1. EEHG 101: The Basics of Echo-7
Joel
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
Pierre

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
Pierre

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

5. Echo Overview: Analogy with 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
Joel z U

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

7. 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! z U
Pierre

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...
Joel

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

10. 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
Joel +θ -θ p0
p0+δ

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

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

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

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!
Joel

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
Pierre

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
Pierre

17. Echo-7: Phase Space
Joel

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!
Pierre

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