Simulations for linear and fully nonlinear
Thomson Scattering with the TSST code
A. Bacci(1), C. Benedetti (6), A.Giulietti(2),
D. Giulietti(2,3,5), L.A. Gizzi (2),
L. Serafini(1), P.Tomassini(1), V. Petrillo(1)
(1) INFN Sect. of Milano (2) IPCF-CNR, Pisa
(3) Dip. Fisica Univ. di Pisa (4) Dip. Fisica Univ. di Milano
(5) INFN Sect. of Pisa (6) INFN Sect. of Bologna
University
of
Milan
Tomassini, INFN sez. di Milano
1
Outline
• Uncoherent Thomson
in the
linear and nonlinear
30%Scattering
of the total
time
regimes
• High-flux source with
RF-photoinjector
in the quasi-linear regime
20%
of the total time
• Monochromatic source
RF-photoinjector
10%with
of the
total time in the quasi-linear
regime
• Ultra-short quasi-monochromatic
fs source
with RF-photoinjector
20% of the total
time
• All-Optic Source: Ultra-short
fs source
with LWFA e-beams
20% of the
total time
Tomassini, INFN sez. di Milano
2
Thomson Scattering
in the linear and nonlinear regimes
y
q
x
z
X-rays
Most important parameters:
1. Particle energy (controls energy and angular
distribution of the X-rays)
2. Laser pulse normalized amplitude a0=eA/mc2
(controls the nonlinearity in the quivering and
several other issues)
Tomassini, INFN sez. di Milano
3
Thomson Backscattering:
relevant issues
1. Particles in the e.m. field of a plane wave do experience:
1.a Longitudinal ponderomotive forces at the rising and
falling edges of the laser pulse
1.b Transverse ponderomotive forces
1.c Transverse force due to the pulse electric -> off axis
field in the case of short rising front with
a 0
momentum
2. Particles motion is:
2.a Secolar motion is longitudinal, with a transverse drift.
Longitudinal and transverse quivering
Note: In a strong quivering regime several harmonics can
be generated (Nonlinear Thomson regime or multiphoton
absorbtion regime)
4
Tomassini, INFN sez. di Milano
The simple case:
harmonic or quasi-harmonic quivering
Weakly relativistic (g=1.7) on axis particle
Weakly nonlinear (a0=1) pulse
Tomassini, INFN sez. di Milano
5
A trivial effect:
longitudinal ponderomotive force
Longitudinal ponderomotive force
Weakly relativistic (g=1.7) on axis particle
Nonlinear (a0=3.5) pulse
Tomassini, INFN sez. di Milano
6
3D (still) trivial effect:
transverse ponderomotive forces
Transverse ponderomotive force
Weakly relativistic (g=1.7) OFF AXIS particle
Weakly nonlinear (a0=1) pulse
Tomassini, INFN sez. di Milano
7
Less trivial effect
for quasi flat-top pulses
Initial phase for non-adiabatic pulses
Weakly relativistic (g=1.7) on axis particle
Weakly nonlinear (a0=1) pulse
Tomassini, INFN sez. di Milano
8
Scattered photons distributions
• The computation of the angular and spectral distribution of the scattered radiation
can be performed in the classical dynamics framework (provided that the energy
of the electrons is far below 50GeV) by using the retarded potentials:
 
2


 J (n,  )
2
dd
4
d 2 Ng

 


J ( n ,  )  n  ( n   dt (t )e
Direction of emission
 
n r ( t )
i ( t 
)
c
)
Particle speed and position
Tomassini, INFN sez. di Milano
9
Scattered photons distributions
Main features of the scattered radiation:
1. Relativistic effect: It is emitted forward with respect to the
direction of the mean speed, within a cone of aperture qc~1/g.
It is blue shifted of a factor depending on the emission angle q,
the electron energy and the pulse amplitude:
E X  ELaser  4g 2 /(1  g 2 2  a02 / 2)
2. Nonlinear effects (multiphoton absorption): As the normalized
amplitude a0 exceeds unity, a large number of harmonics is
produced and a red shift in the mean energy is induced by the
longitudinal ponderomotive forces
Tomassini, INFN sez. di Milano
10
Fully analytical treatment
paper
withcomplex
analytical
treatment
flat-top
plane• •First
An exact
but very
dependence
of the
X-ray distribution
wave
and angle,
for an
exactly
particle:
on thepulses
scattering
initial
phaseon
andaxis
initial
particle momentum
has been found.
E.Esarey
et al. Phys. Rev. E 48 (1993)
• •First
If the paper
numberintroducing
of cycles is large
spectral
distribution
can be
thethe
initial
phase
effect for
an
decomposed
as aparticle
sum of harmonics,
each harmonic
its own
exact
on axis
and a perfectly
sharphaving
rising
energy and intensity dependence upon the output and particle
front:
al, Phys. Rev. Lett. 95 (2003)
angles. F.He et.
2

d Ng
 V (n, ,  ) (  n )
F
•Full treatement
of
nonlinear
TS
for
flat-top
planedd n 1
pulses
and acan
generic
incidence
angle,
• wave
The exact
solution
be simplified
if output
and particle angles
generalization
of the initial
phase for non-sharp rising
are small or if nonlinearity
is weak
fronts and handling of a realistic e-beam:
etparticle
al., Appl.
Phys.independently.
B 80, 419 (2005).
• P.
ForTomassini
a bunch each
is processed
Tomassini, INFN sez. di Milano
11
Example
Head-on collision of a 100 MeV electron against a flat-top pulse of amplitude a0=1.5,
l = 1mm , T = 20 fs and rising front giving a_bar=1
EF   F    4g 2 /(1  g 2 2  a02 / 2)  75KeV
Emission angle of the main
Tomassini, INFN sez. di Milano
component
12
Scattered photons distributions
Tools for simulating the X-ray distribution
•
Monte Carlo based on the Klein-Nishina formula and its nonlinear
generalization
•
Fully analytical. Full treatement of linear and nonlinear TS for a
plane-wave flat-top laser pulse.
•
Fully
numerical.slow
A numerical
integration
the angular
time history
can be
Extremely
if a good
spectralofand
resolution
performed
with several
schemes.
is needed
for ahigh-order
long pulse
and 103-104 particles
•
Semi-analytical. The laser pulse interactong with the particle is
Relatively
accurate
with slowly
most of
the envelope
TS setup
in of
decomposedfast
as a and
sequence
of flat-top,
varying
slices
the
linear radiation
and nonlinear
regimes.
the pulses. The
produced
[which is
estimatyed analytically
for each slice] is then coherently added in a numerical fashion.
Tomassini, INFN sez. di Milano
13
Realistic TS simulations
A realistic simulation of the TS of a pulse on an electron
bunch must take into account consistently a large amount
of effects:
The pulse is not a plane wave (focusing,
LASER PULSE transverse intensity profile). Phase
mismatch and transverse ponderomotive
forces can then arise.
ELECTRON
BEAM
Each electron has its own energy and
incidence angle. Collective (driven by
electrostatic Coulomb forces) effects
should also taken into account
in the case of dense bunches
Tomassini, INFN sez. di Milano
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A semi-analitic approach: the TSST code
Thomson Scattering Simulation Tools
•
If the laser pulse envelope is adiabatic (rise time>>pulse duration) each
electron will interact with a sequence of flat-top slices with slowly varying
amplitude, wavevector and phase slice-by-slice.
•
The amplitude of the scattered radiation A (NOT the intensity) can be
computed by summing up (with the correct phase) the amplitude slice by
slice Aslice. The X-ray radiation is finally computed as the modulus square
of A
•
With this in mind we can estimate each secular particle trajectory and
computing ANALITICALLY the amplitude for each slice, taking account of
transverse effects too.
• Coherence and a dialog with a self-consistent particle
dynamics code are about to be included for very
accurate simulations in the case of dense electron bunches.
Tomassini, INFN sez. di Milano
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Lets start with the simplest case:
Fundamental relations in the linear regime
• Relativistic upshift
EX
~2
4g 2
2
2
 E0
,





~
e  2e cos(   e )
2 2
(1  g  )
Particle incidence angles
• For an e-bunch the energy spread of the collected photons depends
on
– Collecting angle qM
– Bunch energy spread
– Transverse momentum
  gM
Overlap
E X
g
2
  2
 (g  ) 2
EX
g
 cT
N ( )   N e 
 l
+front
curvature
2
4
2
 2 2 (1    3  )
 a0 
3

1 2
Tomassini, INFN sez. di Milano


16
TS by Relativistic Electron Bunches
the bunch side
A good electron bunch source is characterized by:
1.
A large number of electrons N>108
2. A low energy spread
3. On focus, the bunch size is as small as possible (few microns the
transverse and less of a millimeter the longitudinal size)
4. The bunch divergence qe is as small as possible qeg<<1.
Standard accelerators Laser plasma accelerators
1
Yes
Yes
2
Yes, E/E <0.2%
Yes! Good results have been
recently obtained
3
Not enough, the longitudinal
size can exceeds some mm
Yes, few microns size!
4
Yes
(but not always)
Tomassini, INFN sez. diYes
Milano
17
The Bunch Side
(More on Bunch Requirements)
Not so trivial:
Usually the beam normalized emittance is quoted to
quantify the goodness of an e-beam.
For TS the minimum energy spread is limited by the
normalized acceptance angle
  gM ( 1 for monochroma ticity)
which should exceeds the normalized mean incident
angle of the particles transverse relevant
parameter. The relevant parameter is then the
rms of the transverse momentum of the bunch
and NOT the emittance
di Milano
e Tomassini,
 g e INFN
( psez.
 / mc)  (e n  / r )
18
Coherence properties
• Longitudinal coherence
LLl/2l/l
is negligible unless collective phenomena occur
(->switch to FEL regime…)
• However many application [see e.g. contrast phase
tomography, contrast phase mammography….] need
radiation having some degree of transverse coherence
LTl/2D/r
• Due to the small source size r and large distance D
transverse coherence of TS X-rays can be as high as
several hundreds of micrometers!
Tomassini, INFN sez. di Milano
19
Applications of the TS source
…why is the TS source interesting for real use?
• Extremely short duration (approximately as long as
the electron beam), usually few femtoseconds for laserplasma accelerators, few picoseconds for RF accelerators and few tens of fs for slice-selected beams by RF
accelerators
• Extremely small emission spot (few microns!)
• Quasi monochromatic and continuosly tunable.
• More compact than synchrotron radiation
Tomassini, INFN sez. di Milano
20
Thomson Scattering Activities
in PLASMONX
(coordinator: V. Petrillo, INFN&Univ.MI)
We have optimized the TS source aiming at producing
• HIGH FLUX quasi-monochromatic X/g radiation (energy in the range
10KeV-600KeV for PLASMONX) for medical imaging (e.g.
mammography) with a high-charge (1-2.5 nC e-beam).
• MONOCHROMATIC (2%rms) X/g radiation
• Ultrashort quasi-monochromatic X beams with a low-charge
(20pC) ultrashort (30-50fs) photoinjector e-beam
We are currently studying:
• All-optical HIGH FLUX-Ultrashort tunable X/g sources with
LWFA produced e-beams
• Coherent generation of X photons via optical FEL
• Finally, we plan to use TS as a diagnostics on the LWFA produced ebeam
21
Tomassini, INFN sez. di Milano
TS operating modes
in PLASMONX
• High-Flux-Moderate-Monocromaticity mode (HFM2)
(suitable for applications requiring a high flux quasi monochromatic
source)
• Moderate-Flux-Monochromatic mode (MFM)
(applications where emphasis on monochromaticity and tunability
are needed)
• Short-Monochromatic mode (SM)
(tens of femtoseconds long, monochromatic source)
• Laser-Plasma-Ultrashort mode (LPU)
[ongoing, laser-plasma accelerated electron bunches are employed
producing ultrashort (1fs scale) quasi monochromatic X-rays]
Tomassini, INFN sez. di Milano
22
Outline
• Uncoherent Thomson Scattering in the linear and nonlinear regimes
• High-flux source with RF-photoinjector in the quasi-linear
regime
• Monochromatic source with RF-photoinjector in the quasi-linear
regime
• Ultra-short quasi-monochromatic fs source with RF-photoinjector
• All-Optic Source: Ultra-short fs source with LWFA e-beams
Tomassini, INFN sez. di Milano
23
High Flux operation mode
HFM2
• A long (ps scale) laser pulse is employed (weakly
nonlinear regime) to reduce harmonics and energy
spread
• High charge (1-2.5nC) e-beam. Due to the large charge,
it is difficult to obtain small beams (length of ps scale)
• Current optimization for advanced mammography
sources requiring >1011 g/s with energy spread <12%
rms.
Best working point
Bunch
Pulse
•2.5nC
•8ps long (full size)
•TEM00
•13mm rms tr. Size
•6J in 6ps
•1.5 mm mrad norm emittance
Tomassini, INFN sez. di Milano•w0 = 15 mm
•0.1% energy spread
24
PLASMONX LINAC layout
Features:
•High brightnss e-beam
•Very low transverse momentum
quadrupoles
dipoles
RF deflector
collimator
solenoid
Photoinjector
RF sections
25º
25º
11º
1.5m
10.0 m
5.4 m
14.5 m
Diagnostic
1-6 Undulator
modules
High Flux results
• Optimization of the bunch in progress. Front-to-end
simulations from photo-gun to the final focus.
• Optimization of the pulse parameters: scan of the
distribution with the waist size and duration.
Reduced overlapping
Acceptance: g qmax = 0.5
Tomassini, INFN sez. di Milano
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(E,q) Distribution
Second harmonics
Third harmonics
Tomassini, INFN sez. di Milano
27
22%FWHM
4.5% FWHM
2.1010 g/sec with energy spread
22%FWHM, transverse size 15mm
rms and duration 8ps are
produced
Tomassini, INFN sez. di Milano
28
Outline
• Uncoherent Thomson Scattering in the linear and nonlinear regimes
• High-flux source with RF-photoinjector in the quasi-linear regime
• Monochromatic source with RF-photoinjector in the quasilinear regime
• Ultra-short quasi-monochromatic fs source with RF-photoinjector
• All-Optic Source: Ultra-short fs source with LWFA e-beams
Tomassini, INFN sez. di Milano
29
Moderate-Flux-Monochromatic
operation mode (MFM)
• In the MFM mode the requirement is on monochromaticity so the goal
is the optimization of the TS source so as to reduce the energy
spread of the X-rays down to few percent.
• For an ideal e-beam the energy spread depends only on the
acceptance angle:
 E X

 EX

2
 
2
 1  / 2
where gqM is the normalized acceptance
• To switch in the monochromatic mode just a reduction of the
acceptance angle is needed!
• UNFORTUNATELY the first consequence of the acceptance
reduction is the lowering of the X-ray flux
1   2  2 4 / 3 
NX   

3
Tomassini,
INFN(1sez.
di2 Milano


)


2
30
Minimum TS energy spread
• In the presence of beam energy
Minimum energy spread
ofX 1.5%
rms 
,g



E
2
spread and transverse momentum .  8


2

(
g
)
e
 Ephotons/s

with a flux of 1.9 10
g
X

 min
the minimum energy spread is
=0.1
+ponderomotive broadening
Flux: NX=1.9.108 g/s
• With an energy spread 0.1%, emittance 1.5 mm mrad and beam
E/E=1.5%
focusing size
of 13 mmrms
rms, the contributions are
=0.2
Flux: NX=7.3.108 g/s
rms
g E/E=2.2%
3
2
 2 10 , (ge ) 2  2 10  2
  0.1
g =0.3
Flux: NX=1.5.109 g/s
E/E=4.1% rms
Tomassini, INFN sez. di Milano
31
Outline
• Uncoherent Thomson Scattering in the linear and nonlinear regimes
• High-flux source with RF-photoinjector in the quasi-linear regime
• Monochromatic source with RF-photoinjector in the quasi-linear
regime
• Ultra-short quasi-monochromatic fs source with RFphotoinjector
• All-Optic Source: Ultra-short fs source with LWFA e-beams
Tomassini, INFN sez. di Milano
32
Ultrashort Quasi-monochromatic
Source with Photoinjector e-Beam
• Ultrashort 130MeV, 20pC e-beam
Parameters:
r (rms)=6mm
length (rms)=13mm
E/E=0.1%
en=1.2mm mrad
e  ( p / mc)  (e n / r )  0.2
Tomassini, INFN sez. di Milano
33
TS Distributions
Fundamental at 400KeV
• Since the emphasis is on the monochromaticity we
45fs long (rms) with
choose to collect photonsBunch
in the “natural-aperture”
8 photons/sec
2x10
cone, i.e. the one with e=0.2 (approx. 1 mrad).
E/E=4% FWHM
First harmonics at 800 KeV
energy spread
Monochromaticicy requires minimization of the
harmonics production. The laser pulse is 5ps long and is
focused down to 15 mm of waist size
Tomassini, INFN sez. di Milano
34
Outline
• Uncoherent Thomson Scattering in the linear and nonlinear regimes
• High-flux source with RF-photoinjector in the quasi-linear regime
• Monochromatic source with RF-photoinjector in the quasi-linear
regime
• Ultra-short quasi-monochromatic fs source with RF-photoinjector
• All-Optic Source: Ultra-short fs source with LWFA e-beams
Tomassini, INFN sez. di Milano
35
All-optical source:
LWFA for the e-beam
• A route for a drastic reduction of the e-beam
size is that of switching to Laser Wake Field
Accelerated electrons.
• The laser system for the LWFA can either be
the same of TS or another dedicate system. In
the first case a splitting of the laser pulse is
employed
Tomassini, INFN sez. di Milano
36
e-beam quality:
controlled injection
• We are currently exploring controlled self injection with
density downramp
S. Bulanov et al. [the idea+1D sim.] PRE 58 R5257 (1998)
P. Tomassini et al. [First 2D sim+optimization for
monocromaticity and low emittance] PRST-AB 6 121301 (2003).
T. Hosokai et al., [First experimental paper of LWFA with
injection by density decrease] PRE 67, 036407 (2003).
• Search for working points in the 10-100 MeV energy
range, with
– ultrashort, Few femtoseconds long
– low transverse momentum
For monocromaticity of
The X source
– quasi monochromatic e-beams
Tomassini, INFN sez. di Milano
37
2D PIC results with the ALaDyn code
C.Benedetti, P.Londrillo A.Sgattoni, G. Turchetti
developed @ INFN-BO
•
•
•
•
•
•
To increase accuracy, transversally stretched cells have been used in the
simulation box. Macro-particles move in a moving-window simulation
box of 170x45mm2 with longitudinal and transverse spatial resolution in
the center of l/12 and l/4, respectively, and 80 particle per cell.
The plasma density is large (1.1019cm-3) in order to “freeze” the spacecharge effects and slippage in the early stage of acceleration.
The density transition was (L~10 mm ~ lp). The amplitude of the
transition is low (15%), thus producing a SHORT e-beam
The laser pulse intensity (I=8.5.1018W/cm2) 2.5J in 17fs focused on a
waist of 32.5 mm) 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
The accelerating plateau has a negative density gradient in order to
induce dephasing in the early stage of the acceleration thus producing
quasi-monochromatic e-beams with low transverse momentum
Tomassini, INFN sez. di Milano
38
Longitudinal phase-space plot
First plateau
Tomassini, INFN sez. di Milano
39
Longitudinal phase-space plot
Just after transition:
particle injection
Tomassini, INFN sez. di Milano
40
Longitudinal phase-space plot
Particle acceleration
Tomassini, INFN sez. di Milano
41
Longitudinal phase-space plot
Dephasing
Particles enter in the
de-accelerating region:
dephasing has started
Tomassini, INFN sez. di Milano
42
Longitudinal phase-space plot
Dephasing
Very low momentum spread
Tomassini, INFN sez. di Milano
43
Two dimensional issues
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
44
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
45
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
46
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
47
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
48
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
49
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
50
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
51
Ez
Density of particles with pz>0.8
Tomassini, INFN sez. di Milano
52
Main bunch parameters:
•Charge: 55pC
•Length 0.5mm (rms)
•Transverse size 2.2mm (rms)
•Transverse momentum 0.4 mc (rms)
•Normalized emittance 0.8 mm mrad
•Energy 24MeV
•Energy spread 5% (rms)
Tomassini, INFN sez. di Milano
53
TS Distributions
1.
2.
3.
4.
Since theFundamental
emphasis is on the
we choose to
atmonochromaticity
13.3KeV
collect photons in the “natural-aperture” cone, i.e. the one with
e=0.4 (approx. 8 mrad).
at 26.6
KeV monochromaticicy
As for theFirst
case ofharmonics
the Photoinjector
e-beam,
requires minimization of the harmonics production.
To keep a0 relatively low (below unity) a stretched laser pulse
Second
harmonics
at 40KeV
can be used.
Taking
into account
possible reduction of the
beam-pulse overlapping due pulse diffraction and e-beam
defocusing a satisfying working point with full overlapping
X-ray burst 1.5fs long (rms) with
has been found.
1.3x109 photons/sec
The TS laser pulse is stetched up to 2.6 ps and is focused down
E/E=23%
energy spread
to 12.5 mm
of waist sizeFWHM
with a0 =0.51.
2.2mm rms spot size
Tomassini, INFN sez. di Milano
54
In the fully nonlinear regime?
T=17fs, w=25mm a0=3.1, a_bar=0.01
Tomassini, INFN sez. di Milano
55
Conclusions
•An accurate simulation of a TS source must take into account several
effects if nonlinearities are switched on.
•The Thomson Scattering beamline in PLASMONX can be tuned to produce
high flux quasi-monochromatic X rays. With the optimization of the
parameters for mammography a flux of 2.10^10 photons/s @ 20KeV with
22%FWHM enegy spread is obtained. Higher monochromaticity is
obtainable with a lower acceptance angle (with a proportional reduction of
the flux) down to the minimum energy spread of 2% with 109 photons/s.
•The beamline can be tuned to produce ultrashort e-bunches @130MeV.
TS with the PLASMONX parameters can produce 45fs long (rms) X/g rays
with 2x108 photons/sec with E/E=4% FWHM of energy spread
•An all-optical TS source is being investigated. Preliminary simulations show
that the density downramp self-injection scheme is capable of producing
extremely short (0.5mm->1.5fs) e-beams thus allowing the production of a
femtosecond-scale tunable quasi-monocromatic source of 1.3x109
photons/sec with E/E=23% FWHM energy spread.
Tomassini, INFN sez. di Milano
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