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

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micron

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0

5

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30

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fs

0

0

20

40

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micron

0 5 10 15 20

0

5

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micron

20 40 60 80 100 120 140 160 180

20

40

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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

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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