

e+

2 GeV e+ injection

Linear SuperB Double Pass

1st LNF Workshop on SuperB, Nov. 2005

SuperB ILCDR-like

Compressor

Compressor Decompressor

DeCompressor

IP

OptionalAccelerationand deceleration

OptionalAccelerationand deceleration

FF FF

ILC ring with ILC FFILC compressorColliding every 50 turnAcceleration optionalCrossing angle optional

Optimized Round case

• EP parameter set:– Npart = 7.x1010

– I = 5.6 A (for a 3Km ring)

– x = y = 0.916 m

– z = 0.8 mm

– x = y = 0.55 mm

2 Beams

4 Beams

Round casePhase space after collision(x,x’), (y,y’), (z,E/E)

x,x’ y,y’ z,E/E

x,x’ y,y’y,y’ x,x’z,E/E z,E/E

4 beams, Round case

2 beams, Round case

Optimized Flat case

• PR parameter set:– Npart = 2.x1010

– I = 1.6 A (for a 3Km ring)

– x = 2.670 m

– y = 12.6 nm

– z = 4. mm

– x = 2.5 mm

– y = 80. m

2 beams

4 beams

Flat CasePhase space after collision(x,x’), (y,y’), (z,E/E)

x,x’ z,E/Ey,y’

x,x’ x,x’z,E/E z,E/Ey,y’ y,y’

4 beams, Flat case

Large blow up of all 4 beams

2 beams, Flat case

Smaller blow up of 2 beams

4 Beams conclusions

• 4 beams are more unstable than 2 beams, highly disrupted, with larger emittance blow ups and give lower luminosity

• Not exhaustive analysis not excluded we can find better working parameter set in the future

• Shorter beams seem to work better• Larger horizontal beam size is better• Higher energy definitely works better

Possible choice for ILC !!!!

2 beams asymmetric energies

• Studied the 2-beams scheme with asymmetric energies

• 4x7 GeV case• PR parameter set:

– Npart = 2.x1010

– I = 1.6 A (for a 3Km ring)– x = 2.670 m– y = 12.6 nm– z = 4. mm– x = 2.5 mm– y = 80. m

Symmetric energies

Y emittance blow-up: 3.x10-3

Asymmetric energies (4x7 GeV)

Y emittance blow-up: 4 GeV 5x10-3

7 GeV 3x10-3

Asymmetric energies (4x7 GeV)

with transparency condition (I)

Y emittance blow-up: 4 GeV 3.5x10-3

7 GeV 3.6x10-3

Np(4 GeV) = 2.65x1010

Np(7 GeV) = 1.51x1010

I(4 GeV) = 2.1 AI(7 GeV) = 1.2 A

Asymmetric energies (4x7 GeV)

with asymmetric bunch lengths

Np(4 GeV) = 2x1010

Np(7 GeV) = 2x1010

I(4 GeV) = 1.6 AI(7 GeV) = 1.6 A

z(4 GeV) = 3.02 mm z(7 GeV) = 5.29 mmY emittance blow-up: 4 GeV 4. x10-3

7 GeV 4. x10-3

Alternative scheme for beam-beam compensation of energy

asymmetry

• HER: larger y*, smaller y,x

• LER: smaller y*, larger y,x

• No need for high current in LER • Better for IBS, Touschek in LER• Work in progress, coordination with DR design

z

xe-e+

Conclusions

• More work is needed to understand if the 4 beams scheme can work at low energy

• For the asymmetric energies “equal blow up” can be obtained with transparency condition (asymmetric I, or z)

• Alternative scheme is possible• Optimization work will continue to

finalize the beam-beam parameters