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P. Kuske, BESSY

„Topics in Coherent Synchrotron Radiation (CSR) Workshop : Consequences of Radiation Impedance“ Nov. 1st and 2nd 2010, Canadian Light Source. Temporal Characteristics of CSR Emitted in Storage Rings – Observations and a Simple Theoretical Model. P. Kuske, BESSY. Outline of the Talk.

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P. Kuske, BESSY

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  1. „Topics in Coherent Synchrotron Radiation (CSR) Workshop : Consequences of Radiation Impedance“ Nov. 1st and 2nd 2010, Canadian Light Source Temporal Characteristics of CSR Emitted in Storage Rings – Observations and a Simple Theoretical Model P. Kuske, BESSY

  2. Outline of the Talk I. Motivation II. Observations – at BESSY II III. Theoretical Model – μ-wave Instability „numerical solution of the VFP-equation with BBR-wake“ III. 1 BBR-Impedance III. 2 Vlasov-Fokker-Planck-Equation – „wave function“ approach III. 3 Numerical Solution of this VFP-equation IV. Results IV. 1 Comparison to other Solutions IV. 2 New Features and Predictions IV. 3 Comparison of Experimental and Theoretical Results V. Conclusion and Outlook 2

  3. I. Motivation • open questions and issues • related to CSR directly: • spectral characteristic? • steady-state radiation vs. emission in bursts – temporal characteristics? • how can we improve performance? • more generally: • some kind of impedance seems to play a role • potential instability mechanism • very often we operate with single bunch charges beyond the stability limit • How does instability relate to CSR? 3

  4. II. Observations at BESSY II 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, Frascati 4

  5. II. Observations at BESSY II 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, Frascati 5

  6. II. Observations at BESSY II 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, Frascati 6

  7. II. Observations at BESSY II 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, Frascati 7

  8. II. Observations at BESSY II Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 8

  9. II. Observations at BESSY II Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 9

  10. II. Observations at BESSY II Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 10

  11. II. Observations at BESSY II Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 11

  12. II. Observations at BESSY II Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 12

  13. II. Observations at BESSY II Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 13

  14. Observations at BESSY II with 4 sc IDs in operation Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 14

  15. Observations at BESSY II without sc IDs Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 15

  16. II. Observations at BESSY II Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver 16

  17. III. 1 Theoretical Model – BBR-Impedance 17

  18. III. 1 Theoretical Model – CSR-Impedance ‚featureless curve with local maximum and cutoff at long wavelenght‘ 18

  19. III. 1 Theoretical Model – CSR-Impedance 19

  20. III. 2 Vlasov-Fokker-Planck-Equation (VFP) (M. Venturini) RF focusing Collective Force Damping Quantum Excitation numerical solution based on: R.L. Warnock, J.A. Ellison, SLAC-PUB-8404, March 2000 M. Venturini, et al., Phys. Rev. ST-AB 8, 014202 (2005) S. Novokhatski, EPAC 2000 and SLAC-PUB-11251, May 2005 solution for f(q, p,) can become < 0 requires larger grids and smaller time steps Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005, Frascati 20

  21. III. 2 Vlasov-Fokker-Planck-Equation (VFP) „wave function“ approach original VFP-equation: Ansatz – “wave function” approach: Distribution function, f(q, p,) , expressed as product of amplitude function, g(q, p,): f (q, p,) >= 0 and solutions more stable 21

  22. III. 3 Numerical Solution of the VFP-Equation and BESSY II Storage Ring Parameters solved as outlined by Venturini (2005): function, g(q, p,), is represented locally as a cubic polynomial and a time step requires 4 new calculations over the grid distribution followed over 200 Tsyn and during the last 160 Tsyn the projected distribution (q) is stored for later analysis: determination of the moments and FFT for the emission spectrum grid size 128x128 and up to 8 times larger, time steps adjusted and as large as possible Fsyn = 7.7 kHz ~60 Tsyn per damping time 22 M. Venturini, et al., Phys. Rev. ST-AB 8, 014202 (2005)

  23. Theoretical Results VI. 1 Comparison with other Theories and Simulations K. Oide, K. Yokoya, „Longitudinal Single-Bunch Instability in Electron Storage Rings“, KEK Preprint 90-10, April 1990 K.L.F. Bane, et al., „Comparison of Simulation Codes for Microwave Instability in Bunched Beams“, IPAC’10, Kyoto, Japan and references there in 23

  24. Theoretical Results VI. 1 Comparison with other Theories and Simulations 24

  25. Theoretical Results VI. 2 New Features broad band resonator with Rs=10 kΩ 25

  26. Theoretical Results VI. 2 New Features broad band resonator with Rs=10 kΩ 26

  27. Theoretical Results VI. 2 New Features broad band resonator with Rs=10 kΩ 27

  28. Theoretical Results VI. 2 New Features – Islands of Stability 28

  29. Theoretical Results VI. 2 New Features – Islands of Stability 29

  30. Theoretical Results VI. 2 New Features – Hysteresis Effects 30

  31. Theoretical Results - burst VI. 3 BBR: Rs=10kΩ, Fres=200GHz, Q=4 and Isb=7.9mA 31

  32. Theoretical Results – lowest unstable mode VI. 3 BBR: Rs=10kΩ, Fres=100GHz, Q=1 and Isb=2.275mA 32

  33. Theoretical Results VI. 3 BBR + R + L in Comparison with Observations 33 BBR: Rs=10 kΩ, Fres=40 GHz, Q=1; R= 850 Ω and L=0.2 Ω

  34. Theoretical Results VI. 3 BBR + R + L in Comparison with Observations 34

  35. V. Conclusion and Outlook a simple BBR-model for the impedance combined with the low noise numerical solutions of the VFP-equation can explain many of the observed time dependent features of the emitted CSR: • typically a single (azimuthal) mode is unstable first • frequency increases stepwise with the bunch length • at higher intensity sawtooth-type instability (quite regular, mode mixing) • at even higher intensitiy the instability becomes turbulent, chaotic, with many modes involved Oide‘s and Yokoya‘s results are only in fair agreement with these calculations do not show such a rich variety of behavior – why? are better approaches available? simulation can serve as a benchmark for other theoretical solutions need further studies with more complex assumption on the vacuum chamber impedance the simple model does not explain the amount of CSR emitted at higher photon energy – much higher resonator frequencies required is this produced by a two step process, where a short wavelength perturbation is first created by the traditional wakefield interaction and in a second step another wake with even higher frequency comes into play? (like bursting triggered by slicing) 35

  36. Acknowledgement K. Holldack – detector and THz-beamline J. Kuszynski, D. Engel – LabView and data aquisition U. Schade and G. Wüstefeld – for discussions 36

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