Longitudinal Stability of Short Bunches at BESSY Peter Kuske,

1. Longitudinal Stability of Short Bunches at BESSY Peter Kuske, M. Abo-Bakr, W. Anders, J. Feikes, K. Holldack, U. Schade, G. Wüstefeld (BESSY) H.-W. Hübers (DLR) ICFA Mini-Workshop on „Frontiers of Short Bunches in Storage Rings“ INFN-LNF, Frascati, 7- 8 November 2005

2. Content 1. Introduction 2. Experimental Techniques 2.1 Streak Camera 2.2 Observation of CSR 3. Theoretical Approaches 3.1 Impedance Model 3.2 Haissinski Equation 3.3 Vlasov-Fokker-Planck Equation 3.4 Instability Thresholds 4. Comparison of Experiment and Theory 4.1 Bunch Length 4.2 Turbulent Instability 5. Other “Instabilities” 5.1 Timing Jitter 5.2 Multi Bunch Instability at Small Negative Alpha 6. Summary Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

3. 1. Introduction BESSY: 3rd generation light source, in operation since 1998 Importance of short bunches: Table: BESSY parameter Investigation of fast phenomena Coherent synchrotron radiation (CSR) Accademic interest History of short bunches at BESSY: 1984 Isochronous SR based FEL project at BESSY I (D. Deacon, A. Gaupp) since 1999 more seriously persued at BESSY II (G. Wüstefeld, ...) Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

4. 2. Experimental Techniques 2.1 Streak Camera: Dual sweep SC model C5680 with fast sweep=250 MHz, ±1mrad bending magnet radiation, for “direct” bunch length measurements - PAC ’03: “Bunch Length Measurements at BESSY”, M. Abo-Bakr, et al. ph.noise  2.4 ps stat.res.  1.5 ps Results of bunch length measurements as a function of the synchrotron frequency Fsyn Bunch length as a function of beam current for three different momentum compaction factors Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

5. 2. Experimental Techniques 2.2 Observation of CSR Suppression due to shielding and finite acceptance angles Detector: InSb-FIR detector HDL-5 (QMC Instrum. Ltd.) most sensitive around 20 cm-1, very fast – revolution frequency resolved Time-dependence of CSR-signal indicates instability, CSR-spectra (Martin-Puplett-spectrometer)  bunch shape (K. Holldack, et al., Phys. Rev ST-AB 8, 040704 (2005)) Current dependence of the 1.25 MHz- CSR-component as a function of single bunch current Appearance of CSR-bursts measured in time domain (left) and the corresponding Fourier transformation (right) Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

6. 3. Theoretical Approaches 3.1 Impedance Model Observations: Streak Camera and CSR Inductive impedance: (I) prop. I1/3 Assumption for chamber: Z﴾﴿≈ R - iL with R = 850 Ω Lo = 0.2 ... 0.35 Ω o ≤ 2 ps ... 13 ps Consequences: Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

7. 3. Theoretical Approaches 3.1 Impedance Model CSR-wake (J. B. Murphy, et al. Part. Acc. 1997, Vol. 57, pp 9-64) Radiation wake field Short bunch – 1 ps rms-bunch length Assumption: R = 850 Ω, 0L ≈ 0.2 Ω valid for  ≈ 1 ps, unshielded CSR-wake can be added Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

8. 3. Theoretical Approaches 3.2 Haissinski Equation: induced voltage per turn: Analytical solutions only in some cases  numerical approaches required Solutions exist in most cases, if none can be found use relaxation technique (N. Towne, Phys. Rev. ST-AB Vol 4, 114401 (2001)) - usually numerical difficulties have nothing to do with instability  > 0  < 0 Potential well distortion due to CSR-wake in comparison with results of K. Bane, et al. AIP Conf. Proc. 367, p. 191 Potential well distortion due to CSR- and vacuum chamber impedance (<0) Exception is the purely inductive impedance with negative momentum compaction: Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

9. 3. Theoretical Approaches 3.2 Solution of the Haissinski Equation and CSR-Spectra stationary distribution function  stable coherent SR spectrum Distortorted shapes of short bunches just below instability thresholds and their “free space” CSR-spectra. The strong enhancement of CSR at frequencies>3 THz with <0 could not be observed ( J. Lee, G. Wüstefeld) Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

10. 3. Theoretical Approaches 3.3 Vlasov-Fokker-Planck (VFP) Equation (M. Venturini) RF focusing Collective Force Damping Quantum Excitation Numerical solution based on R.L. Warnock, J.A. Ellison, SLAC-PUB-8404, March 2000 S. Novokhatski, EPAC 2000 and SLAC-PUB-11251, May 2005 My code: limited to 127x127 mesh points and CPU-time 500-2000 time steps per ωs simulation of 200 Tsyn Bunch shape at end of simulation: 1ps bunch with R, L-impedance and CSR-wake. Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

11. 3. Theoretical Approaches 3.3 VFP- Results for 1ps Bunch and  > 0 - only CSR-wake Results of the VFP-calculations in comparison with solution of Haissinski equation. Threshold for energy widening is at 7 A. Instability starts with bunch shape oscillations at 1.8·Fsyn. Shown are the moments of the momentum distribution as a function of time at the end of the numerical calculation. Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

12. 3. Theoretical Approaches 3.3 Bursting VFP - Results for 1ps Bunch and  < 0 – only CSR-wake Some moments of the particle distribution as a function of time Results of the VFP-calculations in comparison with solution of Haissinski equation. Threshold for energy widening is at 25 A. -wave-type instability with density modulation accompanied by a small increase of the momentum spread. Well above threshold random bursts at a rate small compared to Fsyn. Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

13. 3. Theoretical Approaches 3.3 Bursting VFP - Results for 1ps Bunch – Vacuum chamber and CSR-wake Results of the VFP-calculations in comparison with solution of Haissinski equation. Burst rate in units of the synchrotron frequency as a function of intensity Unstable longitudinal particle distribution and their projections just above threshold - periodic bursts of coherent radiation. Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

14. 3. Theoretical Approaches 3.4 Instability Thresholds Stupakov & Heifets applied coasting beam instability analysis with CSR-impedance to bunched beams (Phys. Rev. ST-AB 5, 054402) Results are in agreement with observations if the wavelength of the perturbation = 0 chosen • Good agreement despite: • Vacuum chamber ignored - except for perfectly conducting infinite par. plates • Discrepancy for <0 between this theory and the VFP-calculations and • observed thresholds < thresholds with >0 Comparison of observed and simulated bursting thresholds. At BESSY a 1 ps-long bunch would have Fsyn~500 Hz. Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

15. 4. Comparison of Experimental and Theoretical Results 4.1 Bunch Length: • Chosen vacuum chamber impedance leads to: • very good agreement with the observations in the region of potential well distortion • VFP-simulation give too high thresholds and too small energy widening Comparison of measured and calculated bunch lengths Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

16. 4. Comparison of Experimental and Theoretical Results 4.2 Turbulent Instability time dependent CSR-bursts observed in frequency domain: 0=14 ps, nom. optics, with 7T-WLS  CSR-bursting threshold Stable, time independent CSR Spectrum of the CSR-signal: Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

17. 4. Comparison of Experimental and Theoretical Results 4.2 Turbulent Instability Fourier spectra of the time dependent CSR-signals as a function of single bunch current • With short bunches strong signal at 3·Fsyn • appearance of additional sidebands • with <0 1st and 2nd synchrotron sidebands at small Isb CSR-signal as a function of time at Isb=160 A Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

18. 5. Other „Instabilities“ 5.1 Timing Jitter- Technical Imperfections? Streak Camera measurements at Fsyn=1.7 kHz and Isb=0.85 mA Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

19. 5. Other „Instabilities“ 5.2 Multi Bunch Instability at Small Negative Alpha experimental conditions: Fsyn ~ 300 Hz, 2 mA in 200 buckets Horizontal beam position in the straight section (BPM 1) and in the center of the bending region (BPM 2). There are large energy oscillations at Fsyn and much larger sporadic and slower energy variations. In this case the energy increases at a rate of ~12 Hz. Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005

20. 6. Summary • Rather short, intensity limited bunches can be produced in storage rings • Potential well distortion can lead to enhanced emission of stable CSR • Threshold for energy widening usually accompanied by non-stationary bunch shapes and time dependent CSR emission • Observation of CSR leads to information on small scale variations and fluctuations of the particle density • Diagnostic power of CSR • Problems with threshold predictions – inclusion of vacuum chamber effects • In the region of turbulence our understanding is limited and further studies are required • Numerical solution of the VFP equation in combination with more realistic wakes or impedances is certainly a way to go • There remain technical and intellectual challenges for the production of short bunches in storage rings – timing jitter and “orbit” stability Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005