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: 3 rd 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 Energy  1.72 GeV Natural energy spread   /  8  10 -4 Longitudinal damping time  lon 7.7 ms Momentum compaction factor  5  10 -5.. + 10 -4 Bunch length  o 0.5 … 15 ps Accellerating voltage V rf 1.4 MV RF-frequency  rf 500  2  MHz Gradient of RF-Voltage  V rf /  t 4.63 kV/ps Circumference C 240 m Revolution time T o 800 ns Number of electrons 5  10 6 per µA

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. Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 Results of bunch length measurements as a function of the synchrotron frequency F syn Bunch length as a function of beam current for three different momentum compaction factors  ph.noise  2.4 ps  stat.res.  1.5 ps

5. 2. Experimental Techniques 2.2 Observation of CSRSuppression 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)) Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 Appearance of CSR-bursts measured in time domain (left) and the corresponding Fourier transformation (right) Current dependence of the 1.25 MHz- CSR- component as a function of single bunch current

6. 3. Theoretical Approaches Observations: Streak Camera and CSR Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 Current below thresholdCurrent above threshold Long. particle distributionStationary (non- Gaussian) Non-Gaussian, time dependent Momentum distributionStationary, Gaussian with natural spread Time dependent, non-Gaussian with increasing spread TheoryPotential well distortionTurbulent bunch lengthening (energy widening), longitudinal mode mixing-, µ-wave-, CSR-instability Consequences: 3.1 Impedance Model Inductive impedance:  (I) prop. I 1/3 Assumption for chamber: Z﴾  ﴿ ≈ R - i  L with R = 850 Ω L  o = 0.2... 0.35 Ω  o ≤ 2 ps... 13 ps

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

8. 3. Theoretical Approaches 3.2 Haissinski Equation: Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 Exception is the purely inductive impedance with negative momentum compaction: 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)  > 0  < 0 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

9. 3. Theoretical Approaches 3.2 Solution of the Haissinski Equation and CSR-Spectra stationary distribution function  stable coherent SR spectrum Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 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)

10. 3. Theoretical Approaches 3.3 Vlasov-Fokker-Planck (VFP) Equation Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 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 RF focusingCollective ForceDampingQuantum Excitation My code: limited to 127x127 mesh points and CPU-time 500-2000 time steps per ω s simulation of 200 T syn (M. Venturini) Bunch shape at end of simulation: 1ps bunch with R, L-impedance and CSR-wake.

11. 3. Theoretical Approaches 3.3 VFP- Results for 1ps Bunch and  > 0 - only CSR-wake Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 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·F syn. Shown are the moments of the momentum distribution as a function of time at the end of the numerical calculation.

12. 3. Theoretical Approaches 3.3 Bursting VFP - Results for 1ps Bunch and  < 0 – only CSR-wake Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 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 F syn. Some moments of the particle distribution as a function of time

13. 3. Theoretical Approaches 3.3 Bursting VFP - Results for 1ps Bunch – Vacuum chamber and CSR-wake Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 Unstable longitudinal particle distribution and their projections just above threshold - periodic bursts of coherent radiation. 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

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 Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 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 0 Comparison of observed and simulated bursting thresholds. At BESSY a 1 ps-long bunch would have F syn ~500 Hz.

15. 4. Comparison of Experimental and Theoretical Results 4.1 Bunch Length: Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 Comparison of measured and calculated bunch lengths 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

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 Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 Spectrum of the CSR-signal: CSR-bursting threshold Stable, time independent CSR 

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

18. 5. Other „Instabilities“ 5.1 Timing Jitter- Technical Imperfections? Streak Camera measurements at F syn =1.7 kHz and I sb =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: F syn ~ 300 Hz, 2 mA in 200 buckets Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 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 F syn and much larger sporadic and slower energy variations. In this case the energy increases at a rate of ~12 Hz.

20. 6. Summary Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005 ●Rather short, intensity limited bunches can be produced in storage rings ●Potential well distortion can lead to enhanced emission of stable 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 ●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 ●There remain technical and intellectual challenges for the production of short bunches in storage rings – timing jitter and “orbit” stability