Single-laser scheme for reaching strong field QED regime via direct laser acceleration

We investigate a single-laser scheme for reaching the strong-field QED regime based on direct laser acceleration (DLA) of electrons followed by their head-on collision with the same laser pulse reflected from an overdense foil. In this configuration, electrons are first accelerated inside an underdense plasma by a relativistic laser pulse and subsequently interact with the reflected laser field, emitting high-energy photons via nonlinear Compton scattering which decay into electron-positron pairs through the nonlinear Breit-Wheeler process. Using analytical scalings supported by quasi-3D particle-in-cell simulations including QED effects, we demonstrate that a laser pulse with power as low as 2 PW is sufficient to reach the quantum regime characterized by $χ_e> 1$ . For higher powers, we observe a rapid nonlinear increase in the number of generated positrons, reaching more than 2 nC for a 10 PW laser pulse with energy of approximately 1.1 kJ. A semi-analytical model is employed to estimate the positron yield, showing good agreement with simulation results. We further study the influence of laser depletion and the positioning of the reflecting foil on the efficiency of pair production. The presented scheme provides an experimentally feasible platform for probing strong-field QED effects using currently available multi-petawatt laser systems.

💡 Research Summary

The paper proposes and validates a single‑laser configuration that can reach the strong‑field quantum electrodynamics (SFQED) regime by first accelerating electrons via direct laser acceleration (DLA) in an under‑dense gas and then colliding those electrons head‑on with the same laser pulse after it is reflected from an overdense foil. The authors develop analytical scalings for the maximum electron energy, the required acceleration length, laser front depletion, and the quantum non‑linearity parameter χe. They show that the maximum electron Lorentz factor achievable in DLA is γmax≈2 (a0 εcr)4/3 (ne/nc)−1/3, and that the acceleration distance needed to reach this limit scales as Lacc≈0.78 a0^{2/3} εcr^{5/3}(ne/nc)^{2/3} λL. Laser front etching, described by vfront≈c(1−ωp^2/ω0^2), reduces the effective pulse length and must be accounted for when choosing the gas‑target length.

After the acceleration stage, an overdense thin foil placed a few hundred microns downstream reflects the remaining laser pulse. The reflected pulse collides with the DLA‑accelerated electrons, driving χe=γ E⊥/ES. When χe exceeds unity, electrons emit high‑energy photons via nonlinear Compton scattering (NICS), and those photons subsequently decay into electron‑positron pairs through the nonlinear Breit–Wheeler (NBW) process. Using the formalism of Blackburn et al., the number of pairs generated per electron is expressed in terms of the photon emission probability, the recoil‑corrected quantum parameter, and the photon spectrum. Integrating over the broad DLA electron energy distribution yields the total positron yield.

Quasi‑3D particle‑in‑cell (PIC) simulations with QED modules (EPOCH‑QED) are performed for laser powers of 2 PW, 5 PW, and 10 PW (pulse duration ≈30 fs, spot size 5–10 µm). The simulations confirm the analytical predictions: a 2 PW pulse already reaches χe≈1.2, producing a few positrons; a 5 PW pulse yields χe≈2.5–3 and a positron charge of ~0.3 nC; a 10 PW pulse attains χe≈4–5 and generates >2 nC (≈1.2×10⁹) of positrons. The laser front depletion consumes roughly 20 % of the initial pulse energy, and optimal foil placement (0.5–1 mm behind the gas exit) preserves >70 % of the laser energy for the head‑on collision, maximizing pair production. The simulations also reveal that the DLA process supplies a high‑charge electron beam (10–20 nC), which is crucial because the positron yield grows non‑linearly with the electron charge in the χe>1 regime.

A systematic study of foil positioning shows a trade‑off: moving the foil farther downstream allows electrons to gain higher energy but also increases laser depletion, reducing the field strength at the collision point. The optimal distance depends on laser power and gas density but generally lies within the 0.5–1 mm range for the parameters considered.

The authors compare the DLA‑based scheme with traditional LWFA‑based two‑beam approaches. Advantages of the single‑laser DLA configuration include: (i) no need for separate focusing optics after acceleration, (ii) intrinsic synchronization between electrons and the highest‑intensity part of the pulse, (iii) a much larger electron charge leading to higher positron yields, and (iv) a simpler experimental layout (single laser, gas jet, and reflective foil). The main drawback is the broad electron energy spectrum, which limits the precision of QED tests that require mono‑energetic beams.

In conclusion, the paper demonstrates that current multi‑petawatt laser facilities (≥2 PW) can already access the quantum regime (χe>1) using a compact, all‑optical setup. At 10 PW, the scheme produces experimentally measurable positron charges (>2 nC), opening the door to laboratory studies of radiation‑reaction effects, nonlinear Compton scattering, and nonlinear Breit–Wheeler pair creation, as well as the generation of dense electron‑positron pair plasmas. The authors suggest future work on optimizing laser and gas parameters, employing plasma lenses for post‑acceleration focusing, and investigating collective dynamics of the generated pair plasma.