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Ultra-High Brightness electron beams from laser driven plasma accelerators. Luca Serafini, INFN-Milano. ( A look at the particle beam beyond the source ). 6D Phase Space Density of beams produced by self-injection mechanisms (Brightness, Brilliance). - PowerPoint PPT Presentation
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Coulomb09 , Senigallia, 18-06-2009
Ultra-High Brightness electron beams from laser driven plasma accelerators
Luca Serafini, INFN-Milano
• Brightness Degradation due to Chromaticity blow-out in
ultra-focused beams (p/p> 1% is a danger)
• 6D Phase Space Density of beams produced by self-injection
mechanisms (Brightness, Brilliance)
• Ultra-high brightness in step density gradient plasma injectors
(A look at the particle beam beyond the source)
• Fs to As pulses of Coherent X-rays (the AOFEL)
Coulomb09 , Senigallia, 18-06-2009
Vittoria Petrillo Università degli Studi, Milano (Italy)
Alberto Bacci, Andrea R. Rossi, Luca Serafini, Paolo Tomassini INFN, Milano (Italy)
Carlo Benedetti, Pasquale Londrillo, Andrea Sgattoni,
Giorgio Turchetti Università and INFN Bologna (Italy)
Coulomb09 , Senigallia, 18-06-2009
Brightness and Brilliance5D and 6D phase space density
Figures of Merit for Particle Beams
Coulomb09 , Senigallia, 18-06-2009
n [m]
1013
1014
1015
1016
1017
I [kA]
1018
AOFEL
SPARX
SPARC
X-ray FEL @ 1 pC
€
Bn =2I
εn2
The Brightness Chart [A/(m.rad)2]
Self-Inj
Coulomb09 , Senigallia, 18-06-2009
[]
1014
1015
1016
1017Bn
SPARX
SPARC
The 6D Brilliance Chart [A/((m.rad)20.1%)]
Self-InjExt-Inj
€
B 6D =2I
Δγ
γεn
2=
Bn
Δγ
γ
AOFELX-ray FEL @ 1 pC
€
B 6D ne /(mm.mrad)2 s ⋅0.1%[ ] =γ 21019
1012B 6Dn A /(m ⋅rad)2 s ⋅0.1%[ ]
B 6D − SPARX = 9 ⋅1029
Coulomb09 , Senigallia, 18-06-2009
Rapidity
Coulomb09 , Senigallia, 18-06-2009
electron beam
--------- -- --
Physical Principles of the PlasmaPhysical Principles of the Plasma Wakefield Accelerator Wakefield Accelerator
• Space charge of drive beam displaces plasma electrons
• Transformer ratio
• Wake Phase Velocity = Beam Velocity (like wake on a boat)
• Plasma ions exert restoring force => Space charge oscillations
E Ezacc dec beam. .
• Wake amplitude
€
R∝Nb σ z2 ( )for
nz po
21σ λ≈ ∝
++++++++++++++ ++++++++++++++++
----- ----------------
-- --------
-------- ------- ------------------- - -
-
---- - -- ---
------ -
- -- ---- - - - - - ------ - -
- - - - --- --
- -- - - - - -
---- - ----
------
+ + + + + + + + + + ++ + + + + + + + + + + + + + ++ + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +-
- --
-
EzEz
Courtesy of T. Katsouleas
Plasma acceleration experiments with SPARC/X e- beams
Coulomb09 , Senigallia, 18-06-2009
€
SPARC / X[ ] R ≅1 nC
100 − 300 μm( )2 ≅ 0.01− 0.1
C
m2
€
Self − Inj[ ] R ≅0.6 nC
1.8 μm( )2 ≅185
C
μm2
€
X − ray FEL @ 1 pC[ ] R ≅1 pC
1 μm( )2 ≅1
C
m2
• Self-Injection beams seem to have low phase space density but
high rapidity (suited for relativistic piston applications)
LNF – 29/05/2009
C. Benedetti
€
Q ≅ 0.6 nC
σ z ≅1.8 μm (I ≅ 45 kA)
σ x ≅ 0.5 μm εn ≅ 2 μm
x envelope and emittance free diffraction in vacuum
0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 1 .2
0
5 0 0
1 0 0 0
1 5 0 0
2 0 0 0
2 5 0 0
3 0 0 0
σx (m
)
z(m )
σx
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
3 0 0
x (
m)
x
RETAR (A. Rossi)
no description of plasma
vacuum interface
Bunch length and average current
0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 1 .21 .5
2 .0
2 .5
3 .0
3 .5
4 .0
4 .5
5 .0
5 .5
6 .0 σ
z
σz (m
)
z (m )
6 0 0 0
8 0 0 0
1 0 0 0 0
1 2 0 0 0
1 4 0 0 0
1 6 0 0 0
1 8 0 0 0
2 0 0 0 0
2 2 0 0 0
I (
A)
Av g. current
Energy spread
0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 1 .2
0 .0 2 5 0
0 .0 2 5 2
0 .0 2 5 4
0 .0 2 5 6
0 .0 2 5 8
0 .0 2 6 0
0 .0 2 6 2
z (m )
Transverse and longitudinal phase and configuration spaces @ 1 cm
Transverse and longitudinal phase and configuration spaces @ 92 cm
LNF – 29/05/2009
€
n =εn
σ 0
⎛
⎝ ⎜
⎞
⎠ ⎟
2d
γ
Δγ
γ≅ εn
σ
σ 0
Δγ
γ
SPARC n=1 mm.mrad, σ0= 200 m, =300, =0.6%, d=10 mn =0.005 mm.mrad
Self-Inj n=2 mm.mrad, σ0= 1 m, =2000, =2%, d=1 mn =40 mm.mrad
• Emittance Dilution due to Chromatic Effects on a beam
emerging from a focus of spot size σ0, drifting to a distance d
€
free diffraction
σ = σ 0 1+εnd
σ 02γ
⎛
⎝ ⎜
⎞
⎠ ⎟
2
≅εnd
σ 0γ
€
neff = εn
2 + Δεn2 = σ 0
2 ′ σ 02γ 2 + Δεn
2
€
n
εn
≅σ
σ 0
Δp
p
LNF – 29/05/2009
ASTRA (A. Bacci) : matching with a triplet
LNF – 29/05/2009
Space charge
energy spread
No Space charge
energy spread
LNF – 29/05/2009
No Space charge
No energy spread
SPARC beam
Space charge
energy spread
Coulomb09 , Senigallia, 18-06-2009
How to measure this
emittance blow-up? No
trace on beam envelope…
energy selection?
LNF – 29/05/2009
€
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
€
σTR = εn
2I0γ
I
SPARC 640 m
AOFEL 3 m
SPARX 580 m
acceleration
focusing
beamplasma
emittance
laminarityparameter
Beam-plasmawavelength
betatronlength
transitionspot-size
€
σ >σTR space charge
σ < σ TR emittance
Bubble-self.inj. 80-150 m
Coulomb09 , Senigallia, 18-06-2009
Coherence and Time Duration
Coulomb09 , Senigallia, 18-06-2009
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
AOFEL
•injection by longitudinal nonlinear breaking of the wave at a density downramp looks one of the most promising since it can produce e-beams having both low energy spread and low transverse emittance.
•electromagnetic undulator made by a laser pulse counter propagating respect to the electron beam
First stage:LWFA with a gas jet modulated in areas of different densities with sharp density gradients.
LR
270605020
plateau II(accelerating region)
transition (injection)
plateau I
rising1x1019
6x1018
n e (c
m-3)
z (m, not in scale)
Energy (J) 2
Waist (m) 20
Intensity (W/cm2) 7 10 18
Duration (fs) 20
n01 (cm-3) 1 1019
LR(m) 10
n02 (cm-3) 0.6 1019
λp (m) 13
LR
270605020
plateau II(accelerating region)
transition (injection)
plateau I
rising1x1019
6x1018
n e (c
m-3)
z (m, not in scale)
LR
270605020
plateau II(accelerating region)
transition (injection)
plateau I
rising1x1019
6x1018
n e (c
m-3)
z (m, not in scale)
LR
270605020
plateau II(accelerating region)
transition (injection)
plateau I
rising1x1019
6x1018
n e (c
m-3)
z (m, not in scale)L
R
270605020
plateau II(accelerating region)
transition (injection)
plateau I
rising1x1019
6x1018
n e (c
m-3)
z (m, not in scale)
Coulomb09 , Senigallia, 18-06-2009
<>
<>
Selection of best partin the bunch:40 pC in 2 fs (600 nm)
Longitudinal phase space and density profile
projected rmsn = 0.7 m
VORPAL C. Nieter J. R. CaryJ.Comp.Phys. 196 448 (2004)
New results by ALADYN
Numerical Modelling
Formation of the plasmaFormation of the bunchAcceleration stage
Astra Retar
Beam-CO2 laserInteractionFEL instability
Genesis 1.3EURA
TransitionPlasma-undulator
First stage
Second stage
Third stage
Second stage: Transition from the plasma to the interaction area with the e.m. undulator (analysis by ASTRA)
0 1.20.6
0.01
0.005
0
<σ x>
(mm
)
z (mm)
(b)
(a) 0.4
0.3
n (m
m m
rad)
With space charge
Without space charge
3/1
2u
220
2xA k
JJK1
I
I
16
11
σ
FEL interaction with a e.m. undulator
Pierce ParameterIA=17 103 Amp
Lg1d=λu/( 3 Ideal 1d model
Lgλu Three-dimensional model
Erad=Ebeam
2
2wu
4
)a1(
λ
λ
2
2wu
2
)a1)(2/(
λ
λ = 1.35nm
2.39.22.2
d
9.17.0
d
395.0
d
4.29.226.157.0
d
11404.551
35.0355.045.0
,
)4/(L 2
xd1gd σλ
λσ
22
x
2
x,nd1gL4
λ
u
d1gL4
<1
<1
<1
)3(L4 d1g
u λ
xd1g
x,n L4σ
λ
Generalized Pellegrini criterion
Requirements for the growth
3/1
2u
220
2xA k
JJK1
I
I
16
11
σ
50 20 kA
X 10-6 m
1.15 106 m-1
1.3
=3 10-3
Lg1d=76 m
3102.53
σz=0.2 mmradmm3.0
L4 xd1g
x,n σλ
1,1 1,2 1,3 1,4 1,5 1,60,0
0,2
0,4
0,6
n(m
m m
rad)
s(m)
Lg=200 m
Transverse coherence
d= Lsat*λ/σx= 10*Lg*λ/σx
= 10*200 10-6*10-9/5 10-6=0.4 m
Longitudinal coherence
Lc=λ/( (1+) =0.04 m
1 spike each 10 Lc
3
Third stage: FEL radiation λ=λu(1+aw2)/42
by uploading the particles by VORPAL
Superradiant structure
0.1 m=330 asSingle spike structure
Monochromaticpulse
First peak Saturation
Pmax (W) 2 10 8 1.5 108
E (J) 0.05 0.12
LRm) 0.05 0.5
Lsat mm) 1. 4.5
λR(nm) 1.35
dλR/λR 0.81% 25 micron
25 micron
Laser requirements:250 GW for 5 mmR=30 m E=4.16J
Coulomb09 , Senigallia, 18-06-2009
0,0 5,0x10-4 1,0x10-3 1,5x10-3
104
105
106
107
108P
ma
x(W
)
zeta(m)
I=31 KA σz=1.5 m σx=0.6 um n=0.1 m =45 E/E=0.3% a0=0.8 λ=0.162 nm
Conclusions
• All optical free-electron laser are possible with e-beam produced by LWFA in density downramp + electromagnetic undulators
• Characteristics of radiation: small energy/pulse, quasi transverse coherent, very short pulse, longitudinal coherence, monochromaticity
• Injection of the beam, control of the exit from the plasma, requirements of power and structure of the e. m. undulator
5 10 15 20 25 30 35 400
1
2
3
4
5
6
7
8
<P
> (
x107 W
)
I(kA)
0,00
0,05
0,10
0,15
E(
J)
Coulomb09 , Senigallia, 18-06-2009
Conclusions
• Beams produced by Self-Injection in the bubble regime look
affected by strong chromaticity: serious emittance dilution after
the source, loss of beam brightness
• Possible cures: prompt focusing in mm (plasma lenses?), energy
selection (charge loss), emittance compensation schemes?
• Maximum brightness with step downramp density injection (1D
mech., localized injection) Needs new targets, shock wave gas
jets
• AOFEL: table top X-FEL delivering fs to as quasi-coherent
bright X-ray pulses
Coulomb09 , Senigallia, 18-06-2009
L NLNe−
σ x
Scattered photons in collision
Scattered fluxLuminosity as in HEP collisions
Many photons, electronsFocus tightlyShort laser pulse; <few psec (depth of focus)
Thomson X-section
€
ZR
€
σ z
€
σ x
N =LσT σ T =8π
3re
2
Coulomb09 , Senigallia, 18-06-2009
Coulomb09 , Senigallia, 18-06-2009
€
fig.mer.PWFA
∝Qb
2γ
εnσ z
∝ℑLum
2
€
ℑLum
∝Nb
σ x
∝Nb
εnβ min
γ
∝Qb
εnσ z
γ
€
figm(SPARC ,1kA,2μm) =1250
€
figm(SPARX ) =16700
€
figm(Self − Inj) =14000 − 30000 (160 − 400 MeV )
Rapidity
Coulomb09 , Senigallia, 18-06-2009
• This last group tries to realize the scheme proposed by Gruener et al. (1.74 GeV, 160 kA, 1mm mrad, E/E=0.1%, σx=30 m)
where an electron beam generated by LWFA in the bubble regime is driven in a static undulator
λu=5 mm, λ=0.25nm, Lsat=5m, Lrad=4fs,Psat=58 GW,
• The technology of ultra short, high power lasers has permitted the production and the study of high-brightness, stable, low divergence, quasi mono-energetic electron beams by LWFA.
• These beams are now an experimental reality (for instance: Faure et al.,Leemans et al., Jaroszinski et. al, Geddes et al., ecc.)
• and can be used in applications for driving Free-electron lasers Last experimental results, see, for instance:
• J.Osterhoff et al. PRL 101 085002 (2008)• (mono-energetic fraction: 10 pC@200 MeV, divergence=2.1 mrad FWHM)• Koyama, Hosokai 20 pC @ 100 MeV and density downramp• N. Hafz, Jongmin Lee , Nature photonics• THCAU05 FEL Conf 2008
-1 0 1 2
-60
-40
-20
0
20
40
60r(m
)
z(mm)
electron beam
Ti:Sa pulse
Ti:Sa envelope
Gas jet
Lsat≈10 Lg
CO2 envelope
AOFEL
Lg=10.1 x ( σx2/3/I1/3)x(λw/K0/JJ2)1/3
Coulomb09 , Senigallia, 18-06-2009
Simulation with real bunch
GENESIS Simulations starting from actual phase spacefrom VORPAL (with oversampling)
σ=2.5 m (CO2 laser focus closer to plasma)
After 1 mm : 0.2 GW in 200 attoseconds Lbeff < 2 Lc
Coulomb09 , Senigallia, 18-06-2009
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 σ=3.5 m
Average power (Lsat~500 m, Psat~10 MW)Peak power 100 MWin 100 attoseconds
Field
CoherenceTime duration
Coulomb09 , Senigallia, 18-06-2009
Coulomb09 , Senigallia, 18-06-2009
Slice 8, I=25 kA
€
px2
uncorr≅ 0.2
T⊥ ≅100 keV
σ cat ≅ 0.5 μm
εnth ≅ 0.1 mm ⋅mrad
Equivalent Cathode
€
x 2 px2 >> εn ≡ x 2 px
2 − xpx
2
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