Lorenzo Matteini

WHISTLER MODE WAVES AND THE ELECTRON HEAT FLUX IN THE SOLAR WIND: CLUSTER OBSERVATIONS

The nature of the magnetic field fluctuations in the solar wind between the ion and electron scales is still under debate. Using the Cluster/STAFF instrument, we make a survey of the power spectral density and of the polarization of these fluctuations at frequencies f in [1, 400] Hz, during five years (2001-2005), when Cluster was in the free solar wind. In ~10% of the selected data, we observe narrowband, right-handed, circularly polarized fluctuations, with wave vectors quasi-parallel to the mean magnetic field, superimposed on the spectrum of the permanent background turbulence. We interpret these coherent fluctuations as whistler mode waves. The lifetime of these waves varies between a few seconds and several hours. Here, we present, for the first time, an analysis of long-lived whistler waves, i.e., lasting more than five minutes. We find several necessary (but not sufficient) conditions for the observation of whistler waves, mainly a low level of background turbulence, a slow wind, a relatively large electron heat flux, and a low electron collision frequency. When the electron parallel beta factor β e∥ is larger than 3, the whistler waves are seen along the heat flux threshold of the whistler heat flux instability. The presence of such whistler waves confirms that the whistler heat flux instability contributes to the regulation of the solar wind heat flux, at least for β e∥ ≥ 3, in slow wind at 1 AU.

Heating and cooling of protons in the fast solar wind between 0.3 and 1 AU: Helios revisited

The proton thermal energetics in the fast solar wind between 0.3 and 1 AU is re-investigated using the Helios 1 and 2 data. Closer to the Sun, it is estimated that, to ac- count for the observed radial profiles of the proton parallel and perpendicular temperature, non- negligible parallel cooling and perpendicular heating are necessary. Around 1 AU heating is needed in both directions. We also calculate the corresponding rates and find that in total sig- nificant interplanetary heating is necessary, in agreement with previous results. The possible influence that deceleration of fast solar wind streams due to interaction with slow ones has on the proton thermodynamics is evaluated.

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.

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.

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.

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

Plasma beta dependence of the ion-scale spectral break of solar wind turbulence: high-resolution 2D hybrid simulations

We investigate properties of the ion-scale spectral break of solar wind turbulence 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 add a spectrum of in-plane, large-scale, magnetic and kinetic fluctuations. We perform a set of simulations with different values of the plasma β, distributed over three orders of magnitude, from 0.01 to 10. In all cases, once turbulence is fully developed, we observe a power-law spectrum of the fluctuating magnetic field on large scales (in the inertial range) with a spectral index close to −5/3, while in the sub-ion range we observe another power-law spectrum with a spectral index systematically varying with β (from around −3.6 for small values to around −2.9 for large ones). The two ranges are separated by a spectral break around ion scales. The length scale at which this transition occurs is found to be proportional to the ion inertial length, d i , for β 1 and to the ion gyroradius, , for β 1, i.e., to the larger between the two scales in both the extreme regimes. For intermediate cases, i.e., β ~ 1, a combination of the two scales is involved. We infer an empiric relation for the dependency of the spectral break on β that provides a good fit over the whole range of values. We compare our results with in situ observations in the solar wind and suggest possible explanations for such a behavior.

Dependence of solar wind speed on the local magnetic field orientation: Role of Alfvénic fluctuations

We report an analysis of correlations between magnetic field and velocity fluctuations in the fast solar wind beyond 1 AU at high latitudes. We have found that on scales shorter than the microstream structures, there exists a well-defined dependence of the flow speed on the angle between the magnetic field vector and the radial direction. Solar wind is found to be slightly faster when the measured magnetic field vector is transverse to the velocity, while it is always slower when the magnetic field is parallel, or antiparallel, to the radial direction. We show that this correlation is a direct consequence of the high Alfvenicity of fast wind fluctuations and that it can be reasonably described by a simple model taking into account the main properties of the low-frequency antisunward Alfven fluctuations as observed in the solar wind plasma. We also discuss how switchbacks, short periods of magnetic field reversals, naturally fit in this new observed correlation.

PROTON TEMPERATURE ANISOTROPY AND MAGNETIC RECONNECTION IN THE SOLAR WIND: EFFECTS OF KINETIC INSTABILITIES ON CURRENT SHEET STABILITY

We investigate the role of kinetic instabilities driven by a proton anisotropy on the onset of magnetic reconnection by means of two-dimensional hybrid simulations. The collisionless tearing of a current sheet is studied in the presence of a proton temperature anisotropy in the surrounding plasma. Our results confirm that anisotropic protons within the current sheet region can significantly enhance/stabilize the tearing instability of the current. Moreover, fluctuations associated with linear instabilities excited by large proton temperature anisotropies can significantly influence the stability of the plasma and perturb the current sheets, triggering the tearing instability. We find that such a complex coupling leads to a faster tearing evolution in the T_\Vert