1. 1 Strong-Strong Beam-Beam Simulations Ji Qiang Lawrence Berkeley National Laboratory 3 rd JLEIC Collaboration Meeting March 31 st, Jlab 2016

2. 2 The probability of event is proportional to the luminosity of colliding beams. Luminosity depends on: Larger luminosity wants higher repetition rate, larger beam-beam parameters, smaller crossing angle and beam separation. However, beam-beam effects limit these factors and eventually luminosity. High Energy Collider Needs Large Luminosity for Physics Study

3. 3 Beam-Beam Effects Can Cause Beam Blow-up/Emittance Growth Limiting Final Luminosity

4. 4 Beam-Beam Physical Models = - L:f 1 (r,p) = 0 L:f 2 (r,p) = 0 Coupled Poisson-Vlasov Equations = -

5. 5 x y Particle Domain -R2RR 0 A Schematic Plot of the Geometry of Two Colliding Beams Field Domain Head-on collision Long-range collision Crossing angle collision

6. 6 Particle-In-Cell (PIC) Simulation Advance positions & momenta a half step using H ext Advance momenta using H space charge  Field solution on grid  Charge deposition on grid  Field interpolation at particle positions Setup and solve Poisson equation Initialize particles (optional) diagnostics Advance positions & momenta a half step using H ext

7. 7 Radial Electric Field vs. Distance inside the Field Domain with Gaussian Density Distribution in Particle Domain Radial Electric Field vs. Distance inside the Particle Domain with a Gaussian Density Distribution Self-Consistent Calculation of Beam-Beam Field Numerical Solution vs. Analytical Solution

8. 8 Multiple-slice model for finite bunch length New algorithm -- shifted Green function -- efficiently models long- range collisions Parallel particle-field based decomposition to achieve perfect load balance Lorentz boost to handle crossing angle Radiation damping, quantum fluctuation Arbitrary closed-orbit separation Multiple bunches, multiple collision points Linear transfer matrix + one turn chromaticity Conducting wire, crab cavity, e-lens compensation model Feedback model Impedance model BeamBeam3D: Parallel Strong-Strong / Strong-Weak Simulation Code

9. 9 Parallel Implementation Issues: Performance Counts! Example: Scaling of BeamBeam3D # of processors execution time (sec) 1281612 256858 512477 1024303 2048212 Scaling using weak-strong option Performance of different parallelization techniques in strong-strong case

10. 10 32003004 50 1 64003380100 0.89 128003734200 0.80 256003270400 0.92 5120003283800 0.92 # processors time (sec) problem sizeefficiency Parallel Beam-Beam Optimization: Weak Scaling Test on Cray XT-5 at NCCS

11. 11 Parallel Optimization Parallel Luminosity Optimization w.r.p. Tune Working Point for Jlab/ELIC: Time-to-solution: 35 years (serial code, serial optimizer) reduced to 100 days (parallel code, serial optimizer) reduced to 24hrs (parallel code, parallel optimizer) Parallel optimization of Jlab/ELIC luminosity using a differential evolutionary algorithm to select best working point in four dimensional tune space; performed on 12800 processors on Jaguarpf at NCCS; population size = 100, procs/population_member = 128 Peak luminosity as a function of generation. Peak luminosity evolution with nominal and optimal tune working point at the JLab proposed ELIC collider.

12. 12 Pi Mode Tune Shift vs. Horizontal Separation (simulation vs. analytic model I)

13. 13 Kink Instability (simulation vs. analytical solution II) Emittance growth vs. ion intensityAnalytical Model for Instability Threshold Good agreement between numerical simulation results and analytical model analytical model from Y. Hao PRST-AB simulation

14. 14 Simulation of LHC Observation (1) Luminosity vs. Offset 14 Very good agreement between experiment, simulation and theory

15. 15 LHC Observation (II): Working Point Optimization Fill 1990 – 0.31/0.32 Fill 1991 - 0.308/0.318 Fill 1992 - 0.312/0.322 Courtesy of G. Arduini, J. Wenninger

16. 16 Emittance Evolution with 3 Working Points

17. 17 Tune Footprint with Three Working Points (0.308,0.318) (0.31,0.32) (0.312,0.322)

18. 18 LHC Upgrade will Improve the LHC Luminosity by an Order of Magnitude

19. 19 IP5 CAB 21 A Schematic Plot of LHC Upgrade Using Crab Cavities IP IP1 21

20. 20 Luminosity vs. Beta* for LHC Crab Cavity Compensation with crab cavity no crab cavity

21. 21 Analytical Model of White Noise Induced Emittance Growth in Colliding Beams beam-beam parameter 0

22. 22 Some Physical Parameters Used in the Simulations Physical parameters  (normalized) 3.75 um pick-up gain0.02-0.1 Tunes Chromaticity 64.31/59.32 0 β*β* 50 cm 0.0 mrad ξ_tot N IPs 0.003-0.03 1. - 9x10 11 1

23. 23 gain = 0.02 Emittance Growth Rate vs. Beam-Beam Parameter (Simulation vs. Analytical Solution) gain = 0.02 gain = 0.1

24. 24 Horizontal Power Spectral, Emittance, Centroid Evolution (with different gains, beambeam param. = 0.016)

25. 25 white noise offset collision drives emittance growth K. Ohmi, in Proc. Beam-Beam 2013 workshop. RF Noise in the Crab Cavity Causes Emittance Growth and Luminosity Degradation 0 th order error (phase error): 1 st order error (voltage error):

26. 26 Some Physical Parameters Used in the Simulations Physical parameters  (norm.) 2.5 um pick-up gain0.05/0.05 Tunes Chromaticity 62.31/60.32 0 – 4 β*β* 15-60 cm 0.59 mrad ξ_tot N IPs 0.011 - 0.022 1.1 - 2.2x10 11 2

27. 27 Emittance Blow-up due to Phase or Voltage White Noise emittance blow-up from phase error 8e-5 emittance blow-up from voltage error 5e-5. Np = 2.2 x 10 11, beta* = 0.49 m

28. 28J. Qiang et al., in Proc. IPAC2015. Luminosity Degradation due to Phase or Voltage White Noise Lum. degradation rate vs. phase noise amp.Lum. degradation rate vs. voltage noise amp. In order to have a good luminosity lifetime ~ 20 hours, the white noise amplitude needs to be kept below the level of a few 10 -5. crab cavity white noise tolerance level ~10 -5

29. 29 Courtesy of T. Mastori Frequency-Dependent Crab Cavity Noise Power Spectrum (dBc/Hz) frequency (Hz)

30. 30 RMS Emittance Evolution with Different Noise Amplitudes Np = 2.2 x 10 11, beta* = 0.15 m nominal noise amplitude = 3 x 10 -4

31. 31 Peak Luminosity Evolution with Different Noise Amplitudes Np = 2.2 x 10 11, beta* = 0.15 m

32. 32 CC Noise Induced Lumi. Degradation with vs. beta* (with nominal noise amplitude) strong dependence on the beta function at IP

33. 33 CC Noise Induced Lumi. Degradation with vs. Intensity (with nominal noise amplitude) weaker dependence on the beam intensity

34. 34 Lumi. Degradation with Different Chromaticities (and with nominal CC noise amplitude) not quite sensitive to machine linear chromaticity

35. 35 Thank You!