1. Coupled bunch Instabilities at ILC Damping Rings L. Wang SLAC ILC Damping Rings R&D Workshop - ILCDR06 September 26-28, 2006 Cornell University Refer to EPAC06 THPCH077 L. Wang, K.L.F. Bane, T. Raubenheimer and M. Ross

2. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Outline Introduction and Motivation Simulation techniques CBI due to RF HOMs Resistive wall instability (Effects of beam pattern, tune, aperture and material of the beam pipe, coating, feedback, etc.) Summary Outlook

3. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Motivation Non-equidistant filling schemes (effect of train gaps; effect of de-tuning due to variation of bunch frequency) Modeling different impedances (such as, Both long range and intermediate range wake) Interplay between different effects (nonlinearity, feedback, fast ion, etc…) transition procedure Simulation allows:

4. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Simulation Linear transfer matrices & kicks Bellows & other resonators RF Cavity Resistive Wall Feedback kicker  6-Dimensional Model  Radiation damping  RF HOMs, Resistive Wall & other impedance  Linear transfer with nonlinear element, like octupoles  Bunch-by-bunch feedback  Any beam fill pattern &bunch current  Realistic distributed wake along the ring Numerical method allow us to study transition procedure combination effect

5. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Sample I : bunch train instability 4 th bunch Detuning effect

6. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Sample II: Effect of Longitudinal feedback on transverse instability Experimental, TRISTAN Feedback off Longitudinal Feedback on simulation Both Longitudinal and transverse Feedback on Transverse Longitudinal A similar phenomenon was found at ATF (J. Fox, ect)

7. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Fill patterns 5782 bunches : 118 trains 49 bunches per train Bunch spacing 2 RF buckets =3ns Train gap: 25RF buckets=38ns Bunch intensity : 0.97E10 2767 bunches : 1 short train with 22 bunches + 61 long train with two short train in each long train (23 bunches per train+ 22 bunches per train) Bunch spacing: 4 buckets =6ns Train gap: 28 buckets=43ns Bunch intensity : 2.02E10 DescriptionValue Beam energy5.0 GeV Circumference6695 km Harmonic number14516 RF frequency650 MHz Tunes52.28/47.40 Momentum compaction 0.40  10 -3 Number of bunches2767~5782 Bunch intensity 0.97~2.02  10 10 Emittance at injection 5.0  10 -10 m Average betatron function22.5m

8. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 HOMs KEKB superconducting cavity

9. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 CBI due to HOMs 10 cavities are assumed; Alfa=0.405706E-03 Vrf=46.60MV Qs=9.26E-02 Damping time XY=0.026s Damping time s=0.013s(600turn) U0=8.69 [MeV/turn] T0=22  s The instability is damped by radiation damping!

10. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Resistive wall instability & related issues Circumference = 6695.057384 Qx=52.28 Qy=47.40 Harmonic number=14516 (650MHz RF) Optics of New 6km ring  Beam pipe aperture  Material of beam pipe (vacuum & impedance, ecloud)  Vacuum  Electron cloud  instabilities

11. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Options of the beam pipe Aperture of the beam pipe (mm) Material of the beam pipe Option 44/16/100option 50/32/100option 50/46/100 ARC4450 Wiggler163246 Straight100 Effective aperture X/Y34.18/34.1645.75/46.5647.30/48.39 Growth time b: radius of beam pipe  : conductivity  : betatron function MaterialConductivity  -1m-1 SEYOutgassing Pa m/s Stainless steel1.37×10 6 2.6 1×10 -10 Aluminum3.773×10 7 3? Copper5.977×10 7 2 1×10 -11

12. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Secondary Emission Yield (SEY) Al SEY of AL. and Stainless Steel, J. Appl. Phys 88-478 (2000), Carlos Alberto Fonzar Pinta et al. SEY of copper, B. Henrist, et al. Copper Al Stainless steel

13. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Thermal outgassing rate J. Vac. Sci. Technol. A 19.2., Mar/Apr 2001, Fumio Watanabea

14. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Benchmark Even fill pattern 7258 bunches; bunch intensity 7.727E+09 Average Beta function 22.479 m BETATRON TUNE 47.4012 Material: Stainless Steel Aperture of beam pipe: 40mm Analytical Growth time =8.3910 turns Simulated growth time =8.7036 turns

15. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Option 44/16/100 (Arc/Wig/Str) Fill pattern: 5782 bunchesFill pattern: 2767 bunches Option 50/32/100 (Arc/Wig/Str) Double I.D. of wiggler  =8.73turn  =8.67turn  =20.8 turn  =20.7 turn Aperture effect (Stainless steel) Instability due to the wigglers with small aperture is important. Option 50/46/100  =23 turn

16. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Copper-coated stainless steel Real part of impedance for stainless steel, copper and copper-coated stainless steel. t=0.1mm qx=0.28 qy=0.40 The lowest frequency of interest for the resistive-wall instability is q times the revolution frequency. Here q is the fractional part of the betatron tune, A thickness of 0.1mm copper is assumed, which corresponds to a shielding frequency of 0.45MHz. Above 0.45MHz, the impedance is basically determined by the copper layer, while below it, the impedance is influenced by the stainless steel.  =0.58mm  =0.48mm

17. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Option 44/16/100; copper-coated stainless steel Fill pattern: 5782 bunches; Fill pattern: 2767 bunches; Thickness 100 micro-m  = 8.67 turns  =8.73 turns  =36.26 turns  =35.98 turns W.O. coating coated

18. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Summary of the effects of the aperture, fill pattern and material MaterialBeam pattern Option 44/16/100 Option 50/32/100 Option 50/46/100 Stainless steel5782 bunches 8.7320.8222.95 Stainless steel2767 bunches 8.6720.7022.78 Aluminum5782 bunches 45.81109.26120.44 Aluminum2767 bunches 45.50108.6119 Copper-coated Stainless steel 5782 bunches 36.26 Copper-coated Stainless steel 2767 bunches 35.98 Growth time in turn

19. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Effect of work point qx=0.28 qy=0.40 Growth time for different of fractional betatron tune. Copper-coated stainless steel, 2676 bunches, aperture option I.

20. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Bunch-by-bunch Feedback Instability Modes with feedback gain 40turns/0.89ms (a) and 30turns/0.67ms (b). The feedback was turned on at the 100th turn. Copper-coated stainless steel with aperture Option I. Tau0=36.26turns Feedback  Required Bandwidth: 325MHz  Feedback damping time:0.2ms(10 turns) (similar as B- factories)(80~100turns for CBI, FII is faster)  Voltage: >20kV! injected emittance 100nm, beta function=40m, injection offset= 1mm

21. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Summary  Instabilities due to RF HOMs are damped by radiation damping.  Growth time is not sensitive to the beam fill pattern (hence RF frequency)  The effect of q is not much  Growth time with Aluminum pipe is factor of 5 longer than that with stainless steel pipe.  If the I.D. of wiggler > 32mm, the growth time will be longer than 20/100 turns (Stainless steel /Al.)  0.1mm Copper-coated stainless steel can reduce the growth rate by a factor of 4.  High voltage of feedback kick is required at injection

22. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Outlook CBI with future detail model of the impedance Realistic model of feedback with injection beam Integrated simulation of instabilities due to various kinds of sources (impedance, ion-cloud, feedback, nonlinear element, etc.) from injection to extraction.

23. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 FII at ILC L. Wang, T. Raubenheimer, A.Wolski EPAC06 WEPCH103

24. ILC Damping Rings R&D Workshop, Cornell, Sep. 26 Acknowledgement Thanks to all colleagues in the damping ring study, especially thanks to K.L.F. Bane, Y. Cai, A. Chao, J. Fox, S. Heifets, T. Raubenheimer, M. Ross, G. Stupakov, A.Wolski.