CSR-Driven Longitudinal Instability – Comparison of Theoretical

1. CSR-Driven Longitudinal Instability – Comparison of Theoretical and Experimental Results Peter Kuske, Helmholtz-Zentrum Berlin, Germany 3rd Low Emittance Ring Workshop, 8th-10th July, 2013, Oxford, UK

2. Content of the Talk Introduction - Detection of CSR and Signals of Unstable Beams Theoretical Predictions Comparison of Predictions with Observations IV. Summary 2

3. I.1 Observation of CSR @ BESSY II K. Holldack, et al., THPKF013, EPAC‘04

4. I.2 Observation of CSR @ ANKA, MLS, ATF, … S. De Santis, et al., THPCH067, EPAC‘06 Hot Electron Bolometer A.-S. Müller, et al., TU5RFP027, PAC‘09

5. I.3 Observation of CSR @ Diamond G. Rehm, et al., TUPD32,DIPAC‘09

6. I.4 Observations @ Diamond R. Bartolini, et al., THPC068, IPAC‘11

7. I.5 Observations @ ANKA by V. Judin, et al.

8. I.6 Observations @ MLS G. Wüstefeld, et al., WEPA015, IPAC‘10

9. I.7 Observations @ BESSY II BESSY II, Fsyno=1 kHz, o~1.5 ps Many modes visible in the Fourier transformed CSR 9 9

10. II.1 Shielded CSR-Impedance d=2h, plate separation Broad band resonator with low Q: ANKA: Fres ~ 127 GHz BESSY II: Fres ~ 100 GHz MLS: Fres ~ 44 GHz R.L. Warnock, PAC'91, PAC1991_1824, http://www.JACoW.org 10

11. II.2 Theoretical Result

12. II.3 Shielded CSR-Wake – BESSY II Scsr ~ 0.5 + 0.12·X(Bane, et al., IPAC’10)

13. II.3 Shielded CSR-Wake – BESSY II

14. II.3 Shielded CSR-Wake – BESSY II

15. II.4 Shielded CSR-Wake

16. II.5 Frequency of First Unstable Mode vs. norm. 0 BBR-Wake: variation of Fres with constant o and Shielded CSR-Wake: Fres given by geometry and variation of o through α

17. II.6 Bunch Length, inst, at Instability Threshold Broad-Band-Resonator Impedance Shielded CSR Impedance

18. II.7 Frequency of First Unstable Mode vs. norm. inst

19. III.1 First Unstable Modes BESSY II Slope agrees with resonance Fres~100 GHz 19 19

20. III.2 CSR-Threshold Currents for BESSY II In fair agreement with predictions – bunch lengthening explains shift Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010) 20 20

21. III.3 CSR-Threshold Currents for the MLS Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010) 21 21

22. III.4 CSR-Threshold Currents Observed at ANKA Observation at ANKA: Stability between 45 μA and 60 μA, below and above the beam is longitudinally unstable

23. III.5 Parameters for ANKA RMS bunch length: σ = 1.953 ps Bending radius: ρ = 5.593 m Height of dipole chamber: 2·h = 0.032 m Energy: E = 1.3 GeV Momentum compaction factor: α = 2.033 10-4 Accelerating voltage: Vrf = 1.8 MV Longitudinal damping time: Τlong = 10.6 ms Synchrotron frequency: Fsyn = 7.8 kHz Damping/excitation parameter:β = 1.93 10-3 CSR-impedance has first maximum at: Fres = c·(/24)1/2·ρ1/2·h-3/2 = 126.7 GHz Shielding parameter (à la Bane, et al.): Χ = c·σ·ρ1/2·h-3/2 = 0.684 or 2Fres·σ = 1.555 Shielded CSR-Impedance at ANKA Decscription of the code: P. Kuske, “CSR-DRIVEN LONGITUDINAL SINGLE BUNCH INSTABILITY THRESHOLDS”, WEOAB102, IPAC’13, Shanghai, China

24. III.6 Result of the Simulation Beam is longitudinally stable below 20 μA and between ~48 μA and ~59 μA

25. III.7 Result of the Simulation: Normalized Energy Spread vs. Time Stability – thin lines, normalized energy spread = 1.0 Oscillations – thick lines, normalized energy spread > 1.0 Bursts – more or less regular, saw tooth instability

26. III.8Result of the Simulation: CSR-Signal 60 μA

27. III.8Result of the Simulation: CSR-Signal 48 μA

28. IV.1Summary of the Results for ANKA • Very good agreement between the observations at ANKA and the results of the numerical solution of the VFP-equation: • Correct predictions for the regions of longitudinal stability and instability • Correct predictions for the dominant mode of the longitudinal instability: • Dipole mode at 20 μA, above ~36 μA quadrupole mode with a shift to lower frequencies as the current is increased • Quadrupole mode above 60 μA shifting upwards with increasing bunch charge

29. IV.2 Status of CSR-Driven Longitudinal Instability Example for ANKA: 0=5.5 ps, Fsyn=8.5 kHz, Vrf=0.7 MV (E=1.3 GeV, α=6.24e-4): 2Fres·0 = 4.38  Finst ~4.5·Fsyn~ 38 kHz  Scsr ~ 0.8, Ithr ~ 0.32 mA V. Judin, et al., TUPPP010, IPAC’12

30. IV.3 Observations @ ANKA by V. Judin, et al.

31. Predictions using the shielded CSR-wake are in surprisingly good agreement with measurements at BESSY II, MLS, ANKA, and other storage rings. If the bunch length is known then we can estimate the shielding parameter or normalized resonance frequency and predict the threshold current. The observed resonance-like features show the importance of the vertical gap of the dipole vacuum chamber. Increasing the cavity voltage gradient will not necessarily lead to higher threshold currents for shorter bunches – consequences for BESSY-VSR. CSR-driven longitudinal single bunch instability thresholds are of no concern for low emittance rings – coupled multi bunch instabilities could be an issue because of the tube-like vacuum chambers. If bunch length and Finst are known then we can determine the dominant frequency of the impedance. Longitudinal modes below the instability thresholds can be observed - with sensitive detectors. The support of Dennis Engel is acknowledged. IV.4 Summary 31