Laser wakefield accelerators (LWFAs) hold immense potential to revolutionize accelerator science by offering compact and cost-effective alternatives to conventional high-energy accelerators. In an LWFA, an ultra-intense, ultrashort laser pulse propagates through a plasma, generating a wakefield that can accelerate electrons to multi-GeV energies within centimeters. The high accelerating gradients achievable in LWFAs promise to dramatically reduce the size and cost of future accelerators, making them attractive for various applications, including medical imaging and materials science. The X-rays generated by the transverse oscillations of trapped electrons provide compact, ultrafast synchrotron radiation sources. The global effort toward designing a compact plasma-based particle collider further underscores the importance of LWFA development. However, a significant hurdle to the widespread adoption of LWFAs lies in the complexity of controlling and optimizing their output. The process is governed by a complex interplay between numerous input parameters—affecting the laser pulse's spatial and spectral energy distribution and the characteristics of the plasma source—and the dynamically evolving accelerating structure. These parameters are inherently coupled, making optimization challenging. Traditional optimization methods, such as single-variable scans, are often insufficient due to the non-linear nature of the LWFA and the shot-to-shot variations in the experimental outputs. A full multi-dimensional scan is computationally prohibitive. Therefore, a more intelligent and efficient optimization technique is required.

Previous attempts to optimize laser-plasma sources using machine learning have employed genetic algorithms. These studies have focused on optimizing either the spatial phase of the laser to enhance keV electron sources or both spatial and spectral phases (not simultaneously) for MeV electron sources. However, these approaches have limitations. They typically only controlled laser parameters, neglecting the crucial interplay between laser and plasma parameters for complete LWFA optimization. Furthermore, they lacked the incorporation of experimental errors, making them susceptible to distortion by statistical outliers. This study aimed to overcome these limitations by using a more robust and efficient approach.

This research utilizes Bayesian optimization, a powerful machine learning technique well-suited for optimizing noisy, expensive-to-evaluate functions with multiple input parameters. Bayesian optimization constructs a surrogate model of the objective function (the quantity to be optimized), which incorporates uncertainty arising from limited data and measurement noise. This surrogate model, typically implemented using Gaussian Process Regression (GPR), is updated iteratively with each new experimental measurement. The algorithm then uses an acquisition function (e.g., upper confidence bound) to strategically select the next measurement point, balancing exploration of uncharted parameter space and exploitation of promising regions. The experiments were performed using the Gemini TA2 Ti:sapphire laser system at the Central Laser Facility. The experimental setup included a gas cell as the plasma source, with diagnostics to measure electron beam properties (energy distribution, charge, profile) and X-ray characteristics (yield, energy, divergence). The optimization algorithm controlled up to six parameters: the second, third, and fourth-order coefficients of the laser pulse's spectral phase (controlled by an acousto-optic programmable dispersive filter), the laser pulse's spatial phase (controlled by a piezoelectric deformable mirror), the plasma density (controlled by gas pressure), and the plasma length (controlled by the gas cell length). The entire optimization process—control, data analysis, and selection of the next measurement point—was automated. For each measurement, ten shots were taken to calculate the mean and variance of the objective function for a given parameter set. All parameters varied simultaneously during the optimization runs. The researchers developed an augmented Bayesian optimization algorithm based on the scikit-learn platform, incorporating two GPR models to handle input-dependent measurement uncertainty.

The researchers demonstrated the efficacy of their automated system through several optimization runs. Initially, they used the total electron count (charge) above 26 MeV as the objective function, optimizing four parameters (three spectral phase coefficients and the laser focus position) in a nitrogen-helium gas mixture. The algorithm consistently achieved a threefold increase in electron beam charge within 20 measurements (200 shots) across ten independent runs. The average optimized charge was 17 ± 2 pC. Next, the researchers maximized the betatron X-ray yield in a pure helium plasma, optimizing six parameters. They achieved a fivefold increase in X-ray yield within 27 minutes. This result is noteworthy because the laser system's power was considered insufficient for betatron imaging applications in the multi-keV energy range. Analyzing the optimization process revealed that the algorithm tuned the laser compression and focusing, and improved performance by operating at lower plasma density and longer gas cell length. The flexibility of the automated LWFA was further showcased by optimizing different objective functions. One optimization targeted the total electron beam energy, achieving 0.91 ± 0.15 mJ. Another optimization focused on minimizing electron beam divergence within a 3.75 mrad acceptance angle, resulting in a minimum divergence of 3.4 ± 0.2 mrad, though with a lower total beam energy (0.26 ± 0.04 mJ). These results highlight the ability to tailor the electron beam characteristics to specific application needs. Investigation of the model generated by the optimization algorithm revealed a correlation between the second (β(2)) and fourth (β(4)) order coefficients of the spectral phase. This correlation stems from the polynomial representation of the spectral phase, where even orders are coupled. The algorithm found an optimum along a curve representing this correlation. The researchers found that a small amount of positive chirp and a steep rising edge in the laser pulse were optimal for both self-injection and ionization injection, leading to an 80% increase in charge with only a 0.5 fs change in FWHM pulse duration. Particle-in-cell (PIC) simulations using the code FBPIC supported these findings, demonstrating that the sharper rising edge caused by changes in the spectral phase led to increased ionization and charge injection. The study compared Bayesian optimization with other optimization algorithms (sequential 1D scans, genetic algorithm, Nelder-Mead algorithm, and grid search) via Monte Carlo simulations. Bayesian optimization significantly outperformed the other algorithms, demonstrating higher efficiency in reaching the optimum within a limited number of measurements.

This research successfully demonstrated the feasibility and advantages of using Bayesian optimization for the automated control and optimization of LWFAs. The automated system significantly improves the efficiency and effectiveness of optimizing LWFA parameters compared to traditional methods. The ability to simultaneously optimize multiple parameters allows the system to discover optima that might be missed in single-variable scans, revealing subtle relationships between parameters. The development of a surrogate model offers insights into the dynamics of the system, providing valuable information for future LWFA design and development. The flexibility of the system allows for tailoring the accelerator output to specific application needs by simply changing the objective function. This opens up opportunities to explore new experimental parameters and configurations to potentially advance LWFA capabilities. The success of this automated optimization paves the way for future applications, including the development of advanced diagnostics and the optimization of complex, multi-stage LWFA systems.

This study presented a fully automated laser-plasma accelerator controlled by a Bayesian optimization algorithm. This method efficiently optimized electron and X-ray beams by adjusting six laser and plasma parameters simultaneously, outperforming traditional methods and revealing subtle correlations between parameters. This approach facilitates the rapid optimization of complex systems and provides valuable physical insights. Future work could focus on extending this approach to more complex LWFAs and exploring its applications in other areas of accelerator physics and plasma science.

While the study successfully demonstrated the effectiveness of Bayesian optimization for LWFA control, some limitations should be acknowledged. The shot-to-shot variations in laser parameters (pulse energy, duration, and focus position) influenced the optimization results. However, the Bayesian approach robustly identified optima despite these fluctuations. Future implementation on next-generation laser systems with improved stability will likely yield even more precise control and optimization. Furthermore, the study focused on a specific LWFA configuration. The generalizability of this approach to other LWFA designs and operating regimes requires further investigation.