CSFI 2008 - Rimini - Maggio 29, 2008 All Optical Free Electron Lasers : una nuova sfida per i codici di simulazione FEL, Plasma e Fasci A. Bacci, V. Petrillo,
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CSFI 2008 - Rimini - Maggio 29, 2008
All Optical Free Electron Lasers :una nuova sfida per i codici di simulazione
FEL, Plasma e FasciA. Bacci, V. Petrillo, A. R. Rossi, Luca Serafini,
P. Tomassini* - INFN/MI (*and CNR-Pisa),C. Benedetti, P. Londrillo, A. Sgattoni, G. Turchetti - Univ. di Bologna and INFN/BO
• Bubble regime and self-injection schemes with density
downramp analyzed
• Generation of electron beams for FEL’s applications with
plasma injectors, targeting
€
I >10 kA; εn ≤1 μm; σ z ≈1 fs
• FEL simulations showing fs to 100 attosec X-ray pulses (1 Å - 1
nm) using optical undulators
CSFI 2008 - Rimini - Maggio 29, 2008
CO2 envelope
TiSa envelope
e- beamTiSa pulse
plasma
Lsat=10LG=1.3 mm (=0.002)
CO2 focus
Z [m]
rm]
€
λ// bp ≈ 7 cm λ⊥bp ≈ 8 mm
λlas=1 m x,y,z=1 mmesh < 50 nm
CSFI 2008 - Rimini - Maggio 29, 2008
Compare vs. RF Linac driver:SPARX lay-out
160 m 80 m
Fully consistent e.m. simulation: Nmesh=1016, Npart=108-10, Nstep=107
CSFI 2008 - Rimini - Maggio 29, 2008
What is a SASE-FEL Radiation Source?a Bright Electron Beam propagating through an Undulator
Spontaneous Radiation:
peaked at λr λu (1 + K2) / 22 ; K=Buλu ; ≥ 2.103
Beam rms divergence ’ 1/ rad (Compton Backscattering of undulator virtual photons)
I r e ; e number of electrons per bunch ( 109)
1-25 GeVelectrons
100-0.5 Åphotons
und. period λu
CSFI 2008 - Rimini - Maggio 29, 2008
Interaction of e- with Spontaneous Radiation causes Microbunching and SELF-AMPLIFICATION of Spontaneous
Emission (SASE)
In the SASE mode the Intensity: I ph e > 4/3 ; e of electrons (
109)
Amplification gives extraordinary High Photon Flux (diffraction limited beam)Beam rms divergence ’ λ 2e few rad
•Interaction of a bright electron beam with noise in an undulator magnet results in a density modulation of the electron bunch at the optical wavelength: SASE instability leads to COHERENT EMISSION
PFEL =P0 e2z Lg
Resonance Condition
€
λr =λ u
2γ 21+
K 2
2
⎛
⎝ ⎜
⎞
⎠ ⎟
CSFI 2008 - Rimini - Maggio 29, 2008
n [m]
1013
1014
1015
1016
1017
I [kA]
1018
AOFEL
SPARX
SPARCSPARX 1 pC
€
B =2I
εn2
The Brightness Chart [A/(m.rad)2]
CSFI 2008 - Rimini - Maggio 29, 2008
Issues of transporting Ultra-high Currente- beams with brightness preservation
• Longitudinal space charge debunching and correlated energy chirp
• Transverse time-dependent space charge oscillations and rms emittance
compensation/preservation′ σ
′ γ γ
+σΩ2 ′ γ 2
γ2
I2I Aσγ3 +
εn,sl2
σ 3γ2
′ ϑ =−Ksol +pϑ ,o
mcβγR2
€
KzRF ϕ( )σ z
€
KzSC
σ z
€
′ ′
€
′ ′ z
Linear Model forLinear Model for
Plasma BeamsPlasma Beams
(HOMDYN)(HOMDYN)
invariant envelope
vel. bunch.
CSFI 2008 - Rimini - Maggio 29, 2008
€
d2σ
dz2 = −
′ σ ′ γ
γ − ΚFσ + kbp
2 σ + kβ2σ
€
λ⊥bp
4=
π
2kbp
= πσ2γ 3I0
I
€
β* =1
kβ
=γσ 2
εn
€
ν =kbp
kβ
=Iσ 2
2I0γεn2
€
TR = εn
2I0γ
I
SPARC 640 m
AOFEL 3 m
SPARX 580 m
acceleration
focusing
beamplasma
emittance
laminarityparameter
Beam-plasmawavelength
betatronlength
transitionspot-size
€
>TR space charge
σ < σ TR emittance
CSFI 2008 - Rimini - Maggio 29, 2008
€
λ⊥bp = 2πγR2γI0
I
• Transverse beam plasma wavelength : uncontrolled
oscillations over distances > lead to rms (projected)
emittance blow-up
€
I =150 kA
R =10 μm
⎧ ⎨ ⎩
€
λ⊥bp
4 (m)
€
€
λ⊥bp
LCLS 3⋅103 m
SPARC 48 m
⎧ ⎨ ⎩
€
λ⊥bp
€
λ⊥bp
4
CSFI 2008 - Rimini - Maggio 29, 2008
€
λ// bp = 2πγ 2 I0
IR ⋅L
• Longitudinal space charge length λβp (full debunching)
€
€
λ// bp (m)
€
I =150 kA
R =10 μm
L = 2 μm
⎧
⎨ ⎪
⎩ ⎪
€
40 cm
€
λ// bp
LCLS 3.4 ⋅105 m
SPARC 2.6 ⋅103 m
⎧ ⎨ ⎩
CSFI 2008 - Rimini - Maggio 29, 2008
So we would like to operate a SASE FELwith ultra high beam currents, Ip > 10 kA ,
yet in the usual regime
€
LG << λ⊥bp
€
LG << λ // bp
€
λβ << λ⊥bpEmittance dominated beamthrough undulator
€
<< σ TR
CSFI 2008 - Rimini - Maggio 29, 2008
We started exploring two self-injection schemes: a) self-trapping in the bubble regime and b) controlled self injection with density downramp.
• Bubble injection [A. Pukhov, J. M.-ter-Vehn, Appl. Phys. B 74, 355 (2002)]
has been widely investigated, both experimentally and numerically and it has been proved to be able to produce high energetic (GeV-scale), high charge and quasi monochromatic (few-percent) e-beams.
• Self injection with density downramp Main idea+1D sim. [S. Bulanov
et al., PRE 58, 5 R5257], First 2D sim+optimization for monocromaticity and low emittance [P. Tomassini et al. PRST-AB 6 121301 (2003)], First experimental paper of LWFA with injection by density decrease [T. Hosokai et al., PRE 67, 036407 (2003)]. It has been (numerically) proved to be able to produce very low emittance and quasi monochromatic e-beams
Beam GenerationBeam Generation
CSFI 2008 - Rimini - Maggio 29, 2008
2.5D PIC results with the VORPAL code
• Macro-particles move in a moving-window simulation box of 50x60m2 with a spatial resolution of 0.05 λ and 0.15 λ and 20particle/cell
• The plasma density is large (7-12.1018cm-3) in order to “freeze” the space-charge effects and slippage in the early stage of acceleration.
• The density transition was (L~5-10 m ~ λp). The amplitude of the transition is low (20%-40%), thus producing a SHORT e-beam
• The laser pulse intensity (I=7.1018W/cm2) 2J in 25fs focused on a waist of 18 m) was tuned in order to produce a wakefield far from wavebreaking in the flat regions.
• The pulse waist was chosen in order to assure that longitudinal effects do dominate over transverse effects @injection (avoid transverse wavebreaking that will increase the emittance of the bunch)
• A Multi-plateau (three contiguous accelerating regions with increasing densities along the pulse path) is adopted to fix punch slippage along the bucket
CSFI 2008 - Rimini - Maggio 29, 2008
2.5D PIC results withthe VORPAL code
Injected bunch
Accelerating Region
CSFI 2008 - Rimini - Maggio 29, 2008
Best portion of the beam
2.5D PIC results with the VORPAL code
Beaming (x long. axis, y transv.)
CSFI 2008 - Rimini - Maggio 29, 2008
€
Lcoop ≈ λ R /4πρ ≈ 30 − 60nm
Slice analysis: length of each slice
Best slices
CSFI 2008 - Rimini - Maggio 29, 2008
CO2 envelope
TiSa envelope
e- beamTiSa pulse
plasma
Lsat=10LG=1.3 mm (=0.002)
CO2 focus
Z [m]
rm]
€
λ// bp ≈ 7 cm λ⊥bp ≈ 8 mm
CSFI 2008 - Rimini - Maggio 29, 2008
In a conventional FEL the electron beam is generated in the space charge dominated regime ( TR) and is brought,
by acceleration and focusing, into the emittancedominated regime ( TR), where the FEL interaction occurs
€
LG << λ⊥bp
€
λβ << λ⊥bp
€
<< σ TR
In the AOFEL the electron beam is generated in the emittance dominated regime ( TR) and is left
diffracting within the plasma (and in vacuum) into the space charge
dominated regime ( TR), where the FEL interaction occurs
€
λβ < λ⊥bp
€
LG < λ⊥bp
€
> σ TR
CSFI 2008 - Rimini - Maggio 29, 2008
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ASTRA simulation (solid lines) for AOFEL beam in vacuum20 kA, 1 m focal spot size, 0.3 mm.mrad
Red: no space chargeBlack: space charge
Black dashed: numericalintegration of rms envelopeequation with space charge
Red dashed:
€
z( ) = σ 0 1+z2
β 02
CSFI 2008 - Rimini - Maggio 29, 2008
Longitudinal Phase Space distributions show violent blow-up ofuncorrelated energy spread due to transverse space charge field
158 m from plasmaexit, about 3 gain lenghts
€
E redge =
Z0I
2πσI = 20 kA; σ =1 μm
E redge =1 TV /m
CSFI 2008 - Rimini - Maggio 29, 2008
Longitudinal Phase Space after removal of correlation
€
Δ
≅1.• 10−3
CSFI 2008 - Rimini - Maggio 29, 2008
RETAR simulations, 20 kA, 1 m focal spot sizedrift inside plasma and exit through plasma-vacuum interface
focus focus
PLASMA VACUUM
CSFI 2008 - Rimini - Maggio 29, 2008
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Selection of best partin the bunch:40 pC in 2 fs (600 nm)
Longitudinal phase space and density profile
projected rmsn = 0.7 m
CSFI 2008 - Rimini - Maggio 29, 2008
at plasma exit after 1 mm drift
x= 5 m<px
2> = 0.5
€
px2
x= 0≅ 0.03
sphericalwave front
x
px
planewave
€
2θ 2 = px2 =
γεn
βmatched
< ρ plane waves
px2
x= 0=
εn2
σ 2 < ρ spherical wave fronts
€
β
€
β
CSFI 2008 - Rimini - Maggio 29, 2008
Average power (Lsat=2.5 mm)
Peak power 0.7 GWs (micron)
€
λ =10−5 m
a0 = 0.8
P = 500 GW
λ R =1.3 nm
ρ1D =1.8 ⋅10−3
LC = 65 nm
€
=55
I = 20 kA
εn = 0.3 μm
Δγ
γ= 0.9 %
σ = 5 μm ; β = 4.5 mm
GENESIS Simulationsuniform beam over 0.5 m
averaged rms beam parametersCheck 3D effects
CSFI 2008 - Rimini - Maggio 29, 2008
60 nm
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GENESIS Simulations with averaged rms transv. beam parametersActual profiles of current, energy and energy spread
CSFI 2008 - Rimini - Maggio 29, 2008
Simulation with real bunch
GENESIS Simulations starting from actual phase spacefrom VORPAL (with oversampling)
=2.5 m (CO2 laser focus closer to plasma)
After 1 mm : 0.2 GW in 200 attoseconds Lbeff < 2 Lc
CSFI 2008 - Rimini - Maggio 29, 2008
GENESIS Simulations for laser undulator at 1 m
to radiate at 1 Angstrom
€
λ =10−6 m a0 =1.3 P = 8 TW
λ R =1.7 A°
ρ1D = 6 ⋅10−4 Lsat1D = 310 μm LC = 25 nm
Simulation with real bunch =3.5 m
Average power (Lsat~500 m, Psat~10 MW)Peak power 100 MWin 100 attoseconds
Field
CSFI 2008 - Rimini - Maggio 29, 2008
ALADYN vs. VORPAL
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High resolutionΔz=λ/24=33 nmΔx=λ/10=80 nm20 particles per cell
63000 particlesin red circle(160 pC bunch)
z [m]
x [m]
CSFI 2008 - Rimini - Maggio 29, 2008
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W0=23 m, T=17 fs
I=8.5*1018 W/cm2 , E=2.4 J
nota che abbiamo ancora energia laser che possiamo usare per aumentareun po’ la durata fino a valori piu’ realistici oppure il waist per diminuire ulteriormentele forze trasverse e quindi aumentare il raggio del beam
CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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ALADYN vs. VORPAL
CSFI 2008 - Rimini - Maggio 29, 2008
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CSFI 2008 - Rimini - Maggio 29, 2008
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Slice 8, I=25 kA
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px2
uncorr≅ 0.2
T⊥ ≅100 keV
σ cat ≅ 0.5 μm
εnth ≅ 0.1 mm ⋅mrad
CSFI 2008 - Rimini - Maggio 29, 2008
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Slice 9, I=15 kA
CSFI 2008 - Rimini - Maggio 29, 2008
Conclusions
• Feasibility study for exp. at LNF with FLAME (200 TW TiSa
laser available in 2008): perspectives for ELI (600 PW in 2015)
• We presented an exploratory analysis (raising the plasma density we reached 250
kA, Δ 3%, and n 1.5 m, 50 MeV)
• We must set up a reliable start-to-end simulation from plasma to X-rays
(ALADYN3D+GenesysEM?): see C. Benedetti’s talk
• Computational challenge: turn a plasma-code into an accelerator-code,
from plasma vomit to partice beams
• It’s worth to envision and study the future generation of
high brightness beam injectors
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