Classical and quantum electrodynamics in an...
Transcript of 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
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Outline
1 Introduction
2 Modeling the laser field
3 Radiation scattering
Classical/quantum description
Final electron distribution
4 Pair creation
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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]
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Introduction
G. A. Mourou, arXiv:1108.2116
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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
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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).
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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
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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)〉
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Radiation scattering Classical/quantum description
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
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Radiation scattering Classical/quantum description
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!)
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Radiation scattering Classical/quantum description
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)
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Radiation scattering Classical/quantum description
Blue shift/Red shift
η 1 Onset of a different regime: the radiation distribution becomesquasi-continuous for well defined angles.
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Radiation scattering Classical/quantum description
Classical/quantum calculation
Classicality parameter y ∼ ~ω1γηmc2
Head-on collision, ωL = 0.043, E1 = 5.1 GeV, η = 40 (quantum cutt-off reached)
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Radiation scattering Classical/quantum description
Angular distribution
γ ∼ η
Head-on collision, γ1 = 50 , η = 100 Well defined shape of angular distribution,azimuthal symmetry lost
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Radiation scattering Classical/quantum description
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
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Radiation scattering Classical/quantum description
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)
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Radiation scattering Classical/quantum description
Radiation reaction
Quantum description of radiation reaction: incoherent multiple one-photon emission by
the electron [DiPiazza et al, Phys. Rev. Lett. 105, 220403 (2010)]
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Radiation scattering Classical/quantum description
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.
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Radiation scattering Classical/quantum description
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
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Radiation scattering Classical/quantum description
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)]
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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
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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.
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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)
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