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EEHG 101: The Basics of Echo-7

EEHG 101: The Basics of Echo-7. Joel Frederico & Pierre-Louis Pernet | Prof. Tor Raubenheimer | SLAC ARD, 2010. Motivations for Echo-7: The Free Electrons Lasers (FEL). The fourth generation of light sources Many projects around the world The LCLS at SLAC commissioned last year

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EEHG 101: The Basics of Echo-7

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  1. EEHG 101:The Basics of Echo-7 • Joel Frederico & Pierre-Louis Pernet | Prof. Tor Raubenheimer | SLAC ARD, 2010

  2. Motivations for Echo-7:The Free Electrons Lasers (FEL) • The fourth generation of light sources • Many projects around the world • The LCLS at SLAC commissioned last year • Beam of coherent ultrafast high intensity X-rays • One billion time brighter than any previous sources • Resolution of molecular and even atomic processes • Open a new dimension: the time

  3. Motivations for Echo-7:ESASE, HGHG, & EEGH • Self-Amplified Spontaneous Emission (SASE), e.g. LCLS • Radiations are coming from the initial shot in the beam • Excellent spatial coherence • High-Gain Harmonic Generation (HGHG) • FEL seeding with a laser • Needs of shorter undulators • Echo Enhanced Harmonic Generation (EEHG) • Need a proof-of-concept experiment

  4. Echo Overview:The Big Picture • How to get fine energy structure? • Via laser modulator + chicane • Creates energy modulationConvert to density modulation: modulator + chicane

  5. U z Echo Overview:Analogy with Injector • Injector • Laser on cathode produces non-relativistic electron pulse • Accelerated and energy chirped by RF cavity • Pulse compressed by velocity bunching (drift section) • Bunching in accelerator • Beam comes from injector • Energy changed by laser modulator • Pulse compressed by path-length differences in a chicane

  6. Concepts:Accelerator Components • Injector • Subharmonic Buncher • Laser Modulator • Chicane • Radiator

  7. U z Concepts:Subharmonic Buncher • RF Cavity • Head gets too little energy • Tail gets too much energy • Results in linear energy chirp • Pulse in general can be accelerated • Drift (Non-relativistic) • Tail catches up with head • Pulse is compressed!

  8. Concepts:Laser Modulator • Similar to chirping the beam - sinusoidal energy modulation • Beam passes through undulator with a laser • Quasi-sinusoidal path (alternating B-field) • Confusing! So let’s follow a particle...

  9. Concepts:Laser Modulator • Beam travels with βz=c(Unphysical) • Laser field is constant for a particular particle • But the particle oscillates... • In one period, positive and negative work is done • So total work done is zero! • Beam travels slower(Physical) • Light passes, beam sees oscillating laser field • Particle oscillates with the field (synchronism condition) • Positive work is always done • Total work done is positive!

  10. +θ -θ -θ +θ p0 p0+δ Concepts:Laser Modulator • Particles at different phases receive different energies • Sinusoidal modulation in z • But particles are relativistic: • Only energy changes, • Velocity stays ~c • No bunching occurs

  11. +θ -θ -θ +θ p0 p0+δ Concepts:Chicane - Design • Similar to drift in subharmonicbuncher • Composed of four bend magnets • Equal strength and length • Larger momentum particles • Shorter path lengthMove forward in bunch • Vice versa for smaller momentum

  12. Concepts:Chicane - Overcompressing the bunch • Momentum compaction: • Large R56 for the first chicane • Energy strips in phase space • Uniform longitudinal density distribution

  13. Concepts: Energy Strips to Density Modulation • More standard use oflaser modulator + chicane • Laser Modulator: • Larger energy modulation than previously • Not so much that structure washes out

  14. Concepts:Convert Energy Structure to Density • Chicane rotates phase space • Bunches beam • Overbunching would destroy structure • Project to z-axis: Note superharmonic density modulation!

  15. Concepts:Bunching Factor • Indicates amount of bunching at a harmonic n • There is a peak at n = 7. • An undulator tuned to this harmonic should have a decent signal

  16. Concepts:Final Radiator • The last undulator is a radiator • Generation of attosecond X-ray pulses • Saturation of the radiation after only a couple of undulator sections

  17. Echo-7:Phase Space

  18. Echo-7:Phase Space

  19. Echo-7:Phase Space

  20. Echo-7:Phase Space

  21. Echo-7:Phase Space

  22. Echo-7:Phase Space

  23. Echo 7:Preserving Phase Space Structure • CSR, ISR • Laser spot size finite • Doesn’t provide uniform fields • Field errors • Mixes phase space • Can occur in chicane, modulator • Trim errors, misalignments, etc. • Density modulation is delicate!

  24. Citations/Acknowledgements • Papers/Books • Echo-enabled harmonic generation free electron laser,D. Xiang & G. Stupakov, PRSTAB • Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation,G. Stupakov, PRL • Fundamentals of Beam Physics,J. Rosenzweig • Introduction to the Physics of the Free Electron Laser,J. Murphy & C. Pellegrini • Image Credits • http://www.ikp.physik.tu-darmstadt.de/richter/fel/overview.html

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