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On possible design improvements of some XFEL systems

On possible design improvements of some XFEL systems. A.A. Varfolomeev. Introduction. Nonconventional undulator designs as potential for further development of SASE FELs Problems being concerned : reducing of harmful wake field losses shortening of undulator lines internal focusing

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On possible design improvements of some XFEL systems

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  1. On possible design improvements of some XFEL systems A.A. Varfolomeev Russia - Desy Workshop on New Generation Light Sources

  2. Introduction • Nonconventional undulator designs as potential for further development of SASE FELs • Problems being concerned: • reducing of harmful wake field losses • shortening of undulator lines • internal focusing • maximizing of the undulator gaps for high field strengths • helical p.m. undulators • enhancement of spontaneous radiation intensities • self-seeding (semisuperradiance) • enhancement of SASE FEL efficiency by special insertion devices Russia - Desy Workshop on New Generation Light Sources

  3. Content • Undulator constructions and electron energy losses induced by wake fields • Negative phase shifts as a key point for new undulator designs • Enhancement of spontaneous radiation intensity per unit undulator length • Undulator radiator with tunable polarization in wide frequency range • Increase of SASE FEL efficiency due to locally induced negative phase shifts in short bunch limit • Increase of SASE FEL efficiency due to locally induced negative phase shifts in long bunch limit • Total radiation intensity of SASE FEL as a function of local positive phase shifts in long bunch limit • Summary on phase shift effects • Conclusion Russia - Desy Workshop on New Generation Light Sources

  4. Undulator constructions and electron energy losses induced by wakefields • Wake field induced losses and requirements on undulators • Very long undulator devices typical for up-to-date XFEL projects along with very strict limits on e-beam quality are some contradictory requirements • Electron energy losses induced by wake field depend on electron position in the bunch and gives not only uniform energy losses but electron energy spread as well • Contributions to longitudinal wake-field potential: geometric w.f., resistive, roughness From W. Decking FEL2005 Russia - Desy Workshop on New Generation Light Sources

  5. Approaches for making the problem of wakefields easier • To make shorter the total length of undulators by using helical undulators instead of planar ones • To use undulators with internal focusing to shorten beamline • To use special undulator schemes providing required high fields at larger gaps • To use schemes based on harmonic generation like HGHG • To use seeding (or self-seeding) inducing high speed evolution for SASE mode Russia - Desy Workshop on New Generation Light Sources

  6. PM undulators designed for LCLS with higher than nominal gaps • Planar p.m. hybrid undulator designed for LCLS with gap 8.5 mm Magnetic characteristics of the undulator Cut away view of the undulator structure Main simulation results: Undulator gap larger than in LCLS project is possible (AIP Conference Proceedings 581 (2001) 73). For XFEL SASE1 undulator gap 12.5 mm is possible (instead of projected 10 mm gap). Russia - Desy Workshop on New Generation Light Sources

  7. PM undulators designed for LCLS with higher than nominal gaps • Helical p.m. hybrid undulator designed for LCLS with gap 8.5 mm Magnetic characteristics of the undulator Cut away view of the undulator structure Main simulation results: Helical construction is possible which is less sensitive to wake-field losses of electron beam in small gap channels (AIP Conference Proceedings 581 (2001) 73). Russia - Desy Workshop on New Generation Light Sources

  8. Wake field effect estimations for the designed LCLS undulators Radiation power of the projected planar LCLS undulator and helical undulator designed by Kurchatov Institute Solid – no wake fields; Dotted – resistive wall wake fields; Dashed - resistive wall+surface roughness wake fields. Main results: KI helical undulator construction provides shorter saturation length (~62m) in comparison with LCLS one (82m) and almost 1 order higher intensity due to reasonably less sensitivity to wake-fields (AIP Conference Proceedings 581 (2001) 221). Russia - Desy Workshop on New Generation Light Sources

  9. e C A B x y z • Negative phase shifts as a key point for new undulator designs • Thin films with refractive index n(ω)>1 provides retarding of radiation pulse with respect to electron. Slippage compensation is possible for soft X-rays with very thin C plate • Negative phase shifter schematics • Phase delaying by small reflecting angle mirror (total outer reflection). Slippage compensation is obtainable for wide spectrum of X-rays x ' z ' y ' • Conventional drift space or chicane units provide positive phase shifts Reference: NIM A393 (1997) 398 Russia - Desy Workshop on New Generation Light Sources

  10. Enhancement of electron spontaneous radiation per unit undulator length in multisection devices • Phase synchronized radiation • Angular-frequency distribution of radiation power produced by two and three undulator sections, analytical and numerical results (b) one slippage compensating phase shift (c) two slippage compensating phase shifts (a) no phase shifts Reference: NIM A393 (1997) 393 Russia - Desy Workshop on New Generation Light Sources

  11. Characteristics of phase synchronized radiation of undulator sections – semisuperradiance • Two section undulator radiation • – frequency spectrum (b) – angular distribution • Green – no phase shifts, Red – with slippage compensation, Blue – one section • Conclusion: n-fold enhancement due to semisuperradiance is possible with the same total length (n-number of undulator sections) Reference – NIM A393 (1997)393 Russia - Desy Workshop on New Generation Light Sources

  12. Employment of enhanced spontaneous radiation • Quasysuperradiant seeding (or self-seeding) and shorting of the head part of the SASE undulator system • High intensity spontaneous radiation sources on spontaneous radiator lines of XFEL Russia - Desy Workshop on New Generation Light Sources

  13. x x ' z ' y z y ' • Undulator radiator with tunable polarization in wide frequency range • Two separated undulators with crossed polarizations • Schematic of crossed and synchronized undulator system • Characteristics of the system • Wide frequency acceptance due to slippage compensation for basic frequency • Polarization is conserved practically for the entire spontaneous spectrum including harmonics k • No limit typical for nonsynchronized system [K.-J. Kim] which is / « [4k(Nu+ND)]-1 where Nu- number of undulator periods, ND- length of dispersion section in w units • No correction of fields or synchronization is needed for changing the output radiation polarization Reference: NIM A393 (1997) 398 Russia - Desy Workshop on New Generation Light Sources

  14. Some distinctions from Apple II type undulator • Total magnetic field energy in the volume of Apple II undulator does not depend on field polarization. Since that it can’t be recommended for shortening the undulator lines for decreasing wake field losses • Any polarization changing demands correction (tuning) of fields • Tuning of Apple II as p.m. construction is more complicated in comparison with hybrid systems • Small working volume (<100 μm in horizontal direction) [see J.Bahrdt et.al. “Conceptual design of helical undulator…” 2000] • Because of very strong magnetic fields mechanical tuning of polarization is difficult Russia - Desy Workshop on New Generation Light Sources

  15. Increase of SASE FEL efficiency due to locally induced negative phase shifts in short bunch limit • Single pass high gain FEL analysis on slippage changes role for the FEL dynamics • Basic equations and approaches • 1D slowly-varying envelope approximation (SVEA) • |∂a/∂z|<<ka, |∂a/∂t|<<ωa, first order wave equation (R. Bonifacio et al.) • Helical undulator in paraxial approximation • Collective variables b=<exp(iθ)>, P=<p exp(-iθ)>, b2=<exp(2iθ)>, P2=<p exp(-2iθ)> where pj=(γj-<γ0>) ρ<γ0> is relative energy deviation • For short bunch limit variable z1=(z-v//t)/β//ℓc is introduced • Short bunch limit means ℓb<ℓc, ℓc=λ/4πρis cooperation length, ρ– scaling parameter • Field expressed as , where δ=(<γ0>2-γr2)/2ρ γr2 • Special numerical code was written valid for |A|2 ~1 and second harmonics b2, P2 Russia - Desy Workshop on New Generation Light Sources

  16. Increase of SASE FEL efficiency due to locally induced negative phase shifts in short bunch limit • Single pass high gain FEL analysis on slippage changes role for the FEL dynamics • Parameters used for simulations • Phase shifts were introduced at local points ẑs=9, ẑs=8 measured in gain length (w/4ρ) units • Following shifts were made in the ℓc units measured in bunch system Δ=0.6…1.2 – radiation pulse is going ahead; Δ=-2.0…-3.0 – radiation is retarding • For XFEL facility: ρ=3∙10-4, λ=1.0 Å, ℓc=256 Å Russia - Desy Workshop on New Generation Light Sources

  17. Results of simulation • Intensity (dimensionless |A|2) for the short bunch length ℓb=0.6ℓc at the depth ẑ=15 as function z1=(z-v//t)/β//ℓc and phase shift Δℓc introduced at zs=9 • S – total radiation power (square under radiation curves) Significant (up to 50%) intensity enhancement due to single negative phase shift is evident. No enhancement is found for positive phase shifts. Russia - Desy Workshop on New Generation Light Sources

  18. Results of simulation • Intensity of radiation for longer bunch length ℓb=1.2ℓc at the depth ẑ=13 as a function local slippage shifts Δℓc introduced at ẑs=8 Significant (up to 78%) intensity enhancement caused by negative phase shift is evident. Very small enhancement is seen for positive phase shifts. It is seen that for short bunch limit any local negative phase shift at the saturated state of the FEL renew generation of radiation Reference: FEL1997 Procced. p. II-61 Russia - Desy Workshop on New Generation Light Sources

  19. Increase of SASE FEL efficiency due to locally induced negative phase shifts in long bunch limit (ℓb>2ℓc) • Study of SASE FEL evolution starting from noise with subsequently induced slowing down of optical pulse • Simulation approaches • 1D SVEA approximation and first order wave equations valid for |∂a/∂z|<<ka, |∂a/∂t|<<ωa • Steady state approach for long bunch limit • Tracing of model electrons along the undulator depth according to following equations for Compton regime where field amplitude. (No collective variables). • Regular slippage correction with the purpose to increase position correlation between radiation spikes and e.b. density spikes respectively • Study of spatial and temporal evolution of radiation spike structure • To enhance the spikes starting from random noise SASE was simulated Russia - Desy Workshop on New Generation Light Sources

  20. Simulation results • Output radiation power as function of undulator depth ẑ ẑ ẑ Bold red – 0.75 ℓc shift every one gain length up to ẑ=9 followed by phase shift π/2 at ẑ=10 Bold dash blue – no induced phase shifts Thin curves and thin dash curves – respective fluctuation limits Bold red – 0.75 ℓc shift every one gain length up to ẑ=9. Bold dash blue – no induced shifts Thin curves and thin dash curves – respective fluctuation limits Result. Both kinds of phase shifts increase the output radiation power. Maximum gain is reached when both shifts are introduced: 50% enhancement on the same saturation depth ẑ≤11 Reference: Physics of and science with XFEL, AIP 2001 p.78 Russia - Desy Workshop on New Generation Light Sources

  21. Total radiation intensity of SASE FEL as a function of local positive phase shifts in the long bunch limit (ℓb>2ℓc) • Nearly the same as in above presented works • Single pass FEL ID approach, SVEA approximation with constant wiggler parameters in sections are used • |∂a/∂z|<<ka, |∂a/∂t|<<ωa, first order wave equation (Bonifacio et al.) • Helical undulator is considered in paraxial approximation • Local positive phase shifts were introduced between undulator sections in proper way for inducing higher output power limit of the SASE FEL • The purpose of the report to demonstrate some results qualitatively • Basic equations and approaches Russia - Desy Workshop on New Generation Light Sources

  22. 1 . 6 0 1 . 2 0 Y T I S N E 0 . 8 0 T N I 0 . 4 0 0 . 0 0 0 . 0 0 4 . 0 0 8 . 0 0 1 2 . 0 0 1 6 . 0 0 2 0 . 0 0 Z • Results of simulations • Dependence of intensities on primary conditions (as a test of the code) SASE radiation intensity in a uniform undulator as a function of the depth for different initial bunching bo SASE radiation intensity as function of seeding intensity I(0) and the depth ẑ bold: bo = 0 Practically no sensitivity to initial intensity or bunching Russia - Desy Workshop on New Generation Light Sources

  23. Dependence of intensities on localization and positive phase shifts (jumps) values SASE radiation intensity for different induced at ẑ0= ẑmax phase shifts respectively Δ=0 (a), Δ=π/2 (b), Δ=3π/2 (c), and Δ=π (thick curve). SASE radiation intensity at the depth ẑ as function of coordinate ẑ0 where shift Δ=π was introduced c b a Result. Maximum enhancement up to 1.5 is achieved at the phase shifts Δ=π/2 and Δ=π. Result. Real influence on SASE radiation takes place only at ẑ0= ẑmax (saturation depth). Russia - Desy Workshop on New Generation Light Sources

  24. Output SASE radiation intensity of a phase shift tapered undulator as a function of the total undulator length 6 . 0 0 Y T I S N 4 . 0 0 E T N I 2 . 0 0 0 . 0 0 0 . 0 0 4 . 0 0 8 . 0 0 1 2 . 0 0 Z Result. Twice longer tapered undulator can provide 4 times enhancement of output SASE radiation (10 positive phase jumps). Reference: NIM A 407 (1998) 296. Russia - Desy Workshop on New Generation Light Sources

  25. Summary on phase shifts effects • Evolution of SASE FEL dynamics have been investigated for different kinds of phase shifts (negative and positive as well) and for different regimes (short bunch and long bunch limits respectively) • It is shown that nearly in all cases enhancement of the output radiation power is obtainable although mechanisms are probably different. • For short bunch limit negative phase shifts return wave packet to the bunch position and this way enhance their interaction resulting in increasing of radiation intensity. • For long bunches negative phase shifts introduced before saturation depth enlarge correlation between radiation spikes increasing intensity of FEL interaction. Russia - Desy Workshop on New Generation Light Sources

  26. Summary on phase shifts effects • Local positive shifts obtainable with single drift space are efficient if they introduced at saturation depth. Enhancement of radiation intensity 50% and more is possible with additional undulator depth of length compatible with gain length. • Combination of negative and positive phase shifts can provide 50% power enhancement on the same undulator depth (first saturation depth). • Times higher output power can be reached with longer tapered by drift gaps undulators Russia - Desy Workshop on New Generation Light Sources

  27. Conclusion It is shown that further development of SASE FELs is possible. Considered new modifications of undulator are promising for increasing SASE FEL efficiency and enhancement of the output power of XFEL facilities. Russia - Desy Workshop on New Generation Light Sources

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