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A Free Electron Laser Project at A Free Electron Laser Project at LNFLNF
Massimo FerrarioMassimo FerrarioINFN - LNFINFN - LNF
& the SPARC/X Team& the SPARC/X Team
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Atomic LaserAtomic Laser
Synchrotron RadiationSynchrotron Radiation
Free Electron Laser (FEL)Free Electron Laser (FEL)
SPARCSPARC - - SPARXINOSPARXINO - - SPARXSPARX
ApplicationsApplications
Outline Outline
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Atomic LaserAtomic Laser
LLightight A Amplificationmplification by S by Stimulatedtimulated E Emissionmission of of
RRadiationadiation
Spontaneous Spontaneous EmissionEmission
Stimulated EmissionStimulated Emission
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Properties of Stimulated EmissionProperties of Stimulated Emission
The photon which is emitted in the stimulated The photon which is emitted in the stimulated emission process is identical to the incoming emission process is identical to the incoming photon.photon.
They both have:They both have: 1. Identical wavelengths - 1. Identical wavelengths - Monochromaticity.Monochromaticity. 2. Identical directions in space - 2. Identical directions in space - Directionality.Directionality. 3. Identical phase - 3. Identical phase - Coherence.Coherence.
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Atomic LaserAtomic Laser 1. Well known and proven technology1. Well known and proven technology.. 2. One Laser One Color2. One Laser One Color.. 3. Limited by Mirrors ==> No X rays3. Limited by Mirrors ==> No X rays..
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Cosmic MASER Cosmic MASER
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Synchrotron Radiation Synchrotron Radiation
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Charged particle moving on a circle Charged particle moving on a circle
Radiation Simulator – T. Shintake, @ http://www-xfel.spring8.or.jp/Index.htm
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€
δt = tl − t f =2ρ
βcγ−
2ρ sin 1 γ( )c
≈4ρ
3cγ 3 Pulse Pulse Duration Duration
€
δt
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€
ωc ≈1
1
2δt
≈3
2c
γ 3
ρ Cut-Off Frequency of the Cut-Off Frequency of the Spectrum Spectrum
€
To
€
ωo =2π
To
Revolution Revolution Frequency Frequency
€
δt
N
€
δt ≈4ρ
3cγ 3
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Undulator RadiationUndulator Radiation
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Undulator RadiationUndulator Radiation
€
β⊥ ≈K
γ=
e˜ B uλ u
2πγmc 2 €
θ =1
γ
€
K ≤ 1The electron trajectory is inside the radiation cone if
The electron trajectory is determined by the undulator field and The electron trajectory is determined by the undulator field and the electron energythe electron energy
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Relativistic MirrorsRelativistic Mirrors
€
λu' =
λ u
γ //
€
λrad' = λ u
'
€
λrad ≈λ u
2γ //2
€
1
γ //2 =
1
γ 2 + β⊥2
€
λrad ≈λ u
2γ 2 1+ K 2( )
€
// =1
1− β //2
Counter propagating pseudo-Counter propagating pseudo-radiationradiation
Compton back-scattered Compton back-scattered radiation in the moving mirror radiation in the moving mirror
frameframe
Doppler effect in the laboratory Doppler effect in the laboratory frameframe
TUNABILITYTUNABILITY
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16Radiation Simulator – T. Shintake, @ http://www-xfel.spring8.or.jp/Index.htm
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Due to the finite duration the radiation is not monochromatic but contains a frequency spectrum which is obtained by Fourier transformation of a truncated plane wave
€
Lpulse = Nuλ rad
NNu u = 5= 5{{ {{{{ {{ {{
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€
ξ
€
I ω( )∝sinξ
ξ
⎛
⎝ ⎜
⎞
⎠ ⎟
2
€
ξ =ΔωTpulse
2= πNw
ω −ωres
ωres
€
Δωω
≈1
Nw
Spectral IntensitySpectral Intensity
Line width
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€
P1 =Q2
6πεoc3
γ 4˙ v ⊥2
€
PT = Ne
e2
6πεoc3
γ 4˙ v ⊥2
€
PT =Ne
2e2
6πεoc3
γ 4˙ v ⊥2
Peak power of accelerated charge:
different electrons radiate indepedently hence the total power depends linearly on the number Ne of electrons per bunch:
Incoherent Spontaneous Radiation Power:
Coherent Stimulated Radiation Power:
WE NEED micro-BUNCHING !
€
Q = Nee
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€
Psat = ρPbeam ∝Ne4 / 3
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High Gain FEL High Gain FEL
€
dγ
dt= −
e
mc
r E ⋅
r β = −
e
mc
r E ⊥⋅
r β ⊥
Energy exchange occurs only if there is transverse motion
Consider“seeding”by an external light source with wavelength λr
The light wave is co-propagating with the relativistic electron beam
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After one wiggler period the electron sees the radiation with the same phase if the flight time delay is exactly one radiation period:
€
Δt = te − t ph = Trad
€
Δt =λ w
cβ //
−λ w
c=
λ rad
c
€
λrad =1− β //
β //
λ w
€
λrad ≈λ w
2γ 21+ K 2
( )
In a resonant and randomly phased electron beam, nearly one half electrons absorb energy and half lose enrgy, with no net gain
The particles bunch around a phase for which there is no coupling with the radiation
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Question: can there be a continuous energy transfer from electron beam to light wave?
Answer: We need a Self Consistent Treatment
Newton Lorentz Equations
Maxwell Equations
€
J⊥
€
E rad ,Bwλ /2
t>0
t=0
Optical potential
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€
v p =ω − ˙ ϕ
k + kw
< v //
The electron beam acts as a dielectric medium which slows down the phase velocity of the ponderomotive field compared to the average electron longitudinal velocity. Hence resonant electrons bunch around a phase corresponding to gain.
The particles within a micro-bunch radiate coherently. The resulting strong radiationfield enhances the micro-bunching even further.
Result: collective instability, exponential growth of radiation power.
Even if there is no external seeding: Self Amplified Spontaneous Emission
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SASE Saturation ResultsSASE Saturation Results
TTF-FELDESY
98 nm
TTF-FELDESY
98 nm
Since September 2000:3 SASE FEL’s demonstrate saturationSince September 2000:3 SASE FEL’s demonstrate saturation
LEUTLAPS/ANL385 nm
LEUTLAPS/ANL385 nm
September 2000 September 2000
VISAATF/BNL840 nm
VISAATF/BNL840 nm
March 2001
⎟⎟⎠
⎞⎜⎜⎝
⎛=
GL
zPzP exp
9)( 0
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TTF FEL
LEUTLE
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SASE Longitudinal coherence
The radiation “slips” over the electrons for a distance Nuλrad
ζ
independent processes
€
Nuλ radSlippage length
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SASE
Courtesy L. Giannessi (Perseo in 1D mode http://www.perseo.enea.it)
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SEEDING
Courtesy L. Giannessi (Perseo in 1D mode http://www.perseo.enea.it)
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€
Δϑ =1
γ
€
Δϑ =1
Nw
€
Δϑ =λr
4πσ≈ mrad
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High Brightness Electron BeamsHigh Brightness Electron Beams
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Linear AcceleratorsLinear Accelerators
PRINCIPIO:Le particelle emesse da un filamento vengono accelerate dal campo elettrico longitudinale
generato da elettrodi susseguenti.
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fascio
Campo elettrico
Linear Radio-Frequency Linear Radio-Frequency AcceleratorsAccelerators
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Electron Photo-InjectorElectron Photo-Injector
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SPARC - SPARXINO - SPARXSPARC - SPARXINO - SPARX
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0 2 4 6 8 10 12 14 160.1
1
10
100
1 .1031 .1041 .1051 .1061 .1071 .108
( ) Z m
Power (W)
Radiation power growth along the undulator @ 530 nmRadiation power growth along the undulator @ 530 nm
UNDULATOR
Undulator period (cm) 2.8Undulator parameter k 2.143Undulator gap (mm) 9.25# Undulator sections 6# Undulator periods per section 78Drift length between undulator sections (cm) 36.5Additional quadrupole gradient (T/m) 5.438Additional quadrupole length (cm) 8.4FEL radiation wavelength (fundamental, nm) 499.6Average beta function (m) 1.516Expected saturation length (m) < 12
GENESIS simulation of the SPARC SASE-GENESIS simulation of the SPARC SASE-FELFEL
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SPARC
DESYBNL
UCLA
SLAC
UE
MOU
MOU
EEUURROOFFEELL
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Energy [GeV]
λcr [nm]
I = 1 kAI = 1 kAK = 3K = 3e e = 0.1 %= 0.1 %
nn=4=4
nn=1=1
SPARC Injector + DASPARC Injector + DANE LinacNE LinacSPARXINOSPARXINO
a <10 nm SASE FEL source at LNFa <10 nm SASE FEL source at LNF
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The FEL ApplicationsThe FEL Applications
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Scientific case: new research frontiers in
• Atomic, molecular and cluster physics• Plasma and warm dense matter• Condensed matter physics• Material science• Femtosecond chemistry• Life science• Single Biological molecules and clusters• Imaging/holography• Micro and nano lithography • Short PulsesShort Pulses
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Free Electron Lasers: Free Electron Lasers: applicazioniapplicazioni
aumentare potenza media(per λ nell’ IR-UV)
Applicazioni mediche e
industriali
diminuire la lunghezza d’onda(λ-> raggi X)
Impulsi ultra-corti
Struttura della materia,ad es. Dinamica delle molecole,
reazioni chimiche
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E. Muybridge at L. Stanford in E. Muybridge at L. Stanford in 18781878
E. Muybridge, E. Muybridge, Animals in MotionAnimals in Motion, ed. L. S. Brown (Dover Pub. Co., New York 1957), ed. L. S. Brown (Dover Pub. Co., New York 1957)Courtesy Paul Emma (SLAC).Courtesy Paul Emma (SLAC).
used spark photography to freeze this ‘ultra-fast’ processused spark photography to freeze this ‘ultra-fast’ process
E. MuybridgeE. Muybridge
disagree whether all feet leave the ground during gallop…disagree whether all feet leave the ground during gallop…
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Coulomb Explosion of Lysozyme (50 fs)Coulomb Explosion of Lysozyme (50 fs)
JJ. Hajdu,. Hajdu, Uppsala U. Uppsala U.
Atomic and Atomic and molecular molecular dynamics occur dynamics occur at the at the fsecfsec-scale-scale
Single Molecule Imaging with Intense X-raysSingle Molecule Imaging with Intense X-rays
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49X-FEL based on last 1-km of existing SLAC linacX-FEL based on last 1-km of existing SLAC linac
LCLS at SLACLCLS at SLAC1.5-15 Å1.5-15 Å
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TESLA XFEL at DESYTESLA XFEL at DESY
X-FEL Integrated into linear colliderX-FEL Integrated into linear collider
0.85-60 Å0.85-60 Å
user facilityuser facility
multiple undulatorsmultiple undulators
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