All-optical nonlinear Breit-Wheeler pair production with γ-flash photons Alexander J. MacLeod1Prokopis Hadjisolomou1Tae Moon Jeong1and Sergei V. Bulanov1 2 1ELI Beamlines Centre Institute of Physics Czech Academy of Sciences

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All-optical nonlinear Breit-Wheeler pair production with γ-ﬂash photons

Alexander J. MacLeod,1, ∗Prokopis Hadjisolomou,1Tae Moon Jeong,1and Sergei V. Bulanov1, 2

1ELI Beamlines Centre, Institute of Physics, Czech Academy of Sciences,

Za Radnic`ı 835, 25241 Doln`ı Bˇreˇzany, Czech Republic

2National Institutes for Quantum and Radiological Science and Technology (QST),

Kansai Photon Science Institute, 8-1-7 Umemidai, Kizugawa, Kyoto 619-0215, Japan

High-power laser facilities give experimental access to fundamental strong-ﬁeld quantum elec-

trodynamics processes. A key eﬀect to be explored is the nonlinear Breit-Wheeler process: the

conversion of high-energy photons into electron-positron pairs through the interaction with a strong

electromagnetic ﬁeld. A major challenge to observing nonlinear Breit-Wheeler pair production ex-

perimentally is ﬁrst having a suitable source of high-energy photons. In this paper we outline a

simple all-optical setup which eﬃciently generates photons through the so-called γ-ﬂash mechanism

by irradiating a solid target with a high-power laser. We consider the collision of these photons with

a secondary laser, and systematically discuss the prospects for exploring the nonlinear Breit-Wheeler

process at current and next-generation high-power laser facilities.

I. INTRODUCTION

Modern advances in laser technology have brought us

into the multi-PW laser power regime, with a large num-

ber of high-power laser facilities [1] either operational or

in development, e.g. [2–14]. High-power lasers generate

intense electromagnetic ﬁelds, allowing access to the non-

linear regime of quantum electrodynamics (QED), where

the interaction between particles and laser ﬁelds cannot

be described by the usual methods of vacuum perturba-

tion theory. Instead, the electromagnetic ﬁeld must be

taken into account non-perturbatively through a frame-

work typically referred to as strong-ﬁeld QED [15–19].

One of the most important strong-ﬁeld QED phenom-

ena is the nonlinear Breit-Wheeler process (NBW) [20–

23] — the production of an electron-positron pair from

the interaction between a high-energy γ-photon and

strong electromagnetic ﬁeld. High-power lasers are an

ideal source of strong-ﬁelds, with ﬁeld strengths E0∼

10−3ESalready achieved experimentally with PW-class

systems [4], where ES∼1.32 ×1018 Vm−1is the

Schwinger critical ﬁeld of QED at which non-perturbative

pair production occurs [24–26].

With high-power lasers supplying the strong-ﬁelds, one

still requires a source of γ-photons for NBW experiments.

The source should ideally meet the following criteria:

i. High-energy — NBW is exponentially sup-

pressed when the quantum nonlinearity param-

eter for a photon with momentum lµ,χγ=

p−(Fµν lν)2/(mcES)≪1, becoming more proba-

ble as χγ≳1. If the ﬁeld strength of the laser pulse

is parameterised by the dimensionless intensity pa-

rameter, ξ=eE0λC/ℏω0,1this corresponds to a

photon energy ωγ≳m2/(2ω0ξ). Typical multi-PW

∗alexander.macleod@eli-beams.eu

1Here, eis the electron charge, E0is the electric ﬁeld strength,

λc=ℏ/mc is the Compton wavelength of an electron with mass

m, and ω0is the central frequency of the laser pulse.

laser facilities will operate with optical frequencies,

ω0∼1eV, and ﬁeld strengths ξ∼102−103, requir-

ing photons with energy in the MeV—GeV range.

ii. Large numbers — the total number of generated

electron-positron pairs, Ne−e+, is directly propor-

tional to the number of photons which collide with

the laser, Ne−e+∝ Nγ.

iii. Synchronised — multi-PW laser systems reach high

peak power by compressing laser pulses to fem-

tosecond (fs) durations. The photon source should

be easily synchronised with the colliding pulse to

ensure large numbers of photons pass through the

spatio-temporal region of highest ﬁeld strength.

iv. Overlap — high intensities are achieved by fo-

cussing laser pulses to (typically) micron (µm)

beam waists, w0. The photon beam should have

large spatial overlap with the laser focal spot to

mitigate the impact of shot-to-shot ﬂuctuations.

v. Eﬃcient — photon generation mechanism should

eﬃciently convert the total input energy into a com-

parable total energy of photons.

Diﬀerent photon sources suitable for strong-ﬁeld QED ex-

periments have been proposed, which generally fall into

two categories: electron-seeded or laser-driven (for a re-

view see, e.g. [27] and references therein).

Electron-seeded schemes generate γ-photons by collid-

ing electron bunches with electromagnetic ﬁelds or high-

Ztargets. In the former case, photons can be produced

in the perturbative regime, ξ≪1, via inverse Thom-

son/Compton scattering [30], or in the non-perturbative

regime, ξ≳1, via nonlinear Compton scattering [22,

31, 32]. The weak-ﬁeld case, ξ≪1, produces radiation

which is highly monochromatic and polarised [33–35], but

requires high-density electron bunches of GeV energy to

produce the signiﬁcant numbers of MeV photons [33, 36]

required for NBW. In the nonlinear regime, ξ≳1, elec-

tron bunches of comparatively lower density can be used

to generate high-brightness photon beams with energy

comparable to the initial energy of the electrons (see

arXiv:2210.14766v2 [hep-ph] 2 Aug 2023

FIG. 1. Proposed experimental conﬁguration. The total available laser energy, Etotal , is split into two beams: Etotal =

Eﬂash +Epairs. The beam with energy Eﬂash is used to irradiate a solid lithium target, producing high-energy photons via the

so-called γ-ﬂash mechanism [28, 29]. Charged secondary particles from the target are deﬂected to minimise background. The

γ-ﬂash photons propagate from the rear surface of the lithium target and collide with a counter-propagating secondary pulse,

energy Epairs, to produce electron-positron pairs via the nonlinear Breit-Wheeler mechanism [20–23]. Positrons are emitted at

an angle ϑrelative to the axis of the colliding counter-propagating laser.

e.g. [37, 38]), due to the high ﬁeld-strengths causing sig-

niﬁcant portions of the electron energy to be radiated.

Alternatively, electron beams can be collided with high-

Z targets to produce photons via bremsstrahlung [39, 40],

where the maximum photon energy is again comparable

to the initial electron energy. This scheme has shown

promise for the study of NBW [41], and is being con-

sidered as the primary source of photons in several ex-

perimental proposals (see e.g. [42–45]). Novel schemes

have also been proposed utilising electron beam-multifoil

collisions [46] and high-density electron bunch collisions

with solid targets [47] to produce γ-photons with high

conversion eﬃciency.

The key limiting factor of each of these approaches is

the initial step of producing high-energy, high-density,

electron beams. This must be achieved using con-

ventional RF accelerators or laser-wakeﬁeld acceleration

(LWFA) [48–50]. Conventionally accelerated electron

beams were utilised in the ﬁrst experimental demon-

stration of pair production in the weak ﬁeld regime

(ξ≪1) [51, 52], and will be used in the upcoming LUXE

campaign to explore pair production in the transition

regime (ξ≳1) [42]. However, currently no facility exists

which hosts both a conventional accelerator and multi-

PW laser system, putting the non-perturbative multi-

photon regime of NBW (ξ≫1) out of reach with this

approach. Therefore, LWFA will be the primary mech-

anism for producing electron bunches at multi-PW laser

facilities. A typical photon source using LWFA electrons

will require multiple stages. First, the electrons are pro-

duced through a single/multi-stage acceleration scheme

with an initial laser pulse colliding with an under-dense

plasma. Secondly, depending on the properties of the

electron beam such as its transverse size and divergence,

these will need to be focussed/columnated to achieve

higher densities and mitigate undesirable features in the

produced photons (see e.g. [41]). Finally, the electrons

will generate photons via one of the mechanisms outlined

above, requiring either another laser pulse or strong-ﬁeld

source, or collision with a high-Ztarget. At each stage in

the photon generation scheme, nonlinear plasma eﬀects,

shot-to-shot ﬂuctuations in laser parameters and/or elec-

tron beam properties, and the spatio-temporal size of the

produced photon beams can make synchronisation with

another colliding laser pulse extremely challenging. Fur-

thermore, the conversion eﬃciency between the initial

laser energy and the total energy of the produced pho-

tons can be extremely low.

Instead of using electrons to generate γ-photons, one

can instead hope to produce them more directly using

a laser-driven approach. While many of the electron-

seeded schemes described above would require multi-

stage experimental conﬁgurations and access to high-

energy electron sources such as conventional accelera-

tors, laser-driven γ-photon generation can typically be

achieved in a single stage, with the only requirement be-

ing access to a high-power laser. A simple scheme which

uses high-power lasers to irradiate solid targets is the

so-called γ-ﬂash mechanism [28, 29]. The γ-ﬂash mech-

anism meets all of the desired properties i—v outlined

above, producing large numbers of MeV—GeV photons

with very high conversion eﬃciency between the laser

energy and the energy of the produced photons [53–68].

Furthermore, the use of only a single laser-driven stage

to generate the γ-ﬂash, coupled with the short duration

and large transverse size of the photon beam, makes syn-

chronisation to, and overlap with, a secondary laser pulse

particularly simple.

In this paper we investigate the feasibility of using the

γ-ﬂash mechanism for studying nonlinear Breit-Wheeler

pair production through an extremely simple all-optical

two-stage conﬁguration, demonstrated in ﬁg. 1. The key

physical parameter which limits the attainable on-target

peak power at a high-power laser facility is the total avail-

able pulse energy, Etotal. Our scheme assumes Etotal is

split between two laser pulses, Etotal =Eﬂash +Epairs. A

pulse of energy Eﬂash is used to irradiate an over-dense

plasma, chosen as solid lithium (Li), to drive γ-photon

production through the γ-ﬂash mechanism. This pro-

duces a γ-photon beam with large numbers of MeV—

GeV photons, which propagate out from the rear surface

of the target. A second laser pulse, with energy Epairs,

collides head-on with the γ-photons at an interaction dis-

tance, d, from the target rear surface to produce electron-

positron pairs through NBW.

The paper is structured as follows. Firstly, in sec-

tion II we discuss the angular and spectral properties of

photons generated through the γ-ﬂash mechanism. The

spectra are produced using the particle-in-cell (PIC) code

EPOCH [69]. In section III we summarise theoretical

aspects of NBW, giving expressions for the diﬀerential

probability of pair production from the collision of a pho-

ton and a linearly polarised plane wave pulse with Gaus-

sian temporal envelope. In section IV numerical results

are presented for the total number of electron-positron

pairs produced through the interaction of γ-ﬂash pho-

tons with high-power laser pulses. We consider three dif-

ferent cases of total available laser pulse energy, Etotal,

relevant for current and next generation laser facilities,

and discuss the optimal partitioning of this energy into

Eﬂash and Epairs to maximise the overall pair yield. We

also discuss the energy and angular properties of the pro-

duced positrons. Finally, in section V, we summarise our

key ﬁndings and discuss future steps for reﬁning and op-

timising our approach. Throughout the rest of the paper

we work in natural units, ℏ=c= 1, unless otherwise

speciﬁed and use the shorthand notation aµbµ≡a·band

b·b≡b2with metric tensor, gµν = diag(+1,−1,−1,−1).

II. γ-FLASH PHOTON SPECTRUM

At low intensities, over-dense plasmas — where the

electron density ne> ncr with ncr =ϵ0meω2

0/e2the crit-

ical density for frequency ω0— are opaque to laser light.

Irradiating an over-dense plasma with a laser of suﬃ-

ciently high intensity induces relativistic transparency,

allowing the laser to propagate into the plasma and

drive electron motion. A dense “QED plasma” is pro-

duced where there is an interplay between ﬁeld-induced

QED phenomena and collective plasma eﬀects [28, 29].

Copious numbers of high-energy photons are generated

by charged particles in the QED plasma by a com-

bination of nonlinear Compton scattering [28, 29] and

bremsstrahlung [39, 40], in a mechanism often referred

to as a “γ-ﬂash”. Numerical studies primarily utilising

particle-in-cell (PIC) codes [28, 29] have demonstrated

that the laser-to-photon energy conversion eﬃciency, κγ,

for the γ-ﬂash mechanism can be as large as several tens

of percent for single laser [53–61], dual laser [62–64] and

multi-laser conﬁgurations [65–68].

The ﬁrst stage of our setup involves irradiating an over-

Driving pulse Eﬂash

τFWHM [fs] λ0[µm] w0[µm]

17 0.815 1.86

TABLE I. Constant laser parameters for γ-ﬂash driving laser

with energy Eﬂash.

dense plasma with an intense laser pulse to generate high-

energy photons. The plasma is taken to be a solid lithium

(Li) target, density ne≈1.39 ×1029 m−3, with a diam-

eter 12 µm and thickness 10 µm. The choice of target is

twofold. Firstly, thin low-Z targets are known to reduce

secondary particle production by photons in the mate-

rial, compared to thicker and/or higher-Z targets (see

e.g. [70–72]). Secondly, Li has previously been shown to

optimise the laser-to-photon energy conversion eﬃciency

with metallic targets [61]. To increase the eﬃciency of

photon generation the target is ﬁrst irradiated with a long

pre-pulse which generates a conical channel and has a

similar eﬀect to using targets fabricated with cone struc-

tures, see e.g. [61, 72–75]. The three-dimensional electron

number density for the structured target is reproduced

from a publicly available dataset [76] which calculates

the eﬀect of the pre-pulse using radiation hydrodynamic

(RHD) simulations. This data is then used as the initial

conditions for the 3D-PIC simulations which model pho-

ton generation using the code EPOCH [69] compiled with

the Higuera-Cary [77], bremsstrahlung and photons [78]

directives enabled.

We consider the gamma photon spectra generated from

lasers with diﬀerent values of the laser energy, Eﬂash. In

each case the pulse is a linearly polarised laser with full

width half maximum (FWHM) duration of 17 fs focussed

at normal incidence on the target with beam waist w0∼

1.86 µm. The central laser wavelength is λ0= 0.815 µm,

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●5PW

■15PW

★50PW

0 20 40 60 80

0.01

0.10

100

1000

θ[deg]

IΩ[PW sr-1]

FIG. 2. Angular distribution of radiant intensity of γ-ﬂash

photons along laser polarisation axis, averaged over the two-

lobe angular structure. γ-ﬂash produced by interaction with

Li solid target and focussed laser pulses with peak powers

5 PW (blue, circles), 15 PW (orange, squares) and 50 PW

(green, stars). Shaded region denotes β= 10 deg full-angle

divergence which maximises the radiant intensity.

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All-opticalnonlinearBreit-Wheelerpairproductionwithγ-flashphotonsAlexanderJ.MacLeod,1,∗ProkopisHadjisolomou,1TaeMoonJeong,1andSergeiV.Bulanov1,21ELIBeamlinesCentre,InstituteofPhysics,CzechAcademyofSciences,ZaRadnic`ı835,25241Doln`ıBˇreˇzany,CzechRepublic2NationalInstitutesforQuantumandRadiologicalSc...

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All-optical nonlinear Breit-Wheeler pair production with γ-flash photons Alexander J. MacLeod1Prokopis Hadjisolomou1Tae Moon Jeong1and Sergei V. Bulanov1 2 1ELI Beamlines Centre Institute of Physics Czech Academy of Sciences.pdf

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All-optical nonlinear Breit-Wheeler pair production with γ-flash photons Alexander J. MacLeod1Prokopis Hadjisolomou1Tae Moon Jeong1and Sergei V. Bulanov1 2 1ELI Beamlines Centre Institute of Physics Czech Academy of Sciences

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