plasma turbulence

The solar wind contains fast, suprathermal electrons that stream from the sun along the Parker-spiraled magnetic field lines. These electrons experience very weak Coulomb collisions and they get collimated in a narrow beam (strahl). When Coulomb collisions are not efficient, the strahl is broadened by interactions with plasma turbulence. We argue that at high energies, the strahl electrons can efficiently interact with whistler waves. We demonstrate how pitch-angle scattering by whistler turbulence can be incorporated into the kinetic theory of electron strahl broadening. By measuring the strahl width, one can estimate the parameters of whistler turbulence.

Turbulent space and astrophysical plasmas have a complex dynamics, which involve nonlinear coupling across different temporal and spatial scales. There is growing evidence that impulsive events, such as magnetic reconnection instabilities, bring to a spatially localized enhancement of energy dissipation, thus speeding up the energy transfer at small scales. Indeed, capturing such a diverse dynamics is challenging. In this work, we employ the Multidimensional Iterative Filtering (MIF) method, a novel multiscale technique for the analysis of non-stationary non-linear multidimensional signals. Unlike other traditional methods (e.g., based on Fourier or wavelet decomposition), MIF natively performs the analysis without any previous assumption on the functional form of the signal to be identified. Using MIF, we carry out a multiscale analysis of Hall-MHD and Hybrid particle-in-cell numerical simulations of decaying plasma turbulence. Preliminary results assess the ability of MIF to detect localized coherent structures and to separate and characterize their contribution to the turbulent dynamics.

The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize high-resolution observational and simulation data to investigate the nature of waves and structures emerging in a weakly collisional, turbulent kinetic plasma. Observational results are based on in situ solar wind measurements from the Cluster and MMS spacecraft, and the simulation results are obtained from an externally driven, three-dimensional fully kinetic simulation. Using a set of novel diagnostic measures we show that both the large-amplitude structures and the lower-amplitude background fluctuations preserve linear features of kinetic Alfvén waves to order unity. This quantitative evidence suggests that the kinetic turbulence cannot be described as a mixture of mutually exclusive waves and structures but may instead be pictured as an ensemble of localized, anisotropic wave packets or “eddies” of varying amplitudes, which preserve certain linear wave properties during their nonlinear evolution.

We present numerical results from high-resolution hybrid and fully kinetic simulations of plasma turbulence, following the development of the energy cascade from large magnetohydrodynamic scales down to electron characteristic scales. We explore a regime of plasma turbulence where the electron plasma beta is low, typical of environments where the ions are much hotter than the electrons, e.g., the Earth’s magnetosheath and the solar corona, as well as regions downstream of collisionless shocks. In such range of scales, recent theoretical models predict a different behaviour in the nonlinear interaction of dispersive wave modes with respect to what is typically observed in the solar wind, i.e., the presence of so-called inertial kinetic Alfvén waves. We also extend our analysis to scales around and smaller than the electron gyroradius, where hints of a further steepening of the magnetic and electric field spectra have been recently observed by the NASA’s Magnetospheric Multiscale mission, although not yet supported by theoretical models. Our numerical simulations exhibit a remarkable quantitative agreement with recent observations by MMS in the magnetosheath, allowing us to investigate simultaneously the spectral break around ion scales and the two spectral breaks at electron scales, the magnetic compressibility, and the nature of fluctuations at kinetic scales.

Perhaps the most popular and most productive route by which the theoretical machinery of fusion science has been ported to astrophysical plasmas was the application of gyrokinetic theory to the problem of collisionless plasma turbulence in accretion flows and in the heliosphere, in particular to the question of how energy is partitioned between species (ions and electrons) when this turbulence is thermalised. After many years of promising, but perhaps not entirely conclusive advances in this area, the latest news is that we finally have some quantitative grasp on the answer: GK turbulence promotes disequilibration of species: at high beta, ions are preferentially heated; at low beta, electrons are. This conclusion is supported by GK simulations, which are finally able to give us a heating vs. beta and Ti/Te curve [Kawazura et al. 2019, PNAS 116, 771] and, in the case of low beta, also by relatively rigorous theory [Schekochihin et al. 2019, JPP in press/arXiv:1812.09792]. I will review this progress, spell out caveats (of course there are caveats), and describe the next steps, including some theoretical progress on the high-beta regime.

The relationship between a decaying plasma turbulence and proton fire hose instabilities in a slowly expanding plasma is investigated using three-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the radial direction simulation box, and we start with an isotropic spectrum of large-scale, linearly-polarized, random-phase Alfvenic fluctuations with zero cross-helicity. A turbulent cascade rapidly develops and leads to a weak proton heating that is not sufficient to overcome the expansion-driven perpendicular cooling. The plasma system eventually drives the parallel and oblique fire hose instabilities that generate quasi-monochromatic wave packets that reduce the proton temperature anisotropy. The fire hose wave activity has a low amplitude with wave vectors quasi-parallel/oblique with respect to the ambient magnetic field outside of the region dominated by the turbulent cascade and is discernible in one-dimensional power spectra taken only in the direction quasi-parallel/oblique with respect to the ambient magnetic field; at quasi-perpendicular angles the wave activity is hidden by the turbulent background. The fire hose wave activity reduces intermittency and the Shannon entropy but increases the Jensen-Shannon complexity of magnetic fluctuations.

Two textbook physical processes compete to thermalize turbulent fluctuations in collisionless plasmas: Kolmogorov’s “cascade” to small spatial scales, where dissipation occurs, and Landau’s damping, which transfers energy to small scales in velocity space via “phase mixing”, also leading to dissipation. By direct numerical simulations and theoretical arguments, I will show during this presentation that in a magnetized plasma, another textbook process, plasma echo, brings energy back from phase space and on average cancels the effect of phase mixing. Energy cascades effectively as it would in a fluid system and thus Kolmogorov wins the competition with Landau for the free energy in a collisionless turbulent plasma. This reaffirms the universality of Kolmogorov’s picture of turbulence and explains, for example, the broad Kolmogorov-like spectra of density fluctuations observed in the solar wind.

The spectral properties at ion kinetic scales are studied by means of high-resolution three-dimensional numerical simulations using a hybrid codes which integrates the Vlasov system equations for the ions while it treats the electron as a neutralising fluid. We show that the observed anisotropy is less than what expected by theories of plasma turbulence at such scales. More specifically, we observe that the spectral anisotropy is frozen once the magnetic energy cascade reaches the ion kinetic scales. However, the non-linear energy transfer is still in the perpendicular direction with respect to the magnetic field, only advected in the parallel direction as expected balancing the non-linear energy transfer time and the decorrelation time. Such result can be explained by a phenomenological model based on the formation of strong intermittent two-dimensional structures in the plane perpendicular to the local mean field that fulfill some prescribed aspect ratio eventually depending on the scale. This model supports the idea that small scales structures, such as reconnecting current sheets, contribute significantly to the formation of the turbulent cascade at kinetic scales.

Multi-dimensional Eulerian simulations of the hybrid Vlasov-Maxwell model[1] have been employed to investigate the role kinetic effects in turbulent plasmas at typical ion scales. Numerical results suggest that kinetic effects manifest through the deformation of the ion distribution function, with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The velocity-space departure from Maxwellian of the ion velocity distributions has been also recovered in observational data from spacecraft. In a recent paper, Servidio et al.[2] investigated the velocity-space cascade process suggested by the highly structured shape of the ion velocity distribution detected by the NASA Magnetospheric Multiscale mission. Through a tree-dimensional Hermite transform, these authors pointed out a power-law distribution of moments and provided a theoretical prediction for the scaling, based on a Kolmogorov approach. Here, the possibility of a velocity-space cascade is investigated in the strongly magnetized case, in kinetic simulations of turbulence at ion scales. Through the Hermite decomposition of the ion velocity distribution from the simulations, we found that (i) the plasma displays spectral anisotropy in velocity space, due to the presence of the background magnetic field, (ii) the distribution of energy is in agreement with the prediction in Ref. [2] and (iii) the activity in velocity space shows a clear intermittent character in space, being enhanced close to coherent structures, such as the reconnecting current sheets produced by turbulence. Finally, in order to explore the possible role of inter-particle collisions, collisional and collisionless simulations of plasma turbulence have been compared using Eulerian Hybrid Boltzmann-Maxwell simulations, that explicitly model the proton-proton collisions through the nonlinear Dougherty operator.

This talk has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 776262 (AIDA, www.aida-space.eu)

[1] Valentini, F. et al., J. Comput. Phys. 225 2007, 753-770

[2] Servidio, S. et al., Phys. Rev. Lett. 119 2017, 205101