1 / 47

Limits of Beam-Beam Interactions

Limits of Beam-Beam Interactions. Ji Qiang Lawrence Berkeley National Laboratory. Joint EIC2006 & Hot QCD Workshop, BNL, July 17 - 22. Outline. Introduction Experimental observations Physical mechanisms Computational models Validation of computer codes

kimberly
Download Presentation

Limits of Beam-Beam Interactions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Limits of Beam-Beam Interactions Ji Qiang Lawrence Berkeley National Laboratory Joint EIC2006 & Hot QCD Workshop, BNL, July 17 - 22

  2. Outline • Introduction • Experimental observations • Physical mechanisms • Computational models • Validation of computer codes • Beam-beam issues in linac-ring colliders • Summary

  3. Beam Blow-Up during the Collision

  4. Beam-Beam Interactions • Limit the peak luminosity • Reduce the beam lifetime • Cause extra background • Large number of particles loss may quench superconducting machine

  5. Luminosity and Beam-Beam Parameter

  6. Beam-Beam Limits • First beam-beam limit • Saturation of beam-beam parameter • Luminosity scales linearly with current • Second beam-beam limit • Ultimate limit of luminosity • Loss of particles and reduce of beam lifetime

  7. x & Luminosity vs. Current for e+e- Rings (J. Seeman, 1983) CESR PETRA PEP SPEAR 2ndb-b limit due to tails! 1st beam-beam limit (max. x)

  8. Background Noise and Scraper Location vs. Current (J. Seeman, 1983)

  9. Luminosity vs. Current Square at PEP-II (J. Seeman et al, 2001)

  10. Transverse Size vs. Current Square at PEP-II (J. Seeman et al, 2001)

  11. Observation of Flip-Flop at PEP-II: Transverse Beam vs. Bunch Number (R. Holtzapple, et al (2002)

  12. Observation of Flip-Flop at PEP-II: Luminosity vs. Bunch Number (R. Holtzapple, et al, 2002)

  13. Observation of Flip-Flop at PEP-II: Horizontal Width vs. Snap Picture Number at LER R. Holtzapple, et al (2002)

  14. Lepton Beam-Beam Tune shift vs. Proton Current at HERA(F. Willeke 2002)

  15. e+ Beam-Beam Limit at HERAtune footprint appears to be limited by 3rd & 4th order resonances H1 and Zeus spec. lumi vs time beams separated in South IP luminosity in the North increases 3Qy 2Qx+2Qy 4Qx

  16. RHIC Working Point and Background (W. Fischer, 2003) Deuteron-gold collisions, x / IP  0.001, 4 head-on collisions Lowest order resonances are of order 9 between 0.2 and 0.25 High background rates near 9th order resonaces Low background rates near 13th resonances

  17. Contour Plots of Background Halo Rates for Protons and Antiprotons at Tevatron (V. Shiltsev et al 2005) 5th 12th 12th 7th 5th

  18. Beam-Beam Parameters in Hadron Accelerators (W. Fischer, 2003)

  19. Beam-Beam Parameters in Lepton Accelerators (F. Zimmermann, 2003)

  20. Physical Mechanisms • Collective/Coherent Resonance (Keil 1981, Dikansk and Pestrikov 1982, Chao and Ruth 1985, Hirata 1987, Krishnagopal and Siemann, 1991, Shi and Yao, 2000) • Dipole mode instability • Quadrupole model instability • Flip-flop • Period n oscillation higher mode instability • Blow-up • Higher order modes

  21. Stability Region of Coherent Dipole Mode (Keil, Chao, Hirata) tune

  22. Stability Diagram for Coherent Resonance up to 2 and 4 (Chao and Ruth, 1985) 0.20 x Max Mode =2 x Unstable 0.10 Max Mode =4 Unstable 1 0 n0 0 n0

  23. Particle Loss due to Incoherent Diffusion IBS Touschek orbit noise Arnold diffusion background scattering tune fluctuation resonance overlap beam-beam bremsstrahlung quantumn excitation resonance trapping nonlinear resonance random fluctuation collision diffusion particle loss

  24. Resonance Traping: Particle Transport by Slow Phase Space Topology Change (A. Chao 1979)

  25. Resonance overlap: Phase Space Evolution vs. Increasing Beam-Beam Tune Shift (J. Tennyson 1979)

  26. Computational Models • Weak-Strong • One beam (weak beam) is subject to the electromagnetic fields of the other beam (strong beam) while the effects of weak beam on strong beam are neglected • Strong-Strong • The electromagnetic fields from both oppositely rotating beams are included

  27. Weak-Strong Model • Advantages • Only one electromagnetic field calculation is needed. This model is fast and many macroparticles can be used in tracking studies. • The model is useful for halo/lifetime calculations or some quick machine parameter scan • Disadvantages • Sensitive only to incoherent effects • Not self-consistent

  28. Strong-Strong Model • Advantages • Sensitive to both incoherent and coherent effects • Self-consistently modeling of beam-beam interaction • Disadvantages • Electromagnetic fields from each beam have to be calculated at each collision • Computational expensive • Need advanced algorithms and computers

  29. Strong-Strong Model • Soft-Gaussian model • The particle distribution is assumed as a Gaussian distribution with 1st and 2nd moments updated after each collision • Self-consistent model • PIC: electromagnetic fields are calculated at each collision point based on the charge distribution on a grid from macroparticle deposition • Direct numerical Vlasov-Poisson solver

  30. Particle-In-Cell (PIC) Simulation Initialize particles Setup for solving Poisson equation Advance momenta using radiation damping and quantum excitation map Advance positions & momenta using external transfer map Charge deposition on grid Field solution on grid Field interpolation at particle positions (optional) diagnostics Advance momenta using Hbeam-beam forces

  31. Finite Difference Solution of Poisson’s Equation (S. Krishnagopal, 1996, Y. Cai, et al., 2001) • Five point stencil with Fourier analysis by cyclic reduction (FACR) • Reduced grid: • Before solving the Poisson equation, the potential on the reduced grid boundary is determined by a Green’s function method • Poisson solver uses FFT and cyclic reduction (FACR) • Computational complexity: • Scales as N2log(N) within the domain: N – grid number in each dimension • Needs 4N3to find the boundary condition

  32. Hybrid Fast Multipole Solution of Poisson’s Equation (W. Herr, M. P. Zorzano, F. Jones, 2001) • Divided the solution domain into a grid and a halo area • Charge deposition with the grid • Multipole expansions of the field are computed for each grid point as well as for every halo particle • Computation complexity: • Scales as PN2 or PNp

  33. Green Function Solution of Poisson’s Equation (K. Yokoya, K. Oide, E. Kikutani, 1990, E. Anderson et. al. 1999, K. Ohmi, et. al. 2000, J. Shi, et. al, 2000, J. Qiang, et. al. 2002, A. Kabel, 2003) ; r = (x, y) Direct summation of the convolution scales as N4 !!!! N – grid number in each dimension

  34. Green Function Solution of Poisson’s Equation (cont’d) 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: - Ref: J. Qiang, M. Furman, R. Ryne, PRST-AB, vol. 5, 104402 (2002).

  35. 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., vol. 198, 278 (2004). Ey x (sigma)

  36. Needs for High Performance Computers • Number of particles per bunch: • 1010 – 1011 • Number of turns: • 109 - 1010 • Number of bunches per beam: • 1 - 1000

  37. We are now able to perform 100M particle strong-strong simulation on 1024 processors During the development of BeamBeam3D, several parallelization strategies were tested. The large amount of particle movement between collisions gives the standard approach (domain decomposition, bottom curve) poor scalability for the strong-strong model. A hybrid decomposition approach (top curve) has the best scalability. Scaling on seaborg using strong-strong model (100Mp, 512x512x32 grid, 4 slices)

  38. Synchrobetaron Mode Tunes vs. Beam-Beam Parameter Measurement vs Simulation (BeamBeam3D) Stern and Valishev et. al. SciDAC2006 poster

  39. Specific Luminosity vs. beta* at HERA (J. Shi et al, 2003) b

  40. Luminosity of a Routine Operation of PEP-II: Measurement vs Simulation (Y. Cai et. al. 2001)

  41. Linac-Ring Beam-Beam Interaction • Electron beam is re-injected from linac after each turn. This avoids the beam-beam tune shift limit or e-cloud limit to electron intensity inherent in storage ring. • Issues: • Beam-beam head-tail instability • Electron disruption

  42. Schematic Plot of Synchrobetatron Modes E. Perevedentsev and A. Valishev, PRSTAB, 4, 024403 (2001)

  43. Synchrobetatron Mode Increments vs. Beam-Beam Parameter (Zero Chromaticity)

  44. Threshold Value of D_x+/ns vs. Disruption Parameter (R. Li et al, 2001)

  45. Synchrobetatron Mode Increments vs. Beam-Beam Parameter (Finite Chromaticity 0.409) (E. Perevedentsev and A. Valishev)

  46. Summary • Beam-beam limit has been improved by fine tuning of machine, lepton ~ 0.1, hadron ~ 0.01 per IP. • Theoretical models provide a lot of insights to understand beam-beam limits. • Computer codes can reasonably reproduce coherent spectrum and luminosity. However, prediction of beam lifetime is still a challenge. • Linac-ring collider looks promising but detailed study of beam-beam limits including chromaticity and full 3d nonlinearity is needed.

  47. Acknowledgements A. Chao, Y. Cai, W. Fischer, M. Furman, W. Herr, K. Hirata, R. Holtzapple, V. Lebedev, R. Li, L. Merminga, K. Ohmi, E. Perevedentsev, R. Ryne, J. Seeman, J. Shi, C. Siegerist, V. Shiltsev, E. Stern, J. Tennyson, A. Valishev, F. Willeke, F. Zimmermann

More Related