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.

An important limit for energy gain in laser-plasma wakefield accelerators is the dephasing length, after which the electron beam reaches the decelerating region of the wakefield and starts to decelerate. Here, we propose to manipulate the phase of the electron beam in the wakefield, in order to bring the beam back into the accelerating region, hence increasing the final beam energy. This rephasing is operated by placing an upward density step in the beam path. In a first experiment, we demonstrate the principle of this technique using a large energy spread electron beam. Then, we show that it can be used to increase the energy of monoenergetic electron beams by more than 50%.

Laser wakefield acceleration (LWFA) and its particle-driven counterpart, particle or plasma wakefield acceleration (PWFA), are commonly treated as separate, though related, branches of high-gradient plasma-based acceleration. However, novel proposed schemes are increasingly residing at the interface of both concepts where the understanding of their interplay becomes crucial. Here, we present a comprehensive study of this regime, which we may term laser-plasma wakefields. Using datasets of hundreds of shots, we demonstrate the influence of beam loading on the spectral shape of electron bunches. Similar results are obtained using both 100-TW-class and few-cycle lasers, highlighting the scale invariance of the involved physical processes. Furthermore, we probe the interplay of dual electron bunches in the same or in two subsequent plasma periods under the influence of beam loading. We show that, with decreasing laser intensity, beam loading transitions to a beam-dominated regime, where the first bunch acts as the main driver of the wakefield. This transition is evidenced experimentally by a varying acceleration of a low-energy witness beam with respect to the charge of a high-energy drive beam in a spatially separate gas target. Our results also present an important step in the development of LWFA using controlled injection in a shock front. The electron beams in this study reach record performance in terms of laser-to-beam energy transfer efficiency (up to 10%), spectral charge density (regularly exceeding $10\mathrm{pC}{\mathrm{MeV}}^{-1}$), and angular charge density (beyond $300\mathrm{pC}\mu {\mathrm{sr}}^{-1}$ at 220 MeV). We provide an experimental scaling for the accelerated charge per terawatt (TW) of laser power, which approaches 2 nC at 300 TW. With the expanding availability of petawatt-class (PW) lasers, these beam parameters will become widely accessible. Thus, the physics of laser-plasma wakefields is expected to become increasingly relevant, as it provides new paths toward low-emittance beam generation for future plasma-based colliders or light sources.

Plasma wakefield accelerators are capable of sustaining gigavolt-per-centimeter accelerating fields, surpassing the electric breakdown threshold in state-of-the-art accelerator modules by 3-4 orders of magnitude. Beam-driven wakefields offer particularly attractive conditions for the generation and acceleration of high-quality beams. However, this scheme relies on kilometer-scale accelerators. Here, we report on the demonstration of a millimeter-scale plasma accelerator powered by laser-accelerated electron beams. We showcase the acceleration of electron beams to 128 MeV, consistent with simulations exhibiting accelerating gradients exceeding 100 GV m⁻¹. This miniaturized accelerator is further explored by employing a controlled pair of drive and witness electron bunches, where a fraction of the driver energy is transferred to the accelerated witness through the plasma. Such a hybrid approach allows fundamental studies of beam-driven plasma accelerator concepts at widely accessible high-power laser facilities. It is anticipated to provide compact sources of energetic high-brightness electron beams for quality-demanding applications such as free-electron lasers.

Laser-plasma technology promises a drastic reduction of the size of high-energy electron accelerators. It could make free-electron lasers available to a broad scientific community and push further the limits of electron accelerators for high-energy physics. Furthermore, the unique femtosecond nature of the source makes it a promising tool for the study of ultrafast phenomena. However, applications are hindered by the lack of suitable lens to transport this kind of high-current electron beams mainly due to their divergence. Here we show that this issue can be solved by using a laser-plasma lens in which the field gradients are five order of magnitude larger than in conventional optics. We demonstrate a reduction of the divergence by nearly a factor of three, which should allow for an efficient coupling of the beam with a conventional beam transport line.

Recent progress in laser-driven plasma acceleration now enables the acceleration of electrons to several gigaelectronvolts. Taking advantage of these novel accelerators, ultrashort, compact, and spatially coherent x-ray sources called betatron radiation have been developed and applied to high-resolution imaging. However, the scope of the betatron sources is limited by a low energy efficiency and a photon energy in the 10 s of kiloelectronvolt range, which for example prohibits the use of these sources for probing dense matter. Here, based on three-dimensional particle-in-cell simulations, we propose an original hybrid scheme that combines a low-density laser-driven plasma accelerator with a high-density beam-driven plasma radiator, thereby considerably increasing the photon energy and the radiated energy of the betatron source. The energy efficiency is also greatly improved, with about 1% of the laser energy transferred to the radiation, and the $\gamma$-ray photon energy exceeds the megaelectronvolt range when using a 15 J laser pulse. This high-brilliance hybrid betatron source opens the way to a wide range of applications requiring MeV photons, such as the production of medical isotopes with photonuclear reactions, radiography of dense objects in the defense or industrial domains, and imaging in nuclear physics.