I recall a selection of my results of the last 40 years. I first present a theoretical model of absorption of laser light by a plasma, with an emphasis on its dependence on the laser intensity and wavelength. A second topic concerns the nonlinear and nonlocal electron transport in steep temperature gradients. Thirdly, I present the work on the propagation of a short intense laser pulse in tenuous plasmas. Finally, I discuss the plasma expansion into a vacuum, in particular the structure of the ion front and the prediction of the maximum velocity attained by the ions in the expansion.

The continuing development of powerful laser systems has permitted to extend the interaction of laser beams with matter far into the relativistic domain in which extremely high electric and magnetic fields are generated. Thanks to these tremendous fields, that only plasma can support and sustain, new and compact approaches for producing energetic particle beams have been recently achieved. The incredible progress of these laser-plasma accelerators has allowed physicists to produce high quality beams of energetic radiation and particles. These beams have interesting properties such as shortness, brightness and spatial quality, and could lend themselves to applications in many fields, including medicine (radiotherapy, proton therapy, imaging), radiation biology (short-time-scale), chemistry (radiolysis), physics and material science (radiography, electron and photon diffraction), security (material inspection), and of course accelerator science. Stimulated by the advent of compact and powerful lasers, with moderate costs and high repetition rate, this research field has witnessed considerable growth in the past few years, and the promises of laser-plasma accelerators are in tremendous progress. The recent years in particular have seen spectacular progress in the acceleration of electrons and of ions, both in terms of energy and in terms of quality of the beams. To cite this article: V Malka, P Mora, C R. Physique 10 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All fights reserved.

This paper reviews recent experimental activity in the area of optimization, control, and application of laser-accelerated proton beams, carried out at the Rutherford Appleton Laboratory and the Laboratoire pour lpsilaUtilisation des Lasers Intenses 100 TW facility in France. In particular, experiments have investigated the role of the scale length at the rear of the plasma in reducing target-normal-sheath-acceleration acceleration efficiency. Results match with recent theoretical predictions and provide information in view of the feasibility of proton fast-ignition applications. Experiments aiming to control the divergence of the proton beams have investigated the use of a laser-triggered microlens, which employs laser-driven transient electric fields in cylindrical geometry, enabling to focus the emitted protons and select monochromatic beamlets out of the broad-spectrum beam. This approach could be advantageous in view of a variety of applications. The use of laser-driven protons as a particle probe for transient field detection has been developed and applied to a number of experimental conditions. Recent work in this area has focused on the detection of large-scale self-generated magnetic fields in laser-produced plasmas and the investigation of fields associated to the propagation of relativistic electron both on the surface and in the bulk of targets irradiated by high-power laser pulses.

The simulations of the coupling of an incident laser pulse to a capillary tube with a cone-shape entrance are presented. The examples of the perfect Gaussian laser pulses and the experimentally measured radial intensity distributions are studied in a vacuum capillary, as well as the excitation of the wakefield inside a gas-filled tube.

Through the time- and space-resolved interferometry of a short-pulse low-energy probe beam reflecting on the rear surface of a solid target irradiated on its front surface by a high-intensity laser, we have measured a very abrupt expansion of the target rear surface. The experiments were performed using the LULI 100-TW laser facility with a maximum of 10-20 J energy pulses of > 10 19 W ldr cm -2 intensity, wavelength of 1.053 mum irradiating Al targets. The detected phase changes, with a few micrometers spatial resolution and picosecond temporal resolution, are interpreted as induced by the cloud of fast electrons having propagated through the target and expanding into vacuum. The measurements have been performed using a laser-pulse duration of 320 fs and a laser energy of 20 J, varying the target thickness from 25, 14, and 9.4 mum. The experimental phase measurements are compared to simulations obtained by post-processing simulation data, run with a 1-D adiabatic plasma-expansion code. The comparison allows one to access, for the first time, to the dynamics of the density and temperature of laser-accelerated fast electrons in solid targets and expanding into vacuum. The same technique also allows one to have information regarding the cold electrons and the energy-partition dynamics.

Laser-accelerated ion sources have exceptional properties and could stimulate development of compact ion accelerators. For many applications beam control is an essential requirement. A new and interesting technique to control proton beam characteristics has been recently developed. It consists in using an ultrafast laser-triggered micro-lens, which provides simultaneous energy selection and focusing of the incoming ion beam and is tunable. Particle-in-cell simulations coupled with particle tracing are used to model the focusing and energy selection mechanisms, and to study the symmetry of the expanding plasma inside the micro-lens. The model developed is able to reproduce and explain the experimental results obtained at the Laboratoire pour l'Utilisation des Lasers Intenses in France.

Laser‐accelerated ion sources open new opportunities for ion beam generation and control, and could stimulate development of compact ion accelerators for many applications. The mechanisms of proton acceleration with solid targets have been intensively studied over the past years, and new target or laser setups are now needed to obtain even higher maximum proton energies. PIC simulations have shown that using ultra thin targets, the maximum proton energy can be greatly increased. The laser can pass through the target and heat target electrons more efficiently. Experiments were conducted to test the feasibility of ultra thin targets laser interaction. PIC simulations were performed and successfully compared to the experimental results. Recently, experiments have shown that a gaseous target can produce proton beams with characteristics comparable to those obtained with solid targets. PIC simulations were also used to study proton acceleration with an underdense target. The optimum thickness obtained corresponds to the thickness where the laser absorption and transmission are equal, and depends greatly on laser and target parameters. The plasma hot electron temperature has also been found to depend on both laser and target parameters. We developed a simple model for the scaling of the optimum thickness for proton acceleration on target and laser parameters.

In the last few years, intense research has been conducted on laser‐accelerated ion sources and their applications. These sources have exceptional properties, i.e. high brightness and high spectral cut‐oft high directionality and laminarity, short burst duration. These proton sources open new opportunities for ion beam generation and control, and could stimulate development of compact ion accelerators for many applications. We have studied the variations of the proton acceleration characteristic time with target and laser parameters. We used these variations to correct one of the model recently developed to predict maximum energies of laser‐accelerated protons for low energy, short duration laser pulses. We have also developed an ultra‐fast laser‐triggered micro‐lens that allows tunable control of the beam divergence as well as energy selection, therefore solving two of the major problems that these proton beams were facing. We used PIC simulations to explain the focusing and energy selection mechanisms, and to study the symmetry of the expanding plasma inside the cylinder.

The interaction of high‐intensity laser pulses with matter releases instantaneously ultra‐large currents of highly energetic electrons, leading to the generation of highly‐transient, large‐amplitude electric and magnetic fields. We report results of recent experiment in which such charge dynamics have been studied by using proton probing techniques able to provide maps of the electrostatic fields with high spatial and temporal resolution. The dynamics of ponderomotive channelling in underdense plasmas have been studied in this way, as also the processes of Debye sheath formation and MeV ion front expansion at the rear of laser‐irradiated thin metallic foils. An application employing laser‐driven impulsive fields for energy‐selective ion beam focusing is also presented.

The propagation of an intense (up to 10(17) W/cm(2)) and short laser pulse (down to 40 fs) is studied through a well characterized high density Ar cluster jet obtained at the output of a supersonic nozzle. The x-ray emission from the irradiated clusters is measured as a function of the focusing depth inside the jet, with a spatial resolution of the emitting plasma. A strong refraction of the laser pulse is observed, limiting the interaction at the entrance of the jet and decreasing the effective laser intensity on clusters. Calculations indicate that it is due to the ionization of the residual gaseous phase present in the cluster jet. As the focal volume is modified, this effect should be considered for any quantitative analysis of the laser-cluster interaction.

The interaction of an intense beam (1Ore < / < l020Wcm2; with moderately dense plasmas has been investigated by using theoretical analysis as well as numerical simulations. The parametric instabilities of a plane intense light wave have been theoretically studied in this strongly coupled case, with a particular emphasis on filamentation and the generalization of the TPD instability. Then these results are used to discuss numerical simulations. A 2D PIC code is used to study the propagation of picosecond pulses. The theoretical conclusions may be compared with present experimental results. These experiments show that the plasma strongly absorbs the intense radiation for densities where it would be expected to be transparent or reflective via Raman instabilities. Moreover, very high electron temperatures are achieved and multi-Mev particles are generated. These behaviors result from the strong non-linear interaction of the radiation with the plasma.

Channeling of intense optical fields is an important challenge, with possible applications in the context of laser plasma accelerators or X-rays lasers. It has been shown in recent papers that self-channeled pulses are subject to severe instabilities of the Raman type which modulate the laser pulse and erode its tail [1-5]. The simulations of Refs. 1-4 were based on laser-plasma fluid models corresponding to a cold plasma, which prevents from treating situations where the plasma oscillations reach the wavebreaking limit. In addition the models contain a mathematical singularity at zero plasma electron density which prevents its use when the electrons are totally expelled from the axis of the laser propagation (electron cavitation). Such features are strong limitations of the fluid models in the high intensity regime.

It is shown that the non-Maxwellian heating by inverse bremsstrahlung which results in a truncation of the tail of the electron-distribution function is responsible for a reduction of the thermal conductivity in a smooth temperature gradient by a factor of 3 to 4 from the Spitzer-H\"arm conductivity. In a steep temperature gradient, the reduction is still a factor of about 1.5 from the recent nonlinear theories based on a Maxwellian electron-distribution source.

By computing the trajectories of fast electrons in toroidal magnetic fields similar to those measured experimentally, one can reproduce the main results of recent high-flux laser experiments on plane targets: the amount of fast-ion losses, the lateral transport by hot electrons leading to a ring structure, and the decrease of the fraction of absorbed energy coupled inside the focal spot when the laser pulse duration increases.

The Boltzmann equilibrium for electrons has been an ad-hoc assumption of previous work about self-similar plasma expansion in vacuum. Using Boltzmann’s relation, one finds a linear electrostatic potential as a solution of the self-similar expansion. It is first shown that in such a potential, the electron behavior is exactly solvable. As a result, one finds that the exact electron density differs substantially from the Boltzmann equilibrium for moderate values of the self-similar parameter. The complete calculations of the self-similar expansion, without any assumption about the equation of state of the electrons, is presented. It is shown, in particular, that half the electron density depletion in logarithmic units is compensated for by the self-consistent modification of the electric potential. Finally, the effect is analyzed in terms of energy exchange between the electrons and the ions in the expansion.