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)
• Brightness Degradation due to Chromaticity blow-out in
ultra-focused beams (Dp/p> 1% is a danger)
• Ultra-high brightness in step density gradient plasma injectors
• 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
Figures of Merit for
Particle Beams
Brightness and Brilliance
5D and 6D phase space density
Coulomb09 , Senigallia, 18-06-2009
Bn 
2I
n2
1018
17
AOFEL 10
I [kA]

Self-Inj
1016
1015
SPARX
1014
X-ray FEL
@ 1 pC
The Brightness Chart
Coulomb09 , Senigallia, 18-06-2009
SPARC
[A/(m.rad)2]
n [m]
1013
2I
Bn
B6D 

Dg 2 Dg
g
Bn

n
g
1017
X-ray FEL
@ 1 pC
AOFEL
1016
1015
SPARX
SPARC
Self-Inj
Ext-Inj
B6D ne /(mm.mrad) 2 s  0.1%
g 21019
1014
B6Dn A /(m  rad) 2 s  0.1%
1012
B6D  SPARX  9 10 29
Dg/g [0.1%]
The 6D Brilliance Chart
Coulomb09 , Senigallia, 18-06-2009
[A/((m.rad)20.1%)]
Rapidity
Coulomb09 , Senigallia, 18-06-2009
Physical Principles of the Plasma
Courtesy of T. Katsouleas
Wakefield Accelerator
Plasma acceleration experiments with SPARC/X e- beams
• Space charge of drive beam displaces plasma electrons
-- -- ---- -----+----+- + + + + + + +-+-- +--+----+--+ + + + + + + + + -+--+- +--+--+-+- + +
+
+-+- +++ +++ ++ ++++ +-++-+----+--++- ++++ ++++++++++ +++--+--+++ ++++ ++++ ++
---- ------- --- -- -- - ----- -- - - - -- -- - - -- ---- -- -Ez
• Plasma ions exert restoring force => Space charge oscillations
• Wake Phase Velocity = Beam Velocity (like wake on a boat)
2 ( for 2 z   p  1 )
• Wake amplitude
no
b
z
RN 
• Transformer ratio E z acc . E dec . beam
Coulomb09 , Senigallia, 18-06-2009
1 nC
C
R
 0.01 0.1 2
2
m
100  300 m
SPARC / X 
X  ray
FEL @ 1 pC 
Self
 Inj 
1 pC
C
R
1 2
2
m
1 m
0.6 nC
C
R
 185
2
2

m
1.8

m


• Self-Injection beams seem to have low phase space density but
 high rapidity (suited for relativistic piston applications)
Coulomb09 , Senigallia, 18-06-2009
C. Benedetti
Q  0.6 nC
 z 1.8 m (I  45 kA)
 x  0.5 m n  2 m

LNF – 29/05/2009
x envelope and emittance free diffraction in vacuum
3000
300
x
x
2500
250
RETAR (A. Rossi)
no description of plasma
vacuum interface
1500
200
150
1000
100
500
50
0
0.0
0.2
0.4
0.6
z(m)
0.8
1.0
0
1.2
x (m)
x (m)
2000
Bunch length and average current
6.0
z
22000
Avg. current
5.5
20000
5.0
18000
16000
4.0
14000
3.5
3.0
12000
2.5
10000
2.0
8000
1.5
6000
1.2
0.0
0.2
0.4
0.6
z (m)
0.8
1.0
I (A)
z
 (m)
4.5
Energy spread
0.0262
0.0260
g/g
0.0258
0.0256
0.0254
0.0252
0.0250
0.0
0.2
0.4
0.6
z (m)
0.8
1.0
1.2
Transverse and longitudinal phase and configuration spaces @ 1 cm
Transverse and longitudinal phase and configuration spaces @ 92 cm
• Emittance Dilution due to Chromatic Effects on a beam
emerging from a focus of spot size 0, drifting to a distance d
free diffraction
  0
  d 2  d
1  n 2   n
 0 g   0g
n  n  Dn
eff
n  d Dg
 Dg
Dn   
 n
0 g
 0  g g
2
2
2
2
2 2

  0 g  Dn
2
0
Dn
 Dp

n  0 p
SPARC n=1 mm.mrad, 0= 200 m, g=300, Dg/g=0.6%, d=10 m
Dn =0.005 mm.mrad
Self-Inj n=2 mm.mrad, 0= 1 m,
 g=2000, Dg/g=2%, d=1 m
Dn =40 mm.mrad
LNF – 29/05/2009
ASTRA (A. Bacci) :
LNF – 29/05/2009
matching with a triplet
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
LNF – 29/05/2009
How to measure this
emittance blow-up? No
trace on beam envelope…
energy selection?
Coulomb09 , Senigallia, 18-06-2009
acceleration
beam
plasma
d 2
g
2
2






k


k
F
bp

2
dz
g
focusing
Beam-plasma
wavelength

bp
4


2kbp
2g I 0
 
I
laminarity
parameter
   TR space charge
   TR emittance

3
emittance
2
1
g
*  
k
n
kbp
I 2


k 2I0gn2

transition
spot-size
 TR  n
2I0g
I
betatron
length
SPARC 640 m
SPARX 580 m
AOFEL 3 m
Bubble-self.inj. 80-150 m
LNF – 29/05/2009
Coherence and Time Duration
Coulomb09 , Senigallia, 18-06-2009
CO2 envelope
CO2 focus
r
m]
TiSa envelope
TiSa pulse
e- beam
plasma
Lsat=10LG=1.3 mm (=0.002)
Z [m]
// bp  7 cm
Coulomb09 , Senigallia, 18-06-2009
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.
transition
(injection)
1x10
19
rising
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
p (m)
13
plateau II
(accelerating
region)
18
plateau I
-3
ne (cm )
6x10
Energy (J)
LR
20
50
60
z (m, not in scale)
270
transition
(injection)
1x10
rising
plateau II
(accelerating
region)
18
1x10
19
rising
plateau I
ne (cm )
6x10
transition
(injection)
19
18
plateau I
-3
ne (cm )
-3
6x10
plateau II
(accelerating
region)
LR
20
60
50
z (m, not in scale)
LR
270
20
50
60
z (m, not in scale)
270
transition
(injection)
1x10
19
rising
18
transition
(injection)
1x10
19
rising
plateau I
plateau II
(accelerating
region)
-3
ne (cm )
6x10
plateau II
(accelerating
region)
50
60
z (m, not in scale)
plateau I
-3
LR
20
18
ne (cm )
6x10
270
LR
20
50
60
z (m, not in scale)
270
Longitudinal phase space and density profile
Selection of best part
in the bunch:
40 pC in 2 fs (600 nm)
projected rms
n = 0.7 m
<g>
< g>
g/g
Coulomb09 , Senigallia, 18-06-2009
Third stage
First stage
Numerical Modelling
Formation of the plasma
Formation of the bunch
Acceleration stage
VORPAL
C. Nieter J. R. Cary
J.Comp.Phys. 196 448
(2004)
Transition
Plasma-undulator
Astra
Retar
New results by ALADYN
Second stage
Beam-CO2 laser
Interaction
FEL instability
Genesis 1.3
EURA
Second stage: Transition from the plasma to the interaction
area with the e.m. undulator (analysis by ASTRA)
0.01
With space charge
0.4
n(mm mrad)
<x>(mm)
(a)
0.005
(b)
0.3
0
0
1.2
0.6
z (mm)
Without space charge
FEL interaction with a e.m.
undulator

11 I 1
 
g 16 I A 2x
K 02
JJ 
k 2u
Ideal 1d model
Lg1d=u/(
3
4
Lgu 1h/31/24
2
 u (1  a w )

2 2
4g1  a w )
( u / 2)(

= 1.35nm
2
1/ 3
2


2g
Pierce Parameter
IA=17 103 Amp
Erad=Ebeam
Three-dimensional model
h  0.45h d
0.57
 51h d
0.95
 0.55h   3h g  0.35h  h g
1.6
2
2.9
h g  5.4h d h   1140h d h  h g
3
0.7
1.9
hd  Lg1d  /( 4 )
2
x
2.2
4Lg1d 
2
n,x
g
2
x
2
2.9
3.2
<1
,
h 
2.4
<1
L g1d g
hg  4
u g
<1
Requirements for the growth
g
u

(  3)
g 4L g1d
 n ,x 

g x
4L g1d
Generalized
Pellegrini criterion
1.3
11 I 1
 
g 16 I A 2x
2
K0
JJ 
1/ 3
2
k 2u


1.15 106 m-1
50
20 kA
5X 10-6 m
=3 10-3
0.01
g
55
0.005
Lg1d=76 m
54
1.1

g x  0.3 mm mrad
4L g1d
Lg=200 m
1.2
1.3 1.4
s(m)
1.5
1.6
1.1
z=0.2
m
0,6
n(mm mrad)
 n ,x 
g/g
g
 3  5.2 10 3
g
0,4
0,2
0,0
1,1
1,2
1,3
1,4
s(m)
1,5
1,6
Transverse coherence
d= Lsat*/x= 10*Lg*/x
= 10*200 10-6*10-9/5 10-6=0.4 m
Longitudinal coherence
Lc=/(4 (1+h) =0.04 m
3L
1 spike each 10
c
Superradiant
structure
Third stage: FEL radiation =u(1+aw2)/4g2
by uploading the particles by VORPAL
(a)
7
<P>(W)
(b)
8
2x10
P (W)
6x10
7
4x10
8
1x10
7
2x10
0
0
-3
-3
0
2x10
4x10
-3
6x10
0
2x10
-3
-3
4x10
6x10
z (m)
z (m)
(c)
8
(d)
P (a.u.)
P(W)
2x10
-3
8
1x10
0
0
0.2
s (m)
0.4
1.325
 (nm)
1.375
Monochromatic
pulse
Single spike structure
0.1 m=330 as
First peak
Saturation
Pmax (W)
2 10 8
1.5 108
E (J)
0.05
0.12
LRm)
0.05
0.5
Lsat mm)
1.
4.5
R(nm)
1.35
dR/R
0.81%
25 micron
25 micron
Laser requirements:
250 GW for 5 mm
R=30 m E=4.16J
Coulomb09 , Senigallia, 18-06-2009
I=31 KA z=1.5 m x=0.6 um n=0.1 m
g=45 DE/E=0.3% a0=0.8 =0.162 nm
8
10
7
10
Pmax(W)
6
10
5
10
4
10
0,0
-4
5,0x10
-3
1,0x10
zeta(m)
-3
1,5x10
Conclusions
8
0,15
7
5
0,10
7
<P> (x10 W)
6
E(J)
• 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
4
3
0,05
2
1
0
5
10
15
20
25
I(kA)
30
35
0,00
40
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
Coulomb09 , Senigallia, 18-06-2009
Scattered photons in collision
Ng  L T
T 
Scattered flux
Luminosity as in HEP collisions
8 2
re
3
N L N e
Many photons, electrons
L
4  x2
Focus tightly
Short laser pulse; <few psec (depth of focus)
ZR

x

z
Coulomb09 , Senigallia, 18-06-2009
Thomson
X-section
 Lum 
Nb
x

Nb
n  min
g
fig.mer. PW FA 
figm(SPARC,1kA,2m) 1250
Qg
2
b
 n z

Qb
n z
g
  Lum
2
Rapidity
figm(SPARX) 16700
 figm(Self  Inj) 14000  30000 (160  400 MeV )
Coulomb09 , Senigallia, 18-06-2009
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, DE/E=0.1%,
x=30 m)
where an electron beam generated by LWFA in the bubble
regime is driven in a static undulator
u=5 mm, =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 highbrightness, stable, low divergence, quasi monoenergetic 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 Freeelectron 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
Lg=10.1 x (gx2/3/I1/3)x(w/K0/JJ2)1/3
CO2 envelope
60
r(m)
40 Ti:Sa envelope
Ti:Sa
pulse
20
electron
beam
0
-20
-40 Gas jet
Lsat≈10 Lg
-60
-1
0
1
z(mm)
AOFEL
2
GENESIS Simulations starting from actual phase space
from VORPAL (with oversampling)
=2.5 m (CO2 laser focus closer to plasma)
Simulation with real bunch
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
  106 m a0  1.3 P  8 TW

R  1.7 A 1D  6 104
Lsat1D  310 m LC  25 nm
Average power (Lsat~500 m, Psat~10 MW)
Peak power 100 MW
in 100 attoseconds
Simulation with real bunch =3.5 m
Field
Coulomb09 , Senigallia, 18-06-2009
Coherence
Time duration
Coulomb09 , Senigallia, 18-06-2009
Slice 8, I=25 kA
Equivalent Cathode
px2
uncorr
 0.2
T  100 keV
 cat  0.5 m
nth  0.1 mm  mrad
2
2
x
p
Coulomb09 , Senigallia, 18-06-2009
x  n 
x 2 px2  xpx
2