Luca Franci

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.

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.

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.

Plasma turbulence at ion scales: a comparison between particle in cell and Eulerian hybrid-kinetic approaches

Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma models is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning approximately two decades in wavenumber – from the magnetohydrodynamics inertial range to scales well below the ion gyroradius – with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell simulations of freely decaying Alfvenic turbulence, whereas the other consists of Eulerian hybrid Vlasov–Maxwell simulations of turbulence continuously driven with partially compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at

Magnetic Reconnection as a Driver for a Sub-ion-scale Cascade in Plasma Turbulence

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Dynamical bar-mode instability in rotating and magnetized relativistic stars

are observed, where

Mirror Instability in the Turbulent Solar Wind

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Solar Wind Turbulent Cascade from MHD to Sub-ion Scales: Large-size 3D Hybrid Particle-in-cell Simulations

is the fluctuations’ wavenumber perpendicular to the background magnetic field and

Two-dimensional hybrid simulations of kinetic plasma turbulence: Current and vorticity vs proton temperature

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