Beambeam3D and IMPACT: Development and Applications Ji Qiang Lawrence Berkeley National Laboratory

1. Beambeam3D and IMPACT: Development and Applications Ji Qiang Lawrence Berkeley National Laboratory

2. BeamBeam3D

3. BeamBeam3D • Comprehensive parallel PIC code for modeling colliding beams (weak-strong, strong-strong, head-on, crossing angle, long-range) • Recent enhancements • Integrated Green function • Non-uniform grid Green function • Energy variation during collisions • Multi-bunch and multi-collision • Applied to Tevatron, LHC, PEP-II, KEK-B, and RHIC

4. A Schematic Plot of the Geometry of Two Colliding Beams Head-on collision Long-range collision Crossing angle collision y 2R Field Domain 0 -R R 2R x Particle Domain

5. Green Function Solution of Poisson’s Equation ; r = (x, y) Direct summation of the convolution scales as N4 !!!! N – grid number in each dimension

6. Green Function Solution of Poisson’s Equation Hockney’s Algorithm:- scales as (2N)2log(2N) - Ref: Hockney and Easwood, Computer Simulation using Particles, McGraw-Hill Book Company, New York, 1985. Shifted Green function Algorithm for long range beam-beam forces: - Ref: J. Qiang, M. Furman, R. Ryne, PRST-AB, vol. 5, 104402 (2002).

7. Green Function Solution of Poisson’s Equation Integrated Green function Algorithm for large aspect ratio: - Ref: K. Ohmi, Phys. Rev. E, vol. 62, 7287 (2000). J. Qiang, M. Furman, R. Ryne, J. Comp. Phys., 2004 (in press). Ey x (sigma)

8. Green Function Solution of Poisson’s Equation On Non-Uniform Grid

9. Non-Uniform Grid vs. Standard Uniform Grid (Gaussian density distribution with aspect ratio 1 and 128x128 grid) Errors of Er vs. r Er vs. r Non-uniform grid Uniform grid

10. Green Function Solution of Poisson’s Equation • Standard shifted uniform grid method • (2N)2log (2N) • Low aspect ratio • Long range beam-beam • Lower accuracy than the non-uniform grid method • Integrated shifted uniform grid method • (2N)2log (2N) • Large aspect ratio • Long range beam-beam • Costly in calculation of the effective Green function • Non-uniform grid method • 2N2log (2N) • Low aspect ratio

11. Parallel Implementation Issues:Performance Counts! • Example: Scaling of BeamBeam3D Performance of different parallelization techniques in strong-strong case Scaling using weak-strong option Strong-strong beam-beam will be crucial to LHC Optimization

12. Benefit to HEP and NP Programs • Beambeam3D has been applied to: • LHC • RHIC • Tevatron • PEP-II • Effort has involved collaboration with many people: • LBNL: M. Furman, R. Ryne, W. Turner • FNAL: T. Sen, M. Xiao, P. Spentzouris, J. Amundson • BNL: W. Fischer • SLAC: Y. Cai • KEK: K. Ohmi

13. Beam Sweeping Detector for LHC rotating, deliberately displaced beam stationary, accidentally displaced beam

14. Simulated LHC Luminosity Signal and Emittance Growth after One Million Turns LHC beam-beam simulation nx1=nx2= ny1=ny2=0.31, x0=–0.0034 parallel PIC code 128x128 grid 10**6 particles/bunch 1 kick 16 processors 1 bunch/beam Emittance growth vs. Number of Macroparticles

15. Power Spectrum of Horizontal Centroid Motion of Three Bunches in RHIC (Self Consistent Strong-Strong Simulation) Collaboration w/ Wolfram Fischer, BNL s mode p mode

16. Power Spectrum under Different Tunes Horizontal tune of beam 2: 0.21 Horizontal tune of beam 2: 0.20

17. Parameter Studies of Anti-Proton Lifetime of Tevatron at Injection Energy Antiproton Lifetime vs. Beam-Beam Separation Antiproton Lifetime vs. Antiproton Emittance

18. Parameter Studies of Anti-Proton Lifetime of Tevatron at Injection Energy Antiproton Lifetime vs. Proton Intensity simulations raw data Antiproton Lifetime vs. Vertical Chromaticity

19. Beam-Beam Studies of PEP-II • Collaborative study/comparison of beam-beam codes (J. Qiang/LBNL, Y. Cai/SLAC, K. Ohmi/KEK) • Predicted luminosity sensitive to # of slices used in simulation 20 slices 1 slice

20. IMPACT

21. IMPACT (Integrated-Map and Particle Accelerator Tracking) code • A code suite (linac design code, 3D rms envelope code, 2 parallel PIC tracking codes) • Recent enhancements • IMPACT-T: time-based (instead of z-based) version • Cathode emission model • Images from cathode • Poisson solver for high aspect ratio situations • Energy binning for large energy spread • Multi-charge state capability • These enhancements benefit projects • Modeling rf photoinjectors • Modeling beams w/ large energy spread, as for electron bunches emerging from plasma-based accelerators • Multi-charge state for RIA

22. Poisson Solvers • Integrated 3D Green function • Shifted 3D Green function • High aspect ratio Poisson solvers based on Hermite-Gaussian expansion Potential of a beam in a toroidal conducting pipe

23. RAL • PSI • GSI • KEK • SLAC • LBNL • LANL • TX corp • FNAL • ORNL • MSU • BNL • Jlab • Cornell • NIU Impact User-Map

24. Benefit of IMPACT to HEP and NP Programs • Collaboration w/ P. Spentzouris and J. Amundson (FNAL) • FNAL booster modeling reuses portions of IMPACT • Collaboration with LANL, ANL, MSU • Simulation of the RIA driver linac • Studies of space-charge effects, resonances, and equipartitioning in rings • Simulation and analysis of CERN PS experiment • Collaboration w/ P. Piot (FNAL) • Modeling photocathode for linear collider

25. Combining IMPACT and MXYZPLTK for FNAL Booster modeling Booster simulation results and experimental results. P. Spentzouris and J. Amundson, FNAL.

26. Beam Dynamics Modeling of RIA Linac Driver Kinetic Energy vs. Distance RMS Phase Width vs. Distance

27. Physics Study and Code Benchmarking of CERN PS experment using IMPACT-Z • Study of emittance exchange near a 4th order coupling resonance during tune scan (collab. w/ Ingo Hofmann) • Experimental measurements and 3D simulation with IMPACT show that exchange overshoot is reduced with slower ramping • this is a 3D effect involving synch. motion; 2D simulation does not predict this 240 turn ramp 480 turn ramp 960 turn ramp 1920 turn ramp emittance turn #

28. Photoinjector Modeling Several customers are using IMPACT-T for photoinjector studies, and others have expressed interest • Using: • LUX • ALS streak camera • LCLS • Cornell ERL • Fermilab RF photoinjector • Expressed interest: • ANL advanced accelerator project • BNL electron cooling project • JLab

29. RF photoinjector simulation using 3D IMPACT-T • Parallel simulation w/ IMPACT-T using 1M particles is more than 2x faster than PARMELA using 100K particles • Good agreement for test case (azimuthal symmetry) • In general, 3D problems require more particles & mesh points than 2D • Parallel processing makes it possible to perform 3D simulations, and perform parametric studies, with reasonable turnaround time

30. Modeling Collisional Effects • In collaboration w/ J. Wei (BNL), have performed comparisons of the Langevin approach with a finite difference model • Langevin results and FD results are in excellent agreement, but Langevin does not have instability problem present in FD method Finite difference curves are underneath Langevin results

31. Summary • Our new capabilities are benefiting national and international programs • The codes we have developed or helped develop have been applied to many important problems. Examples: • Beam-beam effects at Tevatron, LHC, PEP-II, and RHIC • Dynamics of beams w/ large energy spread from plasma accelerators • RF photocathode simulation • Beam losses at FNAL booster • Understanding beam halo formation, emittance growth, and equipartitioning in high intensity beams

32. Publications (Jan 2002 - Present)Refereed Journals • J. Qiang, R. D. Ryne, I,. Hofmann, “Space-charge driven emittance growth in a 3D mismatched anisotropic beam,” Phys. Rev. Lett. 92, 174801 (2004). • J. Qiang, M. Furman, and R. Ryne, “A Parallel Particle-In-Cell Model for Beam-Beam Interactions in High Energy Ring Colliders,” J. Comp. Phys. (in press) • J. Qiang, R. Gluckstern, "Three-dimensional poisson solver for a charged beam with large aspect ratio in a conducting pipe", Comp. Phys. Comm. 160, 120 (2004). • K. Ohmi, M. Tawada, Y. Cai, S. Kamada, K. Oide, J. Qiang, “Study of the beam-beam limit in e+e- circular colliders, “ Phys. Rev. Lett. 92, 214801 (2004). • J. Qiang, "Halo formation due to beam-beam interactions of beams optically mismatched at injection", PRST-AB, vol 7, 031001 (2004). • T. P. Wangler, C. K. Allen, K. C. D. Chan, P. L. Colestock, K. R. Crandall, R. W. Garnett, J. D. Gilpatrick, W. Lysenko, J. Qiang, J. D. Schneider, M. E. Shulze, R. L. Sheffield, H. V. Smith, “Beam-halo in mismatched proton beams,” Nucl. Instr. Meth. Phys. Res. A 519, 425 (2004). • I. Hofmann, G. Franchetti, O. Boine-Frankenheim, J. Qiang, and R. D. Ryne, "Space Charge Resonances in Two and Three Dimensional Anisotropic Beams," PRST-AB, vol 6, 024202 (February 2003).

33. Publications (Jan 2002 - Present) Refereed Journals (cont.) • J. Qiang and R. W. Garnett, "Smooth Approximation with Acceleration in an Alternating Phase Focusing Superconducting Linac," Nucl. Instr. Meth. Phys. Res. A 496, 33 (2003). • J. Qiang, P. L. Colestock, D. Gilpatrick, H. V. Smith, T. P. Wangler, and M. E. Schulze, "Macroparticle Simulation Studies of a Proton Beam Halo Experiment," PRST-AB, vol 5, 124201 (2002). • C. K. Allen, K. C. D. Chan, P. L. Colestock, K. R. Crandall, R. W. Garnett, J. D. Gilpatrick, W. Lysenko, J. Qiang, J. D. Schneider, M. E. Shulze, R. L. Sheffield, H. V. Smith, and T. P. Wangler, "Beam-Halo Measurements in High-Current Proton Beams," Physics ReviewLetters 89 (21) (November 2002). • J. Qiang, M. Furman, and R. Ryne, "Strong-Strong Beam-Beam Simulation Using a Green Function Approach," PRST-AB, vol 5, 104402 (October 2002). • J. Qiang, R. Ryne, and R. Garnett, "Systematic Comparison of Position and Time Dependent Macroparticle Simulations in Beam Dynamics Studies," PRST-AB, vol 5, 064201 (June 2002).