Large Bandwidth Radiation at XFEL

Transcription

1 Large Bandwidth Radiation at XFEL Usage of corrugated structure for increase of the energy chirp Igor Zagorodnov S2E Meeting DESY 8. April 26

2 Energy spread and Radiation Bandwidth FEL bandwidth for negligible energy spread (D simulation) E E () 2 8 z L g = ω ~ ω ρ ρ ~ at EXFEL ω 2ω ρ Igor Zagorodnov S2E Meeting 8. April 26 Seite 2

3 Energy spread and Radiation Bandwidth ω ~.% ω Igor Zagorodnov S2E Meeting 8. April 26 Seite 3

4 Energy spread and Radiation Bandwidth The energy deviation (of electron) is equivalent to the wavelength deviation (of EM wave) λ u 2 2 K λ = + γ 2 2 γ γ ω ω γ 2ω 3% in bandwidth ~.5% in energy spread For 7.5 GeV we need energy spread of 26 MeV. Igor Zagorodnov S2E Meeting 8. April 26 Seite 4

5 S2E simulations with over-compression Start-to-End simulations done by Guangyao Feng, DESY. At the end of the linac E=7.5 GeV, Ipeak=~5.kA, Q=.5nC Beam energy at some key positions E = 3 MeV E 2 = 7 MeV E 3 = 24 MeV ASTRA+CSRTrack Igor Zagorodnov S2E Meeting 8. April 26 Seite 5

6 S2E simulations with over-compression Start-to-End simulations done by Guangyao Feng, DESY. Parameter settings for the bunch compressors RF settings in accelerating modules Linac3: accelerating on-crest Igor Zagorodnov S2E Meeting 8. April 26 Seite 6

7 S2E simulations with over-compression Start-to-End simulations done by Guangyao Feng, DESY. Over compression CSR impact Igor Zagorodnov S2E Meeting 8. April 26 Seite 7

8 S2E simulations with over-compression E [ GeV] 5 4 I [ ka] s[µm] 5MeV Parameter XFEL Beam energy, GeV 7.5 Charge, pc 5 Beam average current, ka 3.75 FWHM bunch length, um 4 Emittance /, um.64/.9 Energy spread, kev σ E [ MeV] ε y ε s[µm] [ µm] [ µm] Igor Zagorodnov S2E Meeting 8. April 26 Seite 8

9 Flat structure with delayed layer 2a For flat structure (paper of Bane Stupakov, 25) cc Zc 2 tanh( X ) Z ( k, k) = sech ( X ) η ika, X ak 2a = X ss Z c Z ( k, k) = csch ( X ) η ika 2a 2 coth( X ) Z( y, y, k, k) = Z ( k, k)cosh( k y )cosh( k y) + Z ( k, k)sinh( k y )sinh( k y cc ss For rectangular structure X Z(, y,, y, k) = Z( y, y, k, k)sin( k )sin( k ), k =, m, m, m w m= Surface impedance iωµ η = - conductive layer κ η = 2ikw µ ε - dielectric layer ( ) π m 2w Igor Zagorodnov S2E Meeting 8. April 26 Seite 9

10 Corrugated structure.4 mm 2 mm g =.25 mm p =.5 mm 2w = 2 mm 2a =.4 mm h =.5 mm Length = 2&3 m ( ) g η = 2 ikw µ ε, µ =, ε << - equivalent dielectric layer p η << k - high frequency behavior for any delayed layer Igor Zagorodnov S2E Meeting 8. April 26 Seite

11 Corrugated structure wakes cc Zc 2 tanh( X ) Z ( k, k) = sech ( X ) η ika, X ak 2a = X ss Zc 2 coth( X ) Z ( k, k) = csch ( X ) η ika 2a X η << k K. Bane, G. Stupakov, LCLS-II, TN-6-, 26 cc ss Z ( k, k) = Z ( k, k) = i cc ss W ( k, s) = W ( k, s) = Z c ka X 2 2 cosh(x)sinh(x) Zc X 2 2a cosh(x)sinh(x) - independent from s W ( y, y, k, s) = W ( k, s)cosh( k y )cosh( k y) + W ( k, s)sinh( k y )sinh( k y) cc ss π m W (, y,, y, s) = W ( y, y, k, s)sin( k )sin( k ), k = 2w, m, m, m w m= Igor Zagorodnov S2E Meeting 8. April 26 Seite

12 Corrugated structure wakes W y,q 5 4 [MeV] Current[a.u.] analytical -order approimation 3 25 MeV W mm analytical ECHO 5 5 Current[a.u.] ECHO s [µm] s[µm] K. Bane, G. Stupakov, LCLS-II, TN-6-, 26 Igor Zagorodnov S2E Meeting 8. April 26 Seite 2

13 Corrugated structure wakes From paper of K. Bane, K. Yokoya, PAC 999 for chain of pillbo cavities Z αl π Zc 2 a ( ) = + 2 ( + ) = η Z k i i ik πka a kg 4π ca 2 ( + i) π η = α L - surface impedance k g First order in paper of K. Bane, G. Stupakov, I. Zagorodnov, DESY 6-56 cc k Wa ( k, s) = Zc e sinh(2 k a) ss k Wa ( k, s) = Zc e sinh(2 k a) ka s tanh( k a) 4s ka s coth( k a) 4s s g a = 2 π α( g / p) p 2 -order Igor Zagorodnov S2E Meeting 8. April 26 Seite 3

14 Corrugated structure wakes from paper of K.Bane SLAC-PUB-9663, 23 g a s =.54mm 8 = α( g / p) p 4s mm 2 from Bane, Mosnier, Novokhatsky, Yokoya, ICAP a g =.4 =.2mm p 2.4 from fit to ECHO (calculations for bunches with up to 2um RMS) s =.2 mm s.5 ka s.45 cc Zc k tanh( ka) s Wa ( k, s) = e 2 cosh( ka)sinh( ka) k - mm Igor Zagorodnov S2E Meeting 8. April 26 Seite 4

15 Corrugated structure wakes W [MeV] ECHO analytical MeV W y,q mm analytical ECHO s [µm] 5 Current[a.u.] s[µm] MeV W y,d mm analytical ECHO 5 Current[a.u.] s[µm] Igor Zagorodnov S2E Meeting 8. April 26 Seite 5

16 Beam dynamics in corrugated structure Patrameter Theoretical ( order) Numerical, ASTRA ( order) Numerical, ASTRA (st order) Emittance growth Energy spread in tail [kev] Energy loss in tail [MeV] Z ceq Ll = + a E 3 ε π β ε 2 l = 4µm 2π Z ceqls σ σ σ 256a l E ( s) = 4 + y W ( l) = π Z ceql 6a 2 K. Bane, G. Stupakov, LCLS-II, TN-6-, 26 ASTRA tracking with wakefields. M.Dohlus et al. Fast Particle Tracking with Wakefields, 22 Igor Zagorodnov S2E Meeting 8. April 26 Seite 6

17 Beam dynamics in corrugated structure 3 m horizontal 6 vertical quad β [ m] β y [ m] ASTRA tracking with wakefields. M.Dohlus et al. Fast Particle Tracking with Wakefields, 22 z[ m] Igor Zagorodnov S2E Meeting 8. April 26 Seite 7

18 Beam dynamics in corrugated structure 4 3 I [ ka] I [ ka] [ µm] ε y [ µm]. [ kev] ε σ E -2-2 Parameter Before After 6 mod. Emittance Emittance.9.26 Energy spread in tail [kev] 3 Energy loss in tail [MeV] 2 2 ε y ε [ µm] [ µm].σ E [ kev] -2-2 de [ MeV] s[µm] Igor Zagorodnov S2E Meeting 8. April 26 Seite 8

19 Beam dynamics in corrugated structure ε ε y y, ε ε, z[ m] Igor Zagorodnov S2E Meeting 8. April 26 Seite 9

20 Beam dynamics in corrugated structure Parameter Emittance growth, Emittance growth, Energy spread in tail [kev] Energy Loss in tail [MeV] after module as kick after module, kicks after 6 modules, 6 kicks Igor Zagorodnov S2E Meeting 8. April 26 Seite 2

21 Beam dynamics in corrugated structure I [ ka].σ E [ kev] ε [ µm] ε y [ µm] I [ ka].σ E [ kev] ε [ µm] ε y [ µm] Parameter Before After Emittance Emittance.9.37 Energy spread in tail [kev] 5 53 Energy loss in tail [MeV] 5 25 E [ GeV] s[µm] Igor Zagorodnov S2E Meeting 8. April 26 Seite 2

22 Beam dynamics in corrugated structure ε ε y y, ε ε, z[ m] Igor Zagorodnov S2E Meeting 8. April 26 Seite 22

23 SASE ( ideal beam) E[mJ] SASE, ALICE vs. Genesis for ideal beam ALICE Genesis z[m] Igor Zagorodnov S2E Meeting 8. April 26 Seite 23

24 SASE ( ideal beam) Energy distribution at z= m P[GW] current[a.u] Energy distribution at z=75 m P[GW] 4 one shot averaged s[µm] s[µm] Igor Zagorodnov S2E Meeting 8. April 26 Seite 24

25 SASE ( ideal beam) Spectrum at z= m.5 Spectrum[a.u.] averaged.5 Spectrum[a.u.] FWHM.5.5.8% λ[nm] -2-2 ω [%] ω Igor Zagorodnov S2E Meeting 8. April 26 Seite 25

26 SASE ( ideal beam) Spectrum at 75 m.5 Spectrum[a.u.].5 Spectrum[a.u.] averaged FWHM.5.5 2% λ[nm] -2-2 ω [%] ω Igor Zagorodnov S2E Meeting 8. April 26 Seite 26

27 SASE E[mJ] 4 3 SASE, ALICE, for real beam, 5 shots z[m] Igor Zagorodnov S2E Meeting 8. April 26 Seite 27

28 SASE P[GW] Energy distribution at z= m current[a.u] one shot averaged s[µm] Igor Zagorodnov S2E Meeting 8. April 26 Seite 28

29 .5 SASE Spectrum[a.u.] Spectrum at z= m.5 Spectrum[a.u.] averaged FWHM.5.5.7% λ[nm] -2-2 ω [%] ω Igor Zagorodnov S2E Meeting 8. April 26 Seite 29

30 SASE P[GW] 8 Energy distribution at z=75 m current[a.u] one shot 6 4 averaged s[µm] Igor Zagorodnov S2E Meeting 8. April 26 Seite 3

31 SASE.5 Spectrum[a.u.] Spectrum at z=75 m Spectrum[a.u.] averaged FWHM 2.2% lambda [nm] λ[nm] ω [%] ω Igor Zagorodnov S2E Meeting 8. April 26 Seite 3

32 Conclusion With 6 corrugated modules of total length 2 m we can obtain 2% radiation bandwidth at 7.5 GeV (. nm radiation wavelength). Parameter z= m z=75 m Bunch charge, pc 5 Bunch energy, GeV 7.5 Radiation wavelength, nm. Bandwidth (FWHM), % Radiation energy, mj Igor Zagorodnov S2E Meeting 8. April 26 Seite 32