Laser-plasma physics has developed rapidly over the past few decades as lasers have become both more powerful and more widely available. Early experimental and numerical research in this field was dominated by single-shot experiments with limited parameter exploration. However, recent technological improvements make it possible to gather data for hundreds or thousands of different settings in both experiments and simulations. This has sparked interest in using advanced techniques from mathematics, statistics and computer science to deal with, and benefit from, big data. At the same time, sophisticated modeling techniques also provide new ways for researchers to deal effectively with situation where still only sparse data are available. This paper aims to present an overview of relevant machine learning methods with focus on applicability to laser-plasma physics and its important sub-fields of laser-plasma acceleration and inertial confinement fusion.

We study the electric field distribution and current emission in a miniaturized geometrical diode. Using Schwarz-Christoffel transformation, we calculate exactly the electric field inside a finite vacuum cathode-anode (A-K) gap with a single trapezoid protrusion on one of the electrode surfaces. It is found that there is a strong field enhancement on both electrodes near the protrusion, when the ratio of the A-K gap distance to the protrusion height $d/h<2.$ The calculations are spot checked against COMSOL simulations. We calculate the effective field enhancement factor for the field emission current, by integrating the local Fowler-Nordheim current density along the electrode surfaces. We systematically examine the electric field enhancement and the current rectification of the miniaturized geometrical diode for various geometric dimensions and applied electric fields.

The recent advent of deep artificial neural networks has resulted in a dramatic increase in performance for object classification and detection. While pre-trained with everyday objects, we find that a state-of-the-art object detection architecture can very efficiently be fine-tuned to work on a variety of object detection tasks in a high-power laser laboratory. In this paper, three exemplary applications are presented. We show that the plasma waves in a laser–plasma accelerator can be detected and located on the optical shadowgrams. The plasma wavelength and plasma density are estimated accordingly. Furthermore, we present the detection of all the peaks in an electron energy spectrum of the accelerated electron beam, and the beam charge of each peak is estimated accordingly. Lastly, we demonstrate the detection of optical damage in a high-power laser system. The reliability of the object detector is demonstrated over 1000 laser shots in each application. Our study shows that deep object detection networks are suitable to assist online and offline experimental analysis, even with small training sets. We believe that the presented methodology is adaptable yet robust, and we encourage further applications in Hz-level or kHz-level high-power laser facilities regarding the control and diagnostic tools, especially for those involving image data.

There has been growing interest both in studying high intensity ultrafast laser plasma interactions with adaptive control systems as well as using long wavelength driver beams. We demonstrate the coherent control of the dynamics of laser-wakefield acceleration driven by ultrashort (∼ 100 fs) mid-infrared (∼ 3.9 μm) laser pulses. The critical density at this wavelength is 7.3 × 10¹⁹ cm⁻³, which is achievable with an ordinary gas target system. Interactions between mid-infrared laser pulses and such near-critical-density plasma may be beneficial due to much higher absorption of laser energy. In addition, the normalized vector potential of the laser field a₀ increases with longer laser wavelength, lowering the required peak laser intensity to drive non-linear laser-wakefield acceleration. Here, MeV level, collimated electron beams with non-thermal, peaked energy spectra are generated. Optimization of electron beam qualities are realized through adaptive control of the laser wavefront. A genetic algorithm controlling a deformable mirror improves the electron total charge, energy spectra, beam pointing and stability at various plasma density profiles. Particle-in-cell simulations reveal that the optimal wavefront causes an earlier injection on the density up-ramp and thus higher energy gain as well as less filamentation during the interaction, which leads to the improvement in electron beam collimation and energy spectra.

We explore the applications of a variety of machine learning techniques in relativistic laser-plasma experiments beyond optimization purposes. With the trained supervised learning models, the beam charge of electrons produced in a laser wakefield accelerator is predicted given the laser wavefront change caused by a deformable mirror. Feature importance analysis using the trained models shows that specific aberrations in the laser wavefront are favored in generating higher beam charges, which reveals more information than the genetic algorithms and the statistical correlation do. The predictive models enable operations beyond merely searching for an optimal beam charge. The quality of the measured data is characterized, and anomaly detection is demonstrated. The model robustness against measurement errors is examined by applying a range of virtual measurement error bars to the experimental data. This work demonstrates a route to machine learning applications in a highly nonlinear problem of relativistic laser-plasma interaction for in-depth data analysis to assist physics interpretation.