1. November 14, 2004First ILC Workshop1 CESR-c Wiggler Dynamics D.Rubin -Objectives -Specifications -Modeling and simulation -Machine measurements/ analysis

2. November 14, 2004First ILC Workshop2 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

3. November 14, 2004First ILC Workshop3 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)

4. November 14, 2004First ILC Workshop4 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 I B = 200 mA

5. November 14, 2004First ILC Workshop5 Ideal Wiggler Vertical kick ~  B s

6. November 14, 2004First ILC Workshop6 7-pole, 1.3m 40cm period, 161A, B=2.1T Superconducting wiggler prototype

7. November 14, 2004First ILC Workshop7 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

8. November 14, 2004First ILC Workshop8 7 and 8 pole wiggler transfer functions

9. November 14, 2004First ILC Workshop9 Wiggler Field Model -Finite element code -> 3-d field table -Fit analytic form to table

10. November 14, 2004First ILC Workshop10 Wiggler modeling -Phase space mapping Fit parameters of series to field table Analytic form of Hamiltonian -> symplectic integration -> taylor map

11. November 14, 2004First ILC Workshop11 7-pole wiggler

12. November 14, 2004First ILC Workshop12 Measurement and correction of linear lattice Measured - modeled Betatron phase and transverse coupling

13. November 14, 2004First ILC Workshop13 Measurement of wiggler nonlinearity -Measurement of betatron tune vs displacement consistent with modeled field profile and transfer functon

14. November 14, 2004First ILC Workshop14 Wiggler Beam Measurements -Injection 1 sc wiggler (and 2 pm CHESS wigglers) -> 8mA/min 6 sc wiggler -> 50mA/min 1/  = 4.5 s -1 1/  = 10.9s -1

15. November 14, 2004First ILC Workshop15 Wiggler Beam Measurements 6 wiggler lattice -Injection 30 Hz 68mA/80sec60 Hz 67ma/50sec

16. November 14, 2004First ILC Workshop16 Wiggler Beam Measurements -Single beam stability 1/  = 4.5 s -1 1/  = 10.9s -1 2pm + 1 sc wigglers 6 sc wigglers

17. November 14, 2004First ILC Workshop17 Sextupole optics Modeled pretzel dependence of betatron phase due to sextupole feeddown Difference between measured and modelled phase with pretzel after correction of sextupoles

18. November 14, 2004First ILC Workshop18 Optimization of sextupole distribution eliminates synchro-betatron resonance

19. November 14, 2004First ILC Workshop19 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

20. November 14, 2004First ILC Workshop20 Acknowledgement A. Mikhailichenko, S.Temnykh, D. Rice, J. Crittenden, D.Sagan, E. Forest and the CESR operations group

21. November 14, 2004First ILC Workshop21 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

22. November 14, 2004First ILC Workshop22 Transverse RF introduces bunch dependent offsets Transverse RF compensates offsets Circumference = 4km Linear collider damping ring Rich Helms