1. Beam Dynamics and FEL Simulations for FLASH Igor Zagorodnov and Martin Dohlus 08.02.2010 Beam Dynamics Meeting, DESY

2. FLASH I parameters ACC39 FLASH I layout is considered. But the results are equally applicable for FLASH II (SASE). short gain length (for the optimal beta function) high peak current short radiation wavelength high electron energy ~ 6.5 nm In accelerator modules ACC1, ACC2,..., ACC6 the energy of the electrons is increased from 5 MeV (gun) to 1000 MeV (undulator). In compressors the peak current I is increased from 1.5-50 A (gun) to 2500 A (undulator).

3. FLASH I parameters Electron beam properties for good lasing High peak current ~ 2500 A. Small slice emittance  (0.4-1  m). Small slice energy spread  E  (< 300 keV). short gain length (for the optimal beta function) small energy spread small emittance high peak current High harmonic module in 2010

4. FLASH I parameters ACC39 energy 1 GeV radiation wavelength ~ 6.5 nm Only SASE mode of operation is investigated. Charge tuning (20-1000 pC) allows to tune - the radiation pulse energy (30-1400  J), - the pulse width FWHM (2-70 fs).

5. FLASH I parameters ACC39 r 56  0... -0.56 mm Technical constrains V 1  150 MV V 39  26 MV V 2  360 MV How to provide (1) a well conditioned electron beam and (2) what are the properties of the radiation? (1) Self consistent beam dynamics simulations. (2) FEL simulations.

6. FLASH I 3d simulation method (self-consistent) ACC39 W3W3 2W 1 TM 3W 1 TM W 1 TM ASTRA ( tracking with space charge, DESY) CSRtrack (tracking through dipoles, DESY) W1 -TESLA cryomodule wake ( TESLA Report 2003-19, DESY, 2003 ) W3 - ACC39 wake ( TESLA Report 2004-01, DESY, 2004 ) TM - transverse matching to the design optics ( V2+, V.Balandin &N.Golubeva ) ALICE (3D FEL code, DESY )

7. FLASH I simulation methods (looking for working points) 1d tracking with space charge and wakes compressor 3d tracking with all collective effects Astra CSRtrack quasi 3d tracking with all collective effects accelerator matrix transport for x & y CSRtrack ~ 10 h (46 cpu-s) ~ seconds (1 cpu) ~ 30 min (1 cpu) 1d analytical solution without collective effects (8 macroparameters -> 6 RF settings) initial guess ~ 5 iterations final result

8. FLASH I before and after upgrade rollover compression vs. linearized compression ~ 1.5 kA ACC39 ~2.5 kA slice emittance > 2  m slice emittance ~ 0.3 - 1  m Q=1 nC Q=0.5 nC

9. new Optics correction M.Dohlus, T. Limberg, Impact of optics on CSR-related emittance growth in bunch compressor chicanes, PAC 05, 2005 V2+ a small transverse bunch size before the last dipole

10. Working points (8 macroparameters) ? What is the optimal choice? s - particle position before BC2 s 1 - particle position between BC2 and BC3 s 2 - particle position after BC3 s=s 1 =s 2 =0 for the reference particle

11. Working points (8 macroparameters) What is the optimal choice? V 1  150 MV V 2  360 MV 5% reserve 10% reserve

12. Working points (8 macroparameters) - low compression in BC1 and high compression in BC2 - maximal energy chirp transported through BC1for the same C 1 (it looses the voltage requirements on RF system ACC2/ACC3)

13. Working points (8 macroparameters)

14. working point 5% reserve

15. Working points (8 macroparameters) Too strong compression! Local maximum of compression!

16. Working points (8 macroparameters) Tolerances (10 % change of compression) working point

17. Working points (8 macroparameters) working point

18. Working points (8 macroparameters) - a free parameter to move the peak

19. Charge Q, nC Energy in BC2 E 1, [MeV] Energy in BC3 E 2, [MeV] Deflecting radius in BC2 r 1, [m] Deflecting radius in BC3 r 2, [m] Compression in BC2 C 1 Total compression C First derivative p 1, [m -1 ] Second derivative p 2, [m -2 ] 1 1304501.93 62.844812e3 0.56.934.639013.5e3 0.257.86.571500.74e3 0.19.310.324004e3 0.0215.1731.8 (12)1000-0.55e3 Working points (8 macroparameters) scaling for different charges we have used another scaling

20. Working points (6 equations => 6 RF parameters) Analytical solution without self-fields* 8 macroparameters define 6 equations nonlinear operator (defined analytically) *M.Dohlus and I.Zagorodnov, A semi analytical modelling of two-stage bunch compression with collective effects, (in preparation)

21. Analytical solution without self-fields Solution with self-fields nonlinear operator (tracking with self-fields) numerical tracking analytical correction of RF parameters residual in macroscopic parameters

22. FLASH I simulation methods (looking for working points) initial guess ~ 5 iterations final result

23. Working points (6 equations => 6 RF parameters) Charge, nC V 1, [MV]  1, [deg] V 39, [MV]  39, [deg] V 2, [MV]  2, [deg] 1144-4.6622.614535023.4 0.5143.74.04219.65158.435123.65 0.25143.362.49320.81153.9352.623.96 0.1144.8-6.3125.6137.5356.525.62 0.02144.9-3.89425.58141.65339.819.385 RF settings in accelerating modules Analytical solution without self-fields + iterative procedure with them ACC39 8 macroparameters define 6 equations

24. Q=1 nC Phase space Current, emittance, energy spread

25. Q=0.5 nC Phase space Current, emittance, energy spread

26. Q=0.25 nC Phase space Current, emittance, energy spread Space charge impact

27. Q=0.1 nC Current, emittance, energy spread Phase space

28. Q=0.02 nC Current, emittance, energy spread Phase space

29. Q=0.02 nC ACC39 CSR impact

30. Q=0.02 nC ACC39 r 56 =0 [m], t 566 =0.06 [m] Space charge impact

31. Tolerances (analytically) without self fields (10 % change of compression) Tolerances (from tracking) with self fields agree with this table Q, nC10.50.250.10.02 ACC1 |  V|/V ~O(C -1 ) 0.0010.0040.00120.00030.00004 |  |, degree 0.0650.0250.0130.0070.0014 ACC39 |  V|/V 0.0080.010.00260.00080.00013 |  |, degree 0.130.0610.0330.020.004 ACC2/3 |  V|/V ~O(C 2 -1 )0.00420.00330.00260.00240.0016 |  |, degree 0.15 0.17

32. FLASH parameters How to provide (1) a well conditioned electron beam and (2) what are the properties of the radiation? (1) Self consistent beam dynamics simulations. We are able to provide the well conditioned electron beam for different charges. But RF tolerances for small charges are tough. (2) FEL simulations (next slides).

33. Charge Q, nC10.250.02 Longitudinal electron beam size  s,  m 42133.6 Transverse electron beam size  r,  m 806836 Slice parameters for SASE simulations slice emittance Slice parameters are extracted from S2E simulations for SASE simulations current

34. Radiation energy statistics (200-500 runs) 0. 25 nC 1 nC Mean energy 0. 02 nC 1 nC 0.25 nC 0.02 nC Radiation pulse width (RMS) Charge, nC 10.50.250.10.02 Mean radiation energy,  J 1000-140070050020030 Pulse radiation width (FWHM), fs 7030177 2

35. Radiation energy statistics   Gamma distr. Q=0.02 nC     Q=1 nC z=10m z=20m

36. Temporal structure Q= 1 nC Q=0.02 nC z=10m z=20m

37. Summary with harmonic modulewithout* Bunch charge, nC 10.50.250.10.020.5-1 Wavelength, nm 6.56 Beam energy, MeV 1000 Peak current, kA 2.52.11-1.51.3-2.2 Slice emmitance,mm-mrad 1-1.30.7-0.90.5-0.70.4-0.50.3-0.41.5-3.5 Slice energy spread, MeV 0.1-0.2 0.250.2-0.40.250.3 Saturation length, m 131211101122-32 Energy in the rad. pulse,  J 1000- 1400 7005002003050-150 Radiation pulse duration FWHM, fs 7030177215-50 Averaged peak power, GW 5-72-4 Spectrum width, % 0.4-0.60.8-10.4-0.6 Coherence time, fs 4-5--- *) E.L.Saldin at al, Expected properties of the radiation from VUV-FEL at DESY, TESLA FEL 2004-06, 2004.

38. FLASH Simulation results (1) Self consistent beam dynamics simulations We are able to provide the well conditioned electron beam for different charges. But RF tolerances for small charges are tough. (2) FEL simulations The charge tuning (20-1000 pC) in SASE mode allows to tune - the radiation pulse energy (30-1400 mJ) - the pulse width (FWHM 3-70 fs).