Prolific Pair Production in Laser Beams John Kirk - - PowerPoint PPT Presentation

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

1

Introduction

2

Method

3

Results

4

Summary/Outlook

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 1023–1024 W cm−2 available at λ = 1 µm Strength parameter a = Larmor frequency wave frequency = eEλ/mc2 = 855

• I24λ2

µm

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 1023–1024 W cm−2 available at λ = 1 µm Strength parameter a = Larmor frequency wave frequency = eEλ/mc2 = 855

• I24λ2

µm

Strong field QED: in electron rest frame E′ ≈ γE ∼ Ecrit (2I24λµm)

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 (∼ 1020 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

wave Figure-of-eight in linearly polarized wave Periodic in a special frame (ZMF) with γ ∼ a

Introduction Method Results Summary/Outlook

Trajectory in a plane wave

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 factor ≈ a

Introduction Method Results Summary/Outlook

Trajectory in a plane wave

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 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 E = −ˆ z × B Lorentz force vanishes for v → cˆ z Interaction reduced – governed by perpendicular acceleration wave

Introduction Method Results Summary/Outlook

E-M wave in ˆ z direction E along ˆ x E = −ˆ z × B Lorentz force vanishes for v → cˆ z Interaction reduced – governed by perpendicular acceleration More precisely, by η = (/m2c3)

• (dpµ/dτ)(dpµ/dτ)

= (e/m3c4) |F µνpµ| = E/Ecrit

in pick-up frame

|cos φ| wave

Introduction Method Results Summary/Outlook

E-M wave in ˆ z direction E along ˆ x E = −ˆ z × B Lorentz force vanishes for v → cˆ z Interaction reduced – governed by perpendicular acceleration More precisely, by η = (/m2c3)

• (dpµ/dτ)(dpµ/dτ)

= (e/m3c4) |F µνpµ| = E/Ecrit

in pick-up frame

|cos φ| wave Laser beam plays the role of accelerator (to γ ≈ a) but not of target

Introduction Method Results Summary/Outlook

Counter-propagating beams

Circular polarization: simple orbit at B = 0 node Bell & Kirk 2008: eE/γmc = ωlaser η = γE/Ecrit = 3.6 I24λµm e− −eE

Introduction Method Results Summary/Outlook

Counter-propagating beams

Circular polarization: simple orbit at B = 0 node Bell & Kirk 2008: eE/γmc = ωlaser η = γE/Ecrit = 3.6 I24λµm Limited by radiation reaction when γ > γRR =

• 3Ecrit/2αfE

⇒ I24 > 0.13 λ−4/3

µm

e− −eE

Introduction Method Results Summary/Outlook

Counter-propagating beams

Circular polarization: simple orbit at B = 0 node Bell & Kirk 2008: eE/γmc = ωlaser η = γE/Ecrit = 3.6 I24λµm Limited by radiation reaction when γ > γRR =

• 3Ecrit/2αfE

⇒ I24 > 0.13 λ−4/3

µm

e− −eE⊥ −eE

Introduction Method Results Summary/Outlook

Coherence length ℓcoh θ e− γ

sin θ < 1/γ ⇒ ℓcoh = mc2/eE Field quasi-static if ℓcoh ≪ λ ⇒ a ≫ 1 Identical requirement in QED

Introduction Method Results Summary/Outlook

Coherence length ℓcoh θ e− γ

sin θ < 1/γ ⇒ ℓcoh = mc2/eE Field quasi-static if ℓcoh ≪ λ ⇒ a ≫ 1 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 = e2 |F µνkν| /2m3c4 for photons field invariants f = E2 − B2 and g = E · B (both ∼ 10−6 I24)

Introduction Method Results Summary/Outlook

Weak field approximation

In quasi-static limit transition rates depend on

η for electrons, and χ = e2 |F µνkν| /2m3c4 for photons field invariants f = E2 − B2 and g = E · B (both ∼ 10−6 I24)

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 = e2 |F µνkν| /2m3c4 for photons field invariants f = E2 − B2 and g = E · B (both ∼ 10−6 I24)

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 = e2 |F µνkν| /2m3c4 for photons field invariants f = E2 − B2 and g = E · B (both ∼ 10−6 I24)

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

0.5 1

• 4
• 3
• 2
• 1

1 F(η,χ) log(χ) Synchrotron Emissivity η=0.1 η=1

NL Compton scattering: e± + n γlaser → e± + γ for n ≫ 1

Introduction Method Results Summary/Outlook

Shaped pulses

1

• 1

1

• 150 -100 -50

50 100 150 Ex

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 × 1023 W cm−2

• 8
• 6
• 4
• 2

2 4

• 100
• 50

50 t (laser phase) η γ N

• 5

5 10 15 x y z

B = 0 node unstable E = 0 node stable Pair production negligible

Introduction Method Results Summary/Outlook

Aligned, linearly polarized beams

Beam intensity 6 × 1023 W cm−2

• 8
• 6
• 4
• 2

2 4

• 100
• 50

50 t (laser phase) η γ N

• 5

5 10 15 x y z

Stable node less important Pair production significant

Introduction Method Results Summary/Outlook

Crossed, linearly polarized beams

• 5
• 4.5
• 4
• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

Crossed linear polarization 23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 24 log(flux) (W/cm2)

• 10
• 8
• 6
• 4
• 2

2 log(Nreal)

Introduction Method Results Summary/Outlook

Summary/Outlook

Present work

Classical trajectories adequate (η < 1) Physical processes: synchrotron radiation, magnetic pair production (a ≫ 1) Counter-propagating beams in under-dense plasma likely to produce pair avalanche at beam intensity 1024 W cm−2

Introduction Method Results Summary/Outlook

Summary/Outlook

Present work

Classical trajectories adequate (η < 1) Physical processes: synchrotron radiation, magnetic pair production (a ≫ 1) Counter-propagating beams in under-dense plasma likely to produce pair avalanche at beam intensity 1024 W cm−2

Improvements

Discreteness of radiation reaction (“stragglers”) could be important (Shen & White 1971) Monte-Carlo treatment of cascade needed Reflected wave from laser-solid interaction? Hybrid P .I.C.+Monte-Carlo code needed