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 Macroparticle simulation of IBS in SuperB

This study presents a macroparticle simulation of intrabeam scattering (IBS) effects in the SuperB T damping ring, comparing growth rates with conventional theories and examining the evolution of the bunch distribution. The simulation algorithm applies IBS at each lattice element, considering radiation damping and quantum excitation. The results show the impact of IBS on the damping process and the potential generation of non-Gaussian tails. The simulation is implemented in parallel for efficient computation.

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 Macroparticle simulation of IBS in SuperB

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  1.  Macroparticle simulation of IBS in SuperB T. Demma (INFN-LNF) In collaboration with: M. Boscolo (INFN-LNF) A. Chao, M.T.F. Pivi (SLAC).

  2. Introduction Conventional calculation of IBS Multi-particles codes structure Growth rates estimates and comparison with conventional theories Bunch distribution evolution Parallel implementation Conclusions and outlook Plan of Talk

  3. IBS Calculations procedure • Evaluate equilibrium emittances ei and radiation damping times ti at low bunch charge • Evaluate the IBS growth rates 1/Ti(ei) for the given emittances, averaged around the lattice, using K. Bane approximation* • Calculate the "new equilibrium" emittance from: • For the vertical emittance use* : • where r varies from 0 (y generated from dispersion) to 1 (y generated from betatron coupling) • Iterate from step 2 * K. Kubo, S.K. Mtingwa, A. Wolski, "Intrabeam Scattering Formulas for High Energy Beams," Phys. Rev. ST Accel. Beams 8, 081001 (2005)

  4. IBS in SuperB LER (lattice V12) v=5.812 pm @N=6.5e10 h=2.412 nm @N=6.5e10 • Effect is reasonably small. Nonetheless, there are some interesting questions to answer: • What will be the impact of IBS during the damping process? • Could IBS affect the beam distribution, perhaps generating tails? z=4.97 mm @N=6.5e10

  5. Intra-Beam Scattering (IBS) Simulation Algorithm IBS applied at each element of the Ring lattice • Lattice read from MAD (X or 8) files containing Twiss functions and transport matrices • At each element in the ring, the IBS scattering routine is called: • Particles of the beam are grouped in cells. • Particles inside a cell are coupled • Momentum of particles is changed because of scattering. • Invariants and corresponding growth rate are recalculated. • Particles are transported to the next element. • Radiation damping and excitation effects are evaluated at each turn. T. Demma, M. Boscolo, M.Biagini (INFN), M. Pivi , A. Chao (SLAC) Dec 1, 2011 IBS coll. meeting

  6. Zenkevich-Bolshakov Algorithm For two particles colliding with each other, the changes in momentum for particle 1 can be expressed as: with the equivalent polar angle effand the azimuthal angle  distributing uniformly in [0; 2], the invariant changes caused by the equivalent random process are the same as that of the IBS in the time interval ts

  7. Radiation Damping and Quantum Excitation • Normalized coordinates are defined by Twiss (B) and Dispersion (H) matrix : • Synchrotron Radiation is taken into account with the following map: • Switch back to physical coordinates by:

  8. Intrabeam Scattering in SuperB LER Bane Piwinski IBS-Track Bane Piwinski IBS-Track

  9. Emittance Evolution in SuperB LER • SuperB V12 LER Nb= 2x1010 - 12x1010 F=10 tx = 10-1 x 40 ms ty = 10-1x 40 ms ts = 10 -1x 20 ms

  10. Bunch-slice parallel decomposition Computation in parallel - pipeline Each processor deals with the bunch-slice, then send information to the next in the pipeline. The last processor print out the beam information. At each turn, 1 processor gathers all particles and compute Radiation Damping and Quantum Excitation. M. Pivi (SLAC)

  11. IBS – SuperB LER (using C-MAD) • C-MAD parallel code (M. Pivi SLAC) for beam collective effects: • IBS • Electron cloud instability • Benchmark: SuperB lattice ~1800 IPs • sz=5.0*10-3 m • dp=6.3*10-4 • ppb= 5.7 1012 • MacroParticleNumber=3 x 105 • Grid size = 10sy x 10sx • # bunch slices = 64 • # processors for this run = 64 IBS-Track CMAD M. Pivi (SLAC), T. Demma (INFN) Dec 1, 2011

  12. CPU timing studies: SuperB LER 1 turn • Gain not linear: bunch slice decomposition not balanced • Gain @ 64 CPU is only 25 but total execution time is well below 1 min.. • Still working on routines optimization M. Pivi (SLAC)

  13. Emittance Evolution in SuperB LER M. Pivi (SLAC), T. Demma (INFN)

  14. IBS Distribution study M. Pivi (SLAC), T. Demma (INFN)

  15. SIRE: IBS Distribution study: CLIC DR A. Vivoli (CERN)

  16. SuperB Damping Ring A damping ring at 1 GeV is used to reduce the positron beam injected emittance M. Preger

  17. IBS in SuperB Damping Ring Only 1 IP per tun is conidered

  18. The SLS lattice • Picture shows the interpolated beta and h functions. In particular: Sqrt[betax] (magenta), Sqrt[betay] (blue), 20*hx (gold), 105*hy (green). F. Antoniou (CERN)

  19. IBS effect:1 Turn w/ Vertical Dispersion Effect of vertical dispersion has been successfully included!!! MAD-X files including vertical dispersion in SuperB are already available….

  20. Summary • Interesting aspects of the IBS such as its impact on damping process and on generation of non Gaussian tails may be investigated with a multiparticle algorithm. • Two codes implementing the Zenkevich-Bolshakov algorithm to investigate IBS effects have been developed: • Benchmarking with conventional IBS theories gave good results • Evolution of the particle distribution shows deviations from Gaussian behaviour due to IBS effect (SIRE-CERN, CLIC-DR). • Parallel implementation of the algorithm is ready : • IBS routines included in CMAD (thanks to M. Pivi). • Comparison of the code results with measurements at SLS and/or Cesr-TA would provide the possibility of • Benchmarking with real data • Tuning code parameters (number of cells, number of interactions, etc.) • Revision of the theory or theory parameters (Coulomb log, approximations used, etc.)

  21. Spares

  22. Differential equation system for ex and ez Radial and longitudinal emittance growths can be predicted by a model that takes the form of a coupled differential equations: Bane Model N number of particles per bunch a and b coefficients characterizing IBS obtained once by fitting the tracking simulation data for a chosen benchmark case Obtained by fitting the zero bunch intensity case (IBS =0)

  23. Summary plots: SuperB parameters Equilibrium horizontal emittance vs bunch current Equilibrium longitudinal emittance vs bunch current

  24. Summary plots: DAFNE parameters tx = 1000-1 * 0.042 ty = 1000-1 * 0.037 ts = 1000-1 * 0.017 NTurn=1000 (≈10 damping times) MacroParticleNumber=40000 ex=(5.63*10-4)/g ey=(3.56*10-5)/g sz=12.0*10-3 dp=4.8*10-4

  25. SIRE: SLS simulations A. Vivoli, F. Antoniou

  26. SIRE: IBS Distribution study D: IBS A. Vivoli

  27. Bjorken-Mtingwa

  28. Piwinski

  29. Bjorken-Mtingwa solution at high energies Changing the integration variable of B-M to λ’=λσH2/γ2 Bane’s high energy approximation • Approximations • a,b<<1 (if the beam cooler longitudinally than transversally ) The second term in the braces small compared to the first one and can be dropped • Drop-off diagonal terms (let ζ=0) and then all matrices will be diagonal

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