Vlasov-Maxwell Simulations Research Articles

Analysis of intermittent heating in a multi-component turbulent plasma

Kinetic effects and turbulence are two phenomena that characterize the solar wind, and, therefore, kinetic models represent the best tool of investigation for this collisionless plasma. In this work, hybrid Vlasov-Maxwell simulations are performed to investigate the intermittent heating of the solar wind, in a two-dimensional multi-ion plasma composed by protons, alpha particles and fluid electrons. The numerical results show that particle distribution functions depart from the typical Maxwellian configuration under the effect of the turbulence. Both ion species develop temperature anisotropy, with respect to the local magnetic field, that increases during the development of the turbulent cascade. During the nonlinear evolution of the system, coherent structures (vortices and current sheets) appear in physical space, related to the intermittent nature of the magnetic field. Conditioned ion temperature distributions suggest that enhancements of ion temperatures are associated with stronger coherent structures, in agreement with recent solar wind data analyses.

PROTON KINETIC EFFECTS IN VLASOV AND SOLAR WIND TURBULENCE

Kinetic plasma processes have been investigated in the framework of solar wind turbulence, employing Hybrid Vlasov-Maxwell (HVM) simulations. The dependency of proton temperature anisotropy T_{\perp}/T_{\parallel} on the parallel plasma beta \beta_{\parallel}, commonly observed in spacecraft data, has been recovered using an ensemble of HVM simulations. By varying plasma parameters, such as plasma beta and fluctuation level, the simulations explore distinct regions of the parameter space given by T_{\perp}/T_{\parallel} and \beta_{\parallel}, similar to solar wind sub-datasets. Moreover, both simulation and solar wind data suggest that temperature anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. This connection between non-Maxwellian kinetic effects and various types of intermittency may be a key point for understanding the complex nature of plasma turbulence.

On the multistream approach of relativistic Weibel instability. III. Comparison with full-kinetic Vlasov simulations

The saturation of the Weibel instability in the relativistic regime is investigated within the Hamiltonian reduction technique based on the multistream approach developed in paper I in the linear case and in paper II for the nonlinear saturation. In this work, the study is compared with results obtained by full kinetic 1D2V Vlasov-Maxwell simulations based on a semi-Lagrangian technique. For a temperature anisotropy, qualitatively different regimes are realized depending on the excitation of the longitudinal (plasma) electric field, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The emphasis here is on gaining a better understanding of the nonlinear aspects of the Weibel instability. The multistream model offers an alternate way to make calculations or numerical experiments more tractable, when only a few moments of the velocity distribution of the plasma are considered.

Numerical resolution of conservation laws with OpenCL

We present several numerical simulations of conservation laws on recent multicore processors, such as GPU's, using the OpenCL programming framework. Depending on the chosen numerical method, different implementation strategies have to be considered, for achieving the best performance. We explain how to program efficiently three methods: a finite volume approach on a structured grid, a high order Discontinuous Galerkin (DG) method on an unstructured grid and a Particle-In-Cell (PIC) method. The three methods are respectively applied to a two-fluid computation, a Maxwell simulation and a Vlasov-Maxwell simulation.

VLASOV SIMULATIONS OF MULTI-ION PLASMA TURBULENCE IN THE SOLAR WIND

Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the reference frame given by the local magnetic field. Anisotropy is found to be higher in regions of high magnetic stress. Both ion species manifest a preferentially perpendicular heating, although the anisotropy is more pronounced for the alpha particles, according with solar wind observations. Anisotropy of the alpha particle, moreover, is correlated to the proton anisotropy, and also depends on the local differential flow between the two species. Evident distortions of the particle distribution functions are present, with the production of bumps along the direction of the local magnetic field. The physical phenomenology recovered in these numerical simulations reproduces very common measurements in the turbulent solar wind, suggesting that the multi-ion Vlasov model constitutes a valid approach to the understanding of the nature of complex kinetic effects in astrophysical plasmas.

Excitation of nonlinear electrostatic waves with phase velocity close to the ion-thermal speed

Recent hybrid Vlasov–Maxwell simulations predicted the presence of a significant level of electrostatic activity, consisting of ion-acoustic waves and of a new branch of waves (called ion-bulk (IBk) waves), at short spatial scalelengths in the tail of the solar-wind turbulent cascade along the direction of the ambient magnetic field. These waves, driven by particle trapping processes, have phase speed comparable to the ion-thermal speed and acoustic dispersion. In this paper, the hybrid Vlasov–Maxwell code redesigned in the electrostatic configuration is used to reproduce the excitation of the IBk waves. An external driver electric field is applied to the plasma ions in order to create a population of trapped particles. This inhibits Landau damping that would otherwise suppress these low phase speed oscillations. The aim of this work is to show that the IBk waves, like ordinary linear modes, can be excited by general type drivers (even of low amplitude) applied to the plasma. Finally, Vlasov–Poisson simulations, with kinetic ions and Boltzmann electrons, are used to point out the limitations of the quasi-neutrality assumption, on which the hybrid model is based.

SHORT-WAVELENGTH ELECTROSTATIC FLUCTUATIONS IN THE SOLAR WIND

Hybrid Vlasov-Maxwell simulations have been used recently to investigate the dynamics of the solar-wind plasma in the tail at short wavelengths of the energy cascade. These simulations have shown that a significant level of electrostatic activity is detected at wavelengths smaller than the proton inertial scale in the longitudinal direction with respect to the ambient magnetic field. In this paper, we describe the results of a new series of hybrid Vlasov-Maxwell simulations that allow us to investigate in more detail the generation process of these electrostatic fluctuations in terms of the electron-to-proton temperature ratio Te /Tp . This analysis gives evidence for the first time that even in the case of cold electrons, Te Tp (the appropriate condition for solar-wind plasmas), the resonant interaction of protons with large-scale left-hand polarized ion-cyclotron waves is responsible for the excitation of short-scale electrostatic fluctuations with an acoustic dispersion relation. Moreover, through our numerical results we propose a physical mechanism to explain the generation of longitudinal proton-beam distributions in typical conditions of the solar-wind environment.

Stimulated backward Brillouin scattering in two ion-species plasmas

Stimulated Brillouin back-scattering in mixed carbon and hydrogen plasmas is studied using one-dimensional Vlasov–Maxwell simulation. It is found that both the fast and slow ion acoustic waves can scatter the incident light. Carbon ions can be trapped in the slow ion acoustic wave, and the hydrogen ions can be trapped in both the fast and slow waves. The trapped ions tend to reduce the Landau damping of the ion acoustic waves, and both the fast and slow ion acoustic waves can be excited. From the time-integrated scattering spectra, the scattering peaks of the fast and slow ion acoustic waves can be clearly distinguished.

Vlasov – Maxwell, Self-consistent Electromagnetic Wave Emission Simulations in the Solar Corona

1.5D Vlasov-Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the solar physics context. The simulations mimic the plasma emission mechanism and Larmor drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. When density gradient is removed (i.e. when plasma becomes stable to Larmor-drift instability) and a $low$ density, super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, plasma emission mechanism generates non-escaping Langmuir type oscillations which in turn generate escaping electromagnetic radiation. It is found that in the spatial location where the beam is injected, the standing waves, oscillating at the plasma frequency, are excited. These can be used to interpret the horizontal strips observed in some dynamical spectra. Quasilinear theory predictions: (i) the electron free streaming and (ii) the beam long relaxation time, in accord with the analytic expressions, are corroborated via direct, fully-kinetic simulation. Finally, the interplay of Larmor-drift instability and plasma emission mechanism is studied by considering $dense$ electron beam in the Larmor-drift unstable (inhomogeneous) plasma. http://www.maths.qmul.ac.uk/~tsiklauri/movie1.mpg * http://www.maths.qmul.ac.uk/~tsiklauri/movie2.mpg * http://www.maths.qmul.ac.uk/~tsiklauri/movie3.mpg

The kinetic nature of turbulence at short scales in the solar wind

The analysis of the transition from the large-scale fluid regime to the short-scale kinetic range of wavelengths in the development of the turbulent cascade of energy is nowadays subject of fervent discussion in the space plasmas scientific community. We make use of Hybrid Vlasov–Maxwell simulations where the full kinetic dynamics of ions is taken into account, while electrons are treated as a fluid. We investigate the development of turbulence in the solar wind, in 1D–3V phase space configuration and in the frequency range across the ion cyclotron frequency. These simulations allow for the analysis of the role of kinetic effects in the short-scale region of the energy spectra in the direction parallel to the background magnetic field. Our numerical results show the presence of a significant electrostatic activity at small wavelengths, triggered by the resonant interaction of ions with longitudinal waves. Our model does not allow to take into account the evolution of the turbulent spectra in the plane perpendicular to the ambient field, due to limited dimensionality in phase space. On the other hand, this model permits to isolate and study the possibility of transferring the electromagnetic large-scale energy on the small-scale kinetic electrostatic component of the spectrum. Peculiar features observed in the spacecraft data in the solar wind are qualitatively reproduced within the hybrid-Vlasov model, such as the generation of perpendicular temperature anisotropy and accelerated longitudinal beams of ions in the distribution of particle velocities as well as the appearance of a marked peak of electrostatic activity in the short-scale termination of the turbulent spectra.

The transition from plasma gratings to cavitons in laser-plasma interactions

One-dimensional Vlasov–Maxwell simulations of laser-plasma interactions are presented. It is shown that plasma gratings and density cavitons are formed sequentially. There are strong electromagnetic fields in the cavitons and the electromagnetic structures are nearly standing and long-lived. The formation of gratings and cavitons can be explained by a nonlinear second-order differential equation. The electromagnetic fields trapped in cavitons have both subcycle and cycle structures. Plasma whose density is higher than the critical density can be formed around the cavitons. Gratings and high density plasmas can reflect light in a very high level. This may be detrimental to the inertial confinement fusion.

Breakdown of electrostatic predictions for the nonlinear dispersion relation of a stimulated Raman scattering driven plasma wave

The kinetic nonlinear dispersion relation, and frequency shift δωsrs, of a plasma wave driven by stimulated Raman scattering are presented. Our theoretical calculations are fully electromagnetic, and use an adiabatic expression for the electron susceptibility which accounts for the change in phase velocity as the wave grows. When kλD≳0.35 (k being the plasma wave number and λD the Debye length), δωsrs is significantly larger than could be inferred by assuming that the wave is freely propagating. Our theory is in excellent agreement with 1D Eulerian Vlasov–Maxwell simulations when 0.3≤kλD≤0.58, and allows discussion of previously proposed mechanisms for Raman saturation. In particular, we find that no “loss of resonance” of the plasma wave would limit the Raman growth rate, and that saturation through a phase detuning between the plasma wave and the laser drive is mitigated by wave number shifts.

Saturation process induced by vortex-merging in numerical Vlasov-Maxwell experiments of stimulated Raman backscattering

The influence of low-frequency nonlinear Bernstein-Greene-Kruskal (BGK)-type waves induced by trapped electrons in backward stimulated Raman scattering is investigated in optical mixing. Semi-Lagrangian Vlasov-Maxwell simulations show two nonlinear behaviors. First, there is a Morales-O’Neil plasma wave frequency downshift retuned by a small wavenumber shift which maintains the Stimulated Raman Scattering (SRS) resonance. The saturation of Raman backscattering begins with phase space vortex merging followed by a transition to lower wavenumbers following the (nonlinear) dispersion relation, resembling weak turbulence.

Self-induced transparency scenario revisited via beat-wave heating induced by Doppler shift in overdense plasma layer

Maxwell-fluid simulations on a flat-topped moderately overdense plasma slab (typically n0∕nc=1–2) by Berezhiani et al. [Phys. Plasmas 66, 062308 (2005)] {see also the previous work of Tushentsov et al. [Phys. Rev. Lett. 87, 275002 (2001)]} were seen to lead to dynamic penetration of an ultrahigh intensity laser pulse into an overdense plasma. Two qualitatively different scenarios for the penetration of laser pulse into the overdense plasma were presented depending on the background density. In the first one, the penetration of laser energy occurs by soliton-like structures moving into the plasma. In the last one, electron cavitation occurs and the penetration is possible over a finite length only. A kinetic extension is made in this paper using Vlasov-Maxwell simulations. Vlasov simulations revealed a rich variety of new phenomena associated with the trapped particle dynamics, which cannot be described in fluid models. Most notably is the observation, during the penetration phase of the pump electromagnetic wave, of a beat-wave heating scenario induced by the Doppler shift on the reflected wave at the (moving) wave front. This beat-wave generates low-frequency acoustic-like electron modes characterized by coherent trapping-type structures in phase space leading to an efficient (nonstochastic) heating process.

Kinetic enhancement of Raman backscatter, and electron acoustic Thomson scatter

One-dimensional Eulerian Vlasov-Maxwell simulations are presented that show kinetic enhancement of stimulated Raman backscatter (SRBS) due to electron trapping in regimes of heavy linear Landau damping. The conventional Raman Langmuir wave is transformed into a set of beam acoustic modes [L. Yin et al., Phys. Rev. E 73, 025401 (2006)]. A low phase velocity electron acoustic wave (EAW) is seen developing from the self-consistent Raman physics. Backscatter of the pump laser off the EAW fluctuations is reported and referred to as electron acoustic Thomson scatter. This light is similar in wavelength to, although much lower in amplitude than, the reflected light between the pump and SRBS wavelengths observed in single-hot-spot experiments, and previously interpreted as stimulated electron acoustic scatter [D. S. Montgomery et al., Phys. Rev. Lett. 87, 155001 (2001)]. The EAW observed in our simulations is strongest well below the phase-matched frequency for electron acoustic scatter, and therefore the EAW is not produced by it. The beating of different beam acoustic modes is proposed as the EAW excitation mechanism, and is called beam acoustic decay. Supporting evidence for this process, including bispectral analysis, is presented. The linear electrostatic modes, found by projecting the numerical distribution function onto a Gauss-Hermite basis, include beam acoustic modes (some of which are unstable even without parametric coupling to light waves) and a strongly damped EAW similar to the observed one. This linear EAW results from non-Maxwellian features in the electron distribution, rather than nonlinearity due to electron trapping.

Stimulated-Raman-scatter behavior in a relativistically hot plasma slab and an electromagnetic low-order pseudocavity

Particle simulations on a flat-topped somewhat underdense (typically n0/nc = 0.6) plasma slab by Nikolic [Phys. Rev. E 66, 036404 (2002)] were seen to give transient stimulated scattering behavior with frequency shift [omega0 - omegas(approximately omegap)] considerably less than the plasma frequency omegap. This has been linked to the electron acoustic wave (EAW) and the scattering was thus seen as another example of stimulated electron acoustic scattering inferred by Montgomery [Phys. Rev. Lett. 87, 155001 (2001)] from experiments on low-density plasmas. Montgomery had noted the difficulty of how one could have a very narrow observed scattering from a wave whose damping was at least initially very high. Our Vlasov-Maxwell simulations for such somewhat underdense (n0/nc > or = 0.25) plasmas show that the simulation resonance was in fact determined by the beating of the pump with a new "radiating pseudocavity" electromagnetic mode for the slab at a frequency close to omegap with relatively low loss. This allows the initial narrow-band excitation of the kinetic electrostatic electron nonlinear (KEEN) waves (the nonlinear "cousins" of EAWs) at a well-defined frequency (omegaK approximately omega0 - omegap < omegap) which is not necessarily the value given by the EAW dispersion relation. (The KEEN wave characteristics have been discussed by Afeyan [33rd AAAC (2003), #238, IFSA 2003].) The consideration of such a mechanism is relevant to moderately underdense hot plasmas.

Nonlinear kinetic effects induced by electrostatic weak turbulence in Vlasov-Maxwell simulations of stimulated Raman Back-Scattering in optical mixing

We report here semi-lagrangian Vlasov-Maxwell simulations of laser-plasma instabilities in an underdense plasma in which an essential role is played not only by the conventional instabilities as Stimulated Raman Back-Scattering (SRBS) (involving the scattering off of high-frequency electron plasma waves) but also by organized trapped electron modes resulting from such instabilities. Electron hole merging in phase space modifies the nonlinear frequency shift of the electron plasma wave. A Raman-like parametric instability is generated with shifted scattered modes, matching conditions being conserved in time in spite of the shift.

Vlasov-Maxwell simulations of high-frequency longitudinal waves in a magnetized plasma.

The plasma response to the injection of a propagating purely electrostatic wave of finite amplitude is investigated by means of a kinetic code which solves the Vlasov equations for electrons and ions in the three-dimensional (one spatial and two in velocity, 1D2V) phase space, self-consistently coupled to the Maxwell equations. The plasma is uniformly magnetized, and the wave frequency close to the cold upper-hybrid resonance omega(0)=sqrt[omega(2)(pe)+omega(2)(ce)] is considered. Coherent structures are formed in the phase space that would be completely missed by a hydrodynamic analysis. In particular, in the early stage of the interaction, the initially unperturbed equilibrium electron distribution is strongly affected as a whole by the pump, taking a ringlike shape in the velocity plane transverse to the magnetic field. Then, a sort of instability occurs, leading to the broadening and flattening of the electron distribution.

Vlasov-Maxwell kinetic simulations of radio-frequency-driven ion flows in magnetized plasmas.

The generation of a coherent ion flow due to the injection in a plasma of a purely electrostatic wave of finite amplitude, propagating at right angle with the ambient uniform magnetic field, is investigated making use of a kinetic code which solves the fully nonlinear Vlasov equations for electrons and ions, coupled with the Maxwell equations, in one spatial and two velocity dimensions. A uniformly magnetized slab plasma is considered. The wave frequency is assumed in the range of the fourth harmonic of the ion cyclotron frequency, and the wave vector is chosen in order to model the propagation of an ion Bernstein wave. The computation of the first-order moment of the ion distribution function shows that indeed a quasistationary transverse average ion drift velocity is produced. The time evolution of the ion distribution function undergoes a "resonant" interaction of Cherenkov type, even if the plasma ions are magnetized (omega(ci)/omega(pi) approximately 0.5). During the wave-plasma interaction, the electron distribution function remains Gaussian-like, while increasing its energy content.

Two-stage electron acceleration by simultaneous stimulated Raman backward and forward scattering

The coexistence of stimulated Raman forward and backward scattering of intense electromagnetic radiation, which can occur, for instance, in laser fusion plasmas, is investigated. The simultaneous Raman forward and backward scattering is shown to create an electrostatic field structure which is exceptionally efficient in producing highly relativistic electrons. The mechanism of the electron acceleration is analyzed both by Vlasov–Maxwell simulations with self-consistent fields and by test particle calculations with prescribed electrostatic fields. The Vlasov–Maxwell simulations reveal that the two plasma waves generated by the backward and forward scattering are spatially separated, and thus form a two-stage electron ‘‘accelerator.’’