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The excitation of surface plasma waves (SPW) by an intense short laser pulse is a useful tool to enhance the laser absorption and the electron heating in the target. In this work, the influence of the transverse laser profile and the pulse duration used to excited SPW is investigated from Fluid and 2D Particle-in-Cell simulations. We show the existence of a lobe of surface plasma wave modes. Our results highlight surface plasma waves excitation mechanism and define the laser parameters to optimise the SPW excitation and the kinetic energy of the associated electron trapped in the wave. It opens the door to monitor the spectral mode distribution and temporal shape of the excited surface waves in the high relativistic regime. The most important result of the study is that—at least in 2D—the charge and the energy of the electron bunches depend essentially on the laser energy rather than on temporal or spatial shape of the laser pulse.

The distribution function of electrons accelerated by intense laser pulses at steep vacuum-plasma interfaces is investigated by using the Fokker-Planck equation and methods from extreme statistics. The energy spectrum of electrons penetrating into the dense plasma after being accelerated at the interface and in the preplasma shows a systematic cutoff-like decrease in the momentum component p x / m e c along the laser propagation axis. While the distribution associated with the kinetic energy spectrum (Ekin) is often approximated by a thermal distribution, F ( E kin ) ∝ exp ( − E kin / T h ), with a hot particle temperature Th, the nature of the distribution close to the cutoff is clearly nonthermal. Electron distributions are analyzed here from two-dimensional Particle-in-Cell simulations. Via a comparison with solutions derived from a Fokker-Planck equation and based on Chirikov's standard map models, we find that the electron distributions show a clear signature of stochastic heating, due to repeated acceleration in the standing wave in the preplasma. Further analysis of the solutions to the Fokker-Planck equation allows us to describe the cutoff seen in the momentum p of the distributions F(p), which can be expressed as a function of time τ in the form F ( p , τ ) ∝ [ ( p max − p ) / δ p ] exp ( − 2 p 3 / 9 τ ), portraying a time-dependent cutoff at p → p max. This implies that the energetic tail of the distribution belongs to the maximum domain of attraction of the Weibull law, which means that the probability to find high-energy electrons varies abruptly near pmax. The variance of physical observables sensitive to the high-energy tail is consequently considerably higher than when assuming thermal distribution.

The interaction of an ultraintense (2 × 1021 W/cm2) and ultrashort (18 fs) laser pulse with micrometer-scale aluminum foils is studied via the use of two and three dimensional (2D and 3D) particle-in-cell simulations. One shows that for a plane target with a steep density step, total (collisional and collisionless) absorption is weak. On the other hand, the use of structured targets (gratings in our case) or the presence of a sharp density gradient at the front of the slab allows a better coupling between the laser pulse and the target, and this yields a high absorption rate and ultraenergetic aluminum ions (in the 1 GeV range) generated by target normal sheath acceleration. By changing the characteristics of the grating, it is possible to control, to some extent, the absorption rate and the cutoff of the ion spectrum. It is also shown that a relatively simple model based on the adiabatic self-similar expansion of the target in the ultrarelativistic limit provides reasonable agreement with the simulation results. Finally, the comparison of 2D and 3D results for the interaction with gratings shows that 2D simulations accurately describe the absorption by 2D gratings but, on the other hand, they significantly overestimate the ion-spectrum cutoff.

The modulational and Raman instabilities are investigated in the relativistic regime, for a large amplitude electromagnetic wave propagating in a hot plasma of arbitrary density. Temporal growth rates and the number of unstable branches are determined when the plasma temperature, density, and the amplitude of the wave vary. The convective or absolute nature of the Raman instabilities is then determined. The present paper extends previous results by Guerin et al. [Phys. Plasmas 2, 2807 (1995)] and Couairon and Mora [Phys. Plasmas 8, 3434 (2001)]. It is shown that for any temperature, the Raman instability is convectively unstable at low density and low intensity, and absolutely unstable when the intensity or the density exceeds a threshold that we determine as a function of the temperature. In contrast with the cold plasma case, the threshold for absolute instability does not coincide with the merging of branches found by a classical temporal stability analysis.

Stationary plasma thrusters are devices that use crossed electric and magnetic fields to accelerate ions to high velocities. Ions are created by collisional ionization of a propellant gas with electrons injected from a hollow cathode external to the thruster. A major issue is the electron transport through the magnetic field. It is known to exceed considerably the values predicted by the classical theory. Various 2D models have shown that wall collisions, which have often been invoked as the origin of this anomalous transport, are in fact insufficient. Anomalous turbulent transport has to be added to the model to recover an adequate conductivity. In the present paper the first 2D kinetic model that shows that, indeed, plasma turbulence can explain the observed conductivity is presented. Without any free parameter the model is able to reproduce numerous experimental features. At the end of the paper a preliminary theoretical analysis of the observed instability is provided.

The propagation of a short and intense laser pulse (1.057 μm, 350 fs, 1017 W/cm2–2×1019 W/cm2) through preformed undercritical plasmas (≈5%–40% of nc) has been experimentally investigated on the 100-TW laser facility at the Laboratoire pour l’Utilisation des Lasers Intenses. The transmission and reflection of the 1 μm laser pulse, the forward- and backward-Raman (respectively, F-SRS and B-SRS) scattered light and the emission of fast electrons are reported. Significant absorption occurs in these plasmas, which is found to increase with the laser intensity. B-SRS is strongly driven at 1017 W/cm2 and gradually decreases at higher intensities. It is shown that the transmission is low and only weakly dependent on the laser intensity. In contrast, the forward Raman scattering continuously increases with the laser intensity, up to 7% of the incident energy at 2×1019 W/cm2 in the lowest density case. The relativistic electrons accelerated in the forward direction appear to be correlated with the F-SRS. The exper...

The dispersion relation for electronic parametric instabilities of a circularly polarized laser wave is solved in the case where the distribution function is supposed to be cold in the transverse direction and to be a linear combination of a cold distribution function and of a Maxwellian in momentum in the longitudinal direction. Only densities below the critical density are considered. It is shown that the longitudinal temperature as expected reduces the growth rate, but that the existence of a hot tail is not sufficient to significantly reduce the instability. It is the bulk of the distribution function that must be heated to efficiently stabilize the system. Another important effect of the heating is to reduce the backscattered component of the instability. An example of a one-dimensional particle simulation performed in the exact conditions of validity of the theory is discussed.

Propagation of a high-contrast subpicosecond (400–600 fs) relativistic (Iλ2 up to 2×1019 W⋅cm−2⋅μm2) laser pulse through long preformed overdense plasmas is experimentally studied. Transmission values up to 10% are measured in plasmas with initial peak densities above 10×nc. We compare these results with one-dimensional (1D) analytical calculations of the hole boring effect. It is shown that the ponderomotive force of the laser beam can push forward the overdense plasma, create a channel, and lead to transmission levels similar to the experimental ones.

Propagation of a high-contrast frequency-doubled subpicosecond (300 fs) relativistic (Iλ2 up to 5×1018 W⋅cm−2⋅μm2) laser pulse through thin and initially solid foils is studied. Transmission values up to 10% are measured through targets with initial near solid densities. The strong intensity threshold observed for the transmitted energy is correlated with clear modifications of the transmitted and reflected spectra, electron generation, and beam imaging. Two-dimensional Cartesian particle-in-cell (PIC) simulations that qualitatively reproduce the experimental results suggest specific rapid heating of the thin targets by fast electrons, plasma expansion, and density decrease to relativistically transmissive conditions during the pulse.

A new implicit fully electromagnetic particle in cell (PIC) method is presented in which the full ion dynamic and all the electron guiding centre drifts of a highly magnetized plasma are retained. We show that the electron drifts do not have to be described explicitly, and that they can be simulated using a simple but efficient linear direct implicit method. Tests and simulations using the new scheme are presented.

The formation and evolution of density channels created by the interaction of a short bright (600 fs, $5\ifmmode\times\else\texttimes\fi{}{10}^{18}\mathrm{W}{\mathrm{cm}}^{\ensuremath{-}2}\ensuremath{\mu}{\mathrm{m}}^{2}$) laser pulse with a preformed plasma are studied by means of experiments and 2D particle-in-cell (PIC) simulations. Hollow density channels are observed by interferometry, and a fast radial expansion $(5\ifmmode\times\else\texttimes\fi{}{10}^{8}\mathrm{cm}/\mathrm{s})$ is measured. Magnetic fields around 50 MG inferred from Faraday rotation measurements suggest the occurrence of self-focusing. The PIC simulations support this hypothesis and show ion depletion during the laser pulse as well as radial expansion in agreement with experiments.

The dispersion relation for electron parametric instabilities of a circularly polarized laser wave of arbitrary intensity is established without restrictions on the plasma density. It is obtained in an implicit analytical form and solved numerically. The well-known stimulated Raman scattering, relativistic modulational instability, relativistic filamentation instability, and two-plasmon decay are recovered at low intensity. Their behavior in the ultrarelativistic regime is characterized by a wide extent of the unstable region in the wave vector space, with growth rates equal to a fraction of the laser frequency, and a strong harmonic generation. Particle-in-cell simulations confirm these results and show that the instability leads to a very strong heating of the plasma.

The results of a systematic study of the propagation of very high-intensity laser pulses through slabs of plasma of several tens of microns are presented. One-dimensional and two-dimensional electron parametric instabilities are evidenced. They lead to a rapid longitudinal and transverse heating, and to filamentary structures which progressively merge. The heating results in highly energetic electrons with energy of several tens of MeV. Correlatively, a strong attenuation rate of the electromagnetic wave is observed. {copyright} {ital 1997} {ital The American Physical Society}

A general dispersion relation is given for electron parametric instabilities of an ultraintense circularly polarized wave propagating in a plasma. It is valid for any plasma density and wave intensity and corresponds to a generalization of the Raman, relativistic modulational, relativistic filamentation, and two-plasmons instabilities. Its numerical resolution shows different zones of instability in the wave vector space. At high intensities, the zones extend and merge, with growth rates equal to a fraction of the wave frequency. At close-to-critical density and high intensity the instability leads to strong harmonic emission. Particle-in-cell simulations confirm the analytical results.

Due to relativistic effects, a large amplitude electromagnetic wave can propagate in a classically overdense plasma with ω2p≳ω2≳ω2p/γ, where ωp is the plasma frequency, ω the laser frequency, and γ the relativistic factor of an electron in the laser field. Particle‐in‐cell simulations are used to study the interaction of an ultrahigh intensity laser pulse in normal incidence on a one‐dimensional preformed plasma layer. Both electrons and ions dynamics are included. The width of the layer is 10 to 30 μm and the plasma is characterized by (ωp/ω)2=1.5. During the penetration of the electromagnetic wave a large longitudinal electric field is generated. It results in a strong longitudinal heating of electrons which reach relativistic temperatures. This heating further lowers the effective plasma frequency ωp/γ so the layer becomes almost transparent after the plasma crossing by the wave front. Velocity of the wave front, reflection and transmission rates are studied as functions of the incident energy flux, th...

A large amplitude electromagnetic wave propagating in a plasma is known to be subject to severe modulational and Raman instabilities. Previous works were devoted to the weakly relativistic limit and applied mainly to a cold underdense plasma. One extends these works to include the fully relativistic limit for a circularly polarized light for which one derives the dispersion relation in a one‐dimensional plasma. The characteristics of the instabilities are also calculated in the case where the plasma is classically overdense, with 1

In this paper, results of a set of numerical simulations applicable to the problem of particle acceleration by the beating of high‐energy laser waves are presented. The simulations have periodic or open‐ended boundary conditions. The growth rates of the parametric instabilities that are present in both situations are identical. In all cases they yield a destruction of the large amplitude plasma wave in a very short time. The amplitude of the saturation level is shown to be strongly dependent on initial conditions. Finally, some results in the term of the evolution of the distribution function of the background plasma in the context of strong turbulence are shown.

International audience; The development of the Weibel instability during the expansion of a thin plasma foil heated by an intense laser pulse is investigated, using both analytical models and relativistic particle-in-cell simulations. When the plasma has initially an anisotropic electron distribution, this electromagnetic instability develops from the beginning of the expansion. Then it contributes to suppress the anisotropy and eventually saturates. After the saturation, the strength of the magnetic field decreases because of the plasma expansion until it becomes too weak to maintain the distribution isotropic. For this time, the anisotropy rises as electrons give progressively their longitudinal energy to ions, so that a new instability can develop.

International audience; The expansion of a plasma slab into a vacuum is studied using one-dimensional and two-dimensional particle-in-cell simulations. As electrons transfer their longitudinal kinetic energy to ions during the expansion, the electron temperature becomes anisotropic. Once this anisotropy exceeds a threshold value, it drives the Weibel instability, leading to magnetic fields in the megagauss range. These fields induce energy transfer between the longitudinal and transverses directions, which influences the expansion. The impact of a cold electron population on this phenomenon is also investigated. Plasma expansion is a fundamental process which occurs in very different fields, such as astrophysics ͓1,2͔, laser-plasma ion acceleration ͓3–5͔ and thin-film deposition ͓6͔. This phenomenon is usually described by simple one-dimensional models ͓7–9͔. Yet, even when the system is translation-invariant along the plasma surface, several effects ͑e.g., Coulomb collisions ͓10͔͒ can induce momentum transfer between the longitudinal and transverse directions. The purely one-dimensional ͑1D͒ description is thus, in general, inaccurate. In this paper, we show that self-generated magnetic fields can lead to such momentum transfer during the expansion of a collisionless plasma slab. This study is of particular interest in the context of laser-plasma ion acceleration , where an intense laser pulse is focused on a thin foil to create a hot electron population that transfers progressively its energy to ions via the ambipolar electric field at the plasma surface ͓11͔. We assume here that the electron distribution is initially Maxwellian with an isotropic temperature. As the plasma expands, the longitudinal temperature T ʈ decreases and the anisotropy parameter A = T Ќ / T ʈ − 1 increases, which eventually leads to the growth of the Weibel instability ͓12–18͔. The most unstable modes are obtained for k = k x e x , where e x is a unit vector normal to the plasma surface. In this case, the maximum unstable wave vector is k x

The possibility of creating enhanced fast electron bunches via the excitation of surface plasma waves (SPW) in laser overdense plasma interaction has been investigated by mean of relativistic one dimension motion of a test electron in the field of the surface plasma wave study and with two‐dimensional (2D) Particle‐In‐Cell (PIC) numerical simulations. Strong electron acceleration together with a dramatic increase, up to 70%, of light absorption by the plasma is observed.

The effect of ion sound wave (ISW) nonlinearities on the stimulated Brillouin scattering (SBS) in long plasmas is investigated within the framework of the Korteweg–de Vries–Maxwell equations. The nonlinear evolution of the driven ISW results in the localization of the ion density on a scale shorter than the wavelength (λs) of the resonant ISW satisfying SBS three‐wave matching conditions. Since the transverse wave amplitudes vary on a much longer scale, a local–global modeling of SBS is proposed in which this scale separation is exploited. The local part of the procedure includes a solution to the damped KdV equation with periodic boundary conditions and driven by a constant amplitude ponderomotive force. In the global part of the analysis approximate solutions for the transverse waves in long plasmas are constructed using the results from the local part. Particle‐in‐cell simulations have been performed in order to investigate the importance of kinetic effects for the local model. Numerical results obtain...

Implicit electromagnetic PIC codes permit to relax the stability constraints imposed by the resolution of the higher frequency electronic modes of the system. This is particularly valuable when modelling the interaction of high-intensity laser pulses with inhomogeneous over-critical plasmas. Here we will present the relativistic extension of the so-called direct implicit method1, 2 including adjustable damping3 and high-order weight factors. This formalism was implemented in the 2Dx–3Dv code ELIXIRS, and benchmarked against explicit simulations for two kinds of physical problems : plasma expansion into vacuum and high intensity laser plasma interaction. In both cases, we will demonstrate the robustness of the implicit solver for rough discretizations. In particular, our new code is shown to capture the main features of laser-plasma interaction, whether average (laser absorption) or microscopic (bunched electron acceleration, ion acceleration). Eventually, the benefit of using second order weight factor will be highlighted.

International audience; The effect of elastic Coulomb collisions on the one-dimensional expansion of a plasma slab is studied in the classical limit, using an electrostatic particle-in-cell code. Two regimes of interest are identified. For a collision rate of few hundreds of the inverse of the expansion characteristic time $ \tau_e$ the electron distribution function remains isotropic and Maxwellian with a homogeneous temperature, during all the expansion. In this case, the expansion can be approached by a three-dimensional version of the hybrid model developed by Mora [P. Mora, Phys. Rev. E 72, 056401 2005]. When the collision rate becomes somewhat greater than $10^4 \tau_e^{-1}$ the plasma is divided in two parts: an inner part which expands adiabatically as an ideal gas and an outer part which undergoes an isothermal expansion.

We report on highly time- and space-resolved measurements of the evolution of electron plasma waves driven by stimulated Raman scattering of a picosecond, single laser speckle propagating through a preformed underdense plasma. Two-dimensional Thomson scatter spectra indicate that the dominant waves have significant transverse components. These results are supported by particle-in-cell simulations which pinpoint the dominant role of the wave front bowing and of secondary nonlinear electrostatic instabilities in the evolution of the plasma waves.

The one-dimensional expansion of a plasma slab is studied using a kinetic description of the electrons based on an adiabatic invariant. The distribution function of the electrons is determined at any time and any position. Solution of the Poisson equation then enables us to determine the electric potential and the ion acceleration. Special attention is devoted to the disassembly time of the plasma slab which appears shorter than expected, due to the distortion of the electron distribution function. The spatial structures of the ion and electron densities and velocities are presented, together with a prediction of the maximum ion velocity. The model is compared to particle-in-cell simulations and excellent agreement is found.

Nickel nanowires present >90% absorption in an effective skin-depth ~1 mum, making efficient X-ray converters. We present new theoretical and experimental results for intensities from small-signal up to very clean relativistic pulses.

Nickel nanowires present >90% absorption in an absorption depth ~1 µm, making efficient x-ray converters at high energy-densities. We present new theoretical and experimental results for intensities from small-signal up to relativistic ultrafast pulses.

We present a set of 2D collisional particle-in-cell simulations of the interaction of ultra-intense laser pulses with over-dense cold collisional plasmas. The size of these simulations is about 100 times as large as those previously published. This allows studying the transport of energetic particles on time scale of the order of 400 fs without perturbations due to the influence of boundary effects and performing a very detailed analysis of the physics of the transport. We confirm the existence of a threshold in intensity close to the relativistic threshold above which the beam of energetic particles diverges when it penetrates the cold plasma. We also study the applicability of Ohm's law to compute the electric field, which is the method commonly used in hybrid codes. The heating of the cold plasma is then studied and we show that half of the heating is anomalous, i.e., not given by standard Joule effect. We discuss the previously published results in the light of these new simulations.

We study the angular distribution of relativistic electrons generated through laser-plasma interaction with pulse intensity varying from ${10}^{18}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$ up to ${10}^{21}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$ and plasma density ranging from 10 times up to 160 times critical density with the help of 2D and 3D particle-in-cell simulations. This study gives clear evidence that the divergence of the beam is an intrinsic property of the interaction of a laser pulse with a sharp density gradient. It is entirely due to the excitation of large static magnetic fields in the layer of interaction. The energy deposited in this layer increases drastically the temperature of the plasma independently of the initial temperature. This makes the plasma locally collisionless and the simulation relevant for the current experiments.

The excitation and the relaxation of the plasma waves and ion acoustic waves (IAW), respectively, driven by stimulated Raman (SRS) and Brillouin (SBS) backscatterings have been experimentally investigated with short-pulse lasers. The spectra have been obtained with a 0.3 ps time resolution. It is shown that SRS develops before SBS and suddenly decays around the peak of the pump, as the IAW reaches saturation. On this short time scale, electron kinetic effects play a major role for SRS saturation, contrary to ion dynamics. These results are supported by particle-in-cell simulations.

A comprehensive examination of the interaction of a picosecond-long ignition pulse on high-density (40 times critical density) pellets using a two-dimensional particle-in-cell model is described. The global geometry consists of a $50\text{ }\ensuremath{\mu}\mathrm{m}$ diameter pellet surrounded by a corona which is isolated by a vacuum region from the boundary. For cone-attached targets, as much as 67% of the incident laser energy is absorbed with 12% sent forward as fast electrons in a 23\ifmmode^\circ\else\textdegree\fi{} cone. The current filaments are driven by the Weibel instability of the forward-going fast electron flux and its return current with the ions playing an important role of neutralizing the space charge. No global current filament coalescence has been observed. The electron distribution function obeys a power law, which begins at $E\ensuremath{\sim}0.2\text{ }\text{ }\mathrm{M}\mathrm{e}\mathrm{V}$ and falls off as ${E}^{\ensuremath{-}(2--3)}$.

Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation domain, a method which has proven to be effective in other areas (e.g., fluid dynamics simulations) is the mesh refinement technique. A brief discussion of the challenges posed by coupling this technique with plasma particle-in-cell simulations is given, followed by a presentation of examples of application in heavy ion fusion and related fields which illustrate the effectiveness of the approach. Finally, a report is given on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAG’s mesh refinement library Chombo to include the tools needed by particle-in-cell simulation codes.

We present an extension of the B erenger Perfectly Matched Layer with additional terms and tunable coecien ts which introduce some asymmetry in the absorption rate. We show that the discretized version of the new PML oers superior absorption rates than the discretized standard PML under a plane wave analysis. Taking advantage of the high rates of absorption of the new PML, we have devised a new strategy for introducing the technique of Mesh Renemen t into electromagnetic Particle-In-Cell plasma simulations. We present the details of the algorithm as well as a 2-D example of its application to laser-plasma interaction in the context of fast ignition.

International audience; The propagation of an ultra-intense laser pulse in a preformed plasma channel was investigated experimentally. Different regimes of propagation were observed when the pulse duration was varied. For a long pulse and powers lower than the critical power for self-focusing,PL/PC

The interaction of ultraintense laser beams with underdense plasma slabs has been investigated with two-dimensional particle-in-cell numerical simulations, showing a strong absorption and a correlatively low transmission. Energetic electrons in the multi-MeV range are produced. At very high intensities the plasma transparency is recovered. These results are interpreted in terms of the development of electron parametric instabilities in the self-consistently heated plasma.

The general dispersion relation for electron parametric instabilities of an ultra-intense circularly polarized laser wave is established for arbitrary plasma density. It corresponds to a generalization of the stimulated Raman scattering instability, the relativistic modulational instability, the relativistic filamentation instability, and the two plasmons decay instability. In the relativistic regime the generalized instability is characterized by a wide extent of the unstable region in the wave vector space, with growth rates reaching a fraction of the laser frequency, and a strong harmonic generation. One-dimensional and two-dimensional particle-in-cell simulations confirm these results. In particular a systematic study of the propagation of very intense laser pulses through slabs of plasma of several tens of microns are presented. The instability leads to a rapid longitudinal and transverse electron heating, and to filamentary structures which progressively merge in a nonlinear stage. The heating results in highly energetic electrons with energy of several tens of MeV. Correlatively, a strong attenuation rate of the electromagnetic wave is observed.

With the help of an implicit particle-in-cell code, we have shown in a previous paper that the electron-cyclotron drift instability was able to induce anomalous conductivity as well as anomalous heating. As such it can be a major actor among the mechanisms involved in the operation of Hall thrusters. However, experimental results show that the nature of wall material has a significant effect on the behavior of the thruster. The purpose of this paper is to study the plasma-wall interaction in the case where the plasma is heated self-consistently by electrostatic fluctuations induced by the electron-cyclotron drift instability.

We report results of a series of simulations about electron transport in plasma close to solid density performed with a collisional 2D3V PIC code and compare the results to published ones obtained using hybrid codes. We show that the dispersion of energetic particles remains similar to the one observed in the collisionless case and discuss and compare our results in the light of hybrid codes. The transport of fast electrons in dense cold plasmas remains a challenging problem in many situations of interest. The main tool for the study of kinetic effects in the laser-plasma interaction, i.e. PIC code, is at pain in this regime. First it must be extended in the collisional regime, which has proven to be doable but add a significant burden in term of computing time. Second the stability of the model imposes - a priori - severe constraints on the mesh size and the time step usable. In order to alleviate these constraints several kinds of "reduced models" aiming at the replacement of "brute force" by physical insight have been proposed and used. The basic physical assumption of all these models is that for a given temperature of the background plasma, above some value of the density, collisional damping prevails and suppresses collective modes of the plasma (1). The use of this assumption has given rise to various flavours of codes. So-called hybrid models ignore the laser/plasma interaction and merely describe the transport of energetic particles in a background plasma assuming quasi-neutrality. The energetic particles are described by PIC particles, while the background plasma is handled by fluid equations. The electric field is obtained by Ohm law applied to the thermal plasma and the Faraday law then gives the magnetic field. One of the difficulties with this kind of model is the initialization of the high energy electrons, whose distribution function is by essence arbitrary. Several studies showed that the results are dependent on the injection used. Attempts have been made to alleviate these constraints, either by coupling this kind of model with a PIC code (2) or by building directly a PIC code presenting an adequate behaviour for dense plasmas. Two of these codes have been recently published. In one of them (3) the collective behaviour is progressively ignored as the density becomes larger than some critical value ndamp , while in the other one (4) Maxwell equations are replaced by MHD equations-as in an hybrid code- above some critical value ndamp. The study of the published literature shows that the validation of such models is limited to peculiar cases, that a lot of caution has to be exercised in their use and in particular that the hypothesis about collisional damping must remain valid during all the simulation including after heating of the background plasma by energetic particles. Finally the same study of literature shows that similar problems handled with different hybrid codes give different results (2, 5). In the present paper we report results based on a series of reference PIC simulations, in the sense that all standard conditions for stability have been fulfilled. The use of high order spline interpolation combined with fourth order smoothing has allowed us to increase the mesh up to values large as compared to the Debye length (20d) but this point in itself has been validated by comparing

An electromagnetic wave is expected to propagate through an overdense plasma, provided that its amplitude is large enough to bring the electron motion into the relativistic regime. We study this induced transparency by using 1D and 2D particle simulations. We find that large chaotic longitudinal electric fields are generated and strong plasma heating takes place during the propagation. This behavior is attributed to parametric instabilities. In order to support this interpretation, the modulational and Raman instabilities of a relativistic electromagnetic wave are studied analytically as well as with the help of particle simulations. In addition it is found that a finite width beam is strongly self focused

This paper presents recent efforts to better understand and quantify charged particle transport in Hall effect thrusters (HETs). Particle-in-cell (PIC) models, hybrid models, laser induced fluorescence (LIF) measurements and collective scattering (CS) experiments are combined to get a better insight into anomalous electron transport in HETs and to increase the predictive capabilities of simulation codes.PIC models have demonstrated that plasma turbulence associated with the development of a high frequency, short wavelength azimuthal instability can be responsible for anomalous transport. Scaling laws for anomalous electron mobility have not yet been derived and hybrid models, which are more practical than PIC models for parametric studies, must use empirical, adjustable transport coefficients that can be inferred from PIC results or LIF measurements of the ion velocity distribution function. CS experiments are aimed at validating the PIC model predictions of the azimuthal instability. The CS results show the first direct experimental evidence of the azimuthal instability predicted by the PIC code. The paper illustrates the synergy between experiments and models toward a complete and quantitative understanding of the physics of HETs.

A systematic study of a high-frequency electron drift instability is presented. It has very large wave numbers corresponding to wavelengths close to the electron gyroradius. The three-dimensional dispersion relation is derived for a model of a crossed electric and magnetic field configuration existing in the Hall thruster. It is shown that the instability develops in packets of oblique unstable modes perpendicular to the magnetic field. The evolution of the instability is also studied for distorted electron distribution functions obtained in particle-in-cell simulations.

Two-dimensional particle-in-cell simulations of laser-plasma interaction using a plane-wave geometry show strong bursty stimulated Brillouin backscattering, rapid filamentation, and subsequent plasma cavitation. It is shown that the cavitation is not induced by self-focusing. The electromagnetic fields below the plasma frequency that are excited are related to transient soliton-like structures. At the origin of these solitons is a three-wave decay process exciting new modes in the plasma. The cavitation is responsible for a strong local reduction of the reflectivity and goes along with an efficient but transient heating of the electrons. Once heating ceases, transmission starts to increase. Local as well as global average reflectivities attain a very low value due to strong plasma density variations brought about by the cavitation process. On the one hand, the simulations confirm the existence of a new mechanism of cavity and soliton formation in nonrelativistic laser-plasma interaction in two dimensions, which was shown to exist in one-dimensional simulations [S. Weber, C. Riconda, and V. T. Tikhonchuk, Phys. Rev. Lett. 94, 055005 (2005)]. On the other hand, new aspects are introduced inherently related to the additional degree of freedom.

Harmonics of the laser light have been observed from the rear side of solid targets irradiated by a laser beam at relativistic intensities. This emission evidences the acceleration of subfemtosecond electron bunches by the laser pulse in front of the target. These bunches emit coherent transition radiation (CTR) when passing through the back surface of the target. The spectral features of the signal recorded for targets of thicknesses up to several hundred microns are consistent with the electrons being accelerated by both the laser electric field—via vacuum heating and/or resonance absorption,—and the v×B component of the Lorentz force. The spatial study of the radiation shows that the relativistic electrons causing the CTR radiation are coherent and propagate ballistically through the target, originating from a source with a size of the order of the laser focal spot.

An electromagnetic wave is expected to propagate through an overdense plasma, provided that its amplitude is large enough to bring the electron motion into the relativistic regime. We study this induced transparency by using 1D and 2D particle simulations. We find that large chaotic longitudinal electric fields are generated and strong plasma heating takes place during the propagation. This behavior is attributed to parametric instabilities. In order to support this interpretation, the modulational and Raman instabilities of a relativistic electromagnetic wave are studied analytically as well as with the help of particle simulations. In addition it is found that a finite width beam is strongly self focused during its propagation in a plasma layer.

It is known from observations in space plasmas and from numerical simulations that under certain conditions, obliquely propagating shocks generate a standing whistler precursor. A one-dimensional electromagnetic implicit particle code is used to investigate its role during the cyclic reformation of quasi-parallel shocks observed in hybrid simulations. It is shown that the precursor grows until a significant number of ions become trapped, at which time the shock ramp reforms near the leading edge of the whistler wave train. Electron inertial effects are found to be rather unimportant for the reformation mechanism, although some electrons are found to be accelerated to suprathermal velocities by the whistler precursor.

A straightforward modification which reduces by half the computational cost of standard particle-in-cell algorithms for simulation of plasmas is described. The saving is obtained by integrating only the electrons through a number of time steps (sub-cycles) in order to resolve their evolution, while integrating the much slower ions only once per cycle, i.e., to match the time step of each species to their characteristic frequencies. A dispersion relation is derived which describes the numerical instabilities expected by sampling frequency arguments. Simulations support the broad features of the analytical results, viz., the maximum growth rate and domain of the instability, and its stabilization by the addition of weak damping. An implicit sub-cycling algorithm is suggested which may provide further saving while avoiding a limitation of implicit algorithms described elsewhere.