Simone Landi

HIGH-RESOLUTION HYBRID SIMULATIONS OF KINETIC PLASMA TURBULENCE AT PROTON SCALES

We investigate properties of plasma turbulence from magneto-hydrodynamic (MHD) to sub-ion scales by means of two-dimensional, high-resolution hybrid particle-in-cell simulations. We impose an initial ambient magnetic field, perpendicular to the simulation box, and we add a spectrum of large-scale magnetic and kinetic fluctuations, with energy equipartition and vanishing correlation. Once the turbulence is fully developed, we observe a MHD inertial range, where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power-law scaling with spectral indices of -5/3 and -3/2, respectively. This behavior is extended over a full decade in wavevectors and is very stable in time. A transition is observed around proton scales. At sub-ion scales, both spectra steepen, with the former still following a power law with a spectral index of ~-3. A -2.8 slope is observed in the density and parallel magnetic fluctuations, highlighting the presence of compressive effects at kinetic scales. The spectrum of the perpendicular electric fluctuations follows that of the proton bulk velocity at MHD scales, and flattens at small scales. All these features, which we carefully tested against variations of many parameters, are in good agreement with solar wind observations. The turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions. While the parallel proton heating is found to be independent on the resistivity, the number of particles per cell and the resolution employed, the perpendicular proton temperature strongly depends on these parameters.

On the temperature profile and heat flux in the solar corona: Kinetic simulations

In the solar corona the collisional mean free path for a thermal particle (electrons or protons) is of the order of 10 2 to 10 4 times the typical scale of variation H of macroscopic quantities like the density or the temperature. Despite the relative smallness of the ratio =H, an increasingly large number of authors have become convinced that the heat flux in such a plasma cannot be described satisfactorily by theories which suppose that the local particle velocity distribution functions are close to Maxwellian. We address this question through kinetic simulations of the low solar corona by assuming that non thermal velocity distribution functions are present at the base of the corona. In particular, we show that if one assumes that the electron velocity distribution functions at the base of the corona have suciently strong suprathermal power law tails, the heat flux may flow upwards, i.e. in the direction of increasing temperature. Using kappa velocity distribution functions as prototypes for non thermal velocity distributions, we nd that the heat conduction can be properly described by the classical Spitzer &H ¨ (1953) law provided the kappa index is> 5. This value is much smaller than the value previously found by Dorelli & Scudder (1999). In addition we show that, unless extremely strong power law tails are assumed near the base of the corona (i.e. <4), a local heating mechanism (e.g. waves) is needed to sustain the temperature gradient between the base of the corona and the coronal temperature maximum.

SOLAR WIND TURBULENCE FROM MHD TO SUB-ION SCALES: HIGH-RESOLUTION HYBRID SIMULATIONS

We present results from a high-resolution and large-scale hybrid (fluid electrons and particle-in-cell protons) two-dimensional numerical simulation of decaying turbulence. Two distinct spectral regions (separated by a smooth break at proton scales) develop with clear power-law scaling, each one occupying about a decade in wave numbers. The simulation results exhibit simultaneously several properties of the observed solar wind fluctuations: spectral indices of the magnetic, kinetic, and residual energy spectra in the magneto-hydrodynamic (MHD) inertial range along with a flattening of the electric field spectrum, an increase in magnetic compressibility, and a strong coupling of the cascade with the density and the parallel component of the magnetic fluctuations at sub-proton scales. Our findings support the interpretation that in the solar wind large-scale MHD fluctuations naturally evolve beyond proton scales into a turbulent regime that is governed by the generalized Ohms law.

ON THE COMPETITION BETWEEN RADIAL EXPANSION AND COULOMB COLLISIONS IN SHAPING THE ELECTRON VELOCITY DISTRIBUTION FUNCTION: KINETIC SIMULATIONS

We present numerical simulations of the solar wind using a fully kinetic model which takes into account the effects of particles binary collisions in a quasi-neutral plasma in spherical expansion. Starting from an isotropic Maxwellian velocity distribution function for the electrons, we show that the combined effect of expansion and Coulomb collisions leads to the formation of two populations: a collision-dominated cold and dense population almost isotropic in velocity space and a weakly collisional, tenuous field-aligned and antisunward drifting population generated by mirror force focusing in the radially decreasing magnetic field. The relative weights and drift velocities for the two populations observed in our simulations are in excellent agreement with the relative weights and drift velocities for both core and strahl populations observed in the real solar wind. The radial evolution of the main moments of the electron velocity distribution function is in the range observed in the solar wind. The electron temperature anisotropy with respect to the magnetic field direction is found to be related to the ratio between the collisional time and the solar wind expansion time. Even though collisions are found to shape the electron velocity distributions and regulate the properties of the strahl, it is found that the heat flux is conveniently described by a collisionless model where a fraction of the electron thermal energy is advected at the solar wind speed. This reinforces the currently largely admitted fact that collisions in the solar wind are clearly insufficient to force the electron heat flux obey the classical Spitzer-Harm expression where heat flux and temperature gradient are proportional to each other. The presented results show that the electron dynamics in the solar wind cannot be understood without considering the role of collisions.

Resistive Magnetohydrodynamics Simulations of the Ideal Tearing Mode

We study the linear and nonlinear evolution of the tearing instability on thin current sheets by means of two-dimensional numerical simulations, within the framework of compressible, resistive magnetohydrodynamics. In particular we analyze the behavior of current sheets whose inverse aspect ratio scales with the Lundquist number S as S 1=3 . This scaling has been recently recognized to yield the threshold separating fast, ideal reconnection, with an evolution and growth which are independent of S provided this is high enough, as it should be natural having the ideal case as a limit for S! 1. Our simulations conrm that the tearing instability growth rate can be as fast as 0:6 A 1 , where A is the ideal Alfv enic time set by the macroscopic scales, for our least diusive case with S = 10 7 . The expected instability dispersion relation and eigenmodes are also retrieved in the linear regime, for the values of S explored here. Moreover, in the nonlinear stage of the simulations we observe secondary events obeying the same critical scaling with S, here calculated on the local, much smaller lengths, leading to increasingly faster reconnection. These ndings strongly support the idea that in a fully dynamic regime, as soon as current sheets develop, thin and reach this critical threshold in their aspect ratio, the tearing mode is able to trigger plasmoid formation and reconnection on the local (ideal) Alfv enic timescales, as required to explain the explosive aring activity often observed in solar and astrophysical plasmas. Subject headings: plasmas { MHD { methods: numerical.

ALFVEN WAVES AND SHOCK WAVE FORMATION AT AN X-POINT MAGNETIC FIELD CONFIGURATION

We present MHD numerical simulations of the propagation of Alfven waves in inhomogeneous magnetic fields whose topology consists of two-dimensional X-points threaded by a nonvanishing normal component. The coupling of the waves with the background field gradients leads to the development of fast-mode shock trains propagating normal to the average normal magnetic field. The fronts occur with a frequency matching that of the generating Alfven wave. Energy in the original Alfven wave packet is channeled via mode transformation to the fast waves and into the shocks, where it is dissipated at a rate independent of the Reynolds number. Such X-point shock trains might therefore play an important role in the heating of the solar corona plasma and, more generally, in cosmic particle acceleration.

Acceleration of weakly collisional solar-type winds

One of the basic properties of the solar wind, the high speed of the fast wind, is still not satisfactorily explained. This is mainly due to the theoretical difficulty of treating weakly collisional plasmas. The fluid approach implies that the medium is collision dominated and that the particle velocity distributions are close to Maxwellian. However, the electron velocity distributions observed in the solar wind depart significantly from Maxwellian. Recent kinetic collisionless models (called exospheric) using velocity distributions with a suprathermal tail have been able to reproduce the high speeds of the fast solar wind. In this Letter we present new developments of these models by generalizing them over a large range of corona conditions. We also present new results obtained by numerical simulations that include collisions. Both approaches calculate the heat flux self-consistently without any assumption on the energy transport. We show that both approaches—exospheric and collisional—yield a similar variation of the wind speed with the basic parameters of the problem; both produce a fast wind speed if the coronal electron distribution has a suprathermal tail. This suggests that exospheric models contain the necessary ingredients for powering a transonic stellar wind, including the fast solar wind.

Plasma turbulence and kinetic instabilities at ion scales in the expanding solar wind

The relationship between a decaying strong turbulence and kinetic instabilities in a slowly expanding plasma is investigated using two-dimensional (2-D) hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly-polarized, random-phase Alfvenic fluctuations which have energy equipartition between kinetic and magnetic fluctuations and vanishing correlation between the two fields. A turbulent cascade rapidly develops, magnetic field fluctuations exhibit a Kolmogorov-like power-law spectrum at large scales and a steeper spectrum at ion scales. The turbulent cascade leads to an overall anisotropic proton heating, protons are heated in the perpendicular direction, and, initially, also in the parallel direction. The imposed expansion leads to generation of a large parallel proton temperature anisotropy which is at later stages partly reduced by turbulence. The turbulent heating is not sufficient to overcome the expansion-driven perpendicular cooling and the system eventually drives the oblique firehose instability in a form of localized nonlinear wave packets which efficiently reduce the parallel temperature anisotropy. This work demonstrates that kinetic instabilities may coexist with strong plasma turbulence even in a constrained 2-D regime.

On the unconstrained expansion of a spherical plasma cloud turning collisionless: case of a cloud generated by a nanometre dust grain impact on an uncharged target in space

Nano and micrometre sized dust particles travelling through the heliosphere at several hundreds of km?s?1 have been repeatedly detected by interplanetary spacecraft. When such fast moving dust particles hit a solid target in space, an expanding plasma cloud is formed through the vaporization and ionization of the dust particles itself and part of the target material at and near the impact point. Immediately after the impact the small and dense cloud is dominated by collisions and the expansion can be described by fluid equations. However, once the cloud has reached ?m dimensions, the plasma may turn collisionless and a kinetic description is required to describe the subsequent expansion. In this paper we explore the late and possibly collisionless spherically symmetric unconstrained expansion of a single ionized ion?electron plasma using N-body simulations. Given the strong uncertainties concerning the early hydrodynamic expansion, we assume that at the time of the transition to the collisionless regime the cloud density and temperature are spatially uniform. We also neglect the role of the ambient plasma. This is a reasonable assumption as long as the cloud density is substantially higher than the ambient plasma density. In the case of clouds generated by fast interplanetary dust grains hitting a solid target, some 107 electrons and ions are liberated and the in vacuum approximation is acceptable up to meter order cloud dimensions. As such a cloud can be estimated to become collisionless when its radius has reached ?m order dimensions, both the collisionless approximation and the in vacuum approximation are expected to hold during a long lasting phase as the cloud grows by a factor 106. With these assumptions, we find that the transition from the collisional to the collisionless regime could occur when the electron Debye length ?D within the cloud is much smaller than the cloud radius R0, i.e. ?????D/R0???1. This implies a quasi-neutral expansion regime where the radial electron and ion density profiles are equal through most of the cloud except at the cloud?vacuum interface. The consequence of ? being much smaller than unity implies that the electrostatic fields within a cloud generated by a dust impact on a neutral target is ?100 times weaker than in the case of grains hitting a spacecraft, where the positive potential of the target is strong enough to strip-off all the electrons from the expanding cloud leading to a ?Coulomb explosion? like regime (e.g. Peano et al 2007 Phys. Plasmas \bf 14 056704).

Parametric decay of linearly polarized shear Alfvén waves in oblique propagation: One and two‐dimensional hybrid simulations

The parametric instability of a monochromatic shear Alfven wave in oblique propagation with respect the am- bient magnetic field is investigated in a kinetic regime, per- forming one-dimensional (1-D) and two-dimensional (2-D) hybrid simulations. The parallel component of the mother wave is found to be subject to a parametric decay which excites an ion-acoustic wave along the magnetic field and a backward propagating daughter shear Alfven wave, as in the instability for a purely parallel mother wave. At the same time, the acoustic wave generation supports the acceleration of a velocity beam in the ion distribution function, due to the non-linear trapping of protons. Moreover, the instabil- ity leads to the generation of broad band oblique spectra of coupled Alfvenic and compressive modes with variable per- pendicular wavevectors, and, as a consequence, the magnetic field after saturation is characterized by a strong transverse modulation. A 30 0.21 0.33 0.12 0.007 0.008 B 45 0.21 0.33 0.12 0.006 0.008 C 60 0.21 0.33 0.12 0.004 0.008