Beam-beam simulations M.E. Biagini, P. Raimondi LNF/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

Linear SuperB Double Pass e- Gun 2GeV e+ 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 1st LNF Workshop on SuperB, Nov. 2005

SuperB ILCDR-like ILC ring with ILC FF ILC compressor Decompressor DeCompressor IP Optional Acceleration and deceleration FF ILC ring with ILC FF ILC compressor Colliding every 50 turn Acceleration optional Crossing angle optional

Optimized Round case EP parameter set: Npart = 7.x1010 I = 5.6 A (for a 3Km ring) sx = sy = 0.916 mm sz = 0.8 mm bx = by = 0.55 mm

Round case Phase space after collision x,x’ y,y’ z,dE/E Round case Phase space after collision (x,x’), (y,y’), (z,dE/E) 2 Beams x,x’ y,y’ z,dE/E 4 Beams

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) sx = 2.670 mm sy = 12.6 nm sz = 4. mm bx = 2.5 mm by = 80. mm

Flat Case Phase space after collision x,x’ z,dE/E y,y’ Flat Case Phase space after collision (x,x’), (y,y’), (z,dE/E) 2 beams x,x’ z,dE/E y,y’ 4 beams

4 beams, Flat case Large blow up of all 4 beams

2 beams, Flat case Smaller blow up of 2 beams

Possible choice for ILC !!!! 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) sx = 2.670 mm sy = 12.6 nm sz = 4. mm bx = 2.5 mm by = 80. mm

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) Np(4 GeV) = 2.65x1010 Np(7 GeV) = 1.51x1010 I(4 GeV) = 2.1 A I(7 GeV) = 1.2 A Y emittance blow-up: 4 GeV  3.5x10-3 7 GeV  3.6x10-3

Asymmetric energies (4x7 GeV) with asymmetric bunch lengths Np(4 GeV) = 2x1010 Np(7 GeV) = 2x1010 I(4 GeV) = 1.6 A I(7 GeV) = 1.6 A sz(4 GeV) = 3.02 mm sz(7 GeV) = 5.29 mm Y emittance blow-up: 4 GeV  4. x10-3 7 GeV  4. x10-3

Alternative scheme for beam-beam compensation of energy asymmetry z x e- e+ HER: larger by*, smaller ey,ex LER: smaller by*, larger ey,ex No need for high current in LER Better for IBS, Touschek in LER Work in progress, coordination with DR design

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 sz) Alternative scheme is possible Optimization work will continue to finalize the beam-beam parameters