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A sub-grid foam model is developed to describe numerically a sequence of processes transforming solid elements in the foam into a hot plasma under the energy deposition by lasers. We account for three distinct processes: accurate laser energy absorption and scattering on the sub-wavelength cylindrical solid elements, expansion of the foam element due to the energy deposition in its volume, and ablation of the solid element due to the energy deposition on its surface. The foam element dynamics is modeled via a self-similar isothermal expansion combined with a stationary ablation model, and it is described by a set of ordinary differential equations. The microscopic single pore model is incorporated in the macroscopic hydrodynamic codes, and numerical simulations show a good agreement with available experimental data.

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.

International audience; We study with a 1D particle-in-cell (PIC) simulation the evolution of a subcritical perpendicular fast magnetosonic shock. The shock propagates at 1.5 times the fast magnetosonic speed. Some upstream protons are reflected by the shock's electric potential. They form a beam which carries less energy than those that are reflected magnetically by super-critical shocks. The beam triggers the growth of a fast magnetosonic solitary wave upstream of the shock, which reflects the beam protons back to the shock. Extracting the momentum and energy of this beam allows the solitary wave to grow into a proto-shock that is trailed by a short downstream region. Protons from the shock-reflected proton beam increase the density of the plasma between the shock and the proto-shock reducing its potential difference relative to both surrounding structures. Bulk protons, which cross the proto-shock, react to the decreased potential jump. The plasma behind the proto-shock accelerates and so does the shock. The trailing end of the proto-shock speeds up in order to continue reflecting the beam protons and eventually it catches up with its front; the proto-shock collapses and the self-reformation fails. A more energetic proton beam could decrease the potential jump across the shock, let it collapse and replace it with the proto-shock.

The electronic M 1 model is widely used for electron transport studies in a hot collisional plasma. However, the moment extraction of the electron–electron collision operator from the kinetic collision operator, for this angular moments model, is challenging and some approximations are required. In this work a characterisation of the electron–electron and electron–ion collision operators is given and the electron plasma transport coefficients are derived. It is shown that in the high Z limit the electronic M 1 model and the Fokker–Planck–Landau equation coincide in the case of near equilibrium. Also, in general, the electron–electron collision operator proposed for the electronic M 1 model recovers accurate electron transport plasma coefficients.

An exact analytic solution is found for the steady-state distribution function of fast electrons with an arbitrary initial spectrum irradiating a planar low-Z plasma with an arbitrary density distribution. The solution is applied to study the heating of a material by fast electrons of different spectra such as a monoenergetic spectrum, a step-like distribution in a given energy range, and a Maxwellian spectrum, which is inherent in laser-produced fast electrons. The heating of shock- and fast-ignited precompressed inertial confinement fusion (ICF) targets as well as the heating of a target designed to generate a Gbar shock wave for equation of state (EOS) experiments by laser-produced fast electrons with a Maxwellian spectrum is investigated. A relation is established between the energies of two groups of Maxwellian fast electrons, which are responsible for generation of a shock wave and heating the upstream material (preheating). The minimum energy of the fast and shock igniting beams as well as of the beam for a Gbar shock wave generation increases with the spectral width of the electron distribution.

Supersonic plasma jets are ubiquitous in astrophysics. Our study focus on the jets emanated from Herbig-Haro (HH) objects. They have velocities of a few hundred km/s and are extending over the distances more than a parsec. Interaction of the jets with surrounding matter produces two specific structures in the jet head: the bow shock and the Mach disk. The radiative cooling of these shocks affects strongly the jet dynamics.

the date of receipt and acceptance should be inserted later Abstract. The Rayleigh-Taylor instability plays an important role in the dynamics of several astronomical objects, in particular, in supernovae (SN) evolution. In this paper we develop an analytical approach to study the stability analysis of spheric al expansion of the SN ejecta by using a special transformation in the co-moving coordinate frame. We first study a non-stati onary spherical expansion of a gas shell under the pressure of a central source. Then we analyze its stability with respect to a n o radial, non spherically symmetric perturbation of the of the shell. We consider the case where the polytropic constant of the SN shell isγ = 5/3 and we examine the evolution of a arbitrary shell perturbation. The dispersion relation is derived. The growth rate of the perturbation is found and its temporal and spatial evolution is discussed. The stability domain depends on the ejecta shell thickness, its acceleration, and the perturbation wavelen gth.

In laser fusion, the coupling and the propagation of the laser beams in the plasma surrounding the pellet must be well controlled for to succeed in producing a high energy level. To achieve thermonuclear ignition and high gain, the coupling efficiency must be as high as possible, the uniformity of the energy deposition must be very good and the fast electron generation must be minimized. This implies a deep understanding of the laser–plasma interaction mechanisms to keep the nonlinear processes at a low level. Important advances in laser–plasma interaction physics have been achieved thanks to the converging efforts of the experimental and theoretical approaches.Among the different studies of the last few years, we will report results on three themes which are important for future fusion experiments. The first concerns the ability of plasmas to induce temporal and spatial incoherence to the laser beams during their propagation. Beam smoothing, beam spraying and increased incoherence may in turn reduce the level of backscattering instabilities.In laser fusion, multiple beams are used to irradiate the target. The effect of the overlap of the laser beams on parametric instabilities may complicate the problem. Not only is there the interplay between instabilities driven by one beam, but also the interplay between instabilities driven by different beams. In the Laboratoire pour l'Utilisation des Lasers Intenses (LULI) experiment, although the overall stimulated Brillouin scattering (SBS) reflectivity was reduced, a well-defined resonance of the amplitude of ion acoustic waves (IAWs) associated with SBS has been observed for waves propagating along the bisecting direction between two laser beams. Energy transfer between two identical laser beams has been observed and correlated with plasma induced incoherence.The nonlinear saturation of stimulated scattering instabilities is a fundamental ingredient of the understanding of the observed and future reflectivity levels. Using Thomson scattering, the decay of the primary IAWs associated with SBS in secondary IAWs has been observed and correlated with the saturation of SBS.The experiments were performed with the six-beam laser facility of the LULI at Ecole Polytechnique, using one or two 1.053 µm interaction beams in the nanosecond regime and a well-characterized preformed plasma. Multiple diagnostics, including Thomson scattering of a probe beam with spatial, temporal and spectral resolution, were used. The comparison between the experimental results and numerical simulations is used to improve the physics included in the codes.

Laser–plasma interaction (LPI) physics is one the major issues for the realization of inertial fusion. Parametric instabilities may be driven by the incident laser beams during their propagation in the underdense plasma surrounding the fusion capsule. These instabilities may result in various effects detrimental to a good energy transfer from the laser beams to the target: the backscattering of the incident beams, the generation of energetic electrons which might preheat the fusion fuel, and the spoiling of the laser beam alignment. The control of the linear growth of these instabilities, together with the understanding of their nonlinear saturation mechanisms are therefore of fundamental importance for laser fusion. During the past few years, a series of new concepts have emerged, deeply modifying our approach to LPI physics. In particular, LPI experiments are now carried out with laser beams which are optically smoothed by means of random phase plates. Such beams are characterized inside the plasma by randomly distributed intensity maxima. Filamentation instabilities may locally increase the laser intensity maxima and deplete the electron density, leading to an intricate coupling between various nonlinear processes. One of the most striking features of this intricate coupling is the resulting ability of the plasma to induce additional temporal and spatial incoherence to the laser beams during their propagation. The increased incoherence may in turn reduce the level of backscattering instabilities.

The renormalization-group approach is used to obtain an exact solution to the self-consistent Vlasov kinetic equations for plasma particles in the quasi-neutral approximation. This solution describes the one-dimensional adiabatic expansion of a plasma bunch into a vacuum for arbitrary initial particle velocity distributions. Ion acceleration is studied for two-temperature Maxwellian and super-Gaussian initial electron distributions, which predetermine distinctly different ion spectra. The solution found is used to describe the acceleration of ions of two types. The relative acceleration efficiency of light and heavy ions as a function of atomic weights and number densities is analyzed. The solutions obtained are of practical importance in describing ion acceleration during the interaction of an ultrashort laser pulse with nanoplasma, for example, cluster plasma or plasma produced when thin foils are irradiated by a laser.

We present results on laser-driven relativistic electron beam propagation through aluminum samples, which are either solid and cold or compressed and heated by laser-induced shock. A full numerical description of fast electron generation and transport is found to reproduce the experimental absolute K-alpha yield and spot size measurements for varying target thicknesses, and to sequentially quantify the collisional and resistive electron stopping powers. The results demonstrate that both stopping mechanisms are enhanced in compressed Al samples and are attributed to the increase in the medium density and resistivity, respectively. For the achieved time-and space-averaged electronic current density, < j(h)> similar to 8 x 10(10) A/cm(2) in the samples, the collisional and resistive stopping powers in warm and compressed Al are estimated to be 1.5 keV/mu m and 0.8 keV/mu m, respectively. By contrast, for cold and solid Al, the corresponding estimated values are 1.1 keV/mu m and 0.6 keV/mu m. Prospective numerical simulations involving higher j(h) show that the resistive stopping power can reach the same level as the collisional one. In addition to the effects of compression, the effect of the transient behavior of the resistivity of Al during relativistic electron beam transport becomes progressively more dominant, and for a significantly high current density, j(h) similar to 10(12) A/cm(2), cancels the difference in the electron resistive stopping power (or the total stopping power in units of areal density) between solid and compressed samples. Analytical calculations extend the analysis up to j(h) = 10(14) A/cm(2) (representative of the full-scale fast ignition scenario of inertial confinement fusion), where a very rapid transition to the Spitzer resistivity regime saturates the resistive stopping power, averaged over the electron beam duration, to values of similar to 1 keV/mu m. (C) 2014 AIP Publishing LLC.

We present an ion kinetic model describing the transport of suprathermal α-particles in inertial fusion targets. The analysis of the underlying physical model enables us to develop efficient numerical methods to simulate the creation, transport and collisional relaxation of fusion reaction products (α-particles) at a kinetic level. The model assumes spherical symmetry in configuration space and axial symmetry in velocity space around the mean flow velocity. A two-energy-scale approach leads to a self-consistent modeling of the coupling between suprathermal α-particles and the thermal bulk of the imploding plasma. This method provides an accurate numerical treatment of energy deposition and transport processes involving suprathermal particles. The numerical tools presented here are then validated against known analytical results. This enables us to investigate the potential role of ion kinetic effects on the physics of ignition and thermonuclear burn in inertial confinement fusion schemes.

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.

The renormalization group approach is applied to derive an exact solution to self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solution obtained describes the one-dimensional adiabatic expansion into vacuum of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The ion acceleration is investigated for both a Maxwellian two-temperature initial electron distribution and a super-Gaussian initial electron distribution.

The influence of laser beam smoothing on stimulated Brillouin backscattering (SBBS) is studied analytically in the limit of the independent hot spot model. It is shown that the temporal beam smoothing can reduce the SBBS reflectivity significantly even though the laser bandwidth is smaller than the growth rate for the average intensity. The explanation of this reduction effect is given in terms of SBBS growth in the statistically significant hot spots. The minimum laser bandwidth corresponding to an important reduction of the reflectivity is thus determined properly. The dependence of this reduction effect on the acoustic damping for a given laser bandwidth is discussed.

The spectrum of toroidal standing shear Alfven waves (SAWs) is derived for a stretched magnetic field line geometry that is approximated by the Tsyganenko 96 magnetic field model. The model is applied to field lines near the midnight meridional plane. It is demonstrated that the fundamental mode frequency for typical ambient parameters of Earth's magnetosphere is in the 1–4 mHz range. This frequency is in agreement with the measured frequency of magnetospheric field line resonances, and is up to an order of magnitude smaller than for a dipolar magnetic field. We conclude that stretching of Earth's magnetic field offers a possible explanation for anomalously low frequency SAWs observed within diffuse auroral emission (Hβ) produced by energetic proton precipitation in the inner plasma sheet.

Of vital importance for Inertial Confinement Fusion (ICF) are the understanding and control of the nonlinear processes which can occur during the propagation of the laser pulses through the underdense plasma surrounding the fusion capsule. The control of parametric instabilities has been studied experimentally, using the LULI six-beam laser facility, and also theoretically and numerically. New results based on the direct observation of plasma waves with Thomson scattering of a short wavelength probe beam have revealed the occurence of the Langmuir decay instability. This secondary instability may play an imporant role in the saturation of stimulated Raman scattering. Another mechanism for reducing the growth of the scattering instabilities is the so-called `plasma-induced incoherence'. Namely, recent theoretical studies have shown that the propagation of laser beams through the underdense plasma can increase their spatial and temporal incoherence. This plasma-induced beam smoothing can reduce the levels of parametric instabilities. One signature of this process is a large increase of the spectral width of the laser light after propagation through the plasma. Comparison of the experimental results with numerical simulations shows an excellent agreement between the observed and calculated time-resolved spectra of the transmitted laser light at various laser intensities.

The electron kinetic response to an electric current driven by a standing shear Alfven wave (SAW) is considered for the case of a dipolar geometry. The parallel electric field is found from the electron gyrokinetic equation along with the SAW dispersion coefficient. Electron trapping in the dipolar magnetic field significantly reduces the parallel electric conductivity and in this way increases the amplitude of the parallel electric field and SAW dispersion. It is demonstrated that the two-fluid hydrodynamic equations used by many authors significantly underestimate the electron response and, consequently, the magnitude and location of the parallel electric field under conditions where the electron bounce frequency is larger than the SAW frequency. This is especially important in a plasma with density depressions near the Earth’s polar magnetosphere.

A linear theory of stimulated Brillouin scattering and filamentation instabilities has been formulated using nonlocal transport equations for a laser heated plasma, resulting in a model which is fully equivalent to a linearized kinetic description. The inverse-Bremsstrahlung heating, nonlocal energy redistribution, and ponderomotive laser–plasma interactions are correctly taken into account contributing to a new generalized driving force for these instabilities. Temporal and spatial growth rates, thresholds and dominant perturbation wavelengths are obtained. This theory predicts substantial modifications of the ponderomotive results for conditions relevant to many laser plasma interaction experiments. A new nonlocal and nonlinear model of laser propagation in weakly collisional plasmas has been derived.

Solutions to the vortex electron anisotropic hydrodynamic equations are investigated that describe nonlinear helical waves in an anisotropic magnetized plasma. The possibility of constructing such solutions is provided by the symmetry properties of the equations. An optimum family of one-dimensional subgroups of a symmetry group consistent with the equations is constructed that makes it possible to derive other, essentially different solutions.

The propagation of high-amplitude electromagnetic pulses (EMP's) having a pulse length of nanoseconds through the lower atmosphere is studied by using a kinetic model for free electrons. It is shown that an EMP with an amplitude above 1 MV/m can be transported to altitudes of 50 km from the ground without significant energy loss due to the shortness of its pulse length. The distortion of these pulses due to air breakdown and the energy distribution of the electrons in the plasma in the tail of the pulse will also be characterized.

The equations of vortex electron anisotropic hydrodynamics are used to show that, in a plasma with anisotropic pressure, the Weibel instability of short-wavelength perturbations gives rise to a large-amplitude quasi-harmonic magnetic field varying periodically as a function of time. The computed field parameters agree well with the proposed analytic estimates.

The three-dimensional, nonlinear evolution of a shear flow (or Kelvin-Helmholtz (KH)) instability driven by a large-amplitude shear Alfven wave (SAW) in the Earth's magnetosphere is studied by using numerical solutions to the complete set of ideal magnetohydrodynamic equations. An initial setup is chosen to simulate a standing SAW associated with field line resonances (FLRs) in a dipolar magnetosphere. It is shown that KH vortices grow most rapidly in the equatorial plane. In this region, the growth rate is reduced by the ratio of the KH and SAW frequencies when compared to the growth rate predicted by a two-dimensional theory for transient magnetic field lines. For typical parameters of FLRs, this ratio is small. Field-aligned gradients of the KH mode vorticity and azimuthal phase velocity initiate Alfven waves, which carry energy toward the ionosphere. This results in partial restructuring of field-aligned currents with scale size of ∼10 km above the ionosphere. After one period of the SAW, energy in the KH mode returns to the SAW flow. This suggests that vortex formation might be largely periodic in evolution, reconfiguring after each period of the FLR. Finally, we show that this restructuring of field-aligned currents does not depend on the initial phase of the SAW. For example, the model predicts that a ground-based observer in the Northern Hemisphere (looking antiparallel to the Earth's magnetic field) will see that the downward current wraps clockwise and the upward current wraps counterclockwise, though the positions of the currents change latitudes for different phases.

A technique is suggested for triggering nuclear reactions by accelerating ions with a powerful ultrashort laser pulse in a plasma. The underlying idea of the suggested compact “reactor” is utilization of high-energy ions accelerated by the charge-separation electrostatic field in the direction perpendicular to the laser beam axis in a gas-filled capillary. Accelerated ions with energies of several MeV penetrating the target from the inside surface of a channel give rise to nuclear reactions which can be used to create a compact source of fast neutrons and neutrons of intermediate energies for generating various (short-and long-lived, light and heavy) isotopes, for generating gamma radiation over a broad energy range, for making sources of light ion and induced radioactivity. The yield of the corresponding nuclear reactions as a function of the laser beam parameters has been investigated. The suggested technique for triggering nuclear reactions provides a practical tool for studies of nuclear transformation on the pico-and nanosecond scales, which cannot be achieved using other methods.

Exact solutions are found that represent nonlinear nonstationary structures of a helical symmetry in a plasma with anisotropic electron pressure. These are solutions to the system of the equations of vortex electron anisotropic hydrodynamics (VEAH) which describe a nonlinear evolution of the Weibel instability. The symmetry properties of VEAH equations are also studied and an optimal system of one-dimensional sub-groups is constructed that allows one to find other exact nonlinear solutions.

A model is presented that describes the excitation of density perturbations and parallel electric fields by standing shear Alfven waves on dipole fields in Earth's magnetosphere. The model includes the effects of electron inertia and gyro-kinetic dispersion, accounting for field-aligned variations of the electron and ion temperatures and the ambient plasma density. In a model dipole magnetosphere, it is found that dispersion and nonlinearity determine the depth, spatial structure, and temporal evolution of large-amplitude density fluctuations near to the polar ionospheres. The characteristics of magnetospheric density cavities and their relationship to auroral luminosity, or field-aligned currents, is discussed in the context of recent satellite and ground based observations.

A new method of cylindrical cumulation of fast ions undergoing ponderomotive acceleration at the focus of a high-power subpicosecond laser is proposed. When a laser beam is focused in a preionized gas at a ring focus, radial acceleration of ions by the ponderomotive force occurs. The ions accelerated from the inner side of the ring form a cylindrical shock wave converging toward the axis. As the shock wave cumulates, the ion density increases rapidly and the ion-ion collision probability increases along with it. A numerical simulation for a ~100 TW subpicosecond laser pulse predicts the generation of up to 200 keV ions and up to 100-fold volume compression of the plasma in a cylinder ~1 µm in diameter. The lifetime of the dense plasma filament over the length of the laser caustic is several picoseconds. It is suggested that laser cumulation of ions be used for the production of a bright and compact subpicosecond source of fast neutrons, media for x-and γ-ray lasers, and multiply-charged ions and for the initiation of nuclear reactions.

A system of electron-transport equations for small perturbations in a plasma, which is suitable for an arbitrary relation between the electron mean free path and the density gradient length, is formulated. Electron-electron collisions are treated on the basis of the exact Landau collision integral, making it possible to obtain expressions for the potential elements of the Fourier components of electron fluxes, generalized forces, and all the transport coefficients in a plasma with an arbitrary ion charge for the first time. The transport coefficients found, viz., the electrical conductivity, the thermal diffusivity, the thermoelectric coefficient, and the ion convection coefficients, permit the quantitative description of an extensive list of small-scale processes in a completely ionized plasma. The suppression of heat transport and the damping of ion-sound waves in a current-free plasma over the entire range of spatial scales of the perturbations from the high-collisionality limit to the collisionless limit are examined as applications of the theory developed.

A model is presented which describes the nonlinear interaction of dispersive shear Alfven wave (SAW) field line resonances (FLRs) and ion acoustic waves (IAWs), with applications to the Earth’s magnetosphere. Two limits are considered: In low-β plasma (β

We describe nonlinear resonance absorption of compressional Alfven waves in a model magnetosphere. It is shown that the ponderomotive force of excited standing shear Alfven waves can lead to nonlinear saturation and spatial structuring of field line resonances and that in low-beta plasmas ponderomotive saturation may occur before other nonlinear saturation processes such as the Kelvin-Helmholtz instability. The effects of finite electron inertia are also considered, and it is shown that spatial structuring of field line resonances may occur with scale sizes compatible with those found in discrete auroral arcs. Results are discussed in the context of three-dimensional numerical solutions to the resistive magnetohydrodynamic equations and based on a simplified analytical model of nonlinear resonance absorption.

Nonlocal theory of an electron transport in laser-produced plasmas with the large ion charge and arbitrary ratio of the characteristic spatial scale length to the electron mean free path has been developed for small potential perturbations. Closure relations have been derived from the solution to the electron Fokker–Planck equation which includes inverse bremsstrahlung heating and ponderomotive effects. All electron transport coefficients and their dependence on the laser intensity have been found. An expression for the electron heat flux includes laser field and plasma flow contributions. Identification of these different sources is necessary for the unique definition of the thermal transport coefficient which is independent of the particular application. A complete derivation of the potential part of the ponderomotive force in the presence of inverse bremsstrahlung heating has been presented.

Brillouin scattering from a preformed, inhomogeneous, expanding plasma has been investigated. Backscattered light near the incident laser wavelength (λ=1054 nm) from CH planar targets has been spectrally and temporally resolved. By varying the time delay of the interaction beam, the scattering was studied for different plasma conditions. The backscattered light is predominantly blue-shifted and appears before the peak of the laser pulse. The experimental time-integrated reflectivity of backscattered light is in the range of 1%–10% and decreases with the plasma density. The time-resolved spectra and total reflectivity were calculated using a theory of convective stimulated Brillouin scattering (SBS) in a flowing inhomogeneous plasma combined with a statistical hot spot model for the interaction beam. The plasma parameters for these calculations were provided by simulations using a two-dimensional hydrodynamic code. The calculated SBS spectra are similar to the experimental observations. The time-integrated...

This work is concerned with the description of ion acoustic fluctuations in electron-ion plasmas relevant to laser-plasma interaction experiments. A nonlocal closure to the linearized moment equations for the fluctuating hydrodynamic quantities is introduced. These equations are used to construct practical expressions for the dynamical form factor and Thomson scattering cross section, which are valid in the entire region of particle collisionality in plasmas with high Z and large ZTe /Ti . @S1063-651X~98!05403-8#