Longitudinal Impedance Budget and Simulations for XFEL. Igor Zagorodnov DESY
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1 Longitudinal Impedance Budget and Simulations for XFEL Igor Zagorodnov DESY
2 Beam dynamics simulations for the European XFEL Full 3D simulation method (2 CPU, ~1 hours) Gun LH M 1,1 M 1,3 E1 13 MeV E2 7 MeV E3 24 MeV E4 14GeV DL BC1 BC BC 2 3 M M 2 3 M4 W 1 TM W 3 4W 1 TM 12W 1 TM ASTRA ( tracking with 3D space charge, DESY, K. Flötmann) CSRtrack (tracking through dipoles, DESY, M. Dohlus, T. Limberg) 64W 1 z 1.6 km W1 -TESLA cryomodule wake (TESLA Report 23-19, DESY, 23) W3 - ACC39 wake (TESLA Report 24-1, DESY, 24) TM - transverse matching to the design optics
3 Choosing of machine parameters Macro-parameters Charge Q, nc Momentum compaction factor in BC 1 R 56,1, [mm] Compr. in BC 1 C 1 Momentum compaction factor in BC 2 R 56,2, [mm] Compr. in BC 2 C 2 Momentum compaction factor in BC 3 R 56,3, [mm] Total compr. C First derivative Z ', [m -1 ] Second derivative Z '', [m -2 ] E1 13MeV E2 7MeV E3 24 MeV I. Zagorodnov, M. Dohlus, A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects, Physical Review STAB 14 (211), 1443.
4 XFEL beam dynamic simulations for different charges (full) E Phase space Q=1 nc Current, emittance, energy spread I [ka] fs 2 1 E [MeV] y [μm] x [μm] bunch head proj x.9 [μm] proj y 3.5 [μm] We have removed 6% of bad particles in the analysis s [μm]
5 2.5 2 Mismatch and undulator wake Q=1nC W [kv/m] M y bunch I M x [a.u] resistive wake Total wake
6 Optimal taper for Q=1nC ˆ.25 opt Cz ˆ( ˆ) bz ˆˆ bˆ.5 opt opt Cz ˆ ( ˆ).125zˆ dk 1 d 2k.5 2 u ku dz kk dz 2 mc d e kev 16 dz m dk dz opt 4.81 m 5-1
7 SASE radiation Q=1 nc (ALICE, 36 CPU, ~3 min) E mj +Wake+Taper P GW 2 15 z 85m Wake z m Averaged through 8 slices s μm
8 Accelerator wakes. Q=1nC warm pipe 14% 2% 4% 19% collimators 1% 1% 1% 1% 2% 4% cavities 42% COL CAV TDS BPMA OTRA BPMR TORAO KICK PIP2 PUMCL FLANG
9 Accelerator wakes. Q=1nC W [MV] 5 E E E 5.3e 4 current Full wake Cavities wake Cavities wake Full wake s [μm] s [μm]
10 Artificially matched beam. Q=1nC E 1 mj 8 at z=175 m 8 all slices matched 6 current dk dz opt 4.81 m matched in peak current 5-1 z m With full accelerator and undulator wake 2-5 5
11 E mj Artificially matched beam. Q=1nC full wake (full wake) x 4 P GW at z = 85 m current 2 (full wake) x z m -5 5
12 Beam matched in the peak current. Q=1nC E mj 5 full wake P 25 GW at z=85 m 4 3 (full wake) x 4 (full wake) x current z m -5 5
13 Beam matched in the peak current. Q=1nC E E E (full wake) x 8 (full wake) x Normalized spectrum at z=85 m 5.4 full wake FWHM=.14% FWHM=.23% FWHM=.6% %
14 XFEL beam dynamic simulations for different charges (full) E Phase space Q=25 pc Current, emittance, energy spread I 5kA y [μm] fs x [μm] E [MeV] bunch head proj x proj y.45 [μm] 1.5[μm] We have removed 6% of bad particles in the analysis (Q=235 pc!)
15 Mismatch and undulator wake. Q=25 pc 3 2 W [kv/m] bunch M y M x x 1-5 I [a.u] -1-2 resistive wake Total wake
16 SASE radiation. Q=25 pc E mj +Wake+Taper P GW z 6m.5 +Wake dk dz opt 4.81 m 5-1 z m Averaged through 24 slices s μm
17 Accelerator wakes. Q=25 pc. warm pipe 23% 2% 4% collimators 33% 11% 1% 4% 22% cavities COL CAV TDS BPMA KICK PIP2 PUMCL FLANG
18 Accelerator wakes. Q=25 pc W [MV] 3 E E E 5.3e Cavities wake -1-2 Full wake Full wake Cavities wake
19 Artificially matched beam. Q=25 pc E mj 4 P GW 12 at z=175 m all slices matched z m
20 Beam matched in the peak current. Q=25 pc E mj full wake (full wake) x 4 P 4 3 GW at z=6 m (full wake) x z m
21 Beam matched in the peak current. Q=25 pc 15 E E E 1 Normalized spectrum at z=85 m 1 5 (full wake) x 8 (full wake) x full wake FWHM=.29% FWHM=.3% FWHM=.38% %
22 XFEL beam dynamic simulations for different charges (full) Q=2 pc E Phase space Current, emittance, energy spread I 5kA E [MeV].4 2fs.2 y [μm] s [μm] x [μm] bunch head proj x proj y.14 [μm].26 [μm]
23 Mismatch and undulator wake. Q=2 pc 3 4 W [kv/m] M y M x [a.u] x 1-6 I bunch resistive wake Total wake
24 SASE radiation. Q=2 pc E mj +Wake+Taper +Wake P 6 GW z 5m dk dz opt 4.81 m 5-1 z m Averaged through 8 slices s μm
25 Accelerator wakes. Q=2 pc warm pipe 11% 17% 1% 3% collimators 56% 3% 9% cavities COL CAV TDS KICK PIP2 PUMCL FLANG
26 Accelerator wakes. Q=2 pc W [MV] 1 E E E 5.3e 4 5 Full wake Cavities wake Cavities wake -5 Full wake s [μm]
27 Artificially matched beam. Q=2 pc E.5 mj 14 at z=175 m all slices matched z dk dz opt 4.81 m 5-1 m
28 Beam matched in the peak current. Q=2 pc E mj.5.4 full wake (full wake) x 4 P GW at z=6 m (full wake) x z m
29 Beam matched in the peak current. Q=2 pc E E E (full wake) x 8 (full wake) x Normalized spectrum at z=85 m Spectrum at m 2 1 full wake dw/w [%] FWHM=.55% FWHM=.58% FWHM=1.% %
30 Summary Accelerator wake Bunch charge, nc Energy in the radiation pulse at z=175 m, mj Spectrum width at z=85m, % x x x x x x We have considered only the longitudinal wake in a quite coarse model (adding the accelerator wake at the undulator entrance). The transverse wakes are neglected.
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