csfi 2008 - rimini - maggio 29, 2008 all optical free electron lasers : una nuova sfida per i codici...

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


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


Compare vs. RF Linac driver:SPARX lay-out

160 m 80 m

Fully consistent e.m. simulation: Nmesh=1016, Npart=108-10, Nstep=107


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


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

⎛

⎝ ⎜

⎞

⎠ ⎟


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]


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.


€

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


€

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


€

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

⎧ ⎨ ⎩


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


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


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


2.5D PIC results withthe VORPAL code

RISING Region



Plateau I Region


Transition Region

Wave-breaking->injection



Injected bunch

Accelerating Region


Best portion of the beam

2.5D PIC results with the VORPAL code

Beaming (x long. axis, y transv.)


€

Lcoop ≈ λ R /4πρ ≈ 30 − 60nm

Slice analysis: length of each slice

Best slices


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


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


QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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


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


Longitudinal Phase Space after removal of correlation

€

Δ

≅1.• 10−3


518 m from plasmaexit, about 10 gain lenghts


RETAR simulations, 20 kA, 1 m focal spot sizedrift inside plasma and exit through plasma-vacuum interface

focus focus

PLASMA VACUUM


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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


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


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


60 nm

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GENESIS Simulations with averaged rms transv. beam parametersActual profiles of current, energy and energy spread


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


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


ALADYN vs. VORPAL



High resolutionΔz=λ/24=33 nmΔx=λ/10=80 nm20 particles per cell

63000 particlesin red circle(160 pC bunch)

z [m]

x [m]




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




ALADYN vs. VORPAL




Slice 8, I=25 kA

€

px2

uncorr≅ 0.2

T⊥ ≅100 keV

σ cat ≅ 0.5 μm

εnth ≅ 0.1 mm ⋅mrad




Slice 9, I=15 kA


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

csfi 2008 - rimini - maggio 29, 2008 all optical free electron lasers : una nuova sfida per i codici...

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undulator slide

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period u slide

interaction of e