introduction to the physics of free-electron lasers
TRANSCRIPT
![Page 1: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/1.jpg)
1
Introduction to the Physics of Free-Electron Lasers
![Page 2: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/2.jpg)
Outline
Undulator Radiation Radiation from many particles The FEL Instability Advanced FEL concepts
![Page 3: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/3.jpg)
The X-Ray Free-Electron Laser For Angstrom level radiation: High energy linac (~5-15 GeV) + Long Undulator (120 m) X-FEL shares properties of conventional lasers: -High Power (~ 10-100 GW ) -Short Pulse (~4-100 fs ) -Narrow Bandwidth (~0.1% to 0.005%) -Transverse Coherence
10 Billion times brighter than Synchrotron
Radiation Sources!!!!
![Page 4: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/4.jpg)
FEL Physics
FEL physics subject of intense research for 40 years, which produced some ugly looking equations….
![Page 5: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/5.jpg)
Ingredients of an FEL
For a hard x-ray FEL typically γ>104 (Eb>5 GeV)
![Page 6: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/6.jpg)
Undulator
Periodic array of dipole magnets with alternating polarity
![Page 7: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/7.jpg)
Electron Motion in Undulator
![Page 8: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/8.jpg)
Helical Undulator
Trajectory is a helix
![Page 9: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/9.jpg)
Undulator Radiation
Distance between two consecutive wavefronts = wavelength Note: light slips ahead by 1 wavelength per oscillation period
![Page 10: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/10.jpg)
Undulator Radiation
Distance between two consecutive wavefronts = wavelength Note: light slips ahead by 1 wavelength per oscillation period
Dopppler shift of undulator period!
![Page 11: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/11.jpg)
Central Wavelength
![Page 12: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/12.jpg)
Central Wavelength
<<1
![Page 13: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/13.jpg)
Central Wavelength
Helical undulator
Planar undulator
![Page 14: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/14.jpg)
Spontaneous Undulator Radiation
Undulator with NU periods.
Each electron emits a wave train with NU cycles in the forward direction Polarization: linear for linear undulator circular for helical undulator
![Page 15: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/15.jpg)
Incoherent Undulator Radiation
1 particle -> 1 wavetrain
Slippage Length
Forward direction
e-
![Page 16: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/16.jpg)
Incoherent Undulator Radiation
e- e-
e- e-
e- e-
![Page 17: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/17.jpg)
Incoherent Undulator Radiation
Electrons randomly distributed: power number of particles in a wavetrain
![Page 18: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/18.jpg)
What is the coherence length?
Length of e-beam
Slippage length
Length of the undulator One Wavelength
![Page 19: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/19.jpg)
Coherent Emission
Particles are bunched at multiples of the wavelength
power square of number of particles in a wavetrain
For typical x-ray FELs N ~107 Huge gain going from incoherent to coherent emission!
![Page 20: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/20.jpg)
What is the coherence length?
Length of e-beam
Slippage length
Length of the undulator One Wavelength
![Page 21: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/21.jpg)
What is the coherence length?
Length of e-beam
If the beam is perfectly microbunched the phase of the radiation field is constant across the beam
![Page 22: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/22.jpg)
Partially Incoherent Microbunching
-Particles are bunched at multiples of the wavelength. -Bunching phase jumps randomly after Lmb
![Page 23: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/23.jpg)
What is the coherence length?
Slippage length
Coherence length of microbunching
Longest of the two
One Wavelength
![Page 24: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/24.jpg)
What is the coherence length?
Field is a convolution between the charge distribution and the single-particle field. Coherence length adds in quadrature!
Longest of the two
Alternatively think of it in the frequency domain
1/Lmb
1/Slippage
![Page 25: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/25.jpg)
Coherent Emission More generally, an electron beam can have a density modulation defined by bunching factor:
Is the position of the electrons along the bunch: (z-vbt)
![Page 26: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/26.jpg)
Coherent Radiation from Microbunched Beam
1-Dimensional limit: Neglect diffraction
Slowly varying envelope approximation (narrow bandwidth signal)
Position along undulator (proxy for time)
![Page 27: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/27.jpg)
What we learned so far
Microbunching Coherent Radiation
HOW DO YOU GENERATE MICROBUNCHING?
![Page 28: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/28.jpg)
Velocity Modulation vz
ζ
vz
ζ vz
ζ
![Page 29: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/29.jpg)
Velocity Modulation vz
ζ vz
ζ vz
ζ
BUNCHING!
![Page 30: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/30.jpg)
Longitudinal Motion in Undulator
Lower energy -> Longer trajectory -> Slower longitudinal motion
Motion dominated by longitudinal dispersion
Energy modulation Velocity modulation
![Page 31: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/31.jpg)
From Energy Modulation to Bunching
Energy Modulation!
![Page 32: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/32.jpg)
Resonant Interaction
Courtesy of D. Ratner
![Page 33: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/33.jpg)
The Resonance Condition
Courtesy of D. Ratner
![Page 34: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/34.jpg)
Resonant Interaction
Resonant interaction : wave is tuned to the undulator radiation frequency!
Rate of electron energy change:
![Page 35: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/35.jpg)
This is true for every radiation process!
Change in energy due to electron wave interaction
Field radiated by particle
A particle can absorb or lose energy if and only if the wave is tuned to a mode that can be emitted spontaneously
![Page 36: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/36.jpg)
Working Principle
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
![Page 37: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/37.jpg)
Working Principle
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
![Page 38: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/38.jpg)
Working Principle
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
![Page 39: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/39.jpg)
Working Principle
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
![Page 40: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/40.jpg)
Working Principle
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
Process goes unstable, leading to exponential growth of power and bunching
Can start from a coherent seed or by noise in electron distribution!
![Page 41: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/41.jpg)
Microbunching
![Page 42: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/42.jpg)
Words of Warning
Interplay between bunching and collective fields is not necessarily unstable! E.g. Plasma oscillations
Bunching Space-charge field Energy Modulation
![Page 43: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/43.jpg)
Words of Warning
The difference is in the field equation!! Space-charge E-field counteracts existing bunching Radiation E-field Works in favor of existing bunching
![Page 44: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/44.jpg)
Linear One-Dimensional Model
1) Neglect diffraction 2) Small signal ( b << 1 ) 3) Slowly varying envelope (i.e. narrow bandwidth signal) 4) No velocity spread (longitudinal and transverse)
![Page 45: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/45.jpg)
FEL Equations
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
![Page 46: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/46.jpg)
FEL Equations
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
![Page 47: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/47.jpg)
FEL Equations
Resonant Interaction Energy Modulation Density Modulation Coherent Radiation
)
![Page 48: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/48.jpg)
Equilibrium Condition
If particles are uniformly distributed: b = 0 Initial field = 0 Beam perfectly monoenergetic:
System at equilibrium
![Page 49: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/49.jpg)
FEL Instability
Is the equilibrium stable or unstable?
![Page 50: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/50.jpg)
Roots
![Page 51: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/51.jpg)
Roots
Unstable Root -> Exponential Growth
![Page 52: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/52.jpg)
The ρ parameter
High density -> higher gain! (note: scaling typical of all 3-wave instabilities…)
Smaller growth rate at higher energies
Stronger magnetic field -> higher gain
Typically 10-3 to 10-4 for x-ray parameters
![Page 53: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/53.jpg)
The gain-length
What theorists call gain-length:
Because it makes equations look pretty…
What experimentalists call gain-length:
Because it relates to something you can measure…
At LCLS Lg ~2-6 m depending on energy and beam conditions.
![Page 54: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/54.jpg)
That’s Pretty Much it…
![Page 55: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/55.jpg)
What Happens at Saturation?
Saturation b~1
ρ is the extraction efficiency of the FEL
![Page 56: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/56.jpg)
Wait a Minute…
But I promised you that coherent radiation goes like square of # of particles…
![Page 57: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/57.jpg)
WHY? But I promised you that coherent radiation goes like square of # of particles… WHY?
I’m a liar FEL at saturation is different from the simple microbunched beam we analyzed before
Slippage length depends on current OTHER?
![Page 58: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/58.jpg)
Wait a Minute…
What matters is # of particles in a slippage length! PARTICLES PER UNIT LENGTH SLIPPAGE LENGTH
HIGHER CURRENTFASTER GAINSHORTER SLIPPAGE
![Page 59: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/59.jpg)
Wait a Minute…
What matters is # of particles in a slippage length! PARTICLES PER UNIT LENGTH SLIPPAGE LENGTH
HIGHER CURRENTFASTER GAINSHORTER SLIPPAGE
I DIDN’T LIE!
![Page 60: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/60.jpg)
Normalized FEL Equations Normalize everything to saturation value
![Page 61: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/61.jpg)
Normalized FEL Equations Normalize everything to saturation value
Natural scaling of detuning is also ρ
=⊗/2⟩
![Page 62: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/62.jpg)
Dispersion Relation for General Detuning
Assume all quantities Substitute into FEL linear equations
![Page 63: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/63.jpg)
Triggering the FEL Instability
Three coupled equations. An initial non-zero value of any variable can trigger instability!!
![Page 64: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/64.jpg)
Seeded Free-Electron Laser
An initial narrow bandwidth laser is used to initiate the process -> Narrow-bandwidth coherent pulse amplified to saturation
![Page 65: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/65.jpg)
Shot-Noise
Figure from: Avraham Gover et al. Nature Physics 8, 877–880 (2012)
Seeding can’t be done at x-rays: NO LASERS!
Luckily nature gives us a natural initial value for beam microbunching: NOISE
![Page 66: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/66.jpg)
Shot-Noise Microbunching In Frequency Domain
Increasing bunch length: Narrower spikes
![Page 67: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/67.jpg)
Shot-Noise Microbunching
Spectral autocorrelation ~ Fourier transform of longitudinal distribution at k-k’ (Nice derivation in Saldin’s book!)
Inte
nsity
∆Photon Energy
∆T = 30 fs ∆T = 10 fs ∆T = 4.5 fs
![Page 68: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/68.jpg)
SASE Spikes: Spectral Measurements
2ρ
λr/Lb
![Page 69: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/69.jpg)
What is the Coherence Length of SASE?
Slippage length
Lengt of electron bunch
Slippage length acquired in 1 gain-length
OTHER
![Page 70: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/70.jpg)
What is the Coherence Length of SASE?
Coherence length increases as z1/2 since slippage introduces correlation.
Coherence length at saturation is rougly given by slippage in a gain-length.
At LCLS ~1 fs at SXR to ~100 as at HXR
![Page 71: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/71.jpg)
SASE Spikes: Experimental Observation
![Page 72: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/72.jpg)
Bibliography
![Page 73: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/73.jpg)
Things I Want You To Remember a Year From Now
Spontaneous Power ~ N
Coherent Power ~ N2
![Page 74: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/74.jpg)
Things I Want You To Remember a Year From Now
FEL goes from spontaneous to coherent emission by means of a collective instability
![Page 75: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/75.jpg)
Things I Want You To Remember a Year From Now
Rho defines: -the gain-length of the FEL -the relative bandwidth of the FEL -the extraction efficiency of the FEL -the energy acceptance of the FEL
![Page 76: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/76.jpg)
Advanced FEL Concepts
What an FEL does if you leave it alone: High power Good transverse coherence Poor longitudinal coherence What users also ask for: More power Longitudinal coherence Controllable pulse duration Multiple pulses
![Page 77: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/77.jpg)
Seeding
Most straight-forward way to increase longitudinal coherence: Start FEL instability with a coherent signal.
![Page 78: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/78.jpg)
Seed vs Noise
External laser power >> SASE startup level
# particles in the beam # particles in a slippage length
Avogadro’s number Other
![Page 79: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/79.jpg)
External Seeding
Main problem: Availability of seed sources! (if it was that easy we wouldn’t build FELs to begin with!!)
HHG in gas can reach tens of eV energy, still far from direct seeding at X-ray energies.
![Page 80: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/80.jpg)
Alternative: Harmonic Upconversion of FEL itself
First undulator tuned at λ Second undulator tuned at λ/n
![Page 81: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/81.jpg)
HGHG @FERMI (Trieste)
Seed @ 266 nm FEL upconversion down to 32 nm
![Page 82: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/82.jpg)
Harmonic Generation
Highest harmonic: Very high harmonics require large energy modulation, suppressing FEL gain in second stage!
![Page 83: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/83.jpg)
Two-Stage HGHG
Repeat the HGHG process twice using two different regions of a long electron bunch. Extend HGHG energy by another factor ~6 Down to 5 nm
![Page 84: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/84.jpg)
Self-Seeding
Use monochromator in middle of undulator to create narrow bandwidth seed. Amplify seed in 2nd undulator
![Page 85: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/85.jpg)
Echo-Enabled Harmonic Generation
Less sensitive than HGHG to energy spread. Less sensitive than 2-stage HGHG to noise
![Page 86: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/86.jpg)
Echo-Enabled Harmonic Generation
Recently demonstrated 75th harmonic of a 2 um laser at NLCTA (SLAC). Gain in a real FEL at high harmonics not demonstrated yet...
![Page 87: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/87.jpg)
Two-Color FEL Exciting and probing samples above and below edge, imaging at different wavelengths.
![Page 88: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/88.jpg)
Two-Color FELs
Two electron bunches: Full saturation power!
![Page 89: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/89.jpg)
Two-Color FELs
Lower power (~factor 20) using split undulator but LARGE ENERGY SEPARATION!
![Page 90: Introduction to the Physics of Free-Electron Lasers](https://reader033.vdocument.in/reader033/viewer/2022051405/589993381a28abc3468b639f/html5/thumbnails/90.jpg)
That’s all!
• Lecture notes and other material will be made available.
• Feel free to contact me for any questions about FEL physics
• Have fun this week!