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

This paper demonstrates that Bayesian optimisation can effectively navigate the challenges of shot-to-shot laser jitter in simulated all-optical experiments, revealing that optimal conditions for maximizing electron-positron pair production differ from those for gamma-ray energy and remain achievable with high laser energies despite significant timing and pointing instabilities.

The Gist

Imagine trying to create something from nothing—specifically, turning pure light into matter (electron-positron pairs). This is the goal of the Breit-Wheeler process, a phenomenon predicted by physics but incredibly difficult to achieve in a lab.

Think of this experiment like trying to hit a tiny, moving target with a needle while riding a bumpy horse. You have two main ingredients:

1. A super-bright laser (the needle).
2. A beam of high-speed electrons (the horse).

When these two collide perfectly, the intense energy of the laser can rip a pair of particles out of the vacuum. But in the real world, things are messy. The laser might wiggle slightly, or the timing might be off by a fraction of a second (called "jitter"). In a perfect computer simulation, you'd get a great result. In reality, that tiny wobble means the laser and electron beam miss each other, and you get zero results.

Here is how the authors of this paper solved the problem, explained simply:

1. The "Ghost Particle" Trick (Particle Splitting)

Usually, to simulate these collisions, scientists have to track millions of "fake" particles (macroparticles) to see if even one pair gets created. It's like trying to find a specific grain of sand on a beach by looking at every single grain; it takes forever and costs a lot of computer power.

The authors invented a new trick called Particle Splitting.

• The Analogy: Imagine you are a baker testing a recipe that has a 1-in-a-million chance of making a perfect cake. Instead of baking a million loaves to find one perfect cake, you bake one loaf, but you magically "clone" the batter 1,000 times inside the oven. You then check all 1,000 clones at once.
• The Result: This allows the computer to simulate rare events (like creating a particle pair) thousands of times faster without losing accuracy. They proved that their "cloning" math works perfectly, even when the odds are incredibly slim.

2. The "Smart Search" (Bayesian Optimisation)

Once they could run simulations quickly, they needed to find the best settings for the experiment. The problem is that the "perfect" setting changes depending on how much the laser wobbles (jitter).

• The Analogy: Imagine you are looking for the highest point on a foggy mountain. You can't see the whole map.
  • The Old Way (Brute Force): You walk every single step of the mountain, measuring the height everywhere. This takes years.
  • The New Way (Bayesian Optimisation): You take a few steps, guess where the peak might be based on the slope, and then use a "smart compass" (Gaussian Process Regression) to decide exactly where to walk next. It learns as it goes, quickly zooming in on the best spot without checking every inch of the mountain.

3. The Surprising Discovery: "Stand-Off" Distance

The most interesting finding is about where to set up the collision.

• The Intuition: You'd think you want the electron beam to hit the laser focus as tightly as possible, right?
• The Reality: Because the laser wobbles (jitter), if you aim too tightly, the beam often misses the target entirely.
• The Solution: The authors found that you actually want to let the electron beam spread out a bit before it hits the laser. They call this the "stand-off distance."
  • The Metaphor: Imagine trying to throw a dart at a bullseye that is shaking back and forth. If you stand right next to it, you have to be perfect. But if you stand a few meters back, your throw has a wider spread. Even though you are less precise, the "spread" covers the shaking target more often.
  • The Finding: The more the laser wobbles, the further back you should stand (up to a few centimeters). This increases the chance that some electrons will hit the laser, even if the laser is jittering.

4. Two Different Goals

The paper also showed that the "best" settings depend on what you are trying to do:

• If you want to create the most Gamma Rays (light): You want the laser focus to be slightly larger and the beams to hit closer together.
• If you want to create Matter (pairs): You want the laser focus to be as tiny as possible (to get maximum power) and the beams to be further apart (to handle the wobble).

The Bottom Line

Using these new "cloning" math tricks and the "smart search" algorithm, the authors showed that even with realistic, messy lab conditions (where lasers wiggle and timing is slightly off), we can still create matter from light.

They estimate that with current technology (using a 100-joule laser), we could realistically produce one electron-positron pair for every 100 electrons we shoot. It's not a huge number, but it's enough to prove the physics works, even with the "bumpy horse" of real-world experiments.

Technical Summary

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

Problem Statement
The production of electron-positron pairs from pure light via the non-linear Breit-Wheeler process is a primary goal for next-generation high-intensity laser facilities. While idealized simulations suggest high yields, practical all-optical experiments face significant hurdles. Specifically, achieving the necessary many-photon collisions between gamma rays (produced via inverse Compton scattering) and intense laser pulses is hindered by shot-to-shot jitter in laser pointing and timing. This jitter, often on the scale of tens of microns and femtoseconds, reduces the pair production yield by orders of magnitude compared to ideal head-on collisions. Furthermore, the probability of pair production is so low with current laser parameters that standard Monte-Carlo or Particle-In-Cell (PIC) simulations require computationally prohibitive numbers of particles to resolve the rates accurately, especially when exploring multi-dimensional parameter spaces to find optimal experimental conditions.

Methodology
The authors propose a two-pronged approach to address computational inefficiency and experimental uncertainty:

1. Novel Particle Splitting Algorithms: To simulate rare Breit-Wheeler events without tracking millions of unnecessary macroparticles, the authors introduce particle splitting techniques performed during the pair production step. They identify that naive splitting (increasing the emission rate and reducing weight) fails to conserve energy or maintain statistical independence when splitting rates are high. They evaluate three corrected approaches:

   • Full Poisson Sampling: Sampling the full distribution every timestep to allow multiple emissions per macroparticle.
   • Additive Optical Depth: Accumulating random optical depths to maintain emission history and independence.
   • Sub-cycling: Repeating the additive optical depth process within a single timestep to handle high emission rates ($\lambda \sim 1$).
     The authors select the "Additive optical depth with sub-cycling" approach for its balance of computational efficiency and accuracy, noting it allows for simple particle weights while conserving energy on average.

2. Bayesian Optimisation with Gaussian Process Regression (GPR): To navigate the multi-dimensional parameter space (laser spot size, energy split, and stand-off distance) under noisy conditions, the authors employ Bayesian optimisation. They use GPR to build a fast surrogate model of the pair production rate. An "Expected Improvement" acquisition function guides the selection of new simulation points, balancing exploration of uncertain regions with exploitation of known high-yield areas. This replaces brute-force grid searches, which are too expensive given the stochastic nature of the problem.

Key Results

• Algorithmic Efficiency: The particle splitting methods allow for accurate simulation of pair production rates down to $10^{-7}$ pairs per photon. Compared to increasing the number of macroparticles to achieve the same statistical accuracy, the splitting method reduces runtime by three orders of magnitude (e.g., from ~2,800 seconds to ~2.3 seconds per simulation for a specific test case).
• Impact of Jitter: Simulations incorporating realistic jitter (10s of microns spatial, 10s of femtoseconds temporal) show that pair production yields drop by two orders of magnitude compared to ideal collisions.
• Optimal Stand-off Distance: A critical finding is that the optimal experimental configuration depends heavily on the level of jitter.
  • For pair production, the optimal strategy involves a tight laser focus (small waist, e.g., 2 $\mu$m) to maximize the quantum parameter $\chi$, combined with a stand-off distance (several centimeters) that allows the electron beam to expand. This expansion increases the beam size to match the scale of the spatial jitter, ensuring a higher probability of collision despite the beam missing the exact focal point.
  • For synchrotron radiation (gamma-ray production), the optimal strategy differs: it favors a larger laser waist (~16 $\mu$m) and a minimal stand-off distance to maximize the interaction volume and total radiated energy, rather than peak intensity.
• Quantitative Yields: Using 100 J of total laser energy, the authors estimate that realistic pair production rates of approximately 1 pair per 100 electrons are achievable, even with spatial jitter of 10s of microns and temporal jitter of 10s of femtoseconds. The optimal parameters found involve an energy split ($s = E_{coll}/E_{tot}$) of roughly 0.43, resulting in a 5.7 GeV electron beam colliding with a 1.7 PW laser pulse.

Significance and Claims
The paper claims that by combining efficient particle splitting algorithms with Bayesian optimisation, it is now computationally feasible to model and optimise all-optical Breit-Wheeler experiments under realistic, noisy conditions. The work demonstrates that the "best" conditions for producing pairs are distinct from those for maximizing gamma-ray energy, specifically requiring a trade-off between laser intensity and beam expansion to mitigate jitter. The authors assert that these methods enable near-term laser facilities to achieve measurable pair production rates, providing a practical roadmap for experimental design that accounts for the inevitable imperfections of real-world laser systems. The study does not propose new experimental hardware but rather offers a computational framework to maximise the utility of existing and planned facilities (such as ZEUS, CoReLS, and APOLLON).