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Seeing is Believing:Laboratory Visualization of Laser Wakefields
S. S. Bulanov, V. Chvykov, K. KrushelnikG. Kalintchenko, P. Rousseau, T. Matsuoka,
A. Maksimchuk and V. YanovskyCenter for Ultrafast Optical Science, University of Michigan
Mike Downer
Nicholas Matlis,* Peng Dong,Steve Reed, Xiaoming Wang,
S. Kalmykov, G. ShvetsUniversity of Texas at Austin
Collaborators
Lasers and Accelerators: Particle Acceleration with High Intensity LasersStellenbosch Institute of Advanced Study Stiαs
15 January 2009
*Ph.D. ‘06, currently at LBNL
Laser-plasma experiments:lecture 4 of 4
to appear in “The Plasma Universe”(Cambridge U. Press 2008)
Helium Gas Jet
Laser-Plasma Electron Accelerator
Laser Pulse Focuses
Ionize Gas & Make Wave
Gas Jet Fires
Wave Captures andAccelerates Electrons
about3 mm
Tajima & Dawson, Phys. Rev. Lett. 43, 267 (1979)
INVISIBLE
Copper RF acceleratorcavities must be
precision-engineered
Simulations show widely vary-ing plasma wake structures...
...BUT we can’t even see them!
Laser
Electron density
Sinusoidal
50 µm
Distorted sinusoid
Spherical “bubble”
Electron densityLaser
Distorted sinusoid1. Aperture
2. Spacing
3. Micro-structure
DoE’s $0.5 M challengeto me (ca. 1995):
Take a pictureof a wakefield
Visualization ofquasi-static plasma structures:
ne(r,ζ , z) ≈ ne(r,ζ )
plasma gas
r z
0ζ
drivelaser
Simulations using code WAKE,* courtesy S. Kalmykov
*Mora & Antonsen, Phys. Plasmas 4, 217 (97)
THE IMAGING PROBLEM:• our “train” moves at ~0.995c• the “cars” are µm size• it can’t be photographed from
the lab frame
SOLUTION: Ride the train!!
NicholasMatlis
Ph.D.’06
Wakefield ne = n0 + δne(t)
IonizationFront
ChirpedReferencePulse (400nm)
ChirpedProbePulse (400nm)
Ultra-intense Pump Pulse, 1Joule, 30 fs, 800nm
“Frequency Domain Holography” measures Wakefields in a Single-Shot
Fixed Delay, ∆t
CC
D
grating
imagingoptics
mirror
imaging spectrometer
Null HOLOGRAM
Signal HOLOGRAM
Wavelength [nm]
50
-50
0
50
-50
0
dist
ance
[µm
]
390 400 410405395
ionization front
r [µm]-500
500time ζ [fs]
He2+
He+
• Ipump= 1016 W/cm2
• single shot measurement
Holographic snapshot of an ionization frontLeBlanc, Matlis, MCD, Optics Letters 25, 764 (2000)
∆φpr(r,ζ) [rad]
∝ ne(r,ζ)
Wake appears as periodic bunching of interferencefringes in the Frequency Domain Hologram
pumppropagation
axis
0 -200 -400200400600
0
50
100
-50
-100
Rad
ial D
ista
nce
[µm
] a)ne = 0.95 x 1018 cm-3
Time [fs]
Wake Oscillations
Ionization Front
Pump propagation
0 -200 -400200400600
0
50
100
-50
-100
Time [fs]
Rad
ial D
ista
nce
[µm
] b)ne = 0.95 x 1018 cm-3
He2+ He+
WAKE* simulation (11 TW pump)* Antonsen & Mora, Phys. Plasmas 4, 217 (1997)
0 -200 -400200400600
0
50
100
-50
-100
Time [fs]
Rad
ial D
ista
nce
[µm
] c)ne = 5.9 x 1018 cm-3
6e184e182e180e18
80
100
120
60
40
Electron Density [cm-3]
Pla
sma
Per
iod
[fs]
140d)
Holographic snapshots of laser wakefieldsP ~10 TW, I ~ 1018 W/cm2
Ezmax ~ 3x1010 V/m
0
60
120
-60
-120
Time [fs]
Rad
ial D
ista
nce
[µm
]
a)
200 0 -200400600800
ne = 2.17 x 1018 cm-3
Strong wakes have curved wavefrontsP ~30 TW, I ~ 3 x 1018 W/cm2
0
60
120
-60
-120
Time [fs]
Rad
ial D
ista
nce
[µm
] a)
200 0 -200400600800
ne = 2.17 x 1018 cm-3
0
60
120
-60
-120
Rad
ial D
ista
nce
[µm
] b)
200 0 -200400600800
WAKE simulation (40 TW pump)
Time [fs]
a)
background plasma subtracted
n e [1
018cm
-3]
0
1.0
2.0
3.0
4.0
γ ≈ 1
ωp = [nee2/ε0γ me ]1/2
γ ≈ 1.5
Source of wavefront curvature:
• large wave amplitude → large γ• small wave amplitude → small γ
λP (relativistic) > λP (non-relativistic)
0.06
Time ζ [fs]C
urva
ture
ρ-1[1
/µm
]
d)
600 8004002000
∆0 = 0.29
∆0 = 0.37
0.04
0.02
0.00
ρ−1(ζ) ≈ 0.45 ζ [ ∆0/r0 ]2 *
Significance of Wavefront Curvature40 TW
35 TW
30 TW
ne = 2.17x1018 cm-3
Simulated Wakefields
Precipitates wavebreaking (electron injection)
Collimates beam
Helps compress bunch energy spectrum
Curvature determines the peak amplitude of the nonlinear wake
Benefits of Curvature for Electron Beam
* S. Kalmykov et al., Phys. Plasmas 13, 113102 (2006)
Wakefield Photo Gallery
Greyscale Image 3D Map Greyscale Image 3D Maphttp://www.nature.com/nphys/index.html (Supplementary Fig. 1)
Matlis et al., Nature Physics 2, 749 (2006).
GALLERY of WORLD-FAMOUS PHOTOGRAPHS ?
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Our current experiments focus on correlatingwake structures with generated electrons
at ne > 1019 cm-3
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wake reconstructions electron spectra
data of 1/15/09
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single bucket(bubble?)
quasi-monoenergetic peak
3 quasi-monoenergetic peaks
3 buckets
multiple buckets
wide continuous spectrum
Laser: 30 TW, 30 fs
At ne > 1019 cm-3, relativistic nonlinear opticalradiation begins to influence FDH data
0
50
100
-50
-100
Rad
ial D
ista
nce
[µm
] -1.8
-1.4
0.0
Phase Shift [rad]
0 -200 -400200400600Time [fs]
Ipump ~ 1018 W/cm2
ne ~ 1018 cm-3 in He2+
• relativistic nonlinear index modulation*: n = n0 + n2I
• pump second-harmonic & continuum generation
“artifacts” in reconstructed ∆φpr(r,ζ) ⇔ additional diagnostic opportunity
* Max et al., Phys. Rev. Lett. 33, 209 (1974)
Chen, Nature 396, 53 (1998); Phys. Rev. Lett. 84, 5528 (2000)
SHG by diverging pump produces elliptical“Newton rings” in the FD hologram
plasma
unchirped, diverging SH of pump:
exp −(ω − ω0 )2
apu
− ik r2
2R⎡
⎣⎢⎢
⎤
⎦⎥⎥
spectrometer
chirped collimated probe:
exp −(ω − ω0 )2
apr
− i (ω − ω0 )2
bpr
⎡
⎣⎢⎢
⎤
⎦⎥⎥
+
cos (ω − ω0 )2
bpr
+ k r2
2R⎡
⎣⎢
⎤
⎦⎥
elliptical Newton ring:
⇓
shape of rings changesas pump focus moves
• relativistic pump propagation• relativistic harmonic generation
Useful to characterize: Rad
ial D
ista
nce
imaging lens
Reconstructed Ionization Front
0Time behind pump (fs)500
False Structureappears if ringsnot filtered from
raw data.
D. Peng et al. (2007)
Longitudinal Averaging of Evolving Wake
ProbeReference
Pump
[ ]∫ −=∆L
prpr dzz
0),(12)( ζη
λπζφ
Probe phase-shift
),( zζηindex evolves withlongitudinal position z
Integration over z results inaveraging over the indexchanges
Plasma wavelength:jet density profile
Types of EvolutionAmplitude: laser focusing
Wave breaking
Beam loading
Other Sources
⇒ a longitudinal “Abel inversion” problem
Plasma “bubble”*: example of a stronglyevolving laser-plasma structure
Simulations using code WAKE * for plannedLWFA experiment with Texas Petawatt Laser,**
* Mora & Antonsen, Phys. Plasmas 4, 217 (97)
** ne = 2.5 1017 cm-3 ; Plaser/Pcr ≈ 20
* A. Pukhov et al, Appl. Phys B, 74, 355 (2002)• Plasma bubble accelerators can produce nearly mono-energetic electrons• Bubbles have been simulated, but not seen in the laboratory• Bubble & laser pulse evolve considerably during jet transit.
SNAPSHOTS → MOVIES
Visualization of evolving laser-plasma structures
ne(r,ζ , z)
Frequency-Domain “Streak Camera”Records Evolution of Plasma Bubble
• Oblique probe measures bubble evolution• Collinear probe records longitudinally-
averaged bubble structure
0 0
0.5
1
1.5
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
micron
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
0 5 10 15
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16 18
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16 18
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16 18
0
5
10
15
20
25
30
fs
0
0
20
40
60
80
100
120
140
micron
0 5 10 15 20
0
5
10
15
20
25
30
micron
20 40 60 80 100 120 140 160 180
20
40
60
80
100
120
140
160
radi
al d
ista
nce
[µm
]phase shift [rad]
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
WAKE simulation parameters:a0 = 2.15 beam radius = 16 µm plasma density = 1 5
Simulated Phase Streak of a Plasma Bubble
1 - 4: Linear sinusoidal wake generated,drive pulse self-focuses & self-steepens
5: Bubble forms
6-11: Bubble shape stabilizes
12 ff: Bubble shrinks& dissipates
(probe crosses pump at 90o in lab frame)
wakefield
bubble
frame number
phas
e sh
iftal
ong
stre
ak a
xis
[arb
. uni
ts]
(r,ζ )
vgpr
ζ = 0
probeα
vgpu
ηobj (r′r , ′t )
(r,ζ )
vgpr
ζ = 0
probe
vgpu
ηobj (r′r , ′t )
(r,ζ )
vgpr
ζ = 0
probevg
pu
ηobj (r′r , ′t )
(r,ζ )
vgpr
ζ = 0
probe vgpu
ηobj (r′r , ′t )
gas jet
ξ
for point (r,ζ) to sweep across object in direction ξ ...
τ objtransit ≈
Robj
2csinα / 2≈ 10 fs << τ jet
transit• If bubble is quasi-static during time
Slowly varying bubble approximation
• The problem becomes equivalent to conventional computer-aidedtomography (CAT) of stationary object.
... then ² φ pr (r,ζ ) =
2πλpr
ηobj (r′r )dξ
ξ∫ , exactly as if probe had propagated
across stationary object in direction ξ.
Frequency Domain Tomography (FDT)borrows reconstructive algorithms of medical CAT scans
Ledley et al., “Computerized axial tomography of the human body,” Science 186 (1974)
Brooks & Di Chiro, “Principles of Computer Assisted Tomography” Phys. Med. Biol. 21, 689 (1976)
Reconstructive tomography
(a) transmission imaging
(b) scan pattern
Simulated Phase Streak of a Plasma Bubble
WAKE simulation parameters:a0 = 2.15 beam radius = 16 µm plasma density = 1 5
0 0
0.5
1
1.5
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
micron
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
0 5 10 15
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16 18
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16 18
0
5
10
15
20
25
30
0 2 4 6 8 10 12 14 16 18
0
5
10
15
20
25
30
fs
0
0
20
40
60
80
100
120
140
micron
0 5 10 15 20
0
5
10
15
20
25
30
micron
20 40 60 80 100 120 140 160 180
20
40
60
80
100
120
140
160
1. Linear sinusoidal wake generated,drive pulse self-focuses & self-steepens
2. Bubble forms
3. Bubble shape stabilizes
4. Bubble shrinks& dissipates
(probe crosses pump at 90o in lab frame)
• combine w/equivalent
“frame” ofphase streaksat other probeangles.
• reconstructbubble’s in-stantaneousstructure tomo-graphically.
radi
al d
ista
nce
[µm
]phase shift [rad]
micron
mic
ron
0 10 20 30
0
5
10
15
20
25 1
1.01
1.02
1.03
1.04
1.05
Simulations show that evolving, luminal-velocity plasmastructures can be reconstructed tomographically
from multiple-angle phase streaks
3 angles 5 angles0°, 45°, 90°
0°:5°:90°
0°, 20°, 40°,60°, 80°
0°:10°:90°
Single “frame” ofbubble “movie”
Tomographic reconstructions of this framefrom multi-angle phase streaks
10 angles 20 angles
This approach will be essential for visualizing channeled wakes,which cannot be imaged by conventional collinear FDH.
e+ driver:“sucks in”
acceleratede+ bunch
e- driver:“blows out”e- driver:
“blows out”
acceleratede- bunch
acceleratede- bunch
plasma electroniso-density surfaces
e- and e+ driven wakesdiffer greatly in structure
courtesy Frank Tsung (UCLA)
FDH, FDT will be critical incharacterizing & optimizingthese accelerating structures
Plasma Afterburner:Lee et al., “Energy Doubler for Linear Collider,”
Phys. Rev. STAB 5, 011001 (2002)
Blumenfeld et al., “Energy doubling of42 GeV electrons in a metre-scale plasma wakefield accelerator,”Nature 445, 741 (2007)
Petawatt laser wakefield accelerator PIC simulations200 J, 150 fs, 1µm
f/# ~ 40
e-
Self-injectedrelativistic electronsdifferentially pumped gas cell
~5 Torr He, ne ~ 1017 cm-3
a0 ~ 3.3
w0 ≈ 80 µm
3zR~ 6 cm
Laser pulse self-guides stably over > 3 Rayleigh lengths with ~ 10% depletion
z = 0 z = zR z = 2zRLASERPULSE
PROFILE
ELECTRONDENSITYPROFILE
Stable plasma bubble captures, accelerates electrons over > 3 Rayleigh lengths~115 µm
P/Pcrit ~ 8
z = 3zR
S. Kalmykov, G. Shvets
Self-injected electronsreach 3 GeV
after 3zR ≈ 7.6 cmpropagation
2.5 million hours on NERSC*(National Energy Research Scientific Computer)
Estimated computing time required for 3D PIC simulation of
1 GeV channel-guided LWFA* consuming ~ 30 MW of electrical power
SUMMARY1) Holographic snapshots of LWFAs
2) LWFA movies by Frequency Domain Tomography
3) Future applications • particle-bunch- and petawatt-laser-driven wakes• fast igniter tracks in laser fusion targets
• evolving plasma “bubbles”• the only way to “see” channel-guided LWFA
• first direct laboratory visualization of LWFAsMatlis et al., Nature Phys. 2, 749 (2006)Maksimchuk et al., Phys. Plasmas 15, 056703 (2008)
Seeing is believing,but seeing is not always easy
RECONSTRUCTION
“Reading” the Hologram
Εprobe(ω) = |Ε(ω)| e-iφ(ω)
(Full Electric Field Reconstruction)
BASIC SCHEME
1. Reconstruct spectral E-field of probe pulse from holographic spectrum
Hologram
388 390 392 394 396 398 400 402 404 406 408 410
Eprobe(t) = |E(t)| e-iδφ(t)
2. Fourier Transform to the time-domain to recover temporal phase
Εprobe(ω)FFT
Read
δφ(t)
3. Calculate electron density from extracted temporal phase
δne(t)index
Wakefield
TIME DOMAIN
BASIC SCHEME
“Reading” the Hologram(Full Electric Field Reconstruction)
RECONSTRUCTION
Wavelength [nm]
388 390 392 394 396 398 400 402 404 406 408 410
Hologram
FFT of Hologram
Sholo(ω) = |Εprb(ω)|2+|Εref(ω)|2 + Εprb∗(ω)Εref(ω) +
Time [ps]-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
FFTFFT FFTFFT-1
Εprb(ω)Εref∗(ω)
Filtered FFT
= |Εprb(ω)||Εref(ω)|eiφsignal(ω) from FFT side peak
Εprobe(ω) = |Εprb(ω)| e-iφprb(ω)Εprobe(ω) = |Εprb(ω)| e-i[φsignal(ω) + φchirp(ω)]
φprb(ω) = φchirp(ω) + δφsignal(ω)
Reconstruction of Spectral Electric Field
where
TIME DOMAIN
Wavelength [nm]
388 390 392 394 396 398 400 402 404 406 408 410
Spectrum of ReferenceSeparate Measurement
KDPtype I
to spectrometer
Probe
Pump
FFTAnalysis
4J pump PW frontend
LP target PW&LP target
PW target
Long Pulse Laser
LP FE
Compressor
Cleanroom
4J pump PW frontend
LP target PW&LP target
PW target
Long Pulse Laser
LP FE
Compressor
Cleanroom
Texas Petawatt Laser
Todd Ditmire, director
pulse energy: 200 Jpulse duration: 167 fs
peak power: 1.2 PW1st operation: March 2008
World’s most powerful laser
Experimental implementation of Frequency-Domain Streak Camera
Experiments will be performed at University of Michigan using 200TW, 30fs, pump beam and 400nm probe beam.Noncollinear FDH and collinear FDH will be combined as a single shot measurement of bubble structure
Pump beamProbe beam
Deformed Mirror
ParabolaBeam splitter
Gas jetTo spectrometer
Pickoff mirror
Delay
Collinear FDH
90± NoncollinearFDH
KDP KDP
Chirping glass
periscope
To spectrometer
Peng Dong is now runningthis experiment at U Mich
multiple angle probe/reference pulse pairs
glass
∆n = n2Ipu
We are setting up a prototype Frequency Domain Tomographyexperiment based on nonlinear index modulation in glass
As pump self-focuses and broadens temporally by GVD, then2Ipu “bubble” changes shape.
~0.1 mJ pump pulse
Full PIC simulations using Virtual Plasma Laboratory (VPL) codeshow negligible self-injection by TPW pulse at ne ~ 1017 cm-3
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channel-guided9995.75004501015100020
channel-guided991.816.314010163102.0
self-guided5.71.30.08345x1017801.0
Leemans (2006)0.990.180.016141018300.02
commentsEnergy Gain [GeV]
e-charge
[nC]
Int. Length
[m]
Spot Size [µm]
Plasma Density [cm-3]
Pulse Duration
[fs]
Laser Power [PW]
Table entries feature: 1. stable plasma structure 2. Ldephasing = Lpump depletion3. balance between energy extraction & beam quality
Early simulations had shown efficient self-injectionat ne ~5 x 1017 cm-3:
Simulated ∆φpr(r,ζ) agrees with FDH dataMeasured Jet Profile Simulated Wakefield
1.51.00.50z [mm]
2.0
1.1
2.2El
ectr
on D
ensi
ty[1
018cm
-3]
I
II
III
2.5
Comparison of Integrated Phase at r = 0
simulation
measurementData agrees well with simulation when longitudinal averaging is accounted for
Primary 2D structure ∆φprobe(r,ζ)is imprinted in central Leff ~ L/3,
and accurately reflectsne(r,ζ,z≈1 mm)near jet center.
To a good approximation:
ne(r,ζ , z ≈ 1mm)[ ]oscill
=
mcωpr∆φpr (r,ζ )
2πe2Leff
LONGITUDINAL ABEL INVERSION
PULSES OVERLAP!Pulse Duration > Pulse Separation
FDI: Temporal Overlap in Spectrometer
SpectrometerCCDPixels
SpectrometerGrating
1 ps
Interferogram