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

2. 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. 3 IBS Calculations procedure 1.Evaluate equilibrium emittances  i and radiation damping times  i at low bunch charge 2.Evaluate the IBS growth rates 1/T i (  i ) for the given emittances, averaged around the lattice, using K. Bane approximation* 3.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) 4.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. 4 IBS in SuperB LER (lattice V12) 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?  h =2.412 nm @N=6.5e10  v =5.812 pm @N=6.5e10  z =4.97 mm @N=6.5e10

5. 5 Intra-Beam Scattering (IBS) Simulation Algorithm 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. Dec 1, 2011 IBS coll. meeting IBS applied at each element of the Ring lattice T. Demma, M. Boscolo, M.Biagini (INFN), M. Pivi, A. Chao (SLAC)

6. 6 For two particles colliding with each other, the changes in momentum for particle 1 can be expressed as: with the equivalent polar angle  eff and 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 Zenkevich-Bolshakov Algorithm

7. 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. 8 Intrabeam Scattering in SuperB LER ParameterUnitValue EnergyGeV4.18 Bunch population10 6.5 Circumferencem1257 Emittances (H/V)nm/pm1.8/4.5 Bunch Lengthmm3.99 Momentum spread%0.0667 Damping times (H/V/L)ms40/40/20 N. of macroparticles-10 5 N. of grid cells-64x64x64 Bane Piwinski IBS-Track Bane Piwinski IBS-Track

9. 9 Emittance Evolution in SuperB LER SuperB V12 LER Nb= 2x10 10 - 12x10 10 F=10 t x = 10 -1 x 40 ms t y = 10 -1 x 40 ms t s = 10 -1 x 20 ms

10. 10 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. Bunch-slice parallel decomposition M. Pivi (SLAC)

11. 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  z =5.0*10 -3 m  p=6.3*10 -4 ppb= 5.7 10 12 MacroParticleNumber=3 x 10 5 Grid size = 10  y x 10  x # bunch slices = 64 # processors for this run = 64 IBS-Track CMAD M. Pivi (SLAC), T. Demma (INFN) Dec 1, 2011

12. 12 CPU timing studies: SuperB LER 1 turn CPU Time [sec]GainN. of Processors 40011 2501.62 20024 468.716 2416.332 162564 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. 13 Emittance Evolution in SuperB LER M. Pivi (SLAC), T. Demma (INFN)

14. 14 IBS Distribution study Parameter    Confidence  1857.56 <1e-6 X 1455.68 <1e-6 Y 778.228 0.6920 M. Pivi (SLAC), T. Demma (INFN)

15. 15 SIRE: IBS Distribution study: CLIC DR ParameterValue Eq.  x (m rad) 2.001e-10 Eq.  y (m rad) 2.064e-12 Eq.   1.992e-3 Eq.  z (m) 1.687e-3 Parameter    Confidence  p/p 3048.7<1e-15 X1441.7<1e-15 Y1466.9<1e-15 A. Vivoli (CERN)

16. 16 SuperB Damping Ring 5/29/11 A damping ring at 1 GeV is used to reduce the positron beam injected emittance 16 M. Preger Energy (GeV)1 Circumference (m)51.1 Equilibrium horizontal emittance (nm) 23 Equilibrium vertical emittance, k=.01 (nm) 0.2 betatron damping time (ms)7.3 Equilibrium energy spread6.2 10 -4 Momentum compaction5.7 10 -3 RF frequency475 RF voltage (MV)0.5 Bunch length (low current, mm)4.8

17. 17  x (m)  z (m) Injection1100e-91.5e-4 Extraction w/ IBS25e-93.3e-6 Extraction w/o IBS23e-92.97e-6 IBS in SuperB Damping Ring Only 1 IP per tun is conidered

18. 18 The SLS lattice ParameterValue Energy [GeV]2.411 Circumference [m]288 Energy loss/turn [MeV]0.54 RF voltage [MV]2.1 Mom. Comp. factor6.05e -4 Damping times h/v/l [ms]8.59/8.55/4.26 Hor. emittance [nm rad]5.6 Vert. emittance [pm rad]2 Bunch length [mm]3.8 Energy spread [%]0.086  Picture shows the interpolated beta and h functions. In particular: Sqrt[betax] (magenta), Sqrt[betay] (blue), 20*hx (gold), 10 5 *hy (green). 18 F. Antoniou (CERN)

19. 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. 20 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.) Summary

21. 21 SPARES

22. 22 Radial and longitudinal emittance growths can be predicted by a model that takes the form of a coupled differential equations: 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 Differential equation system for  x and  z Obtained by fitting the zero bunch intensity case (IBS =0) Bane Model

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

24. 24 Summary plots: DAFNE parameters  z =12.0*10 -3  p=4.8*10 -4 e x =(5.63*10 -4 )/g e y =(3.56*10 -5 )/g t x = 1000 -1 * 0.042 t y = 1000 -1 * 0.037 t s = 1000 -1 * 0.017 MacroParticleNumber=40000 NTurn=1000 (≈10 damping times)

25. 25 SIRE: SLS simulations 1/Tx (s -1 )1/Ty (s -1 )1/Tz (s -1 ) MADX (B-M)203759 SIRE (compressed) 15.624.547.2 SIRE (not compressed) 14.423.442.2 A. Vivoli, F. Antoniou

26. 26 SIRE: IBS Distribution study D: IBS ParameterValue pp 5.281e+7 pp 1.568 xx 3.840e+10 xx 1.280 yy 4.557e+12 yy 1.196 Parameter    ConfidenceSample %  P/P 38.810.3926 X36.730.4825 Y46.830.1322 A. Vivoli

27. 27 Bjorken-Mtingwa

28. 28 Piwinski

29. 29 Bane’s high energy approximation Bjorken-Mtingwa solution at high energies Changing the integration variable of B-M to λ ’ =λσ H 2 /γ 2  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