EEHG 101:
The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet | Prof. Tor Raubenheimer | SLAC ARD, 2010
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Echo Overview:
The Big Picture
How to get fine energy structure?
Via laser modulator + chicane
Creates energy modulation
Convert to density modulation: modulator + chicane
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Concepts:
Accelerator Components
Injector
Subharmonic Buncher
Laser Modulator
Chicane
Radiator
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Concepts:
Subharmonic Buncher
RF Cavity
U
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!
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
z
Concepts:
Laser Modulator
Similar to chirping the beam sinusoidal energy modulation
Beam passes through undulator with
a laser
Quasi-sinusoidal path (alternating Bfield)
Confusing! So let’s follow a particle...
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
So total work done is zero!
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Positive work is always done
Total work done is positive!
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Concepts:
Chicane - Design
Similar to drift in subharmonic buncher
Larger momentum particles
Shorter path length
Move forward in bunch
Composed of four bend magnets
Equal strength and length
Vice versa for smaller momentum
+θ
θ
-θ
+θ
p
0
p0+δ
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Concepts:
Chicane - Overcompressing the bunch
Momentum compaction:
Large R56 for the first chicane
Energy strips in phase space
Uniform longitudinal density distribution
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Concepts:
Convert Energy Structure to Density
Chicane rotates phase space
Bunches beam
Overbunching would destroy structure
Project to z-axis: Note
superharmonic density modulation!
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Echo-7:
Phase Space
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Echo-7:
Phase Space
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Echo-7:
Phase Space
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Echo-7:
Phase Space
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Echo-7:
Phase Space
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Echo-7:
Phase Space
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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!
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
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
Echo 101: The Basics of Echo-7
Joel Frederico & Pierre-Louis Pernet
Introduction to the Physics of the Free
Electron Laser,
J. Murphy & C. Pellegrini
Image Credits
http://www.ikp.physik.tudarmstadt.de/richter/fel/overview.html