Academia.eduAcademia.edu

Outline

STATUS OF HEAD-ON BEAM-BEAM COMPENSATION IN RHIC *

https://doi.org/10.5170/CERN-2014-004.109

Abstract

In polarized proton operation the RHIC performance is limited by the head-on beam-beam effect. To overcome this limitation two electron lenses are under commission-ing. We give an overview of head-on beam-beam compen-sation in general and the specific design for RHIC, which is based on electron lenses. The status of installation and commissioning are presented along with plans for the fu-ture.

References (81)

  1. G. Arzelia et al., Proc. 8th Int. Conf. High Energy Acc., pp. 150 (1971).
  2. M. Bergher et al., "Status report on D.C.I." proceedings of 1979 Particle Accelerator Conference, San Francisco, CA, USA, pp. 3559-3561 (1979).
  3. Ya.S. Derbenev, "Collective instability of compensated col- liding beams", Nuclear Physics Institute, Siberian Division, Academy of Sciences USSR, Novosibirsk, Report No IYAF 70-72, in Russian (1972), SLAC-TRANS 151 in English.
  4. N.N. Chau and D. Potau, "Stabilit des oscillations transverse dans un anneau charge despace compensée", LAL Orsay (1974 and 1975).
  5. B. Podobedov and R.H. Siemann, "Coherent beam-beam in- teraction with four colliding beams", Phys. Rev. E 52, No 3, pp. 3066-3073 (1995).
  6. E. Tsyganov, R. Meinke, W. Nexsen, A. Zinchenko, "Com- pensation of the beam-beam effect in proton colliders", SSCL-PREPRINT-519 (1993).
  7. E. Tsyganov, E. Tarantin, A. Zinchenko, "Compensation of space charge effect at beam-beam interactions in proton pro- ton colliders", JINR-E9-96-4 (1996).
  8. V. Shiltsev, V. Danilov, D. Finley, and A. Sery, "Consider- ations on compensation of beam-beam effects in the Teva- tron with electron beams", Phys. Rev. ST Accel. Beams 2, 071001 (1999).
  9. E.N. Tsyganov, A. Taratin, and A.I. Zinchenko, "Beam- beam compensation at the LHC", CERN SL-Note-95-116- AP (1995).
  10. W. Scandale and F. Zimmermann, "Head-on compensa- tion in LHC", presentation at US LARP Mini-Workshop on Beam-beam Compensation, SLAC, (2009).
  11. U. Dorda, F. Zimmermann, W. Fischer, and V. Shiltsev, "LHC beam-beam compensation using wires and elec- tron lenses", proceedings of the 2007 Particle Accelerator Conference, Albuquerque, New Mexico; LHC-PROJECT- Report-1023 (2007).
  12. Y. Ohnishi and K. Ohmi, "Beam-beam simulations in four- beam scheme for high-luminosity e+e-collider", proceed- ings of HALO'03 and Beam-Beam'03, Montauk, New York, AIP Conference Proceedings 693 (2003).
  13. A. Burov, V. Danilov, and V. Shiltsev, "Transverse beam sta- bility with an electron lens", Phys. Rev. E 59, 3605 (1999).
  14. S. White, M. Blaskiewicz, and W. Fischer, "Coherent beam- beam effects in experiments and implications for head-on beam-beam compensation", these proceedings.
  15. V. Shiltsev and A. Zinchenko, "Electron beam distortions in beam-beam compensation setup", Phys. Rev. ST Accel. Beams 1, 064001 (1998).
  16. V. Shiltsev, Y. Alexahin, K. Bishofberger, V. Kamerdzhiev, G. Kuznetsov, and X.-L. Zhang, "Experimental demonstra- tion of colliding-beam-lifetime improvement by electron lenses", Phys. Rev. Lett. 99, 244801 (2007).
  17. X.-L. Zhang, K. Bishofberger, V. Kamerdzhiev, V. Lebedev, V. Shiltsev, R. Thurman-Keup, and A. Tollestrup, "Gener- ation and diagnostics of uncaptured beam in the Fermilab Tevatron and its control by electron lenses", Phys. Rev. ST Accel. Beams 11, 051002 (2008).
  18. V. Shiltsev, K. Bishofberger, V. Kamerdzhiev, S. Kozub, M. Kufer, G. Kuznetsov, A. Martinez, M. Olson, H. Pfeffer, G. Saewert, V. Scarpine, A. Seryi, N. Solyak, V. Sytnik, M. Tiunov, L. Tkachenko, D. Wildman, D. Wolff, and X.-L. Zhang, "Tevatron electron lenses: Design and operation", Phys. Rev. ST Accel. Beams 11, 103501 (2008).
  19. G. Stancari, A. Valishev, G. Annala, G. Kuznetsov, V. Shilt- sev, D. A. Still, and L. G. Vorobiev, "Collimation with hol- low electron beams", Phys. Rev. Lett. 107, 084802 (2011).
  20. V. Shiltsev, private communication.
  21. G. Stancari and A. Valishev, "Beam-beam compensation studies in the Tevatron with electron lenses", these proceed- ings.
  22. J. Alessi (editor), "Electron Beam Ion Source Pre-Injector Project (EBIS), Conceptual Design Report", BNL-73700- 2005-IR (2005).
  23. J.G. Alessi, E.N. Beebe, S. Binello, L.T. Hoff, T. Kanesue, K. Kondo, R.F. Lambiase, V. LoDestro, M. Mapes, A. Mc- Nerney, J. Morris, M. Okamura, A.I. Pikin, D. Raparia, U. Ratzinger, J. Ritter, A. Schempp, L. Smart, L. Snydstrup, M. Wilinski, and A. Zaltsman, "Commissioning of the EBIS- based heavy ion preinjector at Brookhaven", proceedings of LINAC2010, Tsukuba, Japan, pp. 1033-1037 (2010)
  24. C. Montag, L. Ahrens, M. Bai, J. Beebe-Wang, M. Blask- iewicz, J.M. Brennan, K.A. Brown, D. Bruno, R. Con- nolly, T. D'Ottavio, A. Drees, A.V. Fedotov, W. Fischer, G. Ganetis, C.J. Gardner, J.W. Glenn, H. Hahn, M. Har- vey, T. Hayes, H. Huang, P. Ingrassia, J. Jamilkowski, D. Kayran, J. Kewisch, R.C. Lee, D. Lowenstein, A.U. Luc- cio, Y. Luo, W.W. MacKay, Y. Makdisi, N. Malitsky, G.J. Marr, A. Marusic, M.P. Menga, R. Michnoff, M. Minty, J. Morris, B. Oerter, F.C. Pilat, P. Pile, E. Pozdeyev, V. Ptitsyn, G. Robert-Demolaize, T. Roser, T. Russo, T. Sato- gata, V. Schoefer, C. Schultheiss, F. Severino, M. Sivertz, K. Smith, S. Tepikian, P. Thieberger, D. Trbojevic, N. Tsoupas, J. Tuozzolo, A. Zaltsman, A. Zelenski, K. Zeno, and S.Y. Zhang, "RHIC Performance as a 100 GeV Polarized Proton Collider in Run-9", proceedings of the 2010 International Particle Accelerator Conference, Kyoto, Japan, pp. 531-533 (2010).
  25. H. Huang, L. Ahrens, I.G. Alekseev, E. Aschenauer, G. Atoian, M. Bai, A. Bazilevsky, M. Blaskiewicz, J.M. Bren- nan, K.A. Brown, D. Bruno, R. Connolly, A. Dion, T. D'Ottavio, K.A. Drees, W. Fischer, C.J. Gardner, J.W. Glenn, X. Gu, M. Harvey, T. Hayes, L. Hoff, R.L. Hulsart, J.S. Laster, C. Liu, Y. Luo, W.W. MacKay, Y. Makdisi, G.J. Marr, A. Marusic, F. Meot, K. Mernick, R.J. Michnoff, M.G. Minty, C. Montag, J. Morris, S. Nemesure, A. Poblaguev, V. Ptitsyn, V. Ranjbar, G. Robert-Demolaize, T. Roser, B. Schmidtke, V. Schoefer, F. Severino, D. Smirnov, K. Smith, D. Steski, D. Svirida, S. Tepikian, D. Trbojevic, N. Tsoupas, J.E. Tuozzolo, G. Wang, M. Wilinski, K. Yip, A. Zaltsman, A. Zelenski, K. Zeno, and S.Y. Zhang, "RHIC polarized proton operation and highlights", proceedings International Particle Accelerator Conference 2011, San Sebastian, Spain, pp. 1888-1890 (2011).
  26. V. Schoefer, L. Ahrens, G. Atoian, M. Bai, J. Beebe-Wang, M. Blaskiewicz, J.M. Brennan, K.A. Brown, D. Bruno, R. Connolly, T. D'Ottavio, K.A. Drees, W. Fischer, C.J. Gard- ner, J.W. Glenn, X. Gu, M. Harvey, T. Hayes, L.T. Hoff, H. Huang, R. Hulsart, J.S. Laster, C. Liu, Y. Luo, G.J. Marr, A. Marusic, F. Meot, K. Mernick, R. Michnoff, M. Minty, C. Montag, J. Morris, S. Nemesure, A. Poblaguev, V. Ptitsyn, V.H. Ranjbar, G. Robert-Demolaize, T. Roser, F. Severino, K. Smith, D. Steski, S. Tepikian, D. Trbojevic, N. Tsoupas, J. Tuozzolo, G. Wang, M. Wilinski, K. Yip, A. Zaltsman, A. Zelenski, K. Zeno, and S.Y. Zhang, "RHIC polarized proton operation in Run 12", proceedings of the International Parti- cle Accelerator Conference 2012, New Orleans, Louisiana, USA, pp. 184-186 (2012).
  27. Y. Luo, M. Bai, W. Fischer, C. Montag, and S. White, "Beam-beam effects in RHIC", BNL C-AD/AP/467 (2012).
  28. Y. Luo, M. Bai, W. Fischer, C. Montag, and S. White, "Beam-beam effects in RHIC", proceedings of the 52th ICFA Advanced Beam Dynamics Workshop on High Inten- sity High Brightness Hadron Beams HB2012, Bejing, China (2012).
  29. S.M. White, W. Fischer, and Y. Luo, "Coherent beam-beam effects observation and mitigation at the RHIC collider", proceedings of the International Particle Accelerator Con- ference 2012, New Orleans, Louisiana, USA, pp. 193-195 (2012).
  30. Y. Luo and W. Fischer, "Beam-beam observations in RHIC", these proceedings.
  31. F. Zimmermann and J. Poole (editors), proceedings of the Workshop on Beam-Beam Effects in Large Hadron Collid- ers, LHC99, CERN, CERN-SL-99-039 AP (1999).
  32. T. Sen and M. Xiao (eds.), proceedings of the Work- shop on Beam-Beam Effects in Circular Colliders, FNAL, FERMILAB-Conf-01/390-T (2001)
  33. W. Fischer and T. Sen (eds.), proceedings of the Work- shop on Beam-Beam effects in Circular Colliders, Beam- Beam'03, Montauk, NY, USA, proceedings of HALO'03 and Beam-Beam'03, Montauk, New York, AIP Conference Proceedings 693 (2003).
  34. V. Shiltsev, Y. Alexahin, V. Lebedev, P. Lebrun, R. S. Moore, T. Sen, A. Tollestrup, A. Valishev, and X. L. Zhang, "Beam- beam effects in the Tevatron", Phys. Rev. ST Accel. Beams 8, 101001 (2005).
  35. W. Fischer (issue editor) and W. Chou (executive editor), "ICFA Beam Dynamics Newsletter No. 52 -Current beam- beam problems", (2010).
  36. W. Herr, E. Metral, and T. Pieloni (eds.), these proceedings.
  37. A. Zelenski, "OPPIS with fast atomic beam source" pre- sentation 2011 Particle Accelerator Conference, New York, USA (2011).
  38. Y. Luo and W. Fischer, "Outline of using an electron lens for the RHIC head-on beam-beam compensation", BNL C- A/AP/286 (2007).
  39. Y. Luo, W. Fischer, and N. Abreu, "Stabiliy of single par- ticle motion with head-on beam-beam compensation in the RHIC", BNL C-A/AP/310 (2008).
  40. Y. Luo, W. Fischer, N. Abreu, E. Beebe, J. Beebe-Wang, C. Montag, M. Okamura, A. Pikin, and G. Robert-Demolaize, "Head-on beam-beam compensation with electron lenses in the Relativistic Heavy Ion Collider", proceedings of the 2008 European Particle Accelerator Conference, Genoa, Italy, pp. 1616-1618 (2008).
  41. Y. Luo, G. Robert-Demolaize, N. Abreu, and W. Fischer, "Multi-particle weak-strong simulation of head-on beam- beam compensation in the RHIC", proceedings of the 2008 European Particle Accelerator Conference, Genoa, Italy, pp. 3125-3127 (2008).
  42. N.P. Abreu, W. Fischer, Y. Luo, and G. Robert-Demolaize, "The effect of head-on beam-beam compensation on the stochastic boundaries and particle diffusion in RHIC", pro- ceedings of the 2008 European Particle Accelerator Confer- ence, Genoa, Italy, pp. 2521-2523 (2008).
  43. W. Fischer, Y. Luo, N. Abreu, R. Calaga, C. Montag, G. Robert-Demolaize, U. Dorda, J.-P. Koutchouk, G. Sterbini, F. Zimmermann, H.-J. Kim, T. Sen, V. Shiltsev, A. Val- ishev, J. Qiang, and A. Kabel, "Long-range and head-on compensation studies in RHIC with lessons for the LHC", proceedings Final CARE-HHH Workshop on Scenarios for the LHC Upgrade and Fair -HHH-2008 -Chavannes- de-Bogis, Switzerland; W. Scandale and F. Zimmermann (eds.), CERN-2009-004 (2009); CARE-Conf-08-032-HHH (2008).
  44. N.P. Abreu, W. Fischer, Y. Luo, and G. Robert-Demolaize, "Stochastic boundary, diffusion, emittance growth and life- time calculation for the RHIC e-lens", BNL C-A/AP/347 (2009).
  45. A. Valishev, Y. Luo, and W. Fischer, "Summary of the LARP mini-workshop on electron lens simulations at BNL", BNL C-A/AP/353 (2009).
  46. Y. Luo, N.P. Abreu, R. de Maria, W. Fischer, G. Robert- Demolaize, and E. McIntosh, "Weak-strong simulation of head-on beam-beam compensation in the RHIC", proceed- ings of the 2009 Particle Accelerator Conference, Vancou- ver, Canada, pp. 94-96 (2009).
  47. W. Fischer, Y. Luo, and C. Montag, "Bunch length effects in the beam-beam compensation with an electron lens", BNL C-AD/AP/359 (2010).
  48. W. Fischer, Y. Luo, and C. Montag, "Bunch length effects in the beam-beam compensation with an electron lens", pro- ceedings of the 2010 International Particle Accelerator Con- ference, Kyoto, Japan, pp. 4755-4757 (2010).
  49. C. Montag, W. Fischer, and D.M. Gassner, "Optimiz- ing the beam-beam alignment in an electron lens using bremsstrahlung", proceedings of the 2010 International Par- ticle Accelerator Conference, Kyoto, Japan, pp. 537-539 (2010).
  50. W. Fischer, E. Beebe, D. Bruno, A.V. Fedotov, D.M. Gassner, X. Gu, R.C. Gupta, J. Hock, A.K. Jain, R. Lambi- ase, Y. Luo, M. Mapes, W. Meng, C. Montag, B. Oerter, M. Okamura, A.I. Pikin, D. Raparia, Y. Tan, R. Than, J. Tuoz- zolo, and W. Zhang, "Status of the RHIC head-on beam- beam compensation project", proceedings of the 2010 Inter- national Particle Accelerator Conference, Kyoto, Japan, pp. 513-515 (2010).
  51. Y. Luo and W. Fischer, "6-D Weak-strong Simulation of head-on beam-beam compensation in the RHIC", proceed- ings of the 2010 International Particle Accelerator Confer- ence, Kyoto, Japan, pp. 4758-4760 (2010).
  52. Y. Luo and W. Fischer, "Simulation study of dynamic aper- ture with head-on beam-beam compensation in the RHIC", BNL C-AD/AP/392 (2010).
  53. Y. Luo, W. Fischer and X. Gu, "Coupling effect on the pro- ton optics from the electron lenses", BNL C-AD/AP/395 (2010).
  54. X. Gu, A. Pikin, M. Okamura, W. Fischer, Y. Luo, R. Gupta, J. Hock, A. Jain, and D. Raparia, "RHIC electron lens beam transport system design considerations", BNL C- AD/AP/409 (2010).
  55. X. Gu, Y. Luo, A. Pikin, M. Okamura, W. Fischer, C. Mon- tag, R. Gupta, J. Hock, A. Jain, and D. Raparia, "Effect of the electron lenses on the RHIC proton beam closed orbit", BNL C-AD/AP/424 (2011).
  56. X. Gu, M. Okamura, A. Pikin, W. Fischer, and Y. Luo, "The effects of realistic pancake solenoids on particle transport", Nucl. Instrum. and Methods A 637, pp. 190-199 (2011).
  57. W. Fischer, M. Anerella, E.N. Beebe, D. Bruno, D.M. Gassner, X. Gu, R.C. Gupta, J. Hock, A.K. Jain, R.F. Lam- biase, C. Liu, Y. Luo,, M. Mapes, T.A. Miller, C. Montag, B. Oerter, M. Okamura, A.I. Pikin, D. Raparia, Y. Tan, R. Than, P. Thieberger, J.E. Tuozzolo, and W. Zhang, "Status of the RHIC head-on beam-beam compensation project", proceedings of the 2011 Particle Accelerator Conference, New York, USA, pp. 2223-2225 (2011).
  58. Y. Luo, W. Fischer, X. Gu, and A.I. Pikin, "Optimizing the electron beam parameters for head-on beam-beam compen- sation in RHIC", proceedings of the 2011 Particle Acceler- ator Conference, New York, USA, pp. 70-72 (2011).
  59. A.I. Pikin, J.G. Alessi, M. Anerella, E.N. Beebe, W. Fischer, D.M. Gassner, R.C. Gupta, J. Hock, R.F. Lambiase, Y. Luo, C. Montag, M. Okamura, D. Raparia, Y. Tan, P. Thieberger, J.E. Tuozzolo, and W. Zhang, "Structure and design of the electron lens for RHIC", proceedings of the 2011 Particle Accelerator Conference, New York, USA, pp. 2309-2311 (2011).
  60. X. Gu, W. Fischer, R.C. Gupta, J. Hock, Y. Luo, M. Oka- mura, A.I. Pikin, and D. Raparia, "Designing a beam trans- port system for RHIC's electron lens", proceedings of the 2011 Particle Accelerator Conference, New York, USA, pp. 1205-1207 (2011).
  61. X. Gu, W. Fischer, R.C. Gupta, J. Hock, Y. Luo, M. Oka- mura, A.I. Pikin, and D. Raparia, "The effects of the RHIC e-lenses' magnetic structure layout on the proton beam tra- jectory", proceedings of the 2011 Particle Accelerator Con- ference, New York, USA, pp. 1202-1204 (2011).
  62. R.C. Gupta, M. Anerella, W. Fischer, G. Ganetis, A.K. Ghosh, X. Gu, A.K. Jain, P. Kovach, A. Marone, A.I. Pikin, S.R. Plate, and P. Wanderer, "Magnetic design of e-lens solenoid and corrector system for RHIC", proceedings of the 2011 Particle Accelerator Conference, New York, USA, pp. 1130-1132 (2011).
  63. P. Thieberger, E.N. Beebe, C. Chasman, W. Fischer, D.M. Gassner, X. Gu, R.C. Gupta, J. Hock, R.F. Lambiase, Y. Luo, M.G. Minty, C. Montag, M. Okamura, A.I. Pikin, Y. Tan, J.E. Tuozzolo, and W. Zhang, "Proposed electron halo detector system as one of the beam overlap diagnostic tools for the new RHIC electron lens", proceedings of the 2011 Particle Accelerator Conference, New York, USA, pp. 489- 491 (2011).
  64. C. Montag, M. Bai, K.A. Drees, W. Fischer, A. Marusic, and G. Wang, "Beam experiments related to the head-on beam- beam compensation project at RHIC", proceedings of the 2011 Particle Accelerator Conference, New York, USA, pp. 2243-2245 (2011).
  65. P. Thieberger, E. Beebe, W. Fischer, D. Gassner, X. Gu, K. Hamdi, J. Hock, M. Minty, T. Miller, C. Montag, and A. Pikin, "Design of a proton-electron beam overlap moni- tor for the new RHIC electron lens, based on detecting en- ergetic backscattered electrons", proceedings Beam Instru- mentation Workshop BIW12, Newport News, VA (2012).
  66. T.A. Miller, J. Aronson, D.M. Gassner, and A. Pikin, "RHIC electron lens beam profile monitoring" proceedings Beam Instrumentation Workshop BIW12, Newport News, VA (2012).
  67. W. Fischer, Z. Altinbas, M. Anerella, E. Beebe, M. Blask- iewicz, D. Bruno, W.C. Dawson, D.M. Gassner, X. Gu, R.C. Gupta, K. Hamdi, J. Hock, L.T. Hoff, A.K. Jain, R. Lambi- ase, Y. Luo, M. Mapes, A. Marone, T.A. Miller, M. Minty, C. Montag, M. Okamura, A.I. Pikin, S.R. Plate, D. Raparia, Y. Tan, C. Theisen, P. Thieberger, J. Tuozzolo, P. Wanderer, S.M. White, and W. Zhang "Construction progress of the RHIC electron lenses", proceedings of the International Par- ticle Accelerator Conference 2012, New Orleans, Louisiana, USA, pp. 2125-2127 (2012).
  68. X. Gu, J. Addessi, Z. Altinbas, J.N. Aronson, E. Beebe, W. Fischer, D.M. Gassner, K. Hamdi, J. Hock, L.T. Hoff, P. Kankiya, R. Lambiase, Y. Luo, M. Mapes, J.-L. Mi, T.A. Miller, C. Montag, S. Nemesure, M. Okamura, R.H. Olsen, A.I. Pikin, D. Raparia, P.J. Rosas, J. Sandberg, Y. Tan, C. Theisen, P. Thieberger, J. Tuozzolo, R. Zapasek, and W. Zhang, "The e-lens test bench for RHIC beam-beam com- pensation", proceedings of the International Particle Accel- erator Conference 2012, New Orleans, Louisiana, USA, pp. 2720-2722 (2012).
  69. X. Gu, W. Fischer, D.M. Gassner, K. Hamdi, J. Hock, Y. Luo, C. Montag, M. Okamura, A.I. Pikin, and P. Thieberger, "A split-electrode for clearing scattered electrons in the RHIC e-lens", proceedings of the International Particle Ac- celerator Conference 2012, New Orleans, Louisiana, USA, pp. 4038-4040 (2012).
  70. Y. Luo, W. Fischer, N.P. Abreu, A. Pikin, and G. Robert- Demolaize, "Six-dimensional weak-strong simulation of head-on beam-beam compensation in the Relativistic Heavy Ion Collider", Phys. Rev. ST Accel. Beams 15, 051004 (2012).
  71. S.M. White, W. Fischer, and Y. Luo, "Simulations of coher- ent beam-beam effects with head-on compensation", pro- ceedings of the International Particle Accelerator Confer- ence 2012, New Orleans, Louisiana, USA, pp. 187-189 (2012).
  72. T.A. Miller, J.N. Aronson, D.M. Gassner, X. Gu, A.I. Pikin, and P. Thieberger, "Electron lens test stand instrumentation progress", proceedings of the 2012 International Beam In- strumentation Conference, Tsukuba, Japan (2012).
  73. X. Gu, F.Z. Altinbas, E. Beebe, B. M. Frak, W. Fischer, D.M. Gassner, K. Hamdi, J. Hock, L. Hoff, P. Kankiya, R. Lambiase, Y. Luo, M. Mapes, J. Mi, T. Miller, C. Mon- tag, S. Nemesure, M. Okamura, R. H. Olsen, A.I. Pikin, D. Raparia, P. J. Rosas, J. Sandberg, Y. Tan, C. Theisen, P. Thieberger, J. Tuozzolo, and W. Zhang, "RHIC electron lens test bench -high intensity electron beam characteristics and hardware commissioning", report in preparation (2013).
  74. D.M. Gassner, E. Beebe, W. Fischer, X. Gu, K. Hamdi, J. Hock, C. Liu, T.A. Miller, A. Pikin, and P. Thieberger, "RHIC electron lens test bench diagnostics", proceedings of DIPAC2011, Hamburg, Germany, pp. 38-40 (2011).
  75. E. Keil, "Beam-beam dynamics", in CERN 95-06, pp. 539- 555 (1995).
  76. E.D. Courant and H. Snyder, "Theory of the Alternating- Gradient Synchrotron", Annals of Physics 281, pp. 360-408 (1957).
  77. D.A. Edwards and M. Syphers, "Linear betatron motion", in "Handbook of accelerator physics and engineering", 3rd printing, World Scientific, p. 65 (2006)
  78. M. Bai, private communication (2011).
  79. G. Kuznezov, BINP Novosibirsk (2011).
  80. A. Jain, "Plans for measurement of field straightness in the solenoids for the electron lens system for RHIC", presen- tation at 17 th International Magnetic Measurement Work- shop, IMMW17, Barcelona, Spain (2011).
  81. P. Görgen, O. Boine-Frankenheim, and W. Fischer, "BTF measurements with beam-beam interactions", these pro- ceedings.