Ultra-High Brightness electron beams from laser driven plasma accelerators

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)


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)


Brightness and Brilliance5D and 6D phase space density

Figures of Merit for Particle Beams


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


[]

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


Rapidity


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


€

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


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


Coherence and Time Duration


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 I

rising1x1019

6x1018

n e (c

m-3)

z (m, not in scale)

LR

270605020



plateau I

rising1x1019

6x1018

n e (c

m-3)

z (m, not in scale)

LR

270605020



plateau I

rising1x1019

6x1018

n e (c

m-3)

z (m, not in scale)L

R

270605020



plateau I

rising1x1019

6x1018

n e (c

m-3)

z (m, not in scale)


<>

<>

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


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)


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


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



€

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


• 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


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


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



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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Ultra-High Brightness electron beams from laser driven plasma accelerators