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CESR-c Wiggler Dynamics

CESR-c Wiggler Dynamics. D.Rubin. -Objectives -Specifications -Modeling and simulation -Machine measurements/ analysis. CESR-c Superconducting Wigglers - Damping and emittance wigglers for 1.8GeV operation Reduce radiation damping time by X 10 (500ms->50ms)

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CESR-c Wiggler Dynamics

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  1. CESR-c Wiggler Dynamics D.Rubin -Objectives -Specifications -Modeling and simulation -Machine measurements/ analysis First ILC Workshop

  2. CESR-c Superconducting Wigglers - Damping and emittance wigglers for 1.8GeV operation Reduce radiation damping time by X 10 (500ms->50ms) • Injection repitition transfer rate from synchrotron is limited by damping time in storage ring • Single and multi-bunch instability thresholds scale inversely with damping rate • Beam beam tune shift limit ~ (damping rate)1/3 • Tolerance to parasitic beambeam effects ~ (damping rate)1/3 Increase horizontal emittance Beam beam current limit ~ emittance Michael Roman First ILC Workshop

  3. CESR-c Electrostatically separated electron-positron orbits accomodate counterrotating trains Electrons and positrons collide with ±~3 mrad horizontal crossing angle 9 5-bunch trains in each beam (768m circumference) First ILC Workshop

  4. Wiggler specifications: - 2.1T peak field (vs 0.2T max bending field) -Uniform over 9cm horizontal aperture, -Long period (40cm) to minimize vertical cubic nonlinearity -Complete installation is 12, 1.6m superconducting wigglers - CESR-c is a wiggler dominated storage ring • (>90% of synchrotron radiation in 768m ring in 19m of • superconducting wigglers) - 3kW/wiggler synchrotron radiation with IB = 200 mA First ILC Workshop

  5. Ideal Wiggler Vertical kick ~  Bs First ILC Workshop

  6. 7-pole, 1.3m 40cm period, 161A, B=2.1T Superconducting wiggler prototype First ILC Workshop

  7. Wiggler model: - Phase space mapping through wigglers required for simulation of dynamical effects - Create field vs position table for wiggler geometry with OPERA-3D finite element code - Measured field in good agreement with computed field table First ILC Workshop

  8. 7 and 8 pole wiggler transfer functions First ILC Workshop

  9. Wiggler Field Model • Finite element code -> • 3-d field table • Fit analytic form to table First ILC Workshop

  10. Wiggler modeling • Phase space mapping Fit parameters of series to field table Analytic form of Hamiltonian -> symplectic integration -> taylor map First ILC Workshop

  11. 7-pole wiggler First ILC Workshop

  12. Measurement and correction of linear lattice Measured - modeled Betatron phase and transverse coupling First ILC Workshop

  13. Measurement of wiggler nonlinearity • Measurement of betatron tune vs displacement consistent with • modeled field profile and transfer functon First ILC Workshop

  14. Wiggler Beam Measurements • Injection 1 sc wiggler (and 2 pm CHESS wigglers) -> 8mA/min 1/ = 4.5 s-1 6 sc wiggler -> 50mA/min 1/ = 10.9s-1 First ILC Workshop

  15. Wiggler Beam Measurements6 wiggler lattice • Injection 30 Hz 68mA/80sec 60 Hz 67ma/50sec First ILC Workshop

  16. Wiggler Beam Measurements • Single beam stability 6 sc wigglers 2pm + 1 sc wigglers 1/ = 10.9s-1 1/ = 4.5 s-1 First ILC Workshop

  17. Sextupole optics Modeled pretzel dependence of betatron phase due to sextupole feeddown Difference between measured and modelled phase with pretzel after correction of sextupoles First ILC Workshop

  18. Optimization of sextupole distribution eliminates synchro-betatron resonance First ILC Workshop

  19. Summary • CESR-c is a wiggler dominated storage ring • Wigglers reduce damping time by a factor of 10 • Injection rate and multibunch instability thresholds • are increased as anticipated • Analytic form for magnetic field (including ends) • yields accurate phase space mapping • Measured and modeled • Linear and nonlinear focusing effects • Emittance • Damping rate • Dynamic aperture • in good agreement • Conclusion: Good understanding of dynamics of wiggler • dominated damping ring First ILC Workshop

  20. Acknowledgement • A. Mikhailichenko, S.Temnykh, D. Rice, J. Crittenden, • D.Sagan, E. Forest • and the CESR operations group First ILC Workshop

  21. ILC Damping Ring R&D • Evaluate dynamic aperture of various alternatives • Determine dependence of acceptance on - linear lattice parameters - sextupole distribution to minimize energy dependence and optimize aperture • Consider dependence on wiggler period/peak field/unit length • Continue study of transverse RF for separation of closely space bunches First ILC Workshop

  22. Linear collider damping ring Transverse RF introduces bunch dependent offsets Transverse RF compensates offsets Circumference = 4km Rich Helms First ILC Workshop

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