Particle acceleration in ultra-intense laser plasma interaction

Patrick Mora

Centre de Physique ThéoriqueEcole Polytechnique, CNRS, Palaiseau, France

ULIS 2007, Bordeaux, October 1-5, 2007

2

Scope

Laser acceleration of particles:- Electrons- Ions (protons or heavier ions)

Even ion acceleration almost always implies a previouselectron heating

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Vacuum electron acceleration (1)

A first question is :- can we have direct particle acceleration by the laserfield ?

Acceleration in the sub-MeV range with focused lasersobtained by Gérard Malka et al., PRL 79, 2053 (1997)

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Vacuum acceleration (2)

2 regimes

- relativistic ponderomotiveacceleration

- phase-dependentacceleration

Quesnel, Mora, PRE 58, 3719 (1978)

a=0.3τ=200 fsw0=10 µmpz0=0.1 mc

a=5.3τ=350 fsw0=5 µmγ0=10

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Vacuum acceleration (3)

Drawbacks:

vacuum acceleration seems to be rather inefficient:- no final acceleration at all for a purely plane wave- no final acceleration in the ultra-relativistic case- weak energy gain in the general case

6

Laser-Plasma accelerator

The combination laser + plasma may lead to a quiteefficient accelerator

Pioneering works:-Tajima and Dawson, PRL 43, 267 (1979)- experimental results on electron spectrum

7

Forward Raman instabilityand electron accelerationwere already observed a longtime ago

Joshi et al., PRL 47, 1285 (1981)

Forward Raman instability and electron acceleration

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Laser wakefield (Tajima and Dawson)

The paradigm is the laser wakefield acceleration: anintense short pulse create a wake of plasma oscillationsthrough the action of the ponderomotive force.Electrons trapped in the wake can be accelerated tohigh energy. Ultra-relativistic electrons get furtherenergy until dephasing stops the acceleration

laser beamwakeTrailing beam

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Laser wakefield

For a gaussian pulse, , the maximum

amplitude of the wake is obtained for

For ne=1019 cm-3, δn is max for FWHM ~ 13 fs!

I(t) = I0 exp "t2

t02

#

$ %

&

' (

!

" pt0 = 2

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Beat wave accelerator

Before the development of ultra-short pulses, the beatwave scheme was used, with the resonant condition

With CO2 lasers (UCLA) or glass lasers (LULI andRAL), efficient acceleration was obtained in the 1-30MeV range- Clayton et al., PRL 70, 37 (1993)- Amiranoff et al., PRL 74, 5220 (1995)

Electric field saturates due to relativistic detuning ormodulational instability (coupling with the ions)

!

" p ="1#"

2

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Electron spectrum in the LULI experiment

Amiranoff et al., PRL 74, 5220 (1995)

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Self modulated laser wakefield acceleration

A moderately short ( ) and ultra-intensepulse experiences Raman-type instabilities whichenhance the wake- N. Andreev et al., JETP 55, 571 (1992)- Sprangle et al., PRL 69, 2200 (1992)- Antonsen & Mora, PRL 69, 2204 (1992)

Electrons can be trapped and accelerated in the wake- Modena et al., Nature 337, 606 (1995)

!

" pt0 # 2 $100

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Self-focusing and Raman scattering

a0/2=0.32kpL=80kpR=16

ξ=ct-z z=0.35zR z=0.5zR

z=2zRz=2zR

/4

/4

/4

Antonsen & Mora,PRL 69, 2204 (1992)

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Experimental observation (RAL-IC-UCLA-LULI)

Modena et al., Nature 337, 606 (1995) P=30 TWτ=800 fs

!

E "1.5 GV/cm

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The bubble (highly nonlinear) regime

- electron cavitation, radial wavebreaking : Mora & Antonsen, PRE 53, 2068 (1996)

- radial wavebreaking, acceleration of fast particles : Bulanov et al., PRL 78, 4205 (1997)

- quasi-monoenergetic electrons : Pukhov & Meyer-ter-Vehn, Appl. Phys B 74, 355(2002)

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Electron cavitation, radial wavebreaking

Code WAKE [Mora & Antonsen,PRE 53, 2068 (1996)]

(ξ=ct-z)

Electron trajectories Electron density

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Radial wavebreaking

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Electron acceleration in the bubble regime

Pukhov & Meyer-ter-Vehn, Appl. Phys B 74, 355 (2002)

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Monoenergetic electrons: experimental results

- Mangles et al., Nature 431, 535 (2004)- Geddes et al., Nature 431, 538 (2004)- Faure et al., Nature 431, 541 (2004)- now many others

-Characteristics of the electron beam:- Energy at the GeV level- Energy spread of a few percent- normalized transverse emittance below π mm mrad- bunch duration below 25 fs

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The LOA experiment

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Main issues

Energy gain, luminosity, beam divergence

Stability

Injection

Staged acceleration

Mixture of LWFA and DLA

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Single beam experiments can be more stable thanfirst experiments - still some way to go though!

Stability• energy ≈ 12%rms• charge ≈ 50-70%• pointing ≈ 6 mrad rms

Mangles et al

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• Beam is most circular at low densities– as the ratio cτ/λp is decreased effect of laser on electron bunch decreases– Implies electrons are within first plasma wave period– Bunch duration must be less than 25 fs

• Effectively a cross-correlation of bunch and laser pulse

Increased stability allowed cross-correlation ofelectron bunch and laser field

2.1 2.4 2.7 x 1019 cm-3

Mangles et al PRL 2006

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Control and stability: external injection using another laser pulse

D. Umstadter et al, PRL 76, 2073 (1996); E. Esarey et al, PRL 79, 2682 (1997); Fubiani PRE 70, 016402 (2004)

Counter-propagating geometry:pump injection

Ponderomotive force of beatwave: Fp ~ 2a0a1/λ0 (a0 et a1 can be “weak”)yBoost electrons locally and injects them: yINJECTION IS LOCAL IN FIRST BUCKET yLINEAR PHENOMENA: no need of self-focusing, no self-trapping

Plasma wave

Principle: Pump beam

Injection beam

electrons

J. Faure’s talk

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Zinj=225 µm

Tunable monoenergetic bunches

Zinj=125 µm

Zinj=25 µm

Zinj=-75 µm

Zinj=-175 µm

Zinj=-275 µm

Zinj=-375 µm

pump injection

pump injection

late injection

early injection

pump injection

middle injection

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Ion acceleration

First experimental results in the ‘70, with CO2 lasers,mainly towards the laser

Much higher energies (10’s of MeV protons inparticular) obtained in 2000 and more recently

Various mechanisms. The dominant mechanism may varywith laser intensity, target material and thickness

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Mechanisms of ion laser-acceleration

- + - + - +- +- + - + - + - +

+ -+ -+ -+ -

- - - - - - - - - - - - - - --

ions

Bulk Target

e-

Incidentlaser e-

e-

e-

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Thin foil expansion

0.1

1

1 10!pit

L=20"D0

Te/Te0

!

T "1/ t2

E0 =kBTe0

e!D0

Efront! 1/ t2

Eplateau!1/ t3

P. Mora, Phys. Rev. E 72, 056401 (2005)!

v final " 2cs ln 0.32L /#D + 4.2( )

adiabatic

isothermal(Mora 2003)

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Observation of the electric peak by proton radiography

L. Romagnani et al., Phys. Rev. Lett. 95, 195001 (2005)See also M Amin’s talk

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M. Borghesi’s talk

32

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Main issues

- Energy, emittance- Quasi-monoenergetic spectrum (multispecies targets,laser piston regime, etc.); see also ZM Sheng’s talk thismorning- Manipulation of the spatial energy distribution ofprotons: see P McKenna’s talk- Laser polarization, contrast dependence, relation withabsorption mechanisms: see A. Lévy and S Ter-Avetisyan talks- Advantages of mass-limited targets: see A. Andreev’stalk

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Conclusion

- well established high quality experimental results(stability, reproducibility, quasimonoenergeticcharacter, emittance)

- number of applications (in particular medicalapplications or for high energy physics, or forsecondary sources of particles)

- still progress have to be made for instance in termsof maximum energy: future lasers will certainly help .

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Acknowledgments

Thanks to M. Borghesi, S. Mangles, C. Toth, and J.Faure who sent me slides

Thanks to past and present collaborators: T. Antonsen,F. Amiranoff, B. Quesnel, T. Grismayer, J. Fuchs, L.Gorbunov, and many others