1. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Simulations of coherent synchrotron radiation effects on beam dynamics G. Dattoli, M. Migliorati, A. Schiavi

2. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Vlasov equation for longitudinal distribution

3. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 TEO code (Transport by Exponential Operators) the formal solution of the Vlasov equation can be written as For small ‘s’ (steps), by using the symmetric split we obtain

4. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 smooth evolution of distribution function (example with CSR without noise)

5. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 CSR effects with initial noise

6. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Example of microbunching due to CSR

7. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Comparison with tracking code

8. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Comparison with tracking code

9. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Phase space distribution

10. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Vlasov equation It is convenient to use dimensionless variables: and

11. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005

12. CSR microbunching instability

13. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 CSR instability threshold

14. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005

15. CSR effect on dynamics (Gaussian bunch) If N / N th and s’ are the same, the beam dynamics is the same (fixed the type of distribution)

16. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 N = 5e10 σ ε0 = 7e-4 σ z0 = 7e-3 m η = 1.4e-3 E 0 = 1.5 GeV L = 1000 m N = 6.35e10 σ ε0 = 1e-3 σ z0 = 1e-3 m η = 5e-3 E 0 = 0.5 GeV L = 28 m λ’λ’ λ’λ’ z’

17. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005

18. Preliminary simulations for Sparxino In 80 cm the wake field does not perturb the uncorrelated gaussian distribution (N/N th ~ 3.2e-3).

19. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Phase space grid 300x300

20. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Phase space grid 300x300

21. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Phase space grid 500x500

22. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Phase space grid 2000x500

23. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Fit of the distribution (work in progress)

24. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Initial distribution (2000x500)

25. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Evolution of longitudinal distribution without noise

26. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Evolution of longitudinal distribution with noise

27. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 phase space distribution

28. The Physics and Applications of High Brightness Electron Beams - Erice, October 9-14, 2005 Work to do Improve the fit of initial distribution Do a more realistic modelization of the compressor (e.g. add drifts, longitudinal space charge effect) …