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Where and under what conditions the transfer of energy between electromagnetic fields and particles takes place in the solar wind remains an open question. We investigate the conditions that promote the growth of kinetic instabilities predicted by linear theory, to infer how turbulence and temperature-anisotropy-driven instabilities are interrelated. Using a large dataset from Solar Orbiter, we introduce the radial rate of strain, a novel measure computed from single-spacecraft data, that we interpret as a proxy for the double-adiabatic strain rate. The solar wind exhibits high absolute values of the radial rate of strain at locations with large temperature anisotropy. We measure the kurtosis and skewness of the radial rate of strain from the statistical moments to show that it is non-Gaussian for unstable intervals and increasingly intermittent at smaller scales with a power-law scaling. We conclude that the velocity field fluctuations in the solar wind contribute to the presence of temperature anisotropy sufficient to create potentially unstable conditions., Comment: Accepted for publication in the Journal of Plasma Physics

The solar wind is highly turbulent, and intermittency effects are observed for fluctuations within the inertial range. By analyzing magnetic field spectra and fourth-order moments, we perform a comparative study of intermittency in different types of solar wind measured during periods of solar minima and a maximum. Using eight fast solar wind intervals measured during solar minima between 0.3 au and 3.16 au, we found a clear signature of two inertial sub-ranges with $f^{-3/2}$ and $f^{-5/3}$ power laws in the magnetic power spectra. The intermittency, measured through the scaling law of the kurtosis of magnetic field fluctuations, further confirms the existence of two different power laws separated by a clear break. A systematic study on the evolution of the said sub-ranges as a function of heliospheric distance shows correlation of the break scale with both the turbulence outer scale and the typical ion scales. During solar maximum, we analyzed five intervals for each of Alfv\'enic fast, Alfv\'enic slow and non-Alfv\'enic slow solar wind. Unlike the case during the solar minima, the two sub-ranges are no longer prominent and the Alfv\'enic slow wind is found to be in an intermediate state of turbulence compared to that of the fast wind and the usual non-Alfv\'enic slow wind., Comment: 16 pages, 11 figures, submitted to ApJ

We analyze in-situ observations of imbalanced solar wind turbulence to evaluate MHD turbulence models grounded in "Critical Balance" (CB) and "Scale-Dependent Dynamic Alignment" (SDDA). At energy injection scales, both outgoing and ingoing modes exhibit a weak cascade; a simultaneous tightening of SDDA is noted. Outgoing modes persist in a weak cascade across the inertial range, while ingoing modes shift to a strong cascade at $\lambda \approx 3 \times 10^{4} d_i$, with associated spectral scalings deviating from expected behavior due to "anomalous coherence" effects. The inertial range comprises two distinct sub-inertial segments. Beyond $\lambda \gtrsim 100 d_i$, eddies adopt a field-aligned tube topology, with SDDA signatures mainly evident in high amplitude fluctuations. The scaling exponents $\zeta_{n}$ of the $n$-th order conditional structure functions, orthogonal to both the local mean field and fluctuation direction, align with the analytical models of Chandran et al. 2015 and Mallet et al. 2017, indicating "multifractal" statistics and strong intermittency; however, scaling in parallel and displacement components is more concave than predicted, possibly influenced by expansion effects. Below $\lambda \approx 100 d_i$, eddies become increasingly anisotropic, evolving into thin current sheet-like structures. Concurrently, $\zeta_{n}$ scales linearly with order, marking a shift towards "monofractal" statistics. At $\lambda \approx 8 d_i$, the increase in aspect ratio halts, and the eddies become quasi-isotropic. This change may signal tearing instability, leading to reconnection, or result from energy redirection into the ion-cyclotron wave spectrum, aligning with the "helicity barrier". Our analysis utilizes 5-point structure functions, proving more effective than the traditional 2-point method in capturing steep scaling behaviors at smaller scales.

The problems of heating and acceleration of solar wind particles are of significant and enduring interest in astrophysics. The interactions between waves and particles are crucial in determining the distributions of proton and alpha particles, resulting in non-Maxwellian characteristics including temperature anisotropies and particle beams. These processes can be better understood as long as the beam can be separated from the core for the two major components of the solar wind. We utilized an alternative numerical approach that leverages the clustering technique employed in Machine Learning to differentiate the primary populations within the velocity distribution, rather than employing the conventional bi-Maxwellian fitting method. Separation of the core and beam revealed new features for protons and alphas. We estimated that the total temperature of the two beams was slightly higher than that of their respective cores, and the temperature anisotropy for the cores and beams was larger than 1. We concluded that the temperature ratio between alphas and protons largely over 4 is due to the presence of a massive alpha beam, which is approximately 50\% of the alpha core. We provided evidence that the alpha core and beam populations are sensitive to Alfv\'enic fluctuations and the surfing effect found in the literature can be recovered only when considering the core and beam as a single population. Several similarities between proton and alpha beams would suggest a common and local generation mechanism not shared with the alpha core, which may not have necessarily been accelerated and heated locally., Comment: paper accepted by APJ on May 4th 2024, 24 pages, 21 figures

Context. The mechanisms regulating the transport and energization of charged particles in space and astrophysical plasmas are still debated. Plasma turbulence is known to be a powerful particle accelerator. Large-scale structures, including flux ropes and plasmoids, may contribute to confine particles and lead to fast particle energization. These structures may also modify the properties of the turbulent nonlinear transfer across scales. Aims. We investigate how large-scale flux ropes are perturbed and, simultaneously, influence the nonlinear transfer of turbulent energy towards smaller scales. We then address how these structures affect particle transport and energization. Methods. We adopt magnetohydrodynamic simulations for perturbing a large-scale flux rope in solar-wind conditions and possibly triggering turbulence. Then, we employ test-particle methods to investigate particle transport and energization in the perturbed flux rope. Results. The large-scale helical flux rope inhibits the turbulent cascade towards smaller scales, especially if the amplitude of the initial perturbations is not large (~5%). In this case, particle transport is inhibited inside the structure. Fast particle acceleration occurs in association with phases of trapped motion within the large-scale flux rope., Comment: 15 pages, 15 figures. Submitted to Astronomy & Astrophysics, comments are welcome!

The complex interaction between shocks and plasma turbulence is extremely important to address crucial features of energy conversion in a broad range of astrophysical systems. We study the interaction between a supercritical, perpendicular shock and pre-existing, fully-developed plasma turbulence, employing a novel combination of magnetohydrodynamic (MHD) and small-scale, hybrid-kinetic simulations where a shock is propagating through a turbulent medium. The variability of the shock front in the unperturbed case and for two levels of upstream fluctuations is addressed.We find that the behaviour of shock ripples, i.e., shock surface fluctuations with short (a few ion skin depths, $d_i$) wavelengths, is modified by the presence of pre-existing turbulence, which also induces strong corrugations of the shock front at larger scales. We link this complex behaviour of the shock front and the shock downstream structuring with the proton temperature anisotropies produced in the shock-turbulence system. Finally, we put our modelling effort in the context of spacecraft observations, elucidating the role of novel cross-scale, multi-spacecraft measurements in resolving shock front irregularities at different scales. These results are relevant for a broad range of astrophysical systems characterised by the presence of shock waves interacting with plasma turbulence., Comment: Submitted to MNRAS

We investigate turbulence in magnetic reconnection jets in the Earth's magnetotail using data from the Magnetospheric Multiscale spacecraft. We show that signatures of a limited inertial range are observed in many reconnection jets. The observed turbulence develops on the time scale of a few ion gyroperiods, resulting in intermittent multifractal energy cascade from the characteristic scale of the jet down to the ion scales. We show that at sub-ion scales, the fluctuations are close to mono-fractal and predominantly kinetic Alfv\'en waves. The observed energy transfer rate across the inertial range is $\sim 10^8~\mathrm{J}~\mathrm{kg}^{-1}~\mathrm{s}^{-1}$, which is the largest reported for space plasmas so far.

Evidence for the presence of ion cyclotron waves, driven by turbulence, at the boundaries of the current sheet is reported in this paper. By exploiting the full potential of the joint observations performed by Parker Solar Probe and the Metis coronagraph on board Solar Orbiter, local measurements of the solar wind can be linked with the large-scale structures of the solar corona. The results suggest that the dynamics of the current sheet layers generates turbulence, which in turn creates a sufficiently strong temperature anisotropy to make the solar-wind plasma unstable to anisotropy-driven instabilities such as the Alfv\'en ion-cyclotron, mirror-mode, and firehose instabilities. The study of the polarization state of high-frequency magnetic fluctuations reveals that ion cyclotron waves are indeed present along the current sheet, thus linking the magnetic topology of the remotely imaged coronal source regions with the wave bursts observed in situ. The present results may allow improvement of state-of-the-art models based on the ion cyclotron mechanism, providing new insights into the processes involved in coronal heating., Comment: 12 pages

The linear scaling of the mixed third-order moment of the magnetohydrodynamic fluctuations is used to estimate the energy transfer rate of the turbulent cascade in the expanding solar wind. In 1976 the Helios 2 spacecraft measured three samples of fast solar wind originating from the same coronal hole, at different distance from the sun. Along with the adjacent slow solar wind streams, these represent a unique database for studying the radial evolution of turbulence in samples of undisturbed solar wind. A set of direct numerical simulations of the MHD equations performed with the Lattice-Boltzmann code FLAME is also used for interpretation. We show that the turbulence energy transfer rate decays approximately as a power law of the distance, and that both the amplitude and decay law correspond to the observed radial temperature profile in the fast wind case. Results from magnetohydrodynamic numerical simulations of decaying magnetohydrodynamic turbulence show a similar trend for the total dissipation, suggesting an interpretation of the observed dynamics in terms of decaying turbulence, and that multi-spacecraft studies of the solar wind radial evolution may help clarifying the nature of the evolution of the turbulent fluctuations in the ecliptic solar wind., Comment: In press on Astron. Astrophys

Solar wind measurements carried out by NASA's Wind spacecraft before, during and after the passing of an interplanetary coronal mass ejection (ICME) detected on 12-14 September 2014 have been used in order to examine several properties of magnetohydrodynamic (MHD) turbulence. Spectral indices and flatness scaling exponents of magnetic field, velocity and proton density measurements were obtained, and provided a standard description of the characteristics of turbulence within different sub-regions of the ICME and its surroundings. This analysis was followed by the validation of the third-order moment scaling law for isotropic, incompressible MHD turbulence in the same sub-regions, which confirmed the fully developed nature of turbulence in the ICME plasma. The energy transfer rate was also estimated in each ICME sub-region and in the surrounding solar wind. An exceptionally high value was found within the ICME sheath, accompanied by enhanced intermittency, possibly related to the powerful energy injection associated with the arrival of the ICME.

In this paper we discuss the results of some Molecular Dynamics simulations of a magnetized One Component Plasma, targeted to estimate the diffusion coefficient $D_{\perp}$ in the plane orthogonal to the magnetic field lines. We find that there exists a threshold with respect to the magnetic field strength $|\vec B|$: for weak magnetic field the diffusion coefficients scales as $1/|\vec B|^2$, while a slower decay appears at high field strength. The relation of this transition with the different mixing properties of the microscopic dynamics is investigated by looking at the behavior of the velocity auto correlation., Comment: 17 pages, 6 figures and 1 Table

Switchbacks are sudden, large radial deflections of the solar wind magnetic field, widely revealed in interplanetary space by the Parker Solar Probe. The switchbacks' formation mechanism and sources are still unresolved, although candidate mechanisms include Alfv\'enic turbulence, shear-driven Kelvin-Helmholtz instabilities, interchange reconnection, and geometrical effects related to the Parker spiral. This Letter presents observations from the Metis coronagraph onboard Solar Orbiter of a single large propagating S-shaped vortex, interpreted as first evidence of a switchback in the solar corona. It originated above an active region with the related loop system bounded by open-field regions to the East and West. Observations, modeling, and theory provide strong arguments in favor of the interchange reconnection origin of switchbacks. Metis measurements suggest that the initiation of the switchback may also be an indicator of the origin of slow solar wind.

This Letter addresses the first Solar Orbiter (SO) -- Parker Solar Probe (PSP) quadrature, occurring on January 18, 2021, to investigate the evolution of solar wind from the extended corona to the inner heliosphere. Assuming ballistic propagation, the same plasma volume observed remotely in corona at altitudes between 3.5 and 6.3 solar radii above the solar limb with the Metis coronagraph on SO can be tracked to PSP, orbiting at 0.1 au, thus allowing the local properties of the solar wind to be linked to the coronal source region from where it originated. Thanks to the close approach of PSP to the Sun and the simultaneous Metis observation of the solar corona, the flow-aligned magnetic field and the bulk kinetic energy flux density can be empirically inferred along the coronal current sheet with an unprecedented accuracy, allowing in particular estimation of the Alfv\'en radius at 8.7 solar radii during the time of this event. This is thus the very first study of the same solar wind plasma as it expands from the sub-Alfv\'enic solar corona to just above the Alfv\'en surface., Comment: 10 pages, 4 figures

Turbulence properties are examined before, during and after a coronal mass ejection (CME) detected by the6Wind spacecraft on July 2012. The power-law scaling of the structure functions, providing information on the7power spectral density and flatness of the velocity, magnetic filed and density fluctuations, were examined. The8third-order moment scaling law for incompressible, isotropic magnetohydrodynamic turbulence was observed9in the preceding and trailing solar wind, as well as in the CME sheath and magnetic cloud. This suggests that10the turbulence could develop sufficiently after the shock, or that turbulence in the sheath and cloud regions11was robustly preserved even during the mixing with the solar wind plasma. The turbulent energy transfer rate12was thus evaluated in each of the regions. The CME sheath shows an increase of energy transfer rate, as13expected from the lower level of Alfv\'enic fluctuations and suggesting the role of the shock-wind interaction as14an additional source of energy for the turbulent cascade.

Numerical simulations and experimental results have shown that current sheets formation in space plasmas can be associated with enhanced vorticity. Also, in simulations the generation of such structures is associated with strong plasma heating. Here, we compare four-point measurements in the terrestrial magnetosheath turbulence from the Multiscale magnetospheric mission (MMS) of the flow vorticity and the magnetic field curlometer versus their corresponding one-point proxies PVI(V) and PVI(B) based on the Partial Variance of Increments (PVI) method. We show that the one-point proxies are sufficiently precise in identifying not only the generic features of the current sheets and vortices statistically, but also their appearance in groups associated with plasma heating. The method has been further applied to the region of the turbulent sheath of an interplanetary coronal mass ejection (ICME) observed at L1 by WIND spacecraft. We observe current sheets and vorticity associated heating in larger groups (blobs), which so far have not been considered in the literature on turbulent data analysis. The blobs represent extended spatial regions of activity with enhanced regional correlations between the occurrence of conditioned currents and vorticity, which at the same time are also correlated with enhanced temperatures. This heating mechanism is substantially different from the plasma heating in the vicinity of the ICME shock, where plasma beta is strongly fluctuating and there is no vorticity. The proposed method describes a new pathway for linking the plasma heating and plasma turbulence, and it is relevant to in-situ observations when only single spacecraft measurements are available., Comment: 21 pages, 7 figures

The high cadence plasma, electric, and magnetic field measurements by the Magnetospheric MultiScale spacecraft allow us to explore the near-Earth space plasma with an unprecedented time and spatial resolution, resolving electron-scale structures that naturally emerge from plasma complex dynamics. The formation of small-scale turbulent features is often associated to structured, non-Maxwellian particle velocity distribution functions that are not at thermodynamic equilibrium. Using measurements in the terrestrial magnetosheath, this study focuses on regions presenting bumps in the power spectral density of the parallel electric field at sub-proton scales. Correspondingly, it is found that the ion velocity distribution functions exhibit beam-like features at nearly the local ion thermal speed. Ion cyclotron waves in the ion-scale range are frequently observed at the same locations. These observations, supported by numerical simulations, are consistent with the generation of ion-bulk waves that propagate at the ion thermal speed. This represents a new branch of efficient energy transfer at small scales, which may be relevant to weakly collisional astrophysical plasmas.

In this work, we present linear exact repair schemes for one or two erasures in decreasing monomial-Cartesian codes DM-CC, a family of codes which provides a framework for polar codes. In the case of two erasures, the positions of the erasures should satisfy a certain restriction. We present families of augmented Reed-Muller (ARM) and augmented Cartesian codes (ACar) which are families of evaluation codes obtained by strategically adding vectors to Reed-Muller and Cartesian codes, respectively. We develop repair schemes for one or two erasures for these families of augmented codes. Unlike the repair scheme for two erasures of DM-CC, the repair scheme for two erasures for the augmented codes has no restrictions on the positions of the erasures. When the dimension and base field are fixed, we give examples where ARM and ACar codes provide a lower bandwidth (resp., bitwidth) in comparison with Reed-Solomon (resp., Hermitian) codes. When the length and base field are fixed, we give examples where ACar codes provide a lower bandwidth in comparison with ARM. Finally, we analyze the asymptotic behavior when the augmented codes achieve the maximum rate.

The recently released spacecraft potential measured by the RPW instrument on-board Solar Orbiter has been used to estimate the solar wind electron density in the inner heliosphere. Solar-wind electron density measured during June 2020 has been analysed to obtain a thorough characterization of the turbulence and intermittency properties of the fluctuations. Magnetic field data have been used to describe the presence of ion-scale waves. Selected intervals have been extracted to study and quantify the properties of turbulence. The Empirical Mode Decomposition has been used to obtain the generalized marginal Hilbert spectrum, equivalent to the structure functions analysis, and additionally reducing issues typical of non-stationary, short time series. The presence of waves was quantitatively determined introducing a parameter describing the time-dependent, frequency-filtered wave power. A well defined inertial range with power-law scaling has been found almost everywhere. However, the Kolmogorov scaling and the typical intermittency effects are only present in part of the samples. Other intervals have shallower spectra and more irregular intermittency, not described by models of turbulence. These are observed predominantly during intervals of enhanced ion frequency wave activity. Comparisons with compressible magnetic field intermittency (from the MAG instrument) and with an estimate of the solar wind velocity (using electric and magnetic field) are also provided to give general context and help determine the cause for the anomalous fluctuations.

A variety of kinetic waves develop in the solar wind. The relationship between these waves and larger-scale structures, such as current sheets and ongoing turbulence remain a topic of investigation. Similarly, the instabilities producing ion-acoustic waves in the solar wind remains an open question. The goals of this paper are to investigate kinetic electrostatic Langmuir and ion-acoustic waves in the solar wind at 0.5 AU and determine whether current sheets and associated streaming instabilities can produce the observed waves. The relationship between these waves and currents is investigated statistically. Solar Orbiter's Radio and Plasma Waves instrument suite provides high-resolution snapshots of the fluctuating electric field. The Low Frequency Receiver resolves the waveforms of ion-acoustic waves and the Time Domain Sampler resolves the waveforms of both ion-acoustic and Langmuir waves. Using these waveform data we determine when these waves are observed in relation to current structures in the solar wind, estimated from the background magnetic field. Langmuir and ion-acoustic waves are frequently observed in the solar wind. Ion-acoustic waves are observed about 1% of the time at 0.5 AU. The waves are more likely to be observed in regions of enhanced currents. However, the waves typically do not occur at current structures themselves. The observed currents in the solar wind are too small to drive instability by the relative drift between single ion and electron populations. When multi-component ion and/or electron distributions are present the observed currents may be sufficient for instability. Ion beams are the most plausible source of ion-acoustic waves. The spacecraft potential is confirmed to be a reliable probe of the background electron density by comparing the peak frequencies of Langmuir waves with the plasma frequency calculated from the spacecraft potential., Comment: 13 pages, 12 figures

We use the plasma density based on measurements of the probe-to-spacecraft potential in combination with magnetic field measurements by MAG to study fields and density fluctuations in the solar wind observed by Solar Orbiter during the first perihelion encounter ($\sim$0.5~AU away from the Sun). In particular we use the polarization of the wave magnetic field, the phase between the compressible magnetic field and density fluctuations and the compressibility ratio (the ratio of the normalized density fluctuations to the normalized compressible fluctuations of B) to characterize the observed waves and turbulence. We find that the density fluctuations are out-of-phase with the compressible component of magnetic fluctuations for intervals of turbulence, while they are in phase for the circular-polarized waves around the proton cyclotron frequency. We analyze in detail two specific events with simultaneous presence of left- and right-handed waves at different frequencies. We compare observed wave properties to a prediction of the three-fluid (electrons, protons and alphas) model. We find a limit on the observed wavenumbers, $10^{-6} < k < 7 \times 10^{-6}$~m$^{-1}$, which corresponds to wavelength $7 \times 10^6 >\lambda > 10^6$~m. We conclude that most likely both the left- and right-handed waves correspond to the low-wavenumber part (close to the cut-off at $\Omega_{c\mathrm{He}++}$) proton-band electromagnetic ion cyclotron (left-handed wave in the plasma frame confined to the frequency range $\Omega_{c\mathrm{He}++} < \omega < \Omega_{c\mathrm{H}+}$) waves propagating in the outwards and inwards directions respectively. The fact that both wave polarizations are observed at the same time and the identified wave mode has a low group velocity suggests that the double-banded events occur in the source regions of the waves., Comment: 13 pages, 9 figures

We reconsider a control theory for Hamiltonian systems, that was introduced on the basis of KAM theory and applied to a model of magnetic field in previous articles. By a combination of Frequency Analysis and of a rigorous (Computer Assisted) KAM algorithm we prove that in the phase space of the magnetic field, due to the control term, a set of invariant tori appear, and it acts as a transport barrier. Our analysis, which is common (but often also limited) to Celestial Mechanics, is based on a normal form approach; it is also quite general and can be applied to quasi-integrable Hamiltonian systems satisfying a few additional mild assumptions. As a novelty with respect to the works that in the last two decades applied Computer Assisted Proofs into the framework of KAM theory, we provide all the codes allowing to produce our results. They are collected in a software package that is publicly available from the {\it Mendeley Data} repository. All these codes are designed in such a way to be easy-to-use, also for what concerns eventual adaptations for applications to similar problems., Comment: Version 2

We propose a perturbation algorithm for Hamiltonian systems on a Lie algebra $\mathbb{V}$, so that it can be applied to non-canonical Hamiltonian systems. Given a Hamiltonian system that preserves a subalgebra $\mathbb{B}$ of $\mathbb{V}$, when we add a perturbation the subalgebra $\mathbb{B}$ will no longer be preserved. We show how to transform the perturbed dynamical system to preserve $\mathbb{B}$ up to terms quadratic in the perturbation. We apply this method to study the dynamics of a non-autonomous symmetric Rigid Body. In this example our algebraic transform plays the role of Iterative Lemma in the proof of a KAM-like statement., Comment: Accepted for publication on DNC

The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include interparticle collisions: the fully kinetic particle-in-cell VPIC, the fully kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov-Maxwell (HVM) code. We differentiate between (i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and (ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is an overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of interparticle collisions on these parameters is finally discussed., Comment: Accepted for publication on MNRAS