Bayesian Optimisation of Non-linear Breit-Wheeler Pair Production in Simulated Laser Experiments

High laser intensities enable the production of electron-positron pairs from bright gamma rays passing through strong fields. Potentially the most promising approach for all-optical experiments in the near term uses dense but higher divergence electron beams from laser wakefield acceleration to produce gamma rays through inverse Compton scattering. Achieving many-photon collisions between these gamma rays and the high intensity laser pulse in practice is extremely difficult, however, due to significant shot-to-shot jitter in laser pointing and timing. We model these practical difficulties using simulated Monte-Carlo experiments. By using a more efficient algorithm for sampling infrequent pair production with particle splitting, we enable the exploration of a multi-dimensional parameter space. Using Gaussian Process Regression we then efficiently find optimal conditions for maximising pair production by changing the laser spot size, the energy in the colliding beam, and the stand-off distance between the laser wakefield accelerator and the focus of the colliding laser pulse. We find that the optimal stand-off distance increases with the degree of laser jitter and that the best conditions for producing electron-positron pairs are not the same as the best conditions for maximising the energy in the gamma rays. With \unit[100]{J} of laser energy, we estimate rates of pair production of around 1 pair per 100 electrons are achievable even with jitter of 10s of microns and 10s of femtoseconds.

💡 Research Summary

The paper addresses the challenge of producing electron‑positron pairs via the non‑linear Breit‑Wheeler process in all‑optical laser experiments, where a high‑intensity laser pulse collides with γ‑rays generated by inverse Compton scattering from a laser‑wakefield‑accelerated (LWFA) electron beam. In realistic laboratory conditions, shot‑to‑shot jitter in laser pointing (tens of microns) and timing (tens of femtoseconds) dramatically reduces the overlap between the γ‑ray beam and the focal region of the high‑intensity laser, suppressing pair‑production yields by orders of magnitude.

To overcome two intertwined computational bottlenecks—(i) the rarity of Breit‑Wheeler events at present laser intensities, and (ii) the need to explore a multi‑dimensional experimental parameter space—the authors develop (a) a novel particle‑splitting algorithm that increases the effective pair‑production probability during the emission step, and (b) a Bayesian optimisation framework based on Gaussian Process Regression (GPR) to efficiently locate the global optimum.

Particle‑splitting methodology
Standard Monte‑Carlo or Particle‑in‑Cell (PIC) codes treat photon emission and pair creation as Poisson processes, sampling a single random number per macro‑particle per timestep. When λ (the mean number of events per step) is ≪ 1, the optical‑depth method works well, but for Breit‑Wheeler the probability per photon is so low that billions of photons must be tracked to obtain a single pair, making the simulation prohibitively expensive. The authors therefore introduce a splitting factor u: each photon is allowed to “attempt” pair creation u times per timestep, effectively scaling λ → u λ. When a pair is created, its macro‑particle weight is reduced to 1/u, and the parent photon weight is reduced by the same amount; if the photon weight reaches zero it is removed.

Three possible implementations are examined: (I) full Poisson sampling (most accurate but costly), (II) additive optical‑depth with a single random number per emission (computationally cheap, accurate on average), and (III) sub‑cycling of the additive optical depth to allow multiple emissions per step. The study adopts the additive‑depth + sub‑cycling scheme, which remains cheap for λ ≤ 1 while preserving independence of emission events and conserving energy on average.

Validation simulations involve a 1 PW, 25 J, 25 fs laser focused to w₀ = 2 µm (peak intensity 2.2 × 10²² W cm⁻²) colliding with a mono‑energetic γ‑ray beam (100 MeV–1 GeV) at a 15° angle. Without splitting, pair yields are zero below ≈ 300 MeV; with splitting, the authors resolve pair yields down to 10⁻⁴–10⁻⁷ pairs per photon and obtain meaningful positron energy spectra even at 400 MeV where only a handful of macroparticles are produced.

Bayesian optimisation
The experimental design space consists of three controllable parameters: laser focal spot size (w₀), energy in the colliding γ‑ray beam (E_beam), and the stand‑off distance L between the LWFA source and the high‑intensity focus. Each simulation is expensive; a brute‑force grid would require thousands of runs. The authors therefore construct a surrogate model using GPR, iteratively selecting new points via an acquisition function (expected improvement). This approach converges to the optimum with an order‑of‑magnitude fewer simulations.

Key findings from the optimisation are:

1. Jitter dependence – As the magnitude of spatial or temporal jitter increases, the optimal stand‑off distance grows (from ~1 cm for sub‑micron jitter to > 2 cm for 20 µm/30 fs jitter). The longer distance allows the divergent γ‑ray beam to spread, reducing sensitivity to mis‑alignment while still intersecting the high‑field region.

2. Non‑coincident objectives – Maximising the total γ‑ray energy does not coincide with maximising pair yield. The latter favours a modestly larger focal spot (to keep the field strength just above the pair‑production threshold) combined with a higher γ‑ray density, whereas the former would push for the smallest possible spot to increase intensity.

3. Quantitative performance – Assuming a 100 J laser, realistic jitter of 10 µm and 10 fs, and an optimal stand‑off of ~2 cm, the simulations predict roughly one electron‑positron pair per 100 incident electrons (or per 100 γ‑photons, depending on the exact conversion efficiency). This translates to a pair‑production rate that is experimentally observable with current high‑repetition‑rate laser systems.

Implications
The work demonstrates that, even with the unavoidable shot‑to‑shot fluctuations of present‑day high‑power laser facilities, careful optimisation of geometry and beam parameters can yield measurable Breit‑Wheeler pair production. The particle‑splitting technique offers a general tool for any rare QED process in PIC or Monte‑Carlo codes, dramatically reducing variance without sacrificing physical fidelity. The Bayesian optimisation framework provides a scalable strategy for navigating high‑dimensional experimental design spaces where each evaluation is costly. Together, these methods pave the way for near‑term all‑optical experiments probing strong‑field QED, potentially enabling compact sources of positrons and advancing our understanding of vacuum non‑linearity.