X-ray Generation in Plasma Using Laser-Accelerated Electrons

Rahul Shah, F. Albert, R. Fitour, K. Taphuoc, and A. Rousse

Laboratoire d’Optique Appliquée (LOA)

LOA laserLOA laser

(similar to (similar to what we will what we will see at NN)see at NN)

Intense Light Fields Cause Electron Motion Along Propagation Direction

Z+ -

Bound Atomic Optics

Light magnetic field negligable

Non-linearities arise from atomic potential

longitudinal

transverse

both transverseand longitudinal

0 1 a

0 ~1 a

0 1 a

Relativistic Optics

Magnetic field causes electron moves in direction of light wave

Non-linearities for free electrons

Relativistics harmonics, Effective force manipulates plasma

a0~E/ω

1. Ultrafast studies (femtosecond)~Å

Bright and Short-Pulse X-rays for Diffraction, Imagery, and Diagnostic

1. Ultrafast studies (femtosecond)~Å

Bright and Short-Pulse X-rays for Diffraction, Imagery, and Diagnostic

x-ray (normal) phase-contrast x-ray 2. Phase Contrast X-rays

of laser-fusion interaction

Be shell fuel layer

1. Ultrafast studies (femtosecond)~Å

Bright and Short-Pulse X-rays for Diffraction, Imagery, and Diagnostic

x-ray (normal) phase-contrast x-ray 2. Phase Contrast X-rays

of laser-fusion interaction

Be shell fuel layer

3. Diagnostic of process (laser-wakefield acceleration)

1 mm

z

simulation1

wave e-

laser

electron energy~10 µm

trapped e-

1A. Pukhov and J. Meyer-ter-VehnAppl. Phys. B, 74, (2002)

magnetic field

electron

ρ (radius of curvature)

Synchrotron RadiationBroad spectrum, narrow beam, 10-100 picoseconds

EX-ray γ3/ρkeV hν mGeV e-

laser

solidx-rays

electrons

Laser on solid targets/Kα

femtosecond but low-brightness

electron

Relativistic Electrons Provides Desirable X-ray Qualities Absent in Line-emission Sources

Laser Wakefield Acceleration Provides MeV-GeV Electrons in Millimeters

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+

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++

-

-

-+-

-

-

-

-

-

-

-

laser

plasma

-

10 µm

100 GeV/m

Electrons pushed by laser force

Pulled back by ions creating plasma wave

Electrons accelerated by electrostatic field, 3 orders larger than conventional

Laser Wakefield Acceleration Provides MeV-GeV Electrons in Millimeters

1 mm

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-+-

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-

-

laser

plasma

-

10 µm

100 GeV/m

Experimentally simple

Various regimes;varying energies

State of the art: GeV, tunable and monochromatic

x

y

< 1°fluorescent screen

electron beam

Relativistic Harmonics

Laser & Plasma Can Generate Low-divergence Ultrafast X-rays from Laser-Accelerated Electrons

Laser overlaps accelerating electrons

Light intensity causes free-electron harmonics

Laser & Plasma Can Generate Low-divergence Ultrafast X-rays from Laser-Accelerated Electrons

Laser creates ionic cylinder

Plasma field causes synchrotron radiation from accelerating electrons

Synchrotron Radiationdue to Plasma

Synchrotronmotion in Plasma

Laser & Plasma Can Generate Low-divergence Ultrafast X-rays from Laser-Accelerated Electrons

ion field

ρ (radius of curvature)

relativistic electronRelativistic electrons collimate radiation

Synchrotron radiation

RelativisticHarmonics

longitudinal

transverse

both transverseand longitudinal

0 1 a

0 ~1 a

0 1 a

Relativistic Harmonicslaser plasma

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

θ (deg)

norm

aliz

ed in

tens

ity

a0=0.01rest electron

Relativistic Intensity results in higher order radiation

fundamental 6th harmonic

11th harmonic 16th harmonic

longitudinal

transverse

both transverseand longitudinal

0 1 a

0 ~1 a

0 1 a

Relativistic Harmonicslaser plasma

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

θ (deg)

norm

aliz

ed in

tens

ity

a0=2rest electron

Relativistic Intensity results in higher order radiation

Previously 2nd, 3rd reported

fundamental 6th harmonic

11th harmonic 16th harmonic

longitudinal

transverse

both transverseand longitudinal

0 1 a

0 ~1 a

0 1 a

Relativistic Harmonicslaser plasma

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

θ (deg)

norm

aliz

ed in

tens

ity

a0=21 MeV electroncopropagating

fundamental 6th harmonic

11th harmonic 16th harmonic

Relativistic Intensity results in higher order radiation

Energetic electrons result in forward peaking

Relativistic Harmonics: Experimental Setup

Laser parameters:400 fs, 1.053 µm, 2 J

2

cmW105 218max

a

I

laser plasma

Relativistic Harmonics: Experimental Setup

Laser parameters:400 fs, 1.053 µm, 2 J

2

cmW105 218max

a

I

laser plasma

Even Harmonics Consistent with Relativistic Process

Relativistic harmonics

Linear ne scaling, even orders

0 5 10 150

200

400

600n

e

2n

e

1.3

Sig

nal

(a.

u.)

n=11 n=12

nex1018 (cm-3)

He at a~2, linear polarization ≈5x1018 e-/cm-3

13th harmonic 12 11

wavelength

sou

rce

imag

e

Atomic harmonics

ne2 scaling, no even orders

Signal vs. Density

laser plasma

I = 5x1017 W cm-2

n = 1018 cm-3

Linear Pol.

I = 4x1018 W cm-2

n = 1019 cm-3

Circular Pol.

RELATIVISTIC

i. Even orders

ATOMIC

i. Odd orders only

Relativistic Process Occurswith Circular Polarization laser plasma

I = 5x1017 W cm-2

n = 1018 cm-3

Linear Pol.

I = 4x1018 W cm-2

n = 1019 cm-3

Circular Pol.

laser plasma

RELATIVISTIC

i. Even orders

ii. Lin/Circ polarization

ATOMIC

i. Odd orders only

ii. Lin pol. only

Relativistic Process Occurswith Circular Polarization

I = 5x1017 W cm-2

n = 1018 cm-3

Linear Pol.

I = 4x1018 W cm-2

n = 1019 cm-3

Circular Pol.

4 μm focal spot

laser plasma

RELATIVISTIC

i. Even orders

ii. Lin/Circ polarization

iii. Generate only at focus

ATOMIC

i. Odd orders only

ii. Lin. pol. Only

iii. Large volume of generation

Relativistic Process Occurswith Circular Polarization

1112source

slit

gratingdetector

wavelength

imag

e

laser plasma

Angular Profile Shows Role of Accelerated Electrons

Take into account energetic electrons and divergence of laser and electrons

Using a0~6 (10x more power)

order 100 harmonic radiation observed. Angular profile similarly depended on 1 MeV electrons.

Banerjee et. al. POP 20:182, 2003Taphuoc et al. PRL 91: 195001, 2003

laser plasmaRelativistic High Harmonics1,2

Laser light itself creates non-linearity in electron motion

Observe characteristics in the radiation supporting relativisticharmonic generation

Laser-accelerated electrons collimate radiation

X-rays though would require a0~10, and the higher harmonicshave even broader angular distribution…

Synchrotron radiation1

50 GeV electrons, ne~1014/cm3, 5-30 keV x-rays

Ex-ray γ2 ne r0

X-ray Generation from Electron Beam Propagation in a Plasma

Beam coulomb field repels ambient electrons

Electron beam self charge and magnetic force cancel

1Esarey et. al. PRE 65,056505, 2002

amplitude

Joshi, et. al. Phys. Plas., 9:1845, 2002.

plasma

D. Whittum. Physics of Fluids B, 4:730, 1992

Ion channel

r0

F=mωp2r/2

laser plasma

Laser-plasma Accelerates & Generates Synchrotron Radiation

PIC after 2 mm propagation

ion core

20 μm

0 2 4 6 8 10

0.4

0.8

1.2

inte

nsity

(ar

b. u

nits

)

energy (keV)

100 MeV, ne=1019 cm-3,r0=2 µm

Matching of laser duration, spot and plasma wave creates cavity regime

keV x-rays with 100 MeV electrons

nC charge 106 photons/eV

3 keV

Faure et. al. Nature 431:541 2004

synchrotron radiation

radius of curvature ~mm

laser plasma

Laser-based Synchrotron Radiation: Experimental Setup

50 cm

magnet

X-ray camera/phosphor

electrons

x-rays

He

laserf=1 m

30fs, 30 TW, 10 Hz laserI=3x1018 W/cm2 (30 μm focus)ne~1019 cm-3

laser plasma

Laser-based Synchrotron Radiation: Experimental Setup laser plasma

0 50 100 150 200

107

108

109

elec

tro

n d

istr

ibu

tio

n (

MeV

-1)

energy (MeV)

experiment assumed exp. drop noise level

•10 shot average •Non-exponential•Plateau near 100 MeV

Laser-based Synchrotron Radiation: Experimental Setup laser plasma

X-ray beam

20 mrad

EX>3 keV

•Narrow (1-2° beam)•109 photons/shot over keV

Broad X-ray Spectrum Measuredwith Crystal and Filters

~200 μm

30 cmx-ray spotafter diffraction

•UPTO ~20% collection (here 1%)•Large spectrum from crystal & filters •Simple model of transverse force and linear acceleration calculates x-rays from electrons (limited specificity)

laser plasma

2 4 6 8 10101

102

103

104

coll

ecte

d x

-ray

yie

ld

(ph

oto

ns/

eV)

energy (keV)

experiment calculation

with electrons

0.0 2.0x1019 4.0x1019 6.0x1019

0

2

4

6

8

10

12

14

Inte

ns

ity

(a

.u)

Electron density (cm-3)

ExperimentPIC

Electron spectrum

X-ray footprint(CCD)

150 MeV

150 MeV

X-ray Variation with Density Matches Simulation

energy

div

erg

en

ce

•resonance consistent with mechanism•simulation (Pukhov group) matches trend•other processes (harmonics/ bremsstrahlung too weak)

laser plasma

fringes

mechanistic detailx-rays

edge

Spatial Coherence Studies X-ray Source & Electron Acceleration

Laser-based-synchrotron

oscillations around central axis, radiation at cusps

no measure of electrons in accelerator

Synchrotrons: Transverse beam monitoring

coherence effects

direct imaging

Thomson scattering

laser plasma

Single Fringe of Edge Diffraction Observed

laser

x-ray

magnet

(horizontal & verticalGaAs (100) edges Be filtered

x-ray camera

electrons

Dλ

2 m0.15 m

Δx ~100 µm(20 µm pixels) Single shot image;

vertically averaged

Laser poynting causes peak position to fluctuate

Δx ~ (Fresnel)(~λD Fraunhoffer)

laser plasma

0 5 100,0

0,2

0,4

0,6

0,8

1,0

dete

cted

pow

er

spec

tral

den

sity

(ar

b. u

nits

)

energy (keV)

Broad Spectrum Contributes to Diffraction

POWER SPECTRUMPower spectrum = source spectrum x Be x CCD

cameraresponse

Be

-200 0 2000,0

0,4

0,8

1,2

inte

nsi

ty (

arb

. u

nits

)

x detector (m)

3 keV

FRESNEL CALCULATION

Large bandwidth washes out higher oscillations

Neg. difference between spectral limits

laser plasma

Use Gaussianradial distribution of oscillation amplitudes;

Synchrotron radiation emission integrated to determine linear source profile

Sharp curvature – Strong emission

weak curvature low emission

0 5 100.0

0.5

1.0

0.000

0.025

0.050

Lin

ear

Dis

trib

utio

n

(ra

diat

ion

or

elec

tron

)

source coordinate x (m)

elec. distribution c=1.0 at FWHM

c=0.1

100 MeV elec.25 MeV elec.

electronbeam

3 keV radiation

PIC self injectionsuggests full rangeof oscillation amplitudes

X-rays Measure Transverse Dimension of Electrons in Plasma

laser plasma

PIC self injectionsuggests full rangeof oscillation amplitudes

X-rays measure upperlimit of electrons

Calculations from simple modeling of radiation indicate >100 MeV electrons dominate

Sharp curvature – Hard x-rays

weak curvature Soft x-rays

electronbeam

electron profile x-ray profiles

energetic electrons

weak electrons

X-rays Measure Transverse Dimension of Electrons in Plasma

laser plasma

-15 0 150,0

0,5

1,0 simulationGaus-

sian fit

elec

tron

s/le

ngth

coordinate (m)

Bandwidth and pixel size limits resolution

Agrees with simulation and simple modeling of radiation

-100 0 100 200 3000.0

0.4

0.8

1.2

inte

nsi

ty (

arb.

un

its)

detector coordinate (m)

experiment point source 5 m FWHM

4 µm

laser plasma

Experimentally < 5 μm Transverse Dimension; Simulation Shows 4 μm

Laser Based Synchrotron Radiation

Shah et. al. PRE 74, 045401(R) 2006Rousse, TaPhuoc, Shah et. al. PRL 93:13005, 2004

Plasma electrostatic field causes transverse oscillations and synchrotron radiation

Broadband keV spectrum, directional femtosecond

Fresnel diffraction gives < 5 μm FWHM x-ray/ electron source diameter (6x smaller than vacuum laser-focus).

laser plasma

X-ray Generation from Laser Accelerated Electrons

Direct relativistic scattering provides VUV-XUV at current intensities; copropagating electrons brighten source

Oscillations of electrons in plasma electrostatic field generate synchrotron radiation

More stable electron beams will lead to counterpropagating geometry for hard bright x-rays and eventually FELs for coherent, compact sources

laser plasma

AcknowledgementsLOA: Davidé Boschetto, Fréderic Burgy, Jean-Philippe Rousseau

Budker Institute of Nuclear Physics: Oleg Shevchenko

Nebraska: Donald Umstadter, Sudeep Banerjee

Heinrich-Heine Universitat: Alexander Pukhov and Sergei Kiselev

FundingNational Science Foundation (International Fellowship)

Centre Nationale de Recherche Scientifique (CNRS)

extra

laser plasma

Relativistic Light Scattering

laser plasmaRelativistic Light Scattering

Far-field Radiation Distributionand Source Size laser plasma

Strictly sinusoidal motion would produce ~5 mrad x-ray beam

Measured 40 mrad x-ray beam from combination of sinusoidal and helical trajectories.