Beam Dynamics and SASE Simulations for XFEL. Igor Zagorodnov DESY

Transcription

1 Beam Dynamics and SASE Simulations for XFEL Igor Zagorodnov 4.. DESY

2 Beam dynamics simulations for the European XFEL Full 3D simulation method ( CPU, ~ hours) Gun LH M, M,3 E = 3 MeV E = 7 MeV E 3 = 4 MeV E 4 = 4 GeV DL BC BC BC 3 M M 3 M4 W TM W 3 4W TM W TM ASTRA ( tracking with 3D space charge, DESY, K. Flötmann) CSRtrack (tracking through dipoles, DESY, M. Dohlus, T. Limberg) 64W z =.6 km W -TESLA cryomodule wake (TESLA Report 3-9, DESY, 3) W3 - ACC39 wake (TESLA Report 4-, DESY, 4) TM - transverse matching to the design optics

3 Choosing of machine parameters Macro-parameters Charge Q, nc Momentum compaction factor in BC R 56,, [mm] Compr. in BC C Momentum compaction factor in BC R 56,, [mm] Compr. in BC C Momentum compaction factor in BC 3 R 56,3, [mm] Total compr. C First derivative Z ', [m - ] Second derivative Z '', [m - ] E = 3 MeV E = 7 MeV E 3 = 4 MeV I. Zagorodnov, M. Dohlus, A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects, Physical Review STAB 4 (), 443.

4 XFEL beam dynamic simulations for different charges RF settings in accelerating modules Charge, nc V,, [MV] ϕ,, [deg] V,3, [MV] ϕ,3, [deg] V, [MV] ϕ, [deg] V 3, [MV] ϕ 3, [deg] Tolerances (analytically) without self fields ( % change of compression) Q, nc V % V,, 5e-4 3e-4 e-4 e-4.5e-5

5 XFEL beam dynamic simulations for different charges (full) δ E Phase space Q= nc Current, emittance, energy spread I [ka] fs σ E [MeV] ε y [µm] ε x [µm] bunch head proj ε x = ε = We have removed 6% of bad particles in the analysis proj y.9 [µm] 3.5 [µm] s [µm]

6 XFEL beam dynamic simulations for different charges (full) δ E Phase space Q=5 pc..8.6 Current, emittance, energy spread ε y [µm] ε x [µm] 7fs I 5kA.4. σ E [MeV] bunch head - proj ε x = proj ε y =.7 [µm]. [µm] s [µm]

7 XFEL beam dynamic simulations for different charges (full) δ E Phase space Q=5 pc Current, emittance, energy spread I 5kA ε y [µm].4. 39fs ε x [µm] σ E [MeV] bunch head - - proj ε x =.45 [µm] ε =.5[µm] We have removed 6% of bad particles in the analysis (Q=35 pc!) proj y

8 XFEL beam dynamic simulations for different charges (full) δ E Phase space Q= pc Current, emittance, energy spread I 5kA bunch head.6.4. σ E [MeV] ε x [µm] proj ε x = proj ε y = 5fs.35 [µm].84 [µm] ε y [µm]

9 XFEL beam dynamic simulations for different charges (full) Q= pc δ E Phase space 4.5 Current, emittance, energy spread I 5kA σ E [MeV].4 fs. ε y [µm] ε x [µm] - - bunch head proj ε x = proj ε y =.4 [µm].6 [µm]

10 Beam parameters from SE simulations Parameter Unit Bunch charge nc Peak current (gun) A Bunch length (gun, FWHM) ps Slice emittance (gun) µm Projected emittance (gun) µm Compression Peak current ka Bunch length (FWHM) fs Slice emittance µm Projected emittance µm Slice energy spread (laser heater off) MeV

11 Mismatch and wake Q=nC.5 M y W [kv/m] 5 bunch I M x [a.u] resistive wake Total wake

12 Radiation Q=nC. Amplifier.4 W[mJ] 5 P[GW].3.. Genesis ALICE 4 3 Genesis ALICE 5 5 z [m]

13 Radiation Q=nC. SASE W [mj] P [GW] ALICE Genesis 5 5 ALICE Genesis z [m] One shot from different particle distributions Averaged through slices

14 Radiation Q=nC. SASE ˆ α opt =.5 C ˆ ( zˆ ) = bz ˆ ˆ bˆ =.5α opt opt C ˆ ( zˆ ) =.5zˆ dk dγ k.5( ) uγ ku ργ dz kk dz

15 ˆΛ mc d e Radiation Q=nC. SASE γ kev dk 5 - = 6 = 4.8 m dz m dz opt P [GW] x -5 dk m dz 4 6 x -5 dk m dz

16 Radiation Q= nc E [ mj] +Wake+Taper P [ GW] 5 z = 85m dk dz opt = 4.8 m 5 - +Wake z[ m] Averaged through 8 slices s[ µm]

17 Mismatch and wake Q=5 pc 3.5 W [kv/m] bunch.5.5 M y M x x -5 I [a.u] - - resistive wake Total wake - -

18 Radiation Q=5 pc E [ mj].5 +Wake+Taper P [ GW] z = 6 m 5.5 +Wake dk dz opt = 4.8 m 5 - z[ m] Averaged through 4 slices s[ µm]

19 Mismatch and wake Q= pc 3 4 W [kv/m] M y M x [a.u] - - x -6 I - -4 bunch resistive wake Total wake mc d e γ kev dk 5 - = 4 =. m dz m dz opt

20 Radiation Q= pc E [ mj] P [ GW ] Wake+Taper 6 5 z = 5 m Wake dk dz opt = 4.8 m 5 - z[ m] - - Averaged through 8 slices s [ µm]

21 Slice parameters for SASE simulations Slice parameters are extracted from SE simulations for SASE simulations γ γ ε ε β β x y x ' y ' α α I x y x y x y ε [ µ m] x slice emittance I 5 [A] current.8.6 Q = nc Q =.5 nc 4 3 Q = nc Q =.5 nc.4 Q =. nc. Q =. nc s σ s -5 5

22 Radiation energy statistics (-5- runs) E [ mj] - Mean energy 5 pc nc σ z fs Radiation pulse width (RMS) nc 5 pc -4 pc 5 5 z [m] 5 pc 5 5 z[ m] Charge, nc.5. Mean radiation energy, mj Pulse radiation width (FWHM), fs

23 Radiation energy statistics Q= pc ( runs) z=5m z=75m 4 3 p( E) Gamma distr. σ=9% 5 p( E) σ=% E E.5.5 E E

24 8 Q= 5 pc Temporal structure 8 Q= pc 6 6 P i GW 4 I [a.u] z=5m 4 P P GW I [a.u] GW -5 5 t[fs] -5 5 t[fs] P i GW 5 GW -5 5 P I [a.u] z=75m t[fs] 5 5 I [a.u] GW -5 5 P t[fs]

25 Q= 5 pc Spectrum Q= pc.4..8 f =.5% z=5m.5 f =.8% f f f [%] f f [%] f f =.3% f z=75m f f [%] f =.5% f f f [%]

26 Summary Bunch charge, nc.5. Wavelength, nm. Beam energy, GeV 4 Peak current, ka ~ 5 Slice emmitance,mm-mrad.5. Saturation length, m Energy in the rad. pulse, mj Radiation pulse duration FWHM, fs Averaged peak power, GW Spectrum width, %