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This article presents the use of artificial neural networks (ANN) to predict nonlocal heat flux transport within hydrodynamic simulations. Several cases of laser driven ablation of a plastic target are considered. The database for the ANN training phase is built using the transport module of the hydrodynamic code CHIC. It covers a range of parameters characteristic of laser experiments in the context of high-energy-density physics. Results show that an ANN can efficiently replace a module of nonlocal transport in one- and two-dimensional hydrodynamic simulations, with an error less than 3% in a radius of 0.5μm and an average computation gain of a factor 433 in two dimensions.

This work consists of the validation of a new Grid Based Boltzmann Solver (GBBS) conceived for the description of the transport and energy deposition by energetic particles for radiotherapy purposes. The entropic closure and a compact mathematical formulation allow our code (M1) to calculate the delivered dose with an accuracy comparable to the Monte-Carlo (MC) codes with a computational time that is reduced to the order of few minutes without any special processing power requirement. A validation protocol with heterogeneity inserts has been defined for different photon sources. The comparison with the MC calculated depth-dose curves and transverse profiles of the beam at different depths shows an excellent accuracy of the M1 model.

One of the big challenges of the emerging MRI-guided radiotherapy is the prediction of an external magnetic field effect on the deposited dose induced by a beam of charged particles. In this paper, we present the results of the implementation of the Lorentz force in the deterministic M1 model. The validation of our code is performed by comparisons with the Monte-Carlo code FLUKA. The relevant examples show a significant modification of the shape of dose deposition volume induced by the external magnetic field in presence of heterogeneities. A gamma-index analysis 3%/3 mm shows a good agreement of our model with FLUKA simulations.

A new deterministic method for calculating the dose distribution in the electron radiotherapy field is presented. The aim of this work was to validate our model by comparing it with the Monte Carlo simulation toolkit, GEANT4. A comparison of the longitudinal and transverse dose deposition profiles and electron distributions in homogeneous water phantoms showed a good accuracy of our model for electron transport, while reducing the calculation time by a factor of 50. Although the Bremsstrahlung effect is not yet implemented in our model, we propose here a method that solves the Boltzmann kinetic equation and provides a viable and efficient alternative to the expensive Monte Carlo modeling.

A new type of proton acceleration stemming from large-scale gradients, low-density targets, irradiated by an intense near-infrared laser is observed. The produced protons are characterized by high-energies (with a broad spectrum), are emitted in a very directional manner, and the process is associated to relaxed laser (no need for high-contrast) and target (no need for ultra-thin or expensive targets) constraints. As such, this process appears quite effective compared to the standard and commonly used Target Normal Sheath Acceleration technique (TNSA), or more exploratory mechanisms like Radiation Pressure Acceleration (RPA). The data are underpinned by 3D numerical simulations which suggest that in these conditions a Low Density Collisionless Shock Acceleration (LDCSA) mechanism is at play, which combines an initial Collisionless Shock Acceleration (CSA) to a boost procured by a TNSA-like sheath field in the downward density ramp of the target, leading to an overall broad spectrum. Experiments performed at a laser intensity of 1020 W/cm2 show that LDCSA can accelerate, from ~1% critical density, mm-scale targets, up to 5 × 109 protons/MeV/sr/J with energies up to 45(±5) MeV in a collimated (~6° half-angle) manner.

International audience; We experimentally investigate the fast ($\atop\sim}$10 ps into a $\approx$ 140 Mbar blast wave, according to hydrodynamic simulations, consistent with our measurements. These experimental and numerical findings pave the way to a short-pulse-laser-based platform dedicated to high-energy-density physics studies.

Laser-produced high-energy-density plasmas may contain strong magnetic fields that affect the energy transport, which can be nonlocal. Models which describe the magnetized nonlocal transport are formally complicated and based on many approximations. This paper presents a more straightforward approach to the description of the electron transport in this regime, based on the extension of a reduced entropic model. The calculated magnetized heat fluxes are compared with the known asymptotic limits and applied for studying of a magnetized nonlocal plasma thermalization.

Collimated transport of ultrahigh intensity electron current was observed in cold and in laser-shocked vitreous carbon, in agreement with simulation predictions. The fast electron beams were created by coupling high-intensity and high-contrast laser pulses onto copper-coated cones drilled into the carbon samples. The guiding mechanism---observed only for times before the shock breakout at the inner cone tip---is due to self-generated resistive magnetic fields of $\ensuremath{\sim}0.5--1\text{ }\text{ }\mathrm{kT}$ arising from the intense currents of fast electrons in vitreous carbon, by virtue of its specific high resistivity over the range of explored background temperatures. The spatial distribution of the electron beams, injected through the samples at different stages of compression, was characterized by side-on imaging of hard x-ray fluorescence.

Introduction The majority of patients affected by cancer are nowadays treated by radiotherapy, which consists in delivering a homogeneous dose with energetic particles. Magnetic Resonance Imaging (MRI)-guided radiotherapy shows precisely the tumor position in real time and allows to direct the photon beams to the tumor while sparing organs at risks. Our work consists in the validation of a new model developped to simulate the energy deposition of the particles used in radiotherapy (electrons, photons and protons) in the presence of strong magnetic field, within human tissues, and its adaptation to this new technology. Material and methods This model is based on a kinetic entropic closure of the linearized Boltzmann equation [1] , which describes the transport of energetic particles in the matter. This equation takes a lot of computation time to be solved due to the high number of variables. To simplify this, we replace fluences by angular moments, which allows getting rid of the angular variables and improve the calculation time. We obtain a set of angular moments equations, and we close this set using the Boltzmann’s principle of entropy maximization on the two first equations of the set. This model has an accuracy comparable to references Monte-Carlo (MC) codes [2] (Geant4, MCNPx, Penelope), and is less time-consuming than these ones. We added the Lorentz force into our code to study the influence of a magnetic field on the dose deposition, and compared it to the reference full MC code FLUKA. To further validate our model, we have carried out an experimental campaign in which we irradiated a composition of materials of different mass densities, with 6 and 18 MV photon beams of a Varian Clinac 21Ex accelerator, without and with the influence of a 0.87 T magnetic field of amplitude induced by a permanent magnet. Results We show a good agreement between our model and the FLUKA code ( Fig. 1 ). We highlight the effects that occur on the propagation of particles in the matter in presence of a magnetic field of a few Tesla. Indeed, it modifies the dose deposition by shifting the deposition of energy, leading to an increased diffusion depending on the orientation of the magnetic field. Moreover, it also leads to an increase or decrease of the dose deposited at the interfaces between materials depending on their difference between mass densities. The results of our experiments lead to the same conclusions. These effects have to be taken into account in order to prevent creation of hot spots or a spread of energy distribution in a human body, within computation times compatible with the clinical environment. Conclusion Our model is a good candidate for future Treatment Planning Systems since it allows a faster and efficient way to plan a viable treatment for a patient in presence of strong magnetic fields. A magnetic field modifies the profile of the dose deposition such as it has to be taken into account in calculations to prevent the dramatic changes which occur at interfaces between media of different density. This work takes place in the framework of POPRA (Programme Optique Physique et Radiotherapie en Aquitaine), which involves several laboratories around problematics on the topic of cancer treatment.

This paper describes the results of a series of experiments conducted with the PALS laser at intensities of interest for the shock ignition approach to inertial fusion. In particular, we addressed the generation of hot electrons (HE) (determining their average energy and number), as well as the parametric instabilities which are producing them. In addition, we studied the impact of HE on the formation and dynamics of strong shocks.

Introduction This work proposes a completely new Grid-Based Boltzmann Solver (GBBS) developed for the transport and energy deposition by energetic particles. Its entropic closure and mathematical formulation allow our entropic model to calculate the delivered dose with an accuracy comparable to Monte Carlo (MC) codes with a computational time that is reduced to the order of few seconds without any special processing power requirement. Methods In contrast to discrete ordinates angular discretization methods, such as Acuros®, our method is based on a reduced number of moment equations closed with Boltzmann’s H-theorem. Keeping a good accuracy of calculations, the algorithm can simulate different treatment techniques such as the external radiotherapy even in presence of magnetic field [1] , [2] (e.g., MRI-guided radiotherapy), brachytherapy or intra-operative radiation therapy. The first validation step consists in simulating dose distributions in complex numerical phantoms including a large number of heterogeneity shapes such as bone, lung and air. For both brachytherapy and external beam radiotherapy, simulations based on CT scan, using the real phase-space of the source, have been performed. The entropic model is validated by a direct comparison with the reference MC code PENELOPE. Results The code is capable of calculating 3D dose distributions with 1 mm3voxels without statistical uncertainties in few seconds instead of several minutes like PENELOPE. In brachytherapy applications the dose distributions significantly differ from those calculated with the TG-43 approximations, thanks to its capability to account for inhomogeneities and strong density gradients. Moreover, for both applications the code shows an excellent agreement with PENELOPE within the 1%/1 mm gamma-index criterion. Conclusions In the comparison with the MC results the excellent accuracy of the model is demonstrated. Thanks to its reduced computational time and its accuracy, this model is a promising candidate to become a real-time dose calculation algorithm.

Fast-electron beam stopping mechanisms in media ranging from solid to warm dense matter have been investigated experimentally and numerically. Laser-driven fast electrons have been transported through solid Al targets and shock-compressed Al and plastic foam targets. Their propagation has been diagnosed via rear-side optical self-emission and Kα X-rays from tracer layers. Comparison between measurements and simulations shows that the transition from collision-dominated to resistive field-dominated energy loss occurs for a fast-electron current density ~5 × 1011 A cm−2. The respective increases in the stopping power with target density and resistivity have been detected in each regime. Self-guided propagation over 200μm has been observed in radially compressed targets due to ~1kT magnetic fields generated by resistivity gradients at the converging shock front.

International audience; The knowledge of the absolute energy distributions of the particles emitted from a clinical accelerator is important for the evaluation of Monte Carlo simulations developed for treatment planning. In this paper, an original approach is presented which allows to measure the absolute energy distribution of the electron beam delivered by a Varian 21Ex medical accelerator. The electron beam was characterized at the isocenter with calibrated image plates covering the exit window of a magnetic spectrometer. The characteristics of the electron beam emitted from an effective source have been inferred from the measurements using the Geant4 Monte Carlo code. The contribution of direct electrons to the absolute depth-dose curve in a water phantom is estimated.

The dynamics of self-generated magnetic B-fields produced following the interaction of a high contrast, high intensity (I > 1019W cm-2) laser beam with thin (3 μm thick) solid (Al or Au) targets is investigated experimentally and numerically. Two main sources drive the growth of B-fields on the target surfaces. B-fields are first driven by laser-generated hot electron currents that relax over ∼10-20 ps. Over longer timescales, the hydrodynamic expansion of the bulk of the target into vacuum also generates B-field induced by non-collinear gradients of density and temperature. The laser irradiation of the target front side strongly localizes the energy deposition at the target front, in contrast to the target rear side, which is heated by fast electrons over a much larger area. This induces an asymmetry in the hydrodynamic expansion between the front and rear target surfaces, and consequently the associated B-fields are found strongly asymmetric. The sole long-lasting (>30 ps) B-fields are the ones growing on the target front surface, where they remain of extremely high strength (∼8-10 MG). These B-fields have been recently put by us in practical use for focusing laser-accelerated protons [B. Albertazzi et al., Rev. Sci. Instrum. 86, 043502 (2015)]; here we analyze in detail their dynamics and structure.

An accurate and rapid kinetic model describing the collisional transport of particles is presented. It is derived from the Fokker-Planck equation and involves an angular closure in the phase space leading to a set of hyperbolic equations for the moments of the distribution function evolving in time, space and energy. This method provides an alternative to the prohibitive cost of a direct solution to the full kinetic equation. Moreover, it is exact for the cases of collimated beams and the quasi-isotropic distributions. It can be approximated with the usual numerical schemes of the non-linear hyperbolic analysis. This model has features that are required to simulate the electron or ion transport for the inertial confinement fusion and the dose deposition for radiation therapy of cancers.

The European High Power laser Energy Research (HiPER) project aims at demonstrating the feasibility of high gain inertial confinement fusion (ICF) using the fast ignitor approach. A baseline target has been recently developed by Atzeni et al. [Phys. Plasmas 14, 052702 (2007)]. The radiative transport have a minor effect on the peak areal density but decreased by 20% the peak density. We have found that with 95 kJ of absorbed laser energy one can assemble the fuel with a peak density around 500 g/cm3 and a peak areal density of 1.2 g/cm2. This implies a total target gain of about 60.

Hydrodynamic simulations of high-energy-density plasmas require a detailed description of energy fluxes. For low and intermediate atomic number materials, the leading mechanism is the electron transport, which may be a nonlocal phenomenon requiring a kinetic modeling. In this paper, we present and test the results of a nonlocal model based on the first angular moments of a simplified Fokker-Planck equation. This multidimensional model is closed thanks to an entropic relation (the Boltzman H-theorem). It provides a better description of the electron distribution function, thus enabling studies of small scale kinetic effects within the hydrodynamic framework. Examples of instabilities of electron plasma and ion-acoustic waves, driven by the heat flux, are presented and compared with the classical formula.

We present a model of nonlocal transport for multidimensional radiation magneto hydrodynamic codes. In laser produced plasmas, it is now believed that the heat transfert can be strongly modified by the nonlocal nature of the electron conduction. Nevertheless other mechanisms as self generated magnetic fields may affect heat transport too. The model described in this work aims at extending the formula of G. Schurtz, Ph. Nicolai and M. Busquet [I] to magnetized plasmas. A system of nonlocal equations is derived from kinetic equations with self-consistent electric and magnetic fields. These equations are analyzed and applied to a physical problem in order to demonstrate the main features of the model.

Controlling the divergence of laser-driven fast electrons is compulsory to meet the ignition requirements in the fast ignition inertial fusion scheme. It was shown recently that using two consecutive laser pulses one can improve the electron-beam collimation. In this paper we propose an extension of this method by using a sequence of several laser pulses with a gradually increasing intensity. Profiling the laser-pulse intensity opens a possibility to transfer to the electron beam a larger energy while keeping its divergence under control. We present numerical simulations performed with a radiation hydrodynamic code coupled to a reduced kinetic module. Simulation with a sequence of three laser pulses shows that the proposed method allows one to improve the efficiency of the double pulse scheme at least by a factor of 2. This promises to provide an efficient energy transport in a dense matter by a collimated beam of fast electrons, which is relevant for many applications such as ion-beam sources and could present also an interest for fast ignition inertial fusion.

Shock ignition concept is a promising approach to inertial confinement fusion that may allow obtaining high fusion energy gains with the existing laser technology. However, the spike driving laser intensities in the range of 1--10 PW/cm${}^{2}$ produces the energetic electrons that may have a significant effect on the target performance. The hybrid numerical simulations including a radiation hydrodynamic code coupled to a rapid Fokker-Planck module are used to asses the role of hot electrons in the shock generation and the target preheat in the time scale of 100 ps and spatial scale of 100 $\ensuremath{\mu}$m. It is shown that depending on the electron energy distribution and the target density profile the hot electrons can either increase the shock amplitude or preheat the imploding shell. In particular, the exponential electron energy spectrum corresponding to the temperature of 30 keV in the present HiPER target design preheats the deuterium-tritium shell and jeopardizes its compression. Ways of improving the target performance are suggested.

International audience; It was recently shown that a promising way to accelerate protons in the forward direction to high energies is to use under-dense or near-critical density targets instead of solids. Simulations have revealed that the acceleration process depends on the density gradients of the plasma target. Indeed, under certain conditions, the most energetic protons are predicted to be accelerated by a collisionless shock mechanism that significantly increases their energy. We report here the results of a recent experiment dedicated to the study of longitudinal ion acceleration in partially exploded foils using a high intensity (similar to 5 x 10(18) W/cm(2)) picosecond laser pulse. We show that protons accelerated using targets having moderate front and rear plasma gradients (up to similar to 8 mu m gradient length) exhibit similar maximum proton energy and number compared to proton beams that are produced, in similar laser conditions, from solid targets, in the well-known target normal sheath acceleration regime. Particle-In-Cell simulations, performed in the same conditions as the experiment and consistent with the measurements, allow laying a path for further improvement of this acceleration scheme. (C) 2014 AIP Publishing LLC.

Resume Nous appliquons ici le principe de minimisation d'entropie a l'equation de transfert radiatif. Comme dans le cadre des equations cinetiques classiques, nous obtenons a l'aide de ce principe une hierarchie de systemes aux moments fermes. Chaque systeme de la hierarchie est hyperbolique, possede un flux limite par la vitesse de la lumiere et dissipe localement l'entropie. Nous analysons plus particulierement les proprietes du premier systeme de la hierarchie.

Resume On demontre le principe d'entropie minimum sur un ensemble de vitesses discret. On utilise ce resultat pour definir des modeles a vitesses discretes de l'equation BGK et des systemes aux moments de Levermore. Enfin, on demontre quelques proprietes essentielles de ces modeles.

A high order practical scheme for a model of nonlocal transport is here proposed to be used in multidimensional radiation hydrodynamic codes. The various investigations on electron heat transport in the Inertial Confinement Fusion (ICF) context, have shown the limits of the classical local SpitzerHarm heat flow model [1]. Monodimensionnal accurate models lying on convolution formulations have been proposed by Luciani and Mora [2] and improved by many other authors [3]. Schurtz, Nicolai and Busquet [4] purposed a practical multidimensional extension of the original convolution formula. The numerical implementation of non local models can be usually very delicate since an implicit resolution is considered. It is of use to force a diffusive formulation by introducing an ill-posed artificial nonlocal conductivity [3]. This choice can lead to mathematical and physical prejudicial anomalies (negative conductivity). An stability analysis leads us to consider an alternative for the implicit discretization of the non local operator. These remarks then led us to naturally set up a high order scheme [5] to solve the nonlocal problems on strongly deformed meshes. The use of such scheme is indeed essential to give a good description of the ablation front and of the hot spot induced by the implosion of the target during a nuclear fusion experience.

Summary form only given. One major issue to address in Inertial Confinement Fusion (ICF) is the detailed description of the kinetic transport of laser generated fast electrons in the time and space scales of the hydrodynamic evolution of the imploded target. We have developed, at CELIA, a fast reduced kinetic model for relativistic electrons transport based on the angular moments of the relativistic Fokker-Planck equation, the M1 model1. This model takes into account the slowing down of fast electrons through collisions with plasma electrons (free and bounded), plasmons and the elastic scattering of fast electrons on plasma ions and electrons. The self-consistent magnetic and electric fields are computed thanks to a generalized Ohm law. This module has been implemented into the 2D radiation hydrodynamic code CHIC2. The M1 model is used as well as for the Fast Ignition (FI) than for the Shock Ignition (SI) schemes. A recent experiment of relativistic electrons transport through Aluminum foils is analyzed thanks to this multi-scales tool. Because of its computing speed, various initial configurations have been tested to reproduce experimental data. In addition, due to its structure, the effects of electric and magnetic fields can easily be highlighted and so the resistive fast electrons losses are directly compared to the collisional losses. Concerning Shock Ignition scheme, it is shown that the energy transfer by fast electrons from the corona to the compressed shell is a important mechanism in the creation of ablation pressure. A 30 keV energy electron beam of 2 - 5 PW/cm2 energy flux may create a pressure amplitude of more than 300 Mbar within few tens of ps in a precompressed solid material3. The dynamics of the ablation layer and the shock evolution are also presented in realistic configurations.

Inertial confinement fusion and specifically shock ignition involve temperatures and temperature gradients for which the classical Spitzer-Harm thermal conduction breaks down and a non-local operator is required. In this article, two non-local electron thermal conduction models are tested against kinetic Vlasov-Fokker-Planck simulations. Both models are shown to reproduce the main features of thermal heat front propagation at kinetic timescales. The reduction of the thermal conductivity as a function of the scalelength of the temperature gradient is also recovered. Comparisons at nanosecond timescales show that the models agree on the propagation velocity of the heat front, but major differences appear in the thermal precursor.

The role of self generated magnetic fields in the transport of a heat wave following a nanosecond laser irradiation of a solid target is investigated. Magnetic fields are expected to localize the electron carrying the heat flux but at the same time are affected in their evolution by the heat flux itself. We performed simultaneous measurements of heat wave propagation velocity within the target and magnetic fields developing on the target surface. These were compared to results obtained by numerical magneto-hydrodynamic modeling, including self-generated B fields. The comparison shows that longitudinal heat flow is overestimated in the simulations. Similarly, but most notably, the radial expansion of the magnetic fields is underestimated by the modeling. The two are likely linked, the more pronounced radial drift of B-fields induces a rotation of heat flux in the radial direction, and corresponding longitudinal heat flux inhibition. This suggests the need for improving present modeling of self-generated magnetic fields evolution in high power laser-matter interaction.

The paper describes the preparation of the short-pulse high-energy laser PETAL that will be coupled to the French megajoule laser (LMJ) of CEA. The LMJ/PETAL facility will be opened to academic access for the international research community. In parallel diagnostics are being developed within the PETAL project and many physical problems are being addressed ranging from the study of the problems of radiation generation and activation issues to the problem of generation of large amplitude electromagnetic pulses.

An intense beam of high energy electrons may create extremely high pressures in solid density materials. An analytical model of ablation pressure formation and shock wave propagation driven by an energetic electron beam is developed and confirmed with numerical simulations. In application to the shock-ignition approach in inertial confinement fusion, the energy transfer by fast electrons may be a dominant mechanism of creation of the igniting shock wave. An electron beam with an energy of 30 keV and energy flux $2--5\text{ }\text{ }\mathrm{PW}/{\mathrm{cm}}^{2}$ can create a pressure amplitude more than 300 Mbar for a duration of 200--300 ps in a precompressed solid material.

Demonstrating ignition and net energy gain in the near future on MJ-class laser facilities will be a major step towards determining the feasibility of Inertial Fusion Energy (IFE), in Europe as in the United States. The current status of the French Laser MégaJoule (LMJ) programme, from the laser facility construction to the indirectly driven central ignition target design, is presented, as well as validating experimental campaigns, conducted, as part of this programme, on various laser facilities. However, the viability of the IFE approach strongly depends on our ability to address the salient questions related to efficiency of the target design and laser driver performances. In the overall framework of the European HiPER project, two alternative schemes both relying on decoupling target compression and fuel heating—fast ignition (FI) and shock ignition (SI)—are currently considered. After a brief presentation of the HiPER project's objectives, FI and SI target designs are discussed. Theoretical analysis and 2D simulations will help to understand the unresolved key issues of the two schemes. Finally, the on-going European experimental effort to demonstrate their viability on currently operated laser facilities is described.

Electrostatic (E) fields associated with the interaction of a well-controlled, high-power, nanosecond laser pulse with an underdense plasma are diagnosed by proton radiography. Using a current 3D wave propagation code equipped with nonlinear and nonlocal hydrodynamics, we can model the measured E-fields that are driven by the laser ponderomotive force in the region where the laser undergoes filamentation. However, strong fields of up to 110 MV/m measured in the first millimeter of propagation cannot be reproduced in the simulations. This could point to the presence of unexpected strong thermal electron pressure gradients possibly linked to ion acoustic turbulence, thus emphasizing the need for the development of full kinetic collisional simulations in order to properly model laser-plasma interaction in these strongly nonlinear conditions., 12 pages, 4 figures, submitted to Physics of Plasmas

International audience; Attraction and fusion between co-propagating light beams, mutually coherent or not, can take place in nonlinear media as a result of the beam power modifying the refractive index of the medium. In the context of high-power light beams, induced modifications of the beam patterns could potentially impact many topics, including long-range laser propagation, the study of astrophysical colliding blast waves and inertial confinement fusion. Here, through experiments and simulations, we show that in a fully ionized plasma, which is a nonlinear medium, beam merging can take place for high-power and mutually incoherent beams that are initially separated by several beam diameters. This is in contrast to the usual assumption that this type of interaction is limited to beams separated by only one beam diameter. This effect, which is orders of magnitude more significant than Kerr-like nonlinearity in gases, demonstrates the importance of potential cross-talk amongst multiple beams in plasma.

This paper describes the first experimental demonstration of the guiding of a relativistic electron beam in a solid target using two co-linear, relativistically intense, picosecond laser pulses. The first pulse creates a magnetic field which guides the higher current fast electron beam generated by the second pulse. The effects of intensity ratio, delay, total energy and intrinsic pre-pulse are examined. Thermal and K{\alpha} imaging showed reduced emission size, increased peak emission and increased total emission at delays of 4 - 6 ps, an intensity ratio of 10 : 1 (second:first) and a total energy of 186 J. In comparison to a single, high contrast shot, the inferred fast electron divergence is reduced by 2.7 times, while the fast electron current density is increased by a factor of 1.8. The enhancements are reproduced with modelling and are shown to be due to the self-generation of magnetic fields. Such a scheme could be of considerable benefit to fast ignition inertial fusion.

In the last few years, intense research has been conducted on laser-accelerated ion sources and their applications. Recently, experiments have shown that a gaseous target can produce proton beams with characteristics comparable to those obtained with solid targets. In underdense laser proton acceleration, volume effects dominate the acceleration, while in target normal sheath acceleration, the electric field value is directly related to the electron surface density. Using Particle-In-Cell simulations, we have studied in detail the effect of an underdense density gradient on proton acceleration with high intensity lasers. Underdense laser ion acceleration strongly depends on the length, the shape and the amplitude of the density gradient and on the laser pulse shape. The accelerated proton beam characteristics in the shock-like regime are very promising.

Recently, a European collaboration has proposed the High Power Laser Energy Research (HiPER) facility, with the primary goal of demonstrating laser driven inertial fusion fast ignition. HiPER is expected to provide 250 kJ in multiple, 3ω (wavelength λ = 0.35 µm), nanosecond beams for compression and 70 kJ in 10–20 ps, 2ω beams for ignition. The baseline approach is fast ignition by laser-accelerated fast electrons; cones are considered as a means to maximize ignition laser–fuel coupling. Earlier studies led to the identification of an all-DT shell, with a total mass of about 0.6 mg as a reference target concept. The HiPER main pulse can compress the fuel to a peak density above 500 g cm−3 and an areal density ρR of about 1.5 g cm−2. Ignition of the compressed fuel requires that relativistic electrons deposit about 20 kJ in a volume of radius of about 15 µm and a depth of less than 1.2 g cm−2. The ignited target releases about 13 MJ. In this paper, additional analyses of this target are reported. An optimal irradiation pattern has been identified. The effects on fuel compression of the low-mode irradiation non-uniformities have been studied by 2D simulations and an analytical model. The scaling of the electron beam energy required for ignition (versus electron kinetic energy) has been determined by 2D fluid simulations including a 3D Monte Carlo treatment of relativistic electrons, and agrees with a simple model. Integrated simulations show that beam-induced magnetic fields can reduce beam divergence. As an alternative scheme, shock ignition is studied. 2D simulations have addressed optimization of shock timing and absorbed power, means to increase laser absorption efficiency and the interaction of the igniting shocks with a deformed fuel shell.

Ultra-intense lasers can nowadays routinely accelerate kiloampere ion beams. These unique sources of particle beams could impact many societal (e.g., proton-therapy or fuel recycling) and fundamental (e.g., neutron probing) domains. However, this requires overcoming the beam angular divergence at the source. This has been attempted, either with large-scale conventional setups or with compact plasma techniques that however have the restriction of short (50 ps), thermoelectric multi-megagauss surface magnetic (B)-fields, compact capturing, and focusing of a diverging laser-driven multi-MeV ion beam can be achieved over a wide range of ion energies in the limit of a 5° acceptance angle.

Correct modeling of the electron-energy transport is essential for inertial confinement fusion target design. Various transport models have been proposed in order to extend the validity of a hydrodynamical description into weakly collisional regimes, taking into account the nonlocality of the electron transport combined with the effects of self-generated magnetic fields. We have carried out new experiments designed to be highly sensitive to the modeling of the heat flow on the Ligne d'Integration Laser facility, the prototype of the Laser Megajoule. We show that two-dimensional hydrodynamic simulations correctly reproduce the experimental results only if they include both the nonlocal transport and magnetic fields.

A hybrid reduced model for relativistic electron beam transport based on the angular moments of the relativistic kinetic equation with a special closure is presented. It takes into account collective effects with the self-generated electromagnetic fields as well as collisional effects with the slowing down of the relativistic electrons by plasmons, bound and free electrons and their angular scattering on both ions and electrons. This model allows for fast computations of relativistic electron beam transport while describing their energy distribution evolution. Despite the loss of information concerning the angular distribution of the electron beam, the model reproduces analytical estimates in the academic case of a monodirectional and monoenergetic electron beam propagating through a warm and dense plasma and hybrid particle-in-cell simulation results in a realistic laser-generated electron beam transport case.

The paper describes the preparation of the short-pulse high-energy laser PETawatt Aquitaine Laser (PETAL), which will be coupled to the Laser Megajoule (LMJ) laser of CEA. The LMJ/PETAL facility will be opened for the academic access of European researchers. In parallel, diagnostics are being developed within the PETAL + project and many physical problems are being addressed ranging from the study of the problems of radiation generation and activation issues to the problem of generation of large electromagnetic pulses.

Intense research is being conducted into sources of laser-accelerated ions and their application. Particular attention is now given to the low-density regime of laser ion acceleration. In this regime, volume effects are expected to dominate, while for solid foils, ion acceleration is directly related to the electron surface density and the number of accelerated ions is limited. Simulations therefore show that it is possible to reach high ion energies with a high number of accelerated ions and a high conversion efficiency. This scheme also leads to less debris than solid foils and is more adapted to high repetition lasers. Due to the difficulty in generating short and dense gas jets experimentally, we have decided to study this regime using very thin foils exploded by a longer, lower intensity pulse. As this regime scales well with laser energy, experiments were recently performed with a high laser energy (∼180 J) on the LLNL Titan laser. A secondary long pulse laser was used to control the density profile of the target. Preliminary analysis suggests that, in this high-energy regime, protons of high energies and with good beam quality were obtained when exploding the foil. We present new simulation results exploring the laser ion acceleration mechanism in laser and plasma conditions close to those of these experiments. These results demonstrate that low-density targets are a promising candidate for an efficient proton source. This source can be optimized by choosing appropriate plasma conditions.

Process of shock ignition in inertial confinement fusion implies creation of a high pressure shock with a laser spike having intensity of the order of a few PW/cm2. However, the collisional (Bremsstrahlung) absorption at these intensities is inefficient and a significant part of laser energy is converted in a stream of energetic electrons. The process of shock formation in a dense plasma by an intense electron beam is studied in this paper in a planar geometry. The energy deposition takes place in a fixed mass target layer with the areal density determined by the electron range. A self-similar isothermal rarefaction wave of a fixed mass describes the expanding plasma. Formation of a shock wave in the target under the pressure of expanding plasma is described. The efficiency of electron beam energy conversion into the shock wave energy depends on the fast electron energy and the pulse duration. The model is applied to the laser produced fast electrons. The fast electron energy transport could be the dominant mechanism of ablation pressure creation under the conditions of shock ignition. The shock wave pressure exceeding 1 Gbar during 200–300 ps can be generated with the electron pulse intensity in the range of 5–10 PW/cm2. The conclusions of theoretical model are confirmed in numerical simulations with a radiation hydrodynamic code coupled with a fast electron transport module.

An analytical model and numerical simulations demonstrate that pulses with intensities exceeding 1022 W/cm2 may penetrate deeply into the plasma and accelerate efficiently ions in the forward direction. We propose a new scheme for fast ignition of precompressed DT fusion targets by using two laser pulses. The first pulse (or a sequence of several pulses) creates a channel with diameter ~ 30μm through the plasma corona up to the fuel density ~ 1 g/cm3. The second pulse with a higher intensity accelerates the deuterium and tritium ions at the head of this channel. The overall ignition energy is ~ 100 kJ.

Fast ignition by laser-driven ion beams benefits from the strong collisional interaction of energetic ions with the imploded fuel. However, conditions for an efficient transformation of the laser pulse energy into ion kinetic energy and for the transport of these ions from the acceleration region to the fusion pellet core without significant temporal and angular spread have to be clarified. The laser ponderomotive force may provide efficient ion acceleration in bulk dense targets such as a precompressed DT capsule and evacuate a channel for further laser beam propagation. The main characteristics of ponderomotive ion acceleration and channel formation inferred from analytical theory and confirmed by particle-in-cell simulations are applied for the design of a new scheme of ion fast ignition. Contrary to schemes based on the mechanism of target normal sheath ion acceleration, at least two laser pulses are used in our proposal. The first pulse (or a sequence of several pulses) creates a channel with a diameter of ∼20 µm through the plasma corona up to a fuel density of ∼1 g cm−3. The second pulse with a higher intensity of ∼1022 W cm−2 accelerates the deuterium and tritium ions at the head of this channel to energies 5–25 MeV on a time scale less than 1–3 ps. The overall ignition energy in this proposal is relatively high, ≳100 kJ, but no additional target arrangements will be required. This feature makes the scheme attractive for a high repetition rate operation.