laser-plasma acceleration physics and...
TRANSCRIPT
http://loa.ensta.fr/UMR 7639
Laser-plasma acceleration
Physics and Applications
Jérôme FaureLaboratoire d’Optique Appliquée
Ecole Polytechnique, France
Outline of the class
• First class
• General introduction: what, why and how ?
• Theory of plasma wave driven by a laser pulse
• Second class
• Acceleration/injection of particles in plasma waves
• Applications of laser-plasma accelerators
Electron accelerators in our life / science
X-ray tube
E< 1 MeV
E< 300 keV
Electron microscope
E< 20 MeV
radiotherapy
E> 100 GeV
High-energy physics
E > 1 GeV
Synchrotron light source
Industrial Market for Accelerators
Application
Total
systems
(2007)
approx.
System
sold/yr
Sales/yr
(M$)
System
price (M$)
Cancer Therapy 9100 500 1800 2.0 - 5.0
Ion Implantation 9500 500 1400 1.5 - 2.5
Electron cutting and welding 4500 100 150 0.5 - 2.5
Electron beam and X rays
irradiators2000 75 130 0.2 - 8.0
Radio-isotope production (incl. PET) 550 50 70 1.0 - 30
Non destructive testing (incl.
Security)650 100 70 0.3 - 2.0
Ion beam analysis (incl. AMS) 200 25 30 0.4 - 1.5
Neutron generators (incl. sealed
tubes)1000 50 30 0.1 - 3.0
Total 27500 1400 3680
Total accelerators sales increasing more than 10% per year
The development of state of the art accelerators for HEP has lead to :
research in other field of science (light source, spallation neutron sources…)
industrial accelerators (cancer therapy, ion implant., electron cutting&welding...)
Accelerators : One century of exploration of the infinitively small
Quarks
Atom
Nucleus
Why alternative techniques ?
• Accelerating field in cavities limited to 50 MV/m by breakdown
LHC at CERN is 27 km circumference
ILC (electron-positron collider at several 100 GeVs), will be a LINAC, about 30 km long
• Use plasmas with much higher electric fields: > 100 GV/m
RF cavity: 1 m Plasma wave over 1 mm
Ez = 10-100 MV/m Ez = 10-100 GV/m
Motivation for alternative techniques
A plasma: free electrons and ions: already ionized
mGVnE ez /300 (for electron density ne=1019 cm-3)
z
dn/n0
Ez
z
With a plasma wave, EZ is 104 greater than in a RF cavity
compact accelerators possible
2/1
12
ep
pn
c
vp c
Plasma wave
Why plasmas ?
F ~ -dIlaser
F
Champ E
Laser vg ~ c
• Ponderomotive force pushes electrons:
• In a plasma: creates a plasma wave (wakefield)
A laser pulse to drive the plasma wave
Gas jet
laser
100 MeV
electrons
Experimental principle
plasma
1 mm
Ultra-intense laser
Energy: 1 J
Duration: 30 fs
Focal spot: 10 µm
Accelerating electrons in wakefields
PROS
• Extreme fields
1 MeV / 10 µm
Compact accelerator
Mitigates space charge
• fs bunches
< p/4
• no jitter
Ez
Er
Electron density
Pulsep≈1-10 µm
accelerating
focusing
Tajima & Dawson, PRL 1979
Surfing the wake !!
Injecting electrons in the wakefield
Fluid electrons trapped electrons
Electrons need a kick to catch the plasma wave
A simple solution: wavebreaking
We drive the wakefield so strongly that it breaks,
traps and accelerated the plasma electrons
Resonant condition for wakefield
excitation: ct ≤ p and w0 ≤ p
Bubble formation
Pukhov & Meyer-ter-Vehn, Appl. Phys. B 2002
Self-injection in the bubble regime
Example of self-injection in a simulation
Gas jet
laser
100 MeV
electrons
Experimental principle
plasma
1 mm
Ultra-intense laser
Energy: 1 J
Duration: 30 fs
Focal spot: 10 µm
5-pass amplifier :
200 mJ
8-pass amplifier : 2 mJ
Oscillator : 2 nJ, 15 fs
stretcher : 500 pJ, 400 ps
On target:
1 J, 30 fs, 0.8 mm,
10 Hz, 10 -92 m
Nd:YAG : 10 J
4-pass amplifier:
2.5 J, 400 ps
“Salle Jaune” laser
compressor
Vacuum
chamber
f=1m
w0=18 µm
30 fs
Typical experimental set-up
Gas jet
Si diodes
magnet
ICT
LANEX screen
Probe beamImage of the plasma
laser
Divergence = 6 mrad
6.0 x 1018cm-37.5 x 1018cm-31.0 x 1019cm-3
2.0 x 1019cm-35.0 x 1019cm-3 3.0 x 1019cm-3
7°
Discovery of the bubble regime
We adjust the plasma density to reach the resonant condition
ct ~ p
Energy distribution
ne=7.5×1018 cm-3, maxwellian distribution
ne=6×1018 cm-3, monoenergetic distribution
20 50 100 200Energy (MeV)
Div
erg
ence(°
)
1
0
-1
Div
erg
ence(°
)
20 50 100 200
Energy (MeV)
Div
erg
ence(°
)
1
0
-1
• charge about 100 pC
• dE limited by spectrometer
resolution
First quasi monoenergetic e-beams
Mangles et al, Imperial College:
70 MeV beam
Geddes et al, LBNL:
85 MeV beam
Faure et al, LOA:
170 MeV beam
5-pass amplifier :
200 mJ
8-pass amplifier : 2 mJ
Oscillator : 2 nJ, 15 fs
stretcher : 500 pJ, 400 ps
On target:
1 J, 30 fs, 0.8 mm,
10 Hz, 10 -92 m
Nd:YAG : 10 J
4-pass amplifier:
2.5 J, 400 ps
“Salle Jaune” laser
First conclusions
plasma
1 mm
In the past 10 years, a new technology for particle accelerators has emerged
Laser-plasma acceleration (laser-wakefield acceleration) is based on
- ultra-intense femtosecond laser
- laser-plasma interaction
- Highly nonlinear physics
In 2017:
- Proof-of-principle experiments have been demonstrated
- Physics well understood
- 100 MeV to few GeV beams driven by 100 TW to PW-class lasers
- Low repetition rate: 1 shot per second
- World record: 4 GeV using PW laser @ Berkeley National Lab. (USA)
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Ultra-intense laser-plasma interaction
in the world > 50 groups in the world
Berkeley
California
1 PW
Commercial system
by THALES
South Korea
First multi-PW laser
Saclay, France
First 10 PW
in preparation
Outline of the class
• First class
• General introduction
• Theory of plasma wave driven by a laser pulse
Very basic plasma physics
• Natural plasma oscillation: plasma frequency :
• Plasma wavelength: p=2c/p. p=10 µm for ne=5×1018 cm-3
• EM Wave propagation possible only if > p
: the plasma is underdense
(n < 1021 cm-3 for λ= 1 µm). In most experiments, ne=1018-1019 cm-3
Basics: definition of laser intensity
• Consider a EM field as a plane wave
• Peak intensity is defined as
• For a Gaussian pulse (at focus)
• Example: E=1 J, w0=20 µm, t0=30 fs I0=5×1018 W/cm2
0
2
0
0
2
tw
EI
Relativistic regime of laser-plasma interaction
• Electron in laser field:
• Weakly relativistic case v/c <<1(magnetic component isneglected)
t
A
m
e
m
Ee
dt
dv
ee
Losc
ac
vosc
Relativistic regime is entered when a ~ 1 (I0 ~ 1018 W/cm2)
a: the normalized vector potential
• Laser E field linked to potential vector a by
• Normalized vector potential
• In practical units
• Example: I0=2×1018 W/cm2 (=1µm) a=1.2
t
AEL
cm
eAa
e
0
00
cm
eEa
e
]/[][105.8 22/1
0
10
0 cmWIµma
Fluid model: hypothesis (1)
Fluid model: hypothesis (1)
• Laser driver
– envelope
Definition of the laser pulse
with
Rewrite as: With
Density perturbation caused
by the laser pulse
Poisson equation
Physical meaning of scalar potential
Fluid equations
Some algebra
Motion of electrons in plasma after
averaging over fast oscillations
Ponderomotive force
Some algebra
Plasma wakefield equation
• Write equation on potential using:
Plasma wakefield equation
Plasma wakefield equation becomes:
Moving window
We follow the laser pulse:
Use new variables:
• Neglect derivatives in t compared to derivatives in z
• Physical meaning: the plasma responds adiabatically to slow changes of the driver
laser
1/zR
1/L0
1/p
Quasi-static approximation
• Solution behind the pulse (gaussian shape)
– Potential
– Electric field
– Longitudinal
– Transverse
– E0 wavebreaking field2/1
0 ne
cmE
pe
Solutions
f, Ez/E0, dnz/n0 are normalized quantities and have the same amplitude
Resonance condition
0/ 0 Lf
Maximum amplitude for: 20 Lk p
In practical units:
0 1 2 3 4 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
kpL
0
F / a
02
Accelerating and focusing fields
a=0.5
Electron density
Pulse
Defocusing
Ez
Er
Focusing
Accelerating
Decelerating
1D Model: Plasma wave
• Low intensity limit (a2<<1), the potential is solution of
• One can use a 1D nonlinear fluid theory which works for a > 1
Co-moving coordinate
Plasma wave vector (p plasma frequency)
Integrate numerically this equation for a gaussian pulse
Example of 1D nonlinear plasma wave
a=0.3
f
dn/n0
Ez/E0
a=2
f
dn/n0
Ez/E0
Ez
Er
3D nonlinear wakefields
Focusing
Defocusing
Accelerating
Decelerating
a0=2
Electron density
Pulse
relativistic shift of p
Requires more complex models (fluid or kinetic)
+ computer simulations
Summary
• Intensity and a:
• Wakefield amplitude: proportional to laser intensity
• Wakefield max at resonance
]/[][105.8 22/1
0
10
0 cmWIµma
20 Lk p
http://loa.ensta.fr/UMR 7639
Laser-plasma acceleration
Physics and Applications
2/2
Jérôme FaureLaboratoire d’Optique Appliquée
Ecole Polytechnique, France
Outline of the class
• First class
• General introduction: what, why and how ?
• Theory of plasma wave driven by a laser pulse
• Second class
• Acceleration/injection of particles in plasma waves
• Applications of laser-plasma accelerators
How do we inject electrons into wakefields ?
How are electrons accelerated ?
Electron density
Pulselp≈1-10 µm
Bubble formationFirst class: wavebreaking
Injecting electrons in the wakefield
Fluid electrons trapped electrons
Electrons need a kick to catch the plasma wave
Summary / reminder of notation
• Intensity and normalized
vector potential a (linear pol.)
• Wakefield amplitude: comes from charge separation define scalarpotential for the plasma wave and its normalized counterpart
• Laser group velocity vg, plasma phase velocity vp
• Define Lorentz factor
laser
Plasma wakefield
laser
Plasma wakefield
We use a 1D fluid model for the plasma wave
Electron motion:Transverse longitudinal
z
1D Model: Plasma wave
• Low intensity limit (a2<<1), the potential is solution of
• One can use a 1D nonlinear fluid theory which works for a > 1
Co-moving coordinate
Plasma wave vector (wp plasma frequency)
Integrate numerically this equation for a gaussian pulse
Outline
• 1 D Hamiltonian model for electrons interacting
with laser field and plasma wave
References:E. Esarey and M. Pilloff, Phys. Plasmas 2, 1432 (1995)
E. Esarey et al., IEEE Trans. Plasm. Sci. 24, 252 (1996)
Hamiltonian of electron in laser and
plasma wave with potential F
kinetic energy potential energy
Let’s normalize the Hamiltonian
• H depends on time but in a a particular manner (z-vgt)
– Eliminate time using a canonical transformation
– With generating function
• New Hamiltonian:
Hamiltonian’s basic properties
• New Hamiltonian is then:
• Define the momentum conjugate to the position (or canonical
momentum)
• In our case, q=-qe and A is a transverse laser field. This translates in
normalized units into
• Hamiltonian expressed in terms of canonical momentum
Hamiltonian’s basic properties
• From Hamilton’s equations, one finds that in 1D the transverse
canonical momentum is conserved (constant of motion)
• For electrons initially at rest in front of the laser pulse, Cste=0 and
Trajectories in the wakefield
• The Hamiltonian does not depend on time constant of motion H0
We want to find the electron trajectories in phase space: uz(z)
• Solving the Hamiltonian for uz, one finds
• 2nd degree polynomial equation with solution
• If a(z) and f(z) and H0 are known then the initial conditions are
known the trajectory in phase space uz(z) is known
(Exercise)
Fluid trajectories: electrons
initially at rest in front of the
laser
Fluid electrons
The separatrix: limit of trapped
trajectories
Trapped electrons=Paddling surfer
Trapped orbits
Trapped electrons haveinitial kinetic energy
(Exercise)
Calculate and obtain minimum energy for trapping
We start from
Electrons in front of the laser pulse and on the separatrix
We can easily calculate
Injection threshold
(Exercise)
Injection thresholds
Larger wake amplitudes Slower wakes
Injection threshold is lower for large amplitude and slow wakefields
Wavebreaking ?
Wavebreaking as an injection mechanism
fluid
separatix
Zoom on the fluid trajectory
• As the wake amplitude increases (|fmin| increases), the fluid
trajectory gets closer to the separatrix
• 1D wavebreaking occurs when fluid and separatrix overlap
• All plasma electrons are then injected and accelerated
Wavebreaking / self-injection
Experimentally, wavebreaking is hard to control unstable beamsResearchers are finding ways to control the injection of electrons
Ponderomotive force in the beatwave: Fp ~ 2a0a1/λ0
The beatwave pre-accelerates electrons locally and injects them
INJECTION is local and short (30 fs) monoenergetic beams
Plasma wave
Pump pulse a0
Injection pulse a1
electrons
Principle of colliding pulse injection
Colliding pulse injectionZoom on the fluid trajectory
fluid
separatix
beatwave
The beatwave provides a bridge from the fluid orbit to the trapped orbit
There is no need for wavebreaking
wavebreaking Controlled injection
Injection beam130 mJ, 30 fs ffwhm=28× 23 µmI ~ 4×1017 W/cm2
Pump beam670 mJ, 30 fs, ffwhm=21×18 µmI ~ 4×1018 W/cm2
What it looks like in reality
Statistics (30 shots):
E = 206 +/- 11 MeV
charge = 13+/- 4 pC
dE = 14 +/- 3 MeV
dE/E = 6%
Very little electrons at low energy, dE/E=5% limited by spectrometer
3 mm gas jet
Stable monoenergetic beams
pump injection
pump injection
Jet exit
pump injection
Middle of jet
Zinj=225 μm
Zinj=125 μm
Zinj=25 μm
Zinj=-75 μm
Zinj=-175 μm
Zinj=-275 μm
Zinj=-375 μm
50 100 200 300 400Energy (MeV)
Beginning of jet
Tuning the beam energy
pulse
1 2 3
Effective slow down
1
2
3
Gradient scale length
In the density gradient, lp increases• causes the plasma wave to elongate• effective slow down of the back of the plasma wave• effective decrease of the phase velocity Facilitates trapping Decreases the threshold for self-injection
Other methods for controlling injectionInjection in a density gradient
Ionized electrons are born in the laser and in the wake itself • They have different initial
conditions compared to fluidelectrons
• “Dropping” them at the right phase so they can be trapped
Electrons from N+ to N5+
Electrons from N6+
Main idea:If we drop an electron at rest at this phase, it will be on a trapped orbit
Other methods for controlling injectionInjection using ionization
Outline of the class
• First class
• General introduction: what, why and how ?
• Theory of plasma wave driven by a laser pulse
• Second class
• Acceleration/injection of particles in plasma waves
• Applications of laser-plasma accelerators
• Very compact acceleration
• Source is very small and short:
– Few micron diameter
– Few femtosecond duration
Application using these
unique qualities
Unique properties of laser-plasma source
High resolution radiography of dense object with a low divergence, point-like electron source
Application exploiting small source size
Radiography of dense objects
Y. Glinec et al., PRL 94, 025003 (2005)
50 μm γ source size2010Cut of the object in 3D
Spherical hollow object in tungsten with sinusoidal structures etched on the inner part.
A. Ben-Ismail et al., App. Phys. Lett. 98, 264101 (2011)A. Ben-Ismail et al., Nucl. Instr. and Meth. A 629 (2010)
400 μm γ source size2005
Radiography of dense objects: experiments
Quicker Access
to Physics and
Applications
Laser Plasma Technologies
The market of non-destructive inspection
Airplane partsnuclear plants
X-rays produced by relativistic electrons
β
β.
Electron
mm plasma wigglers
Equipe A. Rousse et K. Ta Phuoc (LOA)
synchrotrons
free electron lasers
A. Rousse, K. Ta Phuoc et al, Phys. Rev. Lett. 2004
20 mrad
E > 3 keV
Characteristics of the source:- 105 photons/shot/0.1% BW @ 1 keV
- divergence: 10’s mrad
- Duration: 10’s fs
- Spectrum: 1-10 keV
- Source size: 1- 2 microns
Perspectives:- Increase radiation energy by controlling electron trajectories
- Use PW lasers
Radiation produced in a laser wakefield accelerator
Betatron radiation: fs X-ray source
Characteristics of the source:- 105 photons/shot/0.1% BW @ 1 keV
- divergence: 10’s mrad
- Duration: 10’s fs
- Spectrum: 10-1000 keV
- Source size: 1- 2 microns
Perspectives:- Produce a tunable and monochromatic source
- Use PW lasers
Radiation produced at the collision between a laser pulse and a relativistic electron
Compton scatteringfs X-ray source
Ta Phuoc et al., Nat. Phot. 2012
Using laser-plasma accelerators for probing matter ?
Time resolved electron diffraction: watching structural dynamicsin real time
Laser plasma accelerators:
- Femtosecond bunches- No jitter
But should be:
Lower energy: 5 MeVkHz (statistics, averaging)
Toward kHz laser-plasma acceleratorswith mJ-class kHz lasers
Laser pulse has to be resonant
with plasma wave:
R≈lp/2, ct≈lp/2
Pulse
R
lp
Lu et al., PRSTAB 10, 0613001 (2007)
Laser energy scaling Electron energy gain
30 fs 1 J 100 MeV-1 GeV3 fs mJ 1-10 MeV
Laser pulses of 5 fs, few mJ possible @ kHz !
Beaurepaire et al., NJP 16, 023023 (2014)
−8 −4 0 4 8 120
20
40
60
80
100
ElectronHspectraa6 b6
c6 ChirpH=H−4fs2 ChirpH=H0fs2 ChirpH=H8fs2
2 4 6 80
0.2
0.4
0.6
0.8
1
EnergyH5MeV6
dN
el/d
EH8fs2
H4fs2
H0fs2
H−4fs2
1
2
1 2
ElectricHfield
Envelope
H5a
.u.6
FWHMHpulseHdurationH5fs6
Cha
rgeH5
fC/s
hot6
3
3
−20HHHHHHH−10HHHHHHHHHHH0HHHHHHHHHHH10HHHHHHHHHH20HHHHH
TimeH5fs6
HHH HHHHHHHHHHHHH−10HHHHHHHHHHH0HHHHHHHHHHH10HHHHHHHHHH20HHHHH
TimeH5fs6
HHHHHHHHHHHHHH−10HHHHHHHHHHH0HHHHHHHHHHH10HHHHHHHHHH20HHHHH
TimeH5fs6
Am
plit
ude
H5a
.u.6
1
0.5
0
−0.5
−1
ChirpH5fs26
6.7 4.3 3.4 4.0 12.1 16.3
Laser:
3.5 fs – 3 mJE-beam
100 fC-20 pC, 5 MeV
Time-resolved diffraction experimentby streaking the Bragg peaks
30 nm Si nano membrane, S. Scott, M. Lagally, Univ. Wisconsin
Diffraction on single cristal nano-membranes
020
220
200
Gold, 20 nm Silicon, 30 nm
Exposure time 500 msHigh quality diffraction patterns
Z. He et al., Appl. Phys. Lett. 102, 064104 (2013)
Demonstration of time-resolved
electron diffraction
sample
CCD
kHz laser
Diffraction
patternpump pulseI1/I0-1(220) Data set I Data set II I1/I0-1(220)
0-order
unpumped
pumped
1mm
fit
data with DC gun
normalized
a
b
c
d
e
f
normalized
3.1 ± 0.8 ps 15.5 ± 0.8 ps
3.0 ± 0.2 ps 7.1 ± 0.4 ps
fit
data with DC gun
Silicon, 30 nmDynamics of (220) peak
220
400
ps resolution obtainedfor fs resolution, relativistic MeV beams are necessary
From engineering to fundamental science
and back
R & D in laser technology
New generation of ultra-intense lasers
Fundamental researchin
Laser-plasma interaction
New generation of particle beams
SOCIETAL APPLICATIONS
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?
Thank you
• If you are interested: contact me !
http://loa.ensta-paristech.fr/appli/
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