1. CSR-driven Single Bunch Instability P. Kuske, Helmholtz Zentrum Berlin ESLS XX, 19/20 November 2012, Berlin

2. Content of the Talk I.Instability for resistive and inductive impedance II.CSR-driven instability Comparison of theoretical and experimental thresholds: II.1MLS II.1.1Similarity between resistive and CSR-wake II.1.2Threshold determination II.2BESSY II III.Instability thresholds with high RF-gradient IV.Summary and Outlook Details on the VFP-simulations in my ICAP ‘12 contribution 2

3. I.1 Results for some Fundamental Interactions – Resistive Impedance 3 Analytical solutions for the Haiissinski equation are known – most obvious features of wake/impedance: V ind (t)=I 0 T 0 ·R·I(t) energy loss per turn increases with intensity, triangular shape of I(t), weak instability above certain threshold (K. Oide, 1995) Result of measurements of the synchronous phase shift at DIAMOND (G. Rehm, et al. DIPAC 2011) Loss factor 50 – 70 V/pC leads to

4. 44 Oide's dimensionless parameter: Instability thresholds: black solid line - weak instability theory by K. Oide, Part. Accel. 51, 43 (1995), numerical results for the Diamond Light Source (DLS) and BESSY II DLS: Vrf=2, 4, 8, and 16 MV BESSY II: Vrf=0.7,.... 14000 MV. weak instability – damping time matters I.1 Results for some Fundamental Interactions – Resistive Impedance Typical values: R ~ 4Ω · circumference [m]

5. I.2 Results for some Fundamental Interactions – Inductive Impedance 5 Wake/impedance: V ind (t)= I 0 T 0 ·L·dI(t)/dt bunch lengthening proportional to I 1/3, amplitude dependent synchrotron tune, instability for neg. mom. compaction factor Bunch length measurements at BESSY II and Diamond (R. Fielder, ESLS 2011): Typical values: L·T 0 /2  ~ 1mΩ · circumference [m]

6. 6 II.CSR-Impedance R.L. Warnock, PAC'91, PAC1991_1824, http://www.JACoW.org Broad band resonator with low Q: F res /c=(  /24h 3 ) 1/2 BESSY II: F res ~ 100 GHz MLS: F res ~ 44 GHz

7. 77 ParameterBESSY IIMLS Energy, E 0 /MeV1700629 Bending radius,  /m 4.351.528 Momentum compaction, α7.3 10 -4 1.3 10 -4 Cavity voltage, V rf /kV1400330 Accelerating frequency,  rf /MHz2  500 Revolution time, T 0 /ns800160 Natural energy spread,  E 7.0 10 -4 4.36 10 -4 Zero current bunch length,  0/ ps 10.531.549 Longitudinal damping time,  l /ms 8.011.1 Synchrotron frequency,  s /kHz2  7.72  5.82 Height of the dipole chamber, 2h/cm3.54.2 II.Storage Ring Parameters for Simulations normal low-alpha mode

8. 88 II.1CSR-Threshold Currents for the MLS Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010) Solution of Vlasov-Fokker-Planck equation

9. 99 II.1CSR-Threshold Currents for the MLS Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010)

10. 10 II.1.1Comparison of CSR- and Resistive Wake

11. 11 II.1.1CSR-Threshold Currents for the MLS Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010)

12. 12 II.1.1CSR-Threshold Currents for the MLS Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010)

13. 13 II.1.2Threshold Determination MLS – Experimental Result M. Ries, et al., IPAC’12, WEPPR046

14. 14 Simulated temporal CSR spectra - tracking with CSR-wake, 1 Mio. particles, α o =1.3·10 -4 and Vrf=330 kV II.1.2Threshold Determination MLS – Theoretical Result

15. 15 II.1.2CSR - Theoretical Threshold Determination

16. 16 II.2CSR-Threshold Current Measurement BESSY II, F syn o =1 kHz,  o ~1.5 ps Many modes visible in the Fourier transformed CSR

17. 17 II.2CSR-Threshold Currents for BESSY II Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010)

18. 18 II.2First Unstable Modes BESSY II Slope agrees with resonance F res ~100 GHz

19. 19 III.Thresholds with High RF-Gradients Target for BESSY-VSR is 100 times increased RF-gradient – MLS-data is a major step already and has triggered these simulations: In certain regions no increase of threshold currents, for short bunches smaller increase than expected. Scaling according to Bane, et al. only valid for long bunches, in region of strong instability. Theoretical MLS threshold currents vs. zero current bunch length:

20. 20 III.High RF-Gradient

21. Predictions using the shielded CSR-wake are in surprisingly good agreement with measurements at BESSY II and the MLS. The observed resonance-like features show the importance of the vertical gap of the dipole vacuum chamber. Simulations demonstrate the weak nature of the CSR driven instability - also in the region of short bunches where the shielding is less important. Below the threshold multi-particle-tracking in better agreement with observations than “noise free” VFP-solutions. Experimental determination and scaling of threshold currents needs more attention. Preliminary results for very high RF-gradients (higher harmonic, double RF- system) have shown not quite the expected increase of instability thresholds. The VFP solver and multi particle tracking are currently used to model the behavior of bunches above the threshold currents. The experiments at BESSY II were supported by Karsten Holldack, Jens Kuszynski, and Fjodor Falkenstern. 21 IV.Summary and Outlook