Introduction Method Results Summary/Outlook Prolific Pair Production in Laser Beams John Kirk Max-Planck-Institut für Kernphysik Heidelberg, Germany Collaborators: Tony Bell (University of Oxford/CLF), Ioanna Arka (MPIK) École Polytechnique, 22nd June 2009
Introduction Method Results Summary/Outlook Outline Introduction 1 Method 2 Results 3 Summary/Outlook 4
Introduction Method Results Summary/Outlook Motivation Physicists are planning lasers powerful enough to rip apart the fabric of space and time (Nature, 446 (2007))
Introduction Method Results Summary/Outlook Motivation Physicists are planning lasers powerful enough to rip apart the fabric of space and time (Nature, 446 (2007)) Within ∼ 1 year, pulses with 10 23 –10 24 W cm − 2 available at λ = 1 µ m Strength parameter Larmor frequency a = wave frequency eE λ/ mc 2 = � I 24 λ 2 855 = µ m
Introduction Method Results Summary/Outlook Motivation Physicists are planning lasers powerful enough to rip apart the fabric of space and time (Nature, 446 (2007)) Within ∼ 1 year, pulses with 10 23 –10 24 W cm − 2 available at λ = 1 µ m Strength parameter Larmor frequency a = wave frequency eE λ/ mc 2 = � I 24 λ 2 855 = µ m Strong field QED: in electron rest frame E ′ ≈ γ E ∼ E crit ( 2 I 24 λ µ m )
Introduction Method Results Summary/Outlook Pair production using lasers I ‘Standard’ method, laser incident on solid surface: electrons accelerated to few MeV in burn-off layer enter high- Z foil and make gamma-rays by bremsstrahlung these produce pairs by Bethe-Heitler process in electrostatic field of nuclei
Introduction Method Results Summary/Outlook Pair production using lasers I ‘Standard’ method, laser incident on solid surface: electrons accelerated to few MeV in burn-off layer enter high- Z foil and make gamma-rays by bremsstrahlung these produce pairs by Bethe-Heitler process in electrostatic field of nuclei Laser used as accelerator, foil used as target Works at relatively low intensity ( ∼ 10 20 W cm − 2 ) Low efficiency ( < 10 − 5 of laser pulse goes into pairs)
Introduction Method Results Summary/Outlook Pair production using lasers II SLAC experiment (Burke et al 1997): ∼ 50 GeV electrons enter laser beam ( a ∼ few) and scatter photons to ∼ GeV (NL Compton) these photons produce pairs by scattering on laser photons (NL Breit-Wheeler process)
Introduction Method Results Summary/Outlook Pair production using lasers II SLAC experiment (Burke et al 1997): ∼ 50 GeV electrons enter laser beam ( a ∼ few) and scatter photons to ∼ GeV (NL Compton) these photons produce pairs by scattering on laser photons (NL Breit-Wheeler process) SLAC accelerates, laser used as target relatively few pairs
Introduction Method Results Summary/Outlook Trajectory in a plane wave Figure-of-eight in linearly polarized wave Periodic in a special frame (ZMF) with γ ∼ a wave
Introduction Method Results Summary/Outlook Trajectory in a plane wave Figure-of-eight in linearly polarized wave Periodic in a special frame (ZMF) with γ ∼ a If picked up at rest in lab. frame, particle recoils ZMF reached by boost in direction of wave, with Lorentz wave factor ≈ a
Introduction Method Results Summary/Outlook Trajectory in a plane wave Figure-of-eight in linearly polarized wave Periodic in a special frame (ZMF) with γ ∼ a If picked up at rest in lab. frame, particle recoils ZMF reached by boost in direction of wave, with Lorentz wave factor ≈ a Boost to ZMF red-shifts ν by factor ∼ a In ZMF, fields weaker: E ′ ∼ E / a , B ′ ∼ B / a
Introduction Method Results Summary/Outlook E-M wave in ˆ z direction E along ˆ x z × B Lorentz force E = − ˆ vanishes for v → c ˆ z Interaction reduced – governed by perpendicular acceleration wave
Introduction Method Results Summary/Outlook E-M wave in ˆ z direction E along ˆ x z × B Lorentz force E = − ˆ vanishes for v → c ˆ z Interaction reduced – governed by perpendicular acceleration More precisely, by � ( � / m 2 c 3 ) ( d p µ / d τ )( d p µ / d τ ) η = ( e � / m 3 c 4 ) | F µν p µ | = wave | cos φ | = E / E crit � �� � in pick-up frame
Introduction Method Results Summary/Outlook E-M wave in ˆ z direction E along ˆ x z × B Lorentz force E = − ˆ vanishes for v → c ˆ z Interaction reduced – governed by perpendicular acceleration More precisely, by � ( � / m 2 c 3 ) ( d p µ / d τ )( d p µ / d τ ) η = ( e � / m 3 c 4 ) | F µν p µ | = wave | cos φ | = E / E crit � �� � in pick-up frame Laser beam plays the role of accelerator (to γ ≈ a ) but not of target
Introduction Method Results Summary/Outlook Counter-propagating beams Circular polarization: e − simple orbit at B = 0 node Bell & Kirk 2008: eE /γ mc = ω laser η = γ E / E crit − eE 3 . 6 I 24 λ µ m =
Introduction Method Results Summary/Outlook Counter-propagating beams Circular polarization: e − simple orbit at B = 0 node Bell & Kirk 2008: eE /γ mc = ω laser η = γ E / E crit − eE 3 . 6 I 24 λ µ m = Limited by radiation reaction when � 3 E crit / 2 α f E γ > γ RR = 0 . 13 λ − 4 / 3 ⇒ I 24 > µ m
Introduction Method Results Summary/Outlook Counter-propagating beams Circular polarization: e − simple orbit at B = 0 node − eE � Bell & Kirk 2008: eE /γ mc = ω laser η = γ E / E crit − eE ⊥ 3 . 6 I 24 λ µ m = Limited by radiation reaction when � 3 E crit / 2 α f E γ > γ RR = 0 . 13 λ − 4 / 3 ⇒ I 24 > µ m
Introduction Method Results Summary/Outlook Coherence length e − θ γ ℓ coh ℓ coh = mc 2 / eE sin θ < 1 /γ ⇒ Field quasi-static if ℓ coh ≪ λ 1 ⇒ a ≫ Identical requirement in QED
Introduction Method Results Summary/Outlook Coherence length e − θ γ ℓ coh ℓ coh = mc 2 / eE sin θ < 1 /γ ⇒ Field quasi-static if ℓ coh ≪ λ 1 ⇒ a ≫ Identical requirement in QED ⇒ instantaneous , local transition rates at each point on classical trajectory for a ≫ 1
Introduction Method Results Summary/Outlook Weak field approximation In quasi-static limit transition rates depend on η for electrons, and χ = e � 2 | F µν k ν | / 2 m 3 c 4 for photons field invariants f = E 2 − B 2 and g = E · B (both ∼ 10 − 6 I 24 )
Introduction Method Results Summary/Outlook Weak field approximation In quasi-static limit transition rates depend on η for electrons, and χ = e � 2 | F µν k ν | / 2 m 3 c 4 for photons field invariants f = E 2 − B 2 and g = E · B (both ∼ 10 − 6 I 24 ) In γ -ray and pair production regime ( η ∼ 1, χ ∼ 1) rates depend only on η and χ
Introduction Method Results Summary/Outlook Weak field approximation In quasi-static limit transition rates depend on η for electrons, and χ = e � 2 | F µν k ν | / 2 m 3 c 4 for photons field invariants f = E 2 − B 2 and g = E · B (both ∼ 10 − 6 I 24 ) In γ -ray and pair production regime ( η ∼ 1, χ ∼ 1) rates depend only on η and χ Equivalent system: static, homogeneous B , electron/photon with p · B = 0, in limit γ → ∞ , B → 0, with η , χ held constant
Introduction Method Results Summary/Outlook Weak field approximation In quasi-static limit transition rates depend on η for electrons, and χ = e � 2 | F µν k ν | / 2 m 3 c 4 for photons field invariants f = E 2 − B 2 and g = E · B (both ∼ 10 − 6 I 24 ) In γ -ray and pair production regime ( η ∼ 1, χ ∼ 1) rates depend only on η and χ Equivalent system: static, homogeneous B , electron/photon with p · B = 0, in limit γ → ∞ , B → 0, with η , χ held constant Magneto-bremsstrahlung and single-photon (magnetic) pair- production — computed in 1950’s (Klepikov, Erber. . . )
Introduction Method Results Summary/Outlook Synchrotron radiation Synchrotron Emissivity 1 F( η , χ) 0.5 0 -4 -3 -2 -1 0 1 log( χ ) η =0.1 η =1 NL Compton scattering: e ± + n γ laser → e ± + γ for n ≫ 1
Introduction Method Results Summary/Outlook Shaped pulses 1 0 E x -1 -150 -100 -50 0 50 100 150 1 Model pulses in cylinder of radius λ Integrate classical equations of motion (including radiation reaction) Evaluate intensity of synchrotron radiation Compute number of pairs produced per electron
Introduction Method Results Summary/Outlook Circularly polarized beams Beam intensity 6 × 10 23 W cm − 2 15 x y 10 z 5 B = 0 node unstable 0 E = 0 node stable -5 4 η Pair production 2 γ 0 N negligible -2 -4 -6 -8 -100 -50 0 50 t (laser phase)
Introduction Method Results Summary/Outlook Aligned, linearly polarized beams Beam intensity 6 × 10 23 W cm − 2 15 x y 10 z 5 Stable node less 0 important -5 4 η Pair production 2 γ 0 N significant -2 -4 -6 -8 -100 -50 0 50 t (laser phase)
Introduction Method Results Summary/Outlook Crossed, linearly polarized beams Crossed linear polarization 2 -0.5 -1 0 -1.5 -2 -2 log(N real ) -2.5 -4 -3 -6 -3.5 -4 -8 -4.5 -10 -5 23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 24 log(flux) (W/cm 2 )
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