Automation and control of laser wakefield accelerators using Bayesian optimization

Laser wakefield accelerators (LWFAs) use an ultrashort intense laser pulse traveling through plasma to drive a wake that can accelerate electrons to multi-GeV energies over centimeters, enabling compact accelerators and ultrafast synchrotron-like X-ray sources. Despite their promise for future facilities and even collider concepts, LWFAs are challenging to control and optimize because the laser’s intensity, shape, and spectrum evolve nonlinearly during acceleration and many input parameters are coupled. Traditional optimization by sequential one-dimensional scans is inefficient and can miss true optima due to parameter coupling and shot-to-shot variability. Full multidimensional scans are impractical. Machine learning approaches, including Bayesian optimization, are well suited for noisy, expensive, multivariate optimization. Prior work using genetic algorithms adjusted only laser parameters and did not account for measurement uncertainties, limiting full source optimization. This study applies Bayesian optimization to realize a fully automated LWFA with simultaneous control of laser spectral and spatial phase and plasma source parameters, building surrogate models that capture uncertainty and correlations to guide efficient optimization.

The paper situates LWFAs within ongoing efforts to build compact accelerators and light sources, noting prior demonstrations and facility plans. It reviews machine learning applications in plasma and accelerator science, highlighting genetic algorithms previously used to optimize laser-plasma sources by controlling spatial or spectral phase, but not simultaneously and without incorporating experimental errors. These approaches optimized only the laser, not the coupled laser-plasma system, and were susceptible to outliers. Bayesian optimization is presented as a robust alternative that can handle noisy measurements and multivariate control, with Gaussian Process Regression providing uncertainty-aware surrogate models. The work builds on these insights to implement a comprehensive, automated optimization of both laser and plasma parameters.

Bayesian optimization framework: The authors implemented an augmented Bayesian optimization procedure (based on scikit-learn) using Gaussian Process Regression (GPR) as a surrogate model. The workflow: (1) construct a GPR prior with a physically sensible covariance kernel; (2) collect initial measurements; (3) update to a posterior; (4) compute an acquisition function; (5) iterate sampling until convergence.

• Two-model approach for heteroscedastic noise: One GPR modeled the mean objective Y(X) with SD σ(X). A second GPR modeled input-dependent measurement variance, predicting the true SD of the objective. Both used an RBF kernel plus white noise; hyperparameters were optimized by marginal likelihood. Measurement positions were scaled to similar ranges to approximate kernel isotropy.
• Augmented acquisition: The expected improvement acquisition was multiplied by a sampling-efficiency factor η = 1 − sqrt(σ^2/ε), where ε is experimental uncertainty and σ the model SD. The white-noise variance was subtracted from σ^2 and added to ε when evaluating η to avoid double-counting noise. The next point was found by sampling the acquisition along many random line segments through existing samples and picking the global maximum across all sampled points.
• Computation: On a Xeon E5-1620 v3, after ~50 measurements GPR fitting took ~260 ms and acquisition maximization ~290 ms per iteration (~20,000 acquisition evaluations).

Experimental setup: Experiments ran on the Gemini TA2 Ti:sapphire laser (Central Laser Facility). On target: ~245 mJ per pulse, ~45 fs transform limit, focused to 16 μm 1/e^2 radius (a0 ≈ 0.55), 1 Hz rep rate, f/18 off-axis parabola, central wavelength 803 nm, 23 nm FWHM bandwidth.

• Plasma source: Custom gas cell with translatable rear aperture for 0–10 mm length; filled via electronically triggered valve; differential pumping maintained ~1e-3 mbar. Post-plasma, a thin tape-based plasma mirror removed the laser; electrons and X-rays passed to diagnostics.
• Diagnostics: Electron spectrometer with permanent dipole (558 mT), Lanex screen, calibrated with image plates; energy range 26–251 MeV. X-rays recorded by a direct-detection CCD 1.23 m from source with Al-coated Mylar foils filtering optical light and soft X-rays; spectral retrieval via filter transmissions.
• Laser metrology: On-shot SPIDER for temporal profile; wavefront sensor for spatial phase; energy monitor for pulse energy.

Controlled parameters and measurement protocol: The algorithm simultaneously varied up to six inputs: three laser spectral phase coefficients β(2), β(3), β(4) via an acousto-optic programmable dispersive filter; spatial phase via a deformable mirror; plasma electron density via backing pressure; plasma length via gas cell length. For each measurement, a burst of 10 shots was acquired to estimate mean and variance of the objective function; all control, analysis, and next-point selection were fully automated. Multiple objective functions were tested, including electron charge (>26 MeV), total X-ray counts, total electron beam energy, and charge within a small angular acceptance to favor low divergence.

Model exploration and simulations: After combining 10 convergence runs (350 measurements/3500 shots) in a 4D space (β(2), β(3), β(4), focus f), the surrogate model’s optimum was at β(2)=60 fs^2, β(3)=9×10^3 fs^3, β(4)=6×10^5 fs^4, f=0.7 mm relative to start. A strong correlation between β(2) and β(4) was identified, consistent with polynomial spectral phase coupling; the relation Δβ(4)=−64 β(2)/(Δω)^2 matched observed gradients. Quasi-3D PIC simulations (FBPIC) initialized with measured laser properties and a density profile from OpenFOAM fluid modeling were used to interpret injection dynamics and the role of subtle temporal pulse-shape differences (e.g., sharper rising edge from positive chirp) on ionization injection and charge yield.

• Automated 4D electron charge optimization: Using β(2), β(3), β(4), and focal position f as inputs in a N2:He (1%:99%) mix, the algorithm reached the local optimum in ~20 bursts (200 shots; ~6.5 min), yielding a ~3× increase in electron charge relative to the starting point. The mean optimized charge across ten runs was 17 ± 2 pC (E > 26 MeV).
• 6D betatron X-ray optimization: Simultaneously varying laser spectral phase, focus, plasma density, and cell length in pure He achieved a fivefold increase in X-ray yield in 27 min. The optimized source enabled clear filter-array imaging despite modest laser energy (5.4 TW class), typically considered insufficient for multi-keV betatron imaging.
• Tailored beam properties via objective choice: • Example A (maximize total electron beam energy, 5D): Achieved 0.91 ± 0.15 mJ average total beam energy in ~20 min, requiring significant variation of all five inputs from a far-from-optimal start. • Example B (minimize divergence by summing charge within 3.75 mrad), 5D: Achieved minimum burst-averaged divergence of 3.4 ± 0.2 mrad with lower total beam energy, 0.26 ± 0.04 mJ. Demonstrates strong dependence of optimal operating point on objective function.
• Model insight on spectral phase: A correlated optimum along β(2)–β(4) enabled maintaining high peak power via compensation of positive chirp with negative fourth-order phase. Moving from an unchirped pulse to a subtly positively chirped pulse with a slightly sharper rising edge increased electron charge by 80%, while the pulse FWHM changed by only ~0.5 fs.
• Physical mechanism (PIC): Small initial temporal-profile differences amplified by nonlinear self-focusing and compression led to higher peak a0 at the point of ionization injection (z ≈ 3.2 mm), with the optimal positively chirped pulse reaching a ≈ 2.3 vs 2.1, injecting ~40% more charge.
• Algorithmic performance vs alternatives: In the 4D surrogate space, Bayesian optimization reached ~94% of model optimum with 60 measurements. Sequential 1D scans reached ~80%, genetic algorithm ~69%, Nelder–Mead ~34% (all with 60 measurements). A 4D grid search required 14,641 measurements (11 per dimension) to reach ~95% convergence.
• Robustness to variability: Despite shot-to-shot fluctuations (pulse energy PV 8%, duration 6%, focus ~1 mm Rayleigh range), the method reliably found optima. Improved laser stability on next-generation systems is expected to yield even finer control.

The study demonstrates that Bayesian optimization can efficiently and autonomously control a laser wakefield accelerator by learning a surrogate model that captures uncertainties and correlations across high-dimensional parameter spaces. By moving beyond sequential 1D scans, the approach uncovers coupled optima—such as the β(2)–β(4) correlation—enabling significant performance gains with subtle laser pulse-shape adjustments. The capability to redefine the objective function enables tailoring of the LWFA output (e.g., maximizing total energy vs minimizing divergence), allowing a single device to serve diverse applications, from secondary photon and positron sources to staging into further acceleration. The learned models also provide physical insight, here into ionization injection dynamics and the role of the laser’s rising edge, informing future accelerator design. Automated global optimization is anticipated to be essential for forthcoming LWFA user facilities to maximize performance and reliability.

This work presents the first fully automated laser-plasma accelerator controlled via Bayesian optimization, simultaneously tuning up to six laser and plasma parameters. The method rapidly optimized electron and X-ray outputs, achieved substantial performance improvements (e.g., 3× electron charge, 5× X-ray yield), and revealed critical parameter correlations (β(2)–β(4)) that enable large charge gains from minimal pulse-length changes. The approach’s flexibility to choose application-specific objectives enables tailoring of beam properties. Future directions include deployment on higher-stability, higher-repetition-rate laser systems to achieve finer control, integrating end-application feedback (e.g., FEL coherence) as the optimization objective, and leveraging the learned models to guide the design of next-generation plasma accelerators.

• Laser stability limited performance and repeatability: observed shot-to-shot PV fluctuations of ~8% in pulse energy, ~6% in pulse duration, and ~1 mm in focal position contributed to spectral and charge variability.
• Low repetition rate (1 Hz) constrained data acquisition speed and may limit the achievable optimization resolution within practical timescales.
• Modest laser energy (5.4 TW class) capped attainable beam and X-ray parameters; higher-power, more stable systems are expected to enhance outcomes.
• Surrogate-model dependence: performance relies on appropriate kernel choice, noise modeling, and acquisition strategy; suboptimal hyperparameter choices could slow convergence or bias exploration.
• Objective function sensitivity: results depend strongly on how the objective is defined; inappropriate choices can steer the optimization away from application-relevant operating points.
• Comparative algorithm performance was reported without extensive hyperparameter tuning for alternatives; while the Bayesian method outperformed in this setting, tuned alternatives could narrow the gap.