classical and quantum electrodynamics in an...

Classical and quantum electrodynamics in an intenselaser field

Madalina Boca

Department of Physics, University of Bucharest2012 annual scientific conference

(FF UB) Intense laser-matter interaction Magurele 2012 1 / 24

Outline

1 Introduction

2 Modeling the laser field

3 Radiation scattering

Classical/quantum description

Final electron distribution

4 Pair creation


Introduction

Processes

Radiation scattering (non-linear Compton/Thomson):

Fundamental for theoryAstrophysics (Freenberg, Primakov, 1963)X and gamma polarimetryX/gamma radiation source (Milburn (1963), Arutyunian (1963);impressive change due to the availability of intense laser sources.)

Pair creation

Theory (QED in the nonperturbative regime)Schwinger mechanism practically unavailable → non-linear processes

Experiment E144 at SLAC (Stanford Linear Accelerator Center) [Bula et al, 1996]


Introduction

G. A. Mourou, arXiv:1108.2116


Introduction

Relevant parameters

Electron energy E ;

γ ∼ E [keV]511

(ELI-NP: γ ∼ 1000)

Laser wavelength

λ ∼ 800 nm (~ω ∼ 0.056 au ∼ 1.5 eV)

laser pulse duration

tens of cycles: τ ∼ 10T (T ∼ 3 fs; ELI-NP: τ ∼ 30 fs)

Laser intensity

I = ε0c2

E 20 = ε0c

2ω2A2

0

η = eA0mc, → I = (ω [au])2 η2 × 6.6× 1020 W/cm2

η ∼ 700, ω = 0.056 au → I = 1024 W/cm2 (ELI-NP)

classicality parameter:

y = ηγ~ωmc2


Introduction

Compton scattering

p1 6= 0:

ω2 = ω1E1 − cn1 · p1

E1 − cn2 · p1 + (1− n1 · n2)~ω1

Thomson (elastic) scattering

p1 6= 0: (elastic scattering in the elec-tron rest frame)

ω2 = ω1E1 − cn1 · p1

E1 − cn2 · p1

Head-on collision, forward scattering, E1 mc2, ~ω1 mc2: ωmax2 ≈ 4γ2ω1

Example: ~ω1 = 2.33 eV (λ ≈ 532 nm), E1 = 600 MeV → ~ωmax2 ≈ 13 MeV (0.02×E1).


Modeling the laser field

The laser field

Semiclassical approximation: A(r, t), Φ(r, t) ↔ E(r, t), B(r, t)

monochromatic

plane wave: E,B functions on φ ≡ ct − n · r

focused laser field


Radiation scattering Classical/quantum description

Classical/quantum description

CED formalism: the electron accelerated by the laser field emits radiation;

Arbitrary laser field (monochromatic/plane-wave/focused)Electron equation of motion (w/wo radiation reaction)Lienard-Wiechert potentialsPlane-wave, no RR: pi = pf

Quantum description: single photon emission in the external field

Dirac equation, semiclassical approximation (laser field: classical,emitted photon: quantized field)plane wave laser field(P − eAL−eAC−mc)Ψ = 0 Exact solutions of the Dirac equation forHe−L (Volkov solutions); Hc : first order perturbation theory

Aif ∼1

i~

∫dt〈ψV (p2)|HC(k2)|ψV (p1)〉



Radiation spectrum

d2W

dω2dΩ2−→

dW

dω2,

dW

dΩ2

Monochromatic approximation: d2W

dω2dΩ2→ an infinite series of lines for any fixed

observation direction.

ω(q)N = NωL

E1 − cn1 · p1

E1 − cn2 · p1 + (1− n1 · n2)[

mc2η2

4(E1−cn1·p1)+ N~ωL

]ω

(cl)N = NωL

E1 − cn1 · p1

E1 − cn2 · p1 + (1− n1 · n2) mc2η2

4(E1−cn1·p1)

η → 0: Compton/Thomson formula for ωL → NωL (simultaneous absorption of Nphotons)

ω(q)1 = NωL

E1 − cn1 · p1

E1 − cn2 · p1 + (1− n1 · n2)N~ωL

η → 0, p→ 0: Compton/Thomson formula for electron initially at rest andωL → NωL



Radiation spectrum

ω(q)N = NωL

E1 − cn1 · p1

E1 − cn2 · p1 + (1− n1 · n2)[

mc2η2

4(E1−cn1·p1)+ N~ωL

]ω

(cl)N = NωL

E1 − cn1 · p1

E1 − cn2 · p1 + (1− n1 · n2) mc2η2

(E1−cn1·p1)

mc2η2

4(E1−cn1·p1): nonlinearity effect “electron dressing”: p → q = p + (mc)2eta2

4(n1·p)n,

m→ m∗ = m√

1 + η2/2

Classicality criterion: small electron recoil y = Neff~ω1(E1−cn1·p1)

mc2η2 1

η . 1→ Neff = O(1), y ∼ ~ω1γmc2η2 η 1→ Neff ≈ η3, y ∼ ~ω1γη

mc2

Quantum cut-off

ω(q)N < ω

(cl)N ; frequency cut-off lim

N→∞~ω(q)

N = E1−cn1·p11−n1·n2

= ~ωcut−off

Head-on collision For head-on collision, backscattering, ultrarelativistic electron:~ωcut−off = E1 (not always observed!)



Blue shift/Red shift

γ1 1 −→ ω2 ωl Blue shift: electron energy converted into the energy of theemitted photon

η > 1 Red shift due to electron dressing

Head-on collision, E1 = 600 MeV, λL = 532 nm (quasi-monochromatic) (ELI-NPgamma source); δθ = ∠(p1, k2)



Blue shift/Red shift

η 1 Onset of a different regime: the radiation distribution becomesquasi-continuous for well defined angles.



Classical/quantum calculation

Classicality parameter y ∼ ~ω1γηmc2

Head-on collision, ωL = 0.043, E1 = 5.1 GeV, η = 40 (quantum cutt-off reached)



Angular distribution

γ ∼ η

Head-on collision, γ1 = 50 , η = 100 Well defined shape of angular distribution,azimuthal symmetry lost



Angular distribution

γ ∼ η

Shape of the distribution given by trajectory of β

Possible field shape reconstruction from β

Identical shape predicted by classical/quantum calculation



Radiation reaction

Lorentz-Abraham-Dirac (LAD) equation:

dpµ

dτ= e

mFµνpν + 2

3

e20

c2(mc)

[d2pµ

dτ2 + pµ

(mc)2

(dpν

dτdpνdτ

)]Landau-Lifshitz (LL) equation: perturbative; in RHS use dpµ

dτ= e

mFµνpν

analytical solution of the LLequation for a plane-wave field[DiPiazza, Lett. Math. Phys. 83, 105 (2008)]

without RR pi = pf

with RR pi 6= pf

∆p depends on: laser intensity,frequency, duration

Not included in the quantumformalism as presented before

λ = 1000 nm, η = 100(I = 1.2× 1022 W/cm2)



Radiation reaction

Quantum description of radiation reaction: incoherent multiple one-photon emission by

the electron [DiPiazza et al, Phys. Rev. Lett. 105, 220403 (2010)]



Time dependence of the emitted fields

Trains of zeptosecond pulses [Galkin et al, Contrib. Plasma Phys. 49,593 (2009)]

λ0 = 532 nm, E1 = 600 MeV, θ1 = 0.8π, η = 0.1, 10.



Focalization effects

Only classical description possible

unlike in the plane-wave case pi 6= pf

Orthogonal collision: effects in theregime γ ∼ η 1; pi 6= pf

Head-on collision: negligible effects inthe regime γ ∼ η 1; pi = pf

Numerical examples for a Gaussian pulse with waist-size w



Focalization effects

Ponderomotive acceleration of electrons by atigthly focused laser pulse

Energy gain ∼ MeV for I ∼ 1019 W/cm2.

[Yu et al, Phys. Rev. E 61, R2220 (2000); Phys. Rev. E 68, 046407

(2003)]


Radiation scattering Final electron distribution

Final electron distribution (γ η ∼ 1)

the monochromatic case: a series of discrete lines for any electron direction

finite pulse: discrete lines → continuous spectrum

λ0 = 800 nm, η = 0.6, E1 = 46 GeV, near head on collision (SLAC)

monochromatic plane wave pulse


Radiation scattering Final electron distribution

Final electron distribution for large η

λ0 = 800 nm, E1 = 5.1 GeV, head-on collision.η = 0.5 η = 5

λ0 = 800 nm, η = 5 (I = 5 ×1019W /cm2), head-on collision; energydistribution of the final electron dp/dE2.


Pair creation

Pair creation

Trident Process

Intermediate photon: off or on shell

off-shell → one step process

e− + NωL → e′− + e− + e+

(Non-linear Bethe-Heitler)

~ωBH ≥ m∗c2

2Nγ

on-shell → two step process

e− + nωL → e′− + ω′

ω′ + (N − n)ωL → e− + e+

(Non-linear Breit-Wheeler)

~ωBW ≥ m∗c2

2(√

N−1)γ

Rates for the two processes:

Hu et al, Phys. Rev. Lett. 105, 080401 (2010), A. Ilderton, Phys. Rev. Lett. 106, 020404 (2011)


Pair creation

Pair creation

SLAC E144 experiment(Non-linear BW dominant)

Hu et al, Phys. Rev. Lett. 105, 080401 (2010)

ELI-NP (η ∼ 1000, MeV electrons) :competing processes

Hu et al, Phys. Rev. Lett. 105, 080401 (2010)


classical and quantum electrodynamics in an...

Documents