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A unified linear theory that includes forced reconnection as a particular case of Alfv\'en resonance is presented. We consider a generalized Taylor problem in which a sheared magnetic field is subject to a time-dependent boundary perturbation oscillating at frequency $\omega_0$. By analyzing the asymptotic time response of the system, the theory demonstrates that the Alfv\'en resonance is due to the residues at the resonant poles, in the complex frequency plane, introduced by the boundary perturbation. Alfv\'en resonance transitions towards forced reconnection, described by the constant-psi regime for (normalized) times $t\gg S^{1/3}$, when the forcing frequency of the boundary perturbation is $\omega_0\ll S^{-1/3}$, allowing the coupling of the Alfv\'en resonances across the neutral line with the reconnecting mode, as originally suggested in [1]. Additionally, it is shown that even if forced reconnection develops for finite, albeit small, frequencies, the reconnection rate and reconnected flux are strongly reduced for frequencies $\omega_0\gg S^{-3/5}$.

Parker Solar Probe observations reveal that the near-Sun space is almost filled with magnetic switchbacks (``switchbacks'' hereinafter), which may be a major contributor to the heating and acceleration of solar wind. Here, for the first time, we develop an analytic model of an axisymmetric switchback with uniform magnetic field strength. In this model, three parameters control the geometry of the switchback: height (length along the background magnetic field), width (thickness along radial direction perpendicular to the background field), and the radial distance from the center of switchback to the central axis, which is a proxy of the size of the switchback along the third dimension. We carry out three-dimensional magnetohydrodynamic simulations to investigate the dynamic evolution of the switchback. Comparing simulations conducted with compressible and incompressible codes, we verify that compressibility, i.e. parametric decay instability, is necessary for destabilizing the switchback. Our simulations also reveal that the geometry of the switchback significantly affects how fast the switchback destabilizes. The most stable switchbacks are 2D-like (planar) structures with large aspect ratios (length to width), consistent with the observations. We show that when plasma beta ($\beta$) is smaller than one, the switchback is more stable as $\beta$ increases. However, when $\beta$ is greater than one, the switchback becomes very unstable as the pattern of the growing compressive fluctuations changes. Our results may explain some of the observational features of switchbacks, including the large aspect ratios and nearly constant occurrence rates in the inner heliosphere.

We investigate the local proton energization at magnetic discontinuities/intermittent structures and the corresponding kinetic signatures in velocity phase space in Alfv\'enic and non-Alfv\'enic wind streams observed by Parker Solar Probe. By means of the Partial Variance of Increments method, we find that the hottest proton populations are localized around compressible, kinetic-scale magnetic structures in both types of wind. Furthermore, the Alfv\'enic wind shows preferential enhancements of $T_\parallel$ as smaller scale structures are considered, whereas the non-Alfvenic wind shows preferential $T_\bot$ enhancements. Although proton beams are present in both types of wind, the proton velocity distribution function displays distinct features. Hot beams, i.e., beams with beam-to-core perpendicular temperature up to three times larger than the total distribution anisotropy, are found in the non-Alfv\'enic wind, whereas colder beams in the Alfv\'enic wind. Our data analysis is complemented by 2.5D hybrid simulations in different geometrical setups, which support the idea that proton beams in Alfv\'enic and non-Alfv\'enic wind have different kinetic properties and origins. The development of a perpendicular nonlinear cascade, favored in balanced turbulence, allows a preferential relative enhancement of the perpendicular plasma temperature and the formation of hot beams. Cold field-aligned beams are instead favored by Alfv\'en wave steepening. Non-Maxwellian distribution functions are found near discontinuities and intermittent structures, pointing to the fact that the nonlinear formation of small-scale structures is intrinsically related to the development of highly non-thermal features in collisionless plasmas.

We conduct 3D magnetohydrodynamic (MHD) simulations of decaying turbulence in the solar wind context. To account for the spherical expansion of the solar wind, we implement the expanding box model. The initial turbulence comprises uncorrelated counter-propagating Alfv\'en waves and exhibits an isotropic power spectrum. Our findings reveal the consistent generation of negative residual energy whenever nonlinear interactions are present, independent of the normalized cross helicity $\sigma_c$. The spherical expansion facilitates this process. The resulting residual energy is primarily distributed in the perpendicular direction, with $[S_2(\mathbf{b})-S_2(\mathbf{u})] \propto l_\perp$ or equivalently $-E_r \propto k_\perp^{-2}$. Here $S_2(\mathbf{b})$ and $S_2(\mathbf{u})$ are second-order structure functions of magnetic field and velocity respectively. In most runs, $S_2(\mathbf{b})$ develops a scaling relation $S_2(\mathbf{b}) \propto l_\perp^{1/2}$ ($E_b \propto k_\perp^{-3/2}$). In contrast, $S_2(\mathbf{u})$ is consistently shallower than $S_2(\mathbf{b})$, which aligns with in-situ observations of the solar wind. We observe that the higher-order statistics of the turbulence, which act as a proxy for intermittency, are strongly affected by the expansion effect but have weak dependence on the initial $\sigma_c$. Generally, the intermittency is more pronounced when the expansion effect is present. Finally, we find that in our simulations although the negative residual energy and intermittency grow simultaneously as the turbulence evolves, there is no obvious causal relation between them because they are generated on different scales.

We investigate dispersive and kinetic effects on the evolution of a two-dimensional kinked Alfv\'en wave packet by comparing results from MHD, Hall-MHD and hybrid simulations of a low-$\beta$ plasma. We find that the Hall term determines the overall evolution of the wave packet over a characteristic time $\tau^*=\tau_a\ell/d_i$ in both fluid and hybrid models. Dispersion of the wave packet leads to the conversion of the wave energy into internal plasma energy. When kinetic protons are considered, the proton internal energy increase has contributions from both plasma compressions and phase space mixing. The latter occurs in the direction parallel to the guiding mean magnetic field, due to protons resonating at the Alfv\'en speed with a compressible mode forced by the wave packet. Implications of our results for switchbacks observations and solar wind energetics are discussed., Comment: In press at PoP for the Special Collection on the Plasma Physics of the Sun in Honor of Eugene Parker

We study the parametric decay instability of parallel propagating Alfv\'en wave in a low-beta plasma using one-dimensional fully kinetic simulations. We focus for the first time on the conversion of the energy stored in the initial Alfv\'en wave into particle internal energy, and on its partition between particle species. We show that compressible fluctuations generated by the decay of the pump wave into a secondary ion-acoustic mode and a reflected Alfv\'en wave contribute to the gain of internal energy via two distinct mechanisms. First, the ion-acoustic mode leads nonlinearly to proton trapping and proton phase space mixing, in agreement with previous work based on hybrid simulations. Second, during the nonlinear stage, a compressible front of the fast type develops at the steepened edge of the backward Alfv\'en wave leading to a field-aligned proton beam propagating backwards at the Alfv\'en speed. We find that parametric decay heats preferentially protons, which gain about 50% of the pump wave energy in the form of internal energy. However, we find that electrons are also energized and that they contribute to the total energy balance by gaining 10% of the pump wave energy. By investigating energy partition and particle heating during parametric decay, our results contribute to determine the role of compressible and kinetic effects in wave-driven models of the solar wind.

Launched on 12 Aug. 2018, NASA's Parker Solar Probe had completed 13 of its scheduled 24 orbits around the Sun by Nov. 2022. The mission's primary science goal is to determine the structure and dynamics of the Sun's coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Parker Solar Probe returned a treasure trove of science data that far exceeded quality, significance, and quantity expectations, leading to a significant number of discoveries reported in nearly 700 peer-reviewed publications. The first four years of the 7-year primary mission duration have been mostly during solar minimum conditions with few major solar events. Starting with orbit 8 (i.e., 28 Apr. 2021), Parker flew through the magnetically dominated corona, i.e., sub-Alfv\'enic solar wind, which is one of the mission's primary objectives. In this paper, we present an overview of the scientific advances made mainly during the first four years of the Parker Solar Probe mission, which go well beyond the three science objectives that are: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles., Comment: 157 pages, 65 figures

The heating and acceleration of the solar wind remains one of the fundamental unsolved problems in heliophysics. It is usually observed that the proton temperature $T_i$ is highly correlated with the solar wind speed $V_{SW}$, while the electron temperature $T_e$ shows anti-correlation or no clear correlation with the solar wind speed. Here we inspect both Parker Solar Probe (PSP) and WIND data and compare the observations with simulation results. PSP observations below 30 solar radii clearly show a positive correlation between proton temperature and wind speed and a negative correlation between electron temperature and wind speed. One year (2019) of WIND data confirm that proton temperature is positively correlated with solar wind speed, but the electron temperature increases with the solar wind speed for slow wind while it decreases with the solar wind speed for fast wind. Using a one-dimensional Alfv\'en-wave-driven solar wind model with different proton and electron temperatures, we for the first time find that if most of the dissipated Alfv\'en wave energy heats the ions instead of electrons, a positive $T_i-V_{SW}$ correlation and a negative $T_e-V_{SW}$ correlation arise naturally. If the electrons gain a small but finite portion of the dissipated wave energy, the $T_e-V_{SW}$ correlation evolves with radial distance to the Sun such that the negative correlation gradually turns positive. The model results show that Alfv\'en waves are one of the possible explanations of the observed evolution of proton and electron temperatures in the solar wind.

Parker Solar Probe and Solar Orbiter data are used to investigate the radial evolution of magnetic turbulence between $0.06 ~ \lesssim R ~\lesssim 1$ au. The spectrum is studied as a function of scale, normalized to the ion inertial scale $d_{i}$. In the vicinity of the Sun, the inertial range is limited to a narrow range of scales and exhibits a power-law exponent of, $\alpha_{B} = -3/2$, independent of plasma parameters. The inertial range grows with distance, progressively extending to larger spatial scales, while steepening towards a $\alpha_{B} =-5/3$ scaling. It is observed that spectra for intervals with large magnetic energy excesses and low Alfv\'enic content steepen significantly with distance, in contrast to highly Alfv\'enic intervals that retain their near-Sun scaling. The occurrence of steeper spectra in slower wind streams may be attributed to the observed positive correlation between solar wind speed and Alfv\'enicity., Comment: Accepted to APJ letters with minor revisions

Parker Solar Probe (PSP) has shown that the solar wind in the inner heliosphere is characterized by the quasi omni-presence of magnetic switchbacks ("switchback" hereinafter), local backward-bends of magnetic field lines. Switchbacks also tend to come in patches, with a large-scale modulation that appears to have a spatial scale size comparable to supergranulation on the Sun. Here we inspect data from the first ten encounters of PSP focusing on different time intervals when clear switchback patches were observed by PSP. We show that the switchbacks modulation, on a timescale of several hours, seems to be independent of whether PSP is near perihelion, when it rapidly traverses large swaths of longitude remaining at the same heliocentric distance, or near the radial-scan part of its orbit, when PSP hovers over the same longitude on the Sun while rapidly moving radially inwards or outwards. This implies that switchback patches must also have an intrinsically temporal modulation most probably originating at the Sun. Between two consecutive patches, the magnetic field is usually very quiescent with weak fluctuations. We compare various parameters between the quiescent intervals and the switchback intervals. The results show that the quiescent intervals are typically less Alfv\'enic than switchback intervals, and the magnetic power spectrum is usually shallower in quiescent intervals. We propose that the temporal modulation of switchback patches may be related to the "breathing" of emerging flux that appears in images as the formation of "bubbles" below prominences in the Hinode/SOT observations.

Magnetic reconnection is a sporadic process responsible for energy release in space and laboratory plasmas. It is believed that the tearing mode instability may be responsible for the onset of reconnection in the magnetotail. However, due to its elusive nature, there is an absence of in-situ observations of the tearing instability prior to magnetic reconnection in our nearest natural plasma laboratory. Using neural network outlier detection methods in conjunction with Cluster spacecraft data, we find unique electron pitch angle distributions that are consistent with simulation predictions of the tearing instability and the subsequent evolution of plasma electrons and reconnection. We confirm that the events identified via our neural network outlier method are well above the tearing stability threshold based on the criterion detailed in this paper. We find signatures of magnetic reconnection minutes after the majority of tearing observations. Our analysis of the tearing instability provides new insights into the fundamental understanding of the mechanism responsible for reconnection, a process that is ubiquitous in different astrophysical plasma regimes across the universe and in laboratory experiments on Earth.

Several generalizations of the well-known fluid model of Braginskii (Rev. of Plasma Phys., 1965) are considered. We use the Landau collisional operator and the moment method of Grad. We focus on the 21-moment model that is analogous to the Braginskii model, and we also consider a 22-moment model. Both models are formulated for general multi-species plasmas with arbitrary masses and temperatures, where all the fluid moments are described by their evolution equations. The 21-moment model contains two "heat flux vectors" (3rd and 5th-order moments) and two "viscosity-tensors" (2nd and 4th-order moments). The Braginskii model is then obtained as a particular case of a one ion-electron plasma with similar temperatures, with de-coupled heat fluxes and viscosity-tensors expressed in a quasi-static approximation. We provide all the numerical values of the Braginskii model in a fully analytic form (together with the 4th and 5th-order moments). For multi-species plasmas, the model makes calculation of transport coefficients straightforward. Formulation in fluid moments (instead of Hermite moments) is also suitable for implementation into existing numerical codes. It is emphasized that it is the quasi-static approximation which makes some Braginskii coefficients divergent in a weakly-collisional regime. Importantly, we show that the heat fluxes and viscosity-tensors are coupled even in the linear approximation, and that the fully contracted (scalar) perturbations of the 4th-order moment, which are accounted for in the 22-moment model, modify the energy exchange rates. We also provide several Appendices, which can be useful as a guide for deriving the Braginskii model with the moment method of Grad., Comment: Updated version. Title change from "Braginskii-type" to "Braginskii Type" to match the published version (accepted to ApJ Supplements, 29 Jan 2022). Bookmarks included, TOC is now at the beginning, numbering in Appendix I is fixed, few typos corrected

The effects of the heliospheric current sheet (HCS) on the evolution of Alfv\'enic turbulence in the solar wind are studied using MHD simulations incorporating the expanding-box-model (EBM). The simulations show that near the HCS, the Alfv\'enicity of the turbulence decreases as manifested by lower normalized cross helicity and larger excess of magnetic energy. The numerical results are supported by a superposed-epoch analysis using OMNI data, which shows that the normalized cross helicity decreases inside the plasma sheet surrounding HCS, and the excess of magnetic energy is significantly enhanced at the center of HCS. Our simulation results indicate that the decrease of Alfv\'enicity around the HCS is due to the weakening of radial magnetic field and the effects of the transverse gradient in the background magnetic field. The magnetic energy excess in the turbulence may be a result of the loss of Alfv\'enic correlation between velocity and magnetic field and the faster decay of transverse kinetic energy with respect to magnetic energy in a spherically expanding solar wind.

One of the most important problems of magnetotail dynamics is the substorm onset and the related instability of the magneotail current sheet. Since the simplest 2D current sheet configuration with monotonic $B_z$ was proven to be stable to the tearing mode, the focus of the instability investigation moved to more specific configurations, e.g. kinetic current sheets with strong transient ion currents and current sheets with non-monotonic $B_z$ (local $B_z$ minima or/and peaks). Stability of the latter current sheet configuration has been studied both within kinetic and fluid approaches, whereas the investigation of the transient ion effects were limited to kinetic models only. This paper aims to provide detailed analysis of stability of a multi-fluid current sheet configuration that mimics current sheets with transient ions. Using the system with two field-aligned ion flows that mimic the effect of pressure non-gyrotropy, we construct 1D current sheet with a finite $B_z$. This model describes well recent findings of very thin intense magnetotail current sheets. The stability analysis of this two-ion model confirms the stabilizing effect of finite $B_z$ and shows that the most stable current sheet is the one with exactly counter-streaming ion flows and zero net flow. Such field-aligned flows may substitute the contribution of the pressure tensor nongyrotropy to the stress balance, but cannot overtake the stabilizing effect of $B_z$. Obtained results are discussed in the context of magnetotail dynamical models and spacecraft observations.

We analyze magnetic field data from the first six encounters of PSP, three Helios fast streams and two Ulysses south polar passes covering heliocentric distances $0.1\lesssim R\lesssim 3$ au. We use this data set to statistically determine the evolution of switchbacks of different periods and amplitudes with distance from the Sun. We compare the radial evolution of magnetic field variances with that of the mean square amplitudes of switchbacks, and quantify the radial evolution of the cumulative counts of switchbacks per km. We find that the amplitudes of switchbacks decrease faster than the overall turbulent fluctuations, in a way consistent with the radial decrease of the mean magnetic field. This could be the result of a saturation of amplitudes and may be a signature of decay processes of large amplitude Alfv\'enic fluctuations in the solar wind. We find that the evolution of switchback occurrence in the solar wind is scale-dependent: the fraction of longer duration switchbacks increases with radial distance whereas it decreases for shorter switchbacks. This implies that switchback dynamics is a complex process involving both decay and in-situ generation in the inner heliosphere. We confirm that switchbacks can be generated by the expansion although other type of switchbacks generated closer to the sun cannot be ruled out., Comment: Accepted for publication on ApJL

The role of solar wind expansion in generating whistler waves is investigated using the EB-iPic3D code, which models solar wind expansion self-consistently within a fully kinetic semi-implicit approach. The simulation is initialized with an electron velocity distribution function modeled after Parker Solar Probe observations during its first perihelion at 0.166 au, consisting of a dense core and an anti-sunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilities are triggered. These instabilities produce sunward whistler waves initially characterized by predominantly oblique propagation with respect to the interplanetary magnetic field. The excited waves interact with the electrons via resonant scattering processes. As a consequence, the strahl pitch angle distribution broadens and its drift velocity reduces. Strahl electrons are scattered in the direction perpendicular to the magnetic field, and an electron halo is formed. At a later stage, resonant electron firehose instability is triggered and further affects the electron temperature anisotropy as the solar wind expands. Wave-particle interaction processes are accompanied by a substantial reduction of the solar wind heat flux. The simulated whistler waves are in qualitative agreement with observations in terms of wave frequencies, amplitudes and propagation angles. Our work proposes an explanation for the observations of oblique and parallel whistler waves in the solar wind. We conclude that solar wind expansion has to be factored in when trying to explain kinetic processes at different heliocentric distances.

Proton energization at magnetic discontinuities generated by phase-steepened fronts of parallel propagating, large-amplitude Alfv\'enic fluctuation is studied using hybrid simulations. We find that dispersive effects yield to the collapse of the wave via phase steepening and the subsequent generation of compressible fluctuations that mediate an efficient local energy transfer from the wave to the protons. Proton scattering at the steepened edges causes non-adiabatic proton perpendicular heating. Furthermore, the parallel electric field at the propagating fronts mediates the acceleration of protons along the mean field. A steady-state is achieved where proton distribution function displays a field-aligned beam at the Alfv\'en speed, and compressible fluctuations are largely damped. We discuss the implications of our results in the context of Alfv\'enic solar wind.

We make use of the Parker Solar Probe (PSP) data to explore the nature of solar wind turbulence focusing on the Alfv\'enic character and power spectra of the fluctuations and their dependence on distance and context (i.e. large scale solar wind properties), aiming to understand the role that different effects such as source properties, solar wind expansion, stream interaction might play in determining the turbulent state. We carry out a statistical survey of the data from the first five orbits of PSP with a focus on how the fluctuation properties at the large, MHD scales, vary with different solar wind streams and distance from the Sun. A more in-depth analysis from several selected periods is also presented. Our results show that as fluctuations are transported outward by the solar wind, the magnetic field spectrum steepens while the shape of the velocity spectrum remains unchanged. The steepening process is controlled by the "age" of the turbulence, determined by the wind speed together with the radial distance. Statistically, faster solar wind has higher "Alfv\'enicity", with more dominant outward propagating wave component and more balanced magnetic/kinetic energies. The outward wave dominance gradually weakens with radial distance, while the excess of magnetic energy is found to be stronger as we move closer toward the Sun. We show that the turbulence properties can vary significantly stream to stream even if these streams are of similar speed, indicating very different origins of these streams. Especially, the slow wind that originates near the polar coronal holes has much lower Alfv\'enicity compared with the slow wind that originates from the active regions/pseudostreamers. We show that structures such as heliospheric current sheets and velocity shears can play an important role in modifying the properties of the turbulence.

The evolution of the electron heat flux in the solar wind is regulated by the interplay between several effects: solar wind expansion, that can potentially drive velocity-space instabilties, turbulence and wave-particle interactions, and, possibly, collisions. Here we address the respective role played by the solar wind expansion and the electron firehose instability, developing in the presence of multiple electron populations, in regulating the heat flux. We carry out fully kinetic, Expanding Box Model simulations and separately analyze the enthalpy, bulk and velocity distribution function skewness contributions for each of the electron species. We observe that the key factor determining electron energy flux evolution is the reduction of the drift velocity of the electron populations in the rest frame of the solar wind. In our simulations, redistribution of the electron thermal energy from the parallel to the perpendicular direction after the onset of the electron firehose instability is observed. However, this process seems to impact energy flux evolution only minimally. Hence, reduction of the electron species drift velocity in the solar wind frame appears to directly correlate with efficiency for heat flux instabilities

The tearing mode instability is one important mechanism that may explain the triggering of fast magnetic reconnection in astrophysical plasmas such as the solar corona and the Earth's magnetosphere. In this paper, the linear stability analysis of the tearing mode is carried out for a current sheet in the presence of a guide field, including the Hall effect. We show that the presence of a strong guide field does not modify the most unstable mode in the two-dimensional wave vector space orthogonal to the current gradient direction, which remains the fastest growing parallel mode. With the Hall effect, the inclusion of a guide field turns the non-dispersive propagation along the guide field direction to a dispersive one. The oblique modes have a wave-like structure along the normal direction of the current sheet and a strong guide field suppresses this structure while making the eigen-functions asymmetric.

Large amplitude Alfv\'en waves tend to be unstable to parametric instabilities which result in a decay process of the initial wave into different daughter waves depending upon the amplitude of the fluctuations and the plasma beta. The propagation angle with respect to the mean magnetic field of the daughter waves plays an important role in determining the type of decay. In this paper, we revisit this problem by means of multi-dimensional hybrid simulations. In particular, we study the decay and the subsequent nonlinear evolution of large-amplitude Alfv\'en waves by investigating the saturation mechanism of the instability and its final nonlinear state reached for different wave amplitudes and plasma beta conditions. As opposed to one-dimensional simulations where the Decay instability is suppressed for increasing plasma beta values, we find that the decay process in multi-dimensions persists at large values of the plasma beta via the filamentation/magnetosonic decay instabilities. In general, the decay process acts as a trigger both to develop a perpendicular turbulent cascade and to enhance mean field-aligned wave-particle interactions. We find indeed that the saturated state is characterized by a turbulent plasma displaying a field-aligned beam at the Alfv\'en speed and increased temperatures that we ascribe to the Landau resonance and pitch angle scattering in phase space.

In many astrophysical environments the plasma is only partially ionized, and therefore the interaction of charged and neutral particles may alter both the triggering of reconnection and its subsequent dynamical evolution. We derive the tearing mode maximum growth rate for partially ionized plasmas in the cases of weak and strong coupling between the plasma and the neutrals. In addition, critical scalings for current sheet aspect ratios are presented in terms of Lundquist number and ion-neutral collision frequencies. In the decoupled regime the standard tearing mode is recovered with a small correction depending on the ion-neutral collision frequency; in the intermediate regime collisions with neutrals are shown to stabilize current sheets, resulting in larger critical aspect ratios for ideal tearing to occur. Nonetheless, the additional electron-neutral collisions, hidden in the definition of the Lundquist number, can shrink the critical aspect ratios below the fully ionized case. In the coupled regime, the growth rate depends on the density ratio between ions and neutrals through the collision frequency between these two species. These provide critical aspect ratios for which the tearing mode instability transitions from slow to ideal, that depend on the neutral-ion density ratio., Comment: 5 pages, 0 figure

In contrast with the fast solar wind, that originates in coronal holes, the source of the slow solar wind is still debated. Often intermittent and enriched with low FIP elements -- akin to what is observed in closed coronal loops -- the slow wind could form in bursty events nearby helmet streamers. Slow winds also exhibit density perturbations which have been shown to be periodic and could be associated with flux ropes ejected from the tip of helmet streamers, as shown recently by the WISPR white light imager onboard Parker Solar Probe (PSP). In this work, we propose that the main mechanism controlling the release of flux ropes is a flow-modified tearing mode at the heliospheric current sheet (HCS). We use MHD simulations of the solar wind and corona to reproduce realistic configurations and outflows surrounding the HCS. We find that this process is able to explain long ($\sim 10-20$h) and short ($\sim 1-2$h) timescales of density structures observed in the slow solar wind. This study also sheds new light on the structure, topology and composition of the slow solar wind, and could be, in the near future, compared with white light and in situ PSP observations., Comment: 8 pages, 5 figures, accepted for publication in ApJL

During Parker Solar Probe's first orbit, the solar wind plasma has been observed in situ closer than ever before, the perihelion on November 6th 2018 revealing a flow that is constantly permeated by large amplitude Alfv\'enic fluctuations. These include radial magnetic field reversals, or switchbacks, that seem to be a persistent feature of the young solar wind. The measurements also reveal a very strong, unexpected, azimuthal velocity component. In this work, we numerically model the solar corona during this first encounter, solving the MHD equations and accounting for Alfv\'en wave transport and dissipation. We find that the large scale plasma parameters are well reproduced, allowing the computation of the solar wind sources at Probe with confidence. We try to understand the dynamical nature of the solar wind to explain both the amplitude of the observed radial magnetic field and of the azimuthal velocities., Comment: Accepted Erratum includeded as an appendix. Updated references. 17 pages, 9 figures total

Parker Solar Probe (PSP) observations during its first encounter at 35.7 $R_\odot$ have shown the presence of magnetic field lines which are strongly perturbed to the point that they produce local inversions of the radial magnetic field, known as switchbacks. Their counterparts in the solar wind velocity field are local enhancements in the radial speed, or jets, displaying (in all components) the velocity-magnetic field correlation typical of large amplitude Alfv\'en waves propagating away from the Sun. Switchbacks and radial jets have previously been observed over a wide range of heliocentric distances by Helios, WIND and Ulysses, although they were prevalent in significantly faster streams than seen at PSP. Here we study via numerical MHD simulations the evolution of such large amplitude Alfv\'enic fluctuations by including, in agreement with observations, both a radial magnetic field inversion and an initially constant total magnetic pressure. Despite the extremely large excursion of magnetic and velocity fields, switchbacks are seen to persist for up to hundreds of Alfv\'en crossing times before eventually decaying due to the parametric decay instability. Our results suggest that such switchback/jet configurations might indeed originate in the lower corona and survive out to PSP distances, provided the background solar wind is sufficiently calm, in the sense of not being pervaded by strong density fluctuations or other gradients, such as stream or magnetic field shears, that might destabilize or destroy them over shorter timescales., Comment: Accepted for publication on APJ PSP special issue

We carry out two-dimensional magnetohydrodynamic (MHD) simulations of an ensemble of Alfv\'enic fluctuations propagating in a structured, expanding solar wind including the presence of fast and slow solar wind streams. Using an appropriate expanding box model, the simulations incorporate the effects of fast-slow stream shear and compression and rarefaction self-consistently. We investigate the radial and longitudinal evolution of the cross-helicity, the total and residual energies and the power spectra of outward and inward Alfv\'enic fluctuations. The stream interaction is found to strongly affect the radial evolution of Alfv\'enic turbulence. The total energy in the Alfv\'en waves is depleted within the velocity shear regions, accompanied by the decrease of the normalized cross-helicity. The presence of stream-compression facilitates this process. Residual energy fluctuates around zero due to the correlation and de-correlation between the inward/outward waves but no net growth or decrease of the residual energy is observed. The radial power spectra of the inward/outward Alfv\'en waves show significant longitudinal variations. Kolmogorov-like spectra are developed only inside the fast and slow streams and when both the compression and shear are present. On the other hand, the spectra along the longitudinal direction show clear Kolmogorov-like inertial ranges in all cases.

We use 2.5D Magnetohydrodynamic simulations to investigate the spectral signatures of the nonlinear disruption of a tearing unstable current sheet via the generation of multiple secondary current sheets and magnetic islands. During the nonlinear phase of tearing mode evolution, there develops a regime in which the magnetic energy density shows a spectrum with a power-law close to $B(k)^2\sim k^{-0.8}$. Such an energy spectrum is found in correspondence of the neutral line, within the diffusion region of the primary current sheet, where energy is conveyed towards smaller scales via a ``recursive'' process of fast tearing-type instabilities. Far from the neutral line we find that magnetic energy spectra evolve towards slopes compatible with the ``standard'' Kolmogorov spectrum. Starting from a self-similar description of the nonlinear stage at the neutral line, we provide a model that predicts a reconnecting magnetic field energy spectrum scaling as $k^{-4/5}$, in good agreement with numerical results. An extension of the predicted power-law to generic current sheet profiles is also given and possible implications for turbulence phenomenology are discussed. These results provide a step forward to understand the ``recursive'' generation of magnetic islands (plasmoids), which has been proposed as a possible explanation for the energy release during flares, but which, more in general, can have an impact on the subsequent turbulent evolution of unstable sheets that naturally form in the high-Lundquist number and collisionless plasmas found in most of the astrophysical environments.

Magnetohydrodynamic (MHD) theory and simulations have shown that reconnection is triggered via a fast "ideal" tearing instability in current sheets whose inverse aspect ratio decreases to $a/L\sim S^{-1/3}$, with $S$ is the Lundquist number defined by the half-length $L$ of the current sheet (of thickness $2a$). Ideal tearing, in 2D sheets, triggers a hierarchical collapse via stretching of X-points and recursive instability. At each step, the local Lundquist number decreases, until the subsequent sheet thickness either approaches kinetic scales or the Lundquist number becomes sufficiently small. Here we carry out a series of Hall-MHD simulations to show how the Hall effect modifies recursive reconnection once the ion inertial scale is approached. We show that as the ion inertial length becomes of the order of the inner, singular layer thickness at some step of the recursive collapse, reconnection transits from the plasmoid-dominant regime to an intermediate plasmoid+Hall regime and then to the Hall-dominant regime. The structure around the X-point, the reconnection rate, the dissipation property and the power spectra are also modified significantly by the Hall effect., Comment: 13 pages, 8 figures

Magnetic reconnection may be the fundamental process allowing energy stored in magnetic fields to be released abruptly, solar flares and coronal mass ejection (CME) being archetypal natural plasma examples. Magnetic reconnection is much too slow a process to be efficient on the large scales, but accelerates once small enough scales are formed in the system. For this reason, the fractal reconnection scenario was introduced (Shibata and Tanuma 2001) to explain explosive events in the solar atmosphere: it was based on the recursive triggering and collapse via tearing instability of a current sheet originally thinned during the rise of a filament in the solar corona. Here we compare the different fractal reconnection scenarios that have been proposed, and derive generalized scaling relations for the recursive triggering of fast, `ideal' - i.e. Lundquist number independent - tearing in collapsing current sheet configurations with arbitrary current profile shapes. An important result is that the Sweet-Parker scaling with Lundquist number, if interpreted as the aspect ratio of the singular layer in an ideally unstable sheet, is universal and does not depend on the details of the current profile in the sheet. Such a scaling however must not be interpreted in terms of stationary reconnection, rather it defines a step in the accelerating sequence of events of the ideal tearing mediated fractal cascade. We calculate scalings for the expected number of plasmoids for such generic profiles and realistic Lundquist numbers., Comment: 11 pages, 2 figures

In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\zeta)$, and the associated plasma response function $R(\zeta)=1+\zeta Z(\zeta)=-Z'(\zeta)/2$. We then consider a 1D (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the 4th-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1D closures at higher-order moments than the 4th-order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the 4th-order moment level. In the Appendix A, we provide comprehensive tables with Pad\'e approximants of $R(\zeta)$ up to the 8th-pole order, with many given in an analytic form., Comment: Improved version, now accepted to JPP Lecture Notes. Some parts were shortened and some parts were expanded. The text now contains Conclusions

We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modeling turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the CGL fluid model in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius (FLR) corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the 4th-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the "normal" closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the "normal" closure, and beyond the 4th-order moment, Landau fluid closures are required., Comment: Improved version, accepted to JPP Lecture Notes. Some parts were shortened and some parts were expanded. The text now contains Conclusions

Incorporation of kinetic effects such as Landau damping into a fluid framework was pioneered by Hammett and Perkins PRL 1990, by obtaining closures of the fluid hierarchy, where the gyrotropic heat flux fluctuations or the deviation of the 4th-order gyrotropic fluid moment, are expressed through lower-order fluid moments. To obtain a closure of a fluid model expanded around a bi-Maxwellian distribution function, the usual plasma dispersion function $Z(\zeta)$ that appears in kinetic theory or the associated plasma response function $R(\zeta)=1 + \zeta Z(\zeta)$, have to be approximated with a suitable Pad\'e approximant in such a way, that the closure is valid for all $\zeta$ values. Such closures are rare, and the original closures of Hammett and Perkins are often employed. Here we present a complete mapping of all plausible Landau fluid closures that can be constructed at the level of 4th-order moments in the gyrotropic limit and we identify the most precise closures. Furthermore, by considering 1D closures at higher-order moments, we show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing convergence of the fluid and collisionless kinetic descriptions., Comment: Phys. Rev. Lett

The nonlinear evolution of Alfv\'enic fluctuations in the firehose unstable regime is investigated numerically and theoretically for an anisotropic plasma described by the one-fluid double adiabatic equations. We revisit the traditional theory of the instability and examine the nonlinear saturation mechanism, showing that it corresponds to evolution towards states that minimize an appropriate energy functional. We demonstrate that such states correspond to broadband magnetic and velocity field fluctuations with an overall constant magnitude of the magnetic field. These nonlinear states provide a basin of attraction for the long-term nonlinear evolution of the instability, a self-organization process that may play a role in maintaining the constant-$B$ Alfv\'enic states seen in the solar wind in the high-$\beta$ regime.

The fast solar wind shows a wide spectrum of transverse magnetic and velocity field perturbations. These perturbations are strongly correlated in the sense of Alfv\'en waves propagating mostly outward, from the Sun to the interplanetary medium. They are likely to be fundamental to the acceleration and the heating of the solar wind. However, the precise origin of the broadband spectrum is to date unknown. Typical periods of chromospheric Alfv\'en waves are limited to a few minutes, and any longer period perturbations should be strongly reflected at the transition region. In this work, we show that minute long Alfv\'enic fluctuations are unstable to the parametric instability. Parametric instability enables an inverse energy cascade by exciting several hours long periods Alfv\'enic fluctuations together with strong density fluctuations (typically between 1 and $20 R_{\odot}$). These results may improve our understanding of the origin of the solar wind turbulent spectrum and will be tested by the Parker Solar Probe., Comment: 11 pages, 11 figures, to appear in the Astrophysical Journal

Magnetohydrodynamic simulations have shown that a non-unique critical Lundquist number $S_c$ exists, hovering around $S_c \sim 10^4$, above which threshold Sweet-Parker type stationary reconnecting configurations become unstable to a fast tearing mode dominated by plasmoid generation. It is known that the flow along the sheet plays a stabilizing role, though a satisfactory explanation of the non-universality and variable critical Lundquist numbers observed is still lacking. Here we discuss this question using 2D linear MHD simulations and linear stability analyses of Sweet-Parker type current sheets in the presence of background stationary inflows and outflows at low Lundquist numbers ($S\le 10^4$). Simulations show that the inhomogeneous outflow stabilizes the current sheet by stretching the growing magnetic islands and at the same time evacuating the magnetic islands out of the current sheet. This limits the time during which fluctuations which begin at any given wave-length can remain unstable, rendering the instability non-exponential. We find that the linear theory based on the expanding-wavelength assumption works well for $S$ larger than $\sim 1000$. However we also find that the inflow and location of the initial perturbation also affect the stability threshold.

In this paper we study the scaling relations for the triggering of the fast, or "ideal", tearing instability starting from equilibrium configurations relevant to astrophysical as well as laboratory plasmas that differ from the simple Harris current sheet configuration. We present the linear tearing instability analysis for equilibrium magnetic fields which a) go to zero at the boundary of the domain and b) contain a double current sheet system (the latter previously studied as a cartesian proxy for the m=1 kink mode in cylindrical plasmas). More generally, we discuss the critical aspect ratio scalings at which the growth rates become independent of the Lundquist number $S$, in terms of the dependence of the $\Delta'$ parameter on the wavenumber $k$ of unstable modes. The scaling $\Delta'(k)$ with $k$ at small $k$ is found to categorize different equilibria broadly: the critical aspect ratios may be even smaller than $L/a \sim S^{\alpha}$ with $\alpha=1/3$ originally found for the Harris current sheet, but there exists a general lower bound $\alpha\ge1/4$., Comment: 7 pages, 5 figures

We study the stability of large amplitude, circularly polarized Alfv\'en waves in an anisotropic plasma described by the double-adiabatic/CGL closure, and in particular the effect of a background thermal pressure anisotropy on the well-known properties of Alfv\'en wave parametric decay in Magnetohydrodynamics (MHD). Anisotropy allows instability over a much wider range of values of parallel plasma beta ($\beta_\parallel$) when $\xi=p_{0\bot}/p_{0\parallel} > 1$. When the pressure anisotropy exceeds a critical value, $\xi\geq\xi^*$ with $\xi^*\simeq2.7$, there is a new regime in which the parametric instability is no longer quenched at high $\beta_\parallel$ and in the limit $\beta_\parallel\gg1$ the growth rate becomes independent of $\beta_\parallel$. In the opposite case of $\xi< \xi^*$, the instability is strongly suppressed with increasing parallel plasma beta, similarly to the MHD case. We analyze marginal stability conditions for parametric decay in the $(\xi,\,\beta_\parallel)$ parameter space, and discuss possible implications for Alfv\'enic turbulence in the solar wind., Comment: 9 pages, 9 figures. Under review

One of the main questions in magnetic reconnection is the origin of triggering behavior with on/off properties that accounts, once it is activated, for the fast magnetic energy conversion to kinetic and thermal energies at the heart of explosive events in astrophysical and laboratory plasmas. Over the past decade progress has been made on the initiation of fast reconnection via the plasmoid instability and what has been called "ideal" tearing, which sets in once current sheets thin to a critical inverse aspect ratio $(a/L)_c$: as shown by Pucci and Velli (2014), at $(a/L)_c \sim S^{-1/3}$ the time scale for the instability to develop becomes of the order of the Alfv\'en time and independent of the Lundquist number (here defined in terms of current sheet length $L$). However, given the large values of $S$ in natural plasmas, this transition might occur for thicknesses of the inner resistive singular layer which are comparable to the ion inertial length $d_i$. When this occurs, Hall currents produce a three-dimensional quadrupole structure of magnetic field, and the dispersive waves introduced by the Hall effect accelerate the instability. Here we present a linear study showing how the "ideal" tearing mode critical aspect ratio is modified when Hall effects are taken into account, including more general scaling laws of the growth rates in terms of sheet inverse aspect ratio: the critical inverse aspect ratio is amended to $a/L \simeq (di/L)^ {0.29} (1/S)^{0.19}$, at which point the instability growth rate becomes Alfv\'enic and does not depend on either of the (small) parameters $d_i/L, 1/S$. We discuss the implications of this generalized triggering aspect ratio for recently developed phase diagrams of magnetic reconnection.

Alfv\'enic fluctuations in the solar wind display many properties reflecting an ongoing nonlinear cascade, e.g. a well-defined spectrum in frequency, together with some characteristics more commonly associated with the linear propagation of waves from the Sun, such as the variation of fluctuation amplitude with distance, dominated by solar wind expansion effects. Therefore both nonlinearities and expansion must be included simultaneously in any successful model of solar wind turbulence evolution. Because of the disparate spatial scales involved, direct numerical simulations of turbulence in the solar wind represent an arduous task, especially if one wants to go beyond the incompressible approximation. Indeed, most simulations neglect solar wind expansion effects entirely. Here we develop a numerical model to simulate turbulent fluctuations from the outer corona to 1 AU and beyond, including the sub-Alfv\'enic corona. The accelerating expanding box (AEB) extends the validity of previous expanding box models by taking into account both the acceleration of the solar wind and the inhomogeneity of background density and magnetic field. Our method incorporates a background accelerating wind within a magnetic field that naturally follows the Parker spiral evolution using a two-scale analysis in which the macroscopic spatial effect coupling fluctuations with background gradients becomes a time-dependent coupling term in a homogeneous box. In this paper we describe the AEB model in detail and discuss its main properties, illustrating its validity by studying Alfv\'en wave propagation across the Alfv\'en critical point., Comment: 19 pages, 6 Figures. In press in the ApJ