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In this study, we use fully kinetic Particle In Cell (PIC) simulations to investigate numerically the dispersion relation of the tearing instability in the kinetic regime, which is at the moment rather poorly explored by theoretical investigations. To reduce the computational cost of the simulations, we use the the semi-implicit, energy conserving ECsim code (Lapenta et al, 2017), that allows us to step over the smaller scales and fastest frequencies and focus on characteristic scales of interest, with excellent energy conservation.We run several simulations with current sheets of fixed length. The current sheet half-thickness is progressively increased from $\delta \sim d_i$ to significantly larger. The other simulation parameters are kept identical.In our simulations, the tearing instability grows without external perturbation from the particle noise of PIC simulations. Later onset times are (predictably) observed when the number of particles per cell is increased.Several modes grow unstable in each simulation. We plot the growth rates of the unstable modes as a function of the current sheet thickness. We obtain a spread around a curve decreasing with increasing current sheet thickness.

We study the parametric decay instability of parallel-propagating Alfvén waves 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 Alfvén 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 Alfvén 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 Alfvén wave leading to a field-aligned proton beam propagating backwards at the Alfvén speed. We find that parametric decay heats preferentially protons, which gain approximately 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 the determination of the role of compressible and kinetic effects in wave-driven models of the solar wind.

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

Parker Solar Probe observations in the inner heliosphere have demonstrated that non-thermal features in solar wind ion distributions are particularly enhanced and dominant in the close-Sun environment. Proton beams and large differential flows of alpha particles are ubiquitously observed, also in slow, though Alfvénic, streams, qualitatively at odds with typical observations at 1AU, where non-Maxwellian features are usually less apparent in the slow solar wind. All this reinforces the idea, also supported by past Helios and Ulysses explorations, that preferential ion heating and acceleration take place already in the Corona and signatures of the kinetic processes involved are gradually washed out during expansion. To explore further properties of ion differential streaming during expansion, as well as associated kinetic instabilities and their possible role in plasma heating, we perform expanding box hybrid simulations of a multi-species solar wind composed by proton core, beam and alpha particles, focussing on the role of wave-particle interactions in shaping distribution functions and controlling relative drifts. Radial trends and typical distributions found in simulations are then compared with PSP and Solar Orbiter observations in the inner Heliosphere.

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.

Context. Parker Solar Probe (PSP) measures the magnetic field and plasma parameters of the solar wind at unprecedentedly close distances to the Sun. These data provide great opportunities to study the early-stage evolution of magnetohydrodynamic (MHD) turbulence in the solar wind. Aims. In this study, we make use of the PSP data to explore the nature of solar wind turbulence focusing on the Alfvénic character and power spectra of the fluctuations and their dependence on the 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, and stream interaction might play in determining the turbulent state. Methods. We carried 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 the distance from the Sun. A more in-depth analysis from several selected periods is also presented. Results. 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, which is determined by the wind speed together with the radial distance. Statistically, faster solar wind has higher “Alfvénicity,” with a more dominant outward propagating wave component and more balanced magnetic and 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 significantly vary from stream to stream even if these streams are of a similar speed, indicating very different origins of these streams. Especially, the slow wind that originates near the polar coronal holes has much lower Alfvénicity compared with the slow wind that originates from the active regions and 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 first radial alignment between Parker Solar Probe and Solar Orbiter spacecraft is used to investigate the evolution of solar wind turbulence in the inner heliosphere. Assuming ballistic propagation, two 1.5 hr intervals are tentatively identified as providing measurements of the same plasma parcels traveling from 0.1 to 1 au. Using magnetic field measurements from both spacecraft, the properties of turbulence in the two intervals are assessed. Magnetic spectral density, flatness, and high-order moment scaling laws are calculated. The Hilbert–Huang transform is additionally used to mitigate short sample and poor stationarity effects. Results show that the plasma evolves from a highly Alfvénic, less-developed turbulence state near the Sun, to fully developed and intermittent turbulence at 1 au. These observations provide strong evidence for the radial evolution of solar wind turbulence.

Alfvénic fluctuations represent the dominant contributions to turbulent fluctuations in the solar wind, especially, but not limited to, the fastest streams with velocity of the order of 600-700 km/s. Alfvénic fluctuations can contribute to solar wind heating and acceleration via wave pressure and turbulent heating. Observations show that such fluctuations are characterized by a nearly constant magnetic field amplitude, a condition which remains largely to be understood and that may be an indication of how fluctuations evolve and relax in the expanding solar wind. Interestingly, measurements from Parker Solar Probe have shown the ubiquitous and persistent presence of the so-called switchbacks. These are magnetic field lines which are strongly perturbed to the point that they produce local inversions of the radial magnetic field. The corresponding signature of switchbacks in the velocity field is that of local enhancements in the radial speed (or jets) that display the typical velocity-magnetic field correlation that characterizes Alfvén waves propagating away from the Sun. While there is not yet a general consensus on what is the origin of switchbacks and their connection to coronal activity, a first necessary step to answer these important questions is to understand how they evolve and how long they can persist in the solar wind. Here we investigate the evolution of switchbacks. We address how their evolution is affected by parametric instabilities and the possible role of expansion, by comparing models with the observed radial evolution of the fluctuations’ amplitude. We finally discuss what are the implications of our results for models of switchback generation and related open questions.

Magnetic reconnection converts the magnetic field energy into thermal and kinetic energies of the plasma. This process usually happens at extremely fast speed and is therefore believed to be a fundamental mechanism to explain various explosive phenomena such as coronal mass ejections and planetary magnetospheric storms. How magnetic reconnection is triggered from the large magnetohydrodynamic (MHD) scales remains an open question, with some theoretical and numerical studies showing the tearing instability to be involved. Observations in the Earth’s magnetotail and near the magnetopause show that a finite normal magnetic field is usually present inside the reconnecting current sheet. Besides, such a normal field may also exist in the solar corona. However, how this normal magnetic field modifies the tearing instability is not thoroughly studied. Here we discuss the linear tearing instability inside a two-dimensional current sheet with a normal component of magnetic field where the magnetic tension force is balanced by ion flows parallel and anti-parallel to the magnetic field. We solve the dispersion relation of the tearing mode with wave vector parallel to the reconnecting magnetic field. Our results confirm that the finite normal magnetic field stabilizes the tearing mode and makes the mode oscillatory instead of purely growing.

Already several decades ago, it was suggested that kinetic instabilities play a fundamental role in heat flux regulation at relatively large distances from the Sun, R> 1 AU [Scime et al, 1994]. Now, Parker Solar Probe observations have established that this is the case also closer to it [Halekas et al, 2020].Electron scale instabilities in the solar wind are driven and affected in their evolution by the slow, large scale process of solar wind expansion, as demonstrated observationally [Stverak et al, 2008; Bercic et al, 2020], and via fully kinetic Expanding Box Model simulations [Innocenti et al, 2019b].Now, connecting the dots, we examine an indirect role of plasma expansion in heat flux regulation in the solar wind. We show, as a proof of principle, that plasma expansion can modify heat flux evolution as a function of heliocentric distance, with respect to what is expected within an adiabatic framework, due to the onset of kinetic instabilities, in this case, an oblique firehose instability developing self consistently in the presence of a core and suprathermal electron population [Innocenti et al, 2020].This result highlights, once again, the deeply multi scale nature of the heliospheric environment, that calls for advanced simulation techniques. In this work, the simulations are done with the fully kinetic, semi-implicit [Markidis et al, 2010], Expanding Box Model [Velli et al, 1992] code EB-iPic3D [Innocenti et al, 2019a].

Parker Solar Probe (PSP) measures the magnetic field and plasma parameters of the solar wind at unprecedentedly close distances to the Sun, providing a great opportunity to study the early-stage evolution of magnetohydrodynamic (MHD) turbulence in the solar wind. Here we use PSP data to explore the nature of solar wind turbulence focusing on the Alfvénic character and power spectra of the fluctuations and their dependence on heliocentric 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, and stream interaction might play in determining the turbulent state. We carried 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 the 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, which is determined by the wind speed together with the radial distance. Statistically, faster solar wind has higher Alfvénicity with a more dominant outward propagating wave component and more balanced magnetic and 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 significantly vary from stream to stream even if these streams are of a similar speed, indicating very different origins of these streams. Especially, the slow wind that originates near the polar coronal holes has much lower Alfvénicity compared with the slow wind that originates from the active regions and pseudostreamers. We show that structures such as the heliospheric current sheet and wind stream velocity shears can play an important role in modifying the properties of the turbulence.*The PSP Team: Stuart D.Bale, Justin Kasper, Kelly Korreck, J. W. Bonnell, Thierry Dudok de Wit, Keith Goetz, Peter R. Harvey, Robert J. MacDowall, David Malaspina, Marc Pulupa, Anthony W.Case, Davin Larson, Jenny Verniero, Roberto Livi, Michael Stevens, PhyllisWhittlesey, Milan Maksimovic, and Michel Moncuquet

The onset of magnetic reconnection in space, astrophysical and laboratory plasmas is reviewed discussing results from theory, numerical simulations and observations. After a brief introduction on magnetic reconnection and approach to the question of onset, we first discuss recent theoretical models and numerical simulations, followed by observations of reconnection and its effects in space and astrophysical plasmas from satellites and ground-based detectors, as well as measurements of reconnection in laboratory plasma experiments. Mechanisms allowing reconnection spanning from collisional resistivity to kinetic effects as well as partial ionization are described, providing a description valid over a wide range of plasma parameters, and therefore applicable in principle to many different astrophysical and laboratory environments. Finally, we summarize the implications of reconnection onset physics for plasma dynamics throughout the Universe and illustrate how capturing the dynamics correctly is important to understanding particle acceleration. The goal of this review is to give a view on the present status of this topic and future interesting investigations, offering a unified approach.

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

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., 8 pages, 5 figures, accepted for publication in ApJL

Observations of solar wind electron properties, as displayed in the Tperp/Tpar vs βpar plane, appear to be constrained both in the Tperp/Tpar perp/Tpar >1 regimes by the electron firehose instability (EFI) and by the whistler instability respectively [Štverák 2008]. The onset mechanism of the EFI is established: solar wind expansion results in an electron thermal anisotropy, which in turns promotes the development of the instability that contributes to limit that same anisotropy [Innocenti 2019a]. However, if this were the only mechanism at work in the expanding solar wind, electron observations would pool at the EFI marginal instability line. Instead, they populate the “stable” interval bound by EFI and whistler marginal instability lines. It is not fully clear which role fully kinetic processes have in lifting the observed data points above the EFI marginal stability line and into the “stable” area. Other competing processes redistributing excess parallel energy into the perpendicular direction, such as collisions, may be at work as well [Yoon 2019].We investigate this issue with Particle In Cell, Expanding Box Model simulations [Innocenti 2019b] of EFI developing self consistently in the expanding solar wind. Our results show that after the EFI marginal stability line is reached, further collisionless evolution brings our simulated data points in the “stable” area. We thus demonstrate that, at least under certain circumstances, purely collisionless processes may explain observed solar wind observations, without the need of invoking collisions as a way to channel excess parallel energy into the perpendicular direction. Štverák, Štěpán, et al. "Electron temperature anisotropy constraints in the solar wind." Journal of Geophysical Research: Space Physics 113.A3 (2008).Innocenti, Maria Elena, et al. "Onset and Evolution of the Oblique, Resonant Electron Firehose Instability in the Expanding Solar Wind Plasma." The Astrophysical Journal 883.2 (2019): 146.Yoon, P. H., et al. "Solar Wind Temperature Isotropy." Physical review letters 123.14 (2019): 145101.Innocenti, Maria Elena, Anna Tenerani, and Marco Velli. "A Semi-implicit Particle-in-cell Expanding Box Model Code for Fully Kinetic Simulations of the Expanding Solar Wind Plasma." The Astrophysical Journal 870.2 (2019): 66.

Context.Turbulence dominated by large-amplitude, nonlinear Alfvén-like fluctuations mainly propagating away from the Sun is ubiquitous in high-speed solar wind streams. Recent studies have demontrated that slow wind streams may also show strong Alfvénic signatures, especially in the inner heliosphere.Aims.The present study focuses on the characterisation of an Alfvénic slow solar wind interval observed by Solar Orbiter between 14 and 18 July 2020 at a heliocentric distance of 0.64 AU.Methods.Our analysis is based on plasma moments and magnetic field measurements from the Solar Wind Analyser (SWA) and Magnetometer (MAG) instruments, respectively. We compared the behaviour of different parameters to characterise the stream in terms of the Alfvénic content and magnetic properties. We also performed a spectral analysis to highlight spectral features and waves signature using power spectral density and magnetic helicity spectrograms, respectively. Moreover, we reconstruct the Solar Orbiter magnetic connectivity to the solar sources both via a ballistic and a potential field source surface (PFSS) model.Results.The Alfvénic slow wind stream described in this paper resembles, in many respects, a fast wind stream. Indeed, at large scales, the time series of the speed profile shows a compression region, a main portion of the stream, and a rarefaction region, characterised by different features. Moreover, before the rarefaction region, we pinpoint several structures at different scales recalling the spaghetti-like flux-tube texture of the interplanetary magnetic field. Finally, we identify the connections between Solar Orbiter in situ measurements, tracing them down to coronal streamer and pseudostreamer configurations.Conclusions.The characterisation of the Alfvénic slow wind stream observed by Solar Orbiter and the identification of its solar source are extremely important aspects for improving the understanding of future observations of the same solar wind regime, especially as solar activity is increasing toward a maximum, where a higher incidence of this solar wind regime is expected.

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 observations of the Parker Solar Probe during its first perihelion at 0.166 au, consisting of a dense core and an antisunward 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. The 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.

Fast solar wind streams are known to be dominated by Alfvenic turbulence, i.e. large amplitude magnetic field and quasi-incompressible velocity fluctuations with a correlation corresponding to wave...

During Parker Solar Probe’s first orbit, the solar wind plasma was observed in situ closer than ever before, the perihelion on 2018 November 6 revealing a flow that is constantly permeated by large-amplitude Alfvénic 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 Alfvén 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.

This paper discusses the transition to fast growth of the tearing instability in thin current sheets in the collisionless limit where electron inertia drives the reconnection process. It has been previously suggested that in resistive MHD there is a natural maximum aspect ratio (ratio of sheet length and breadth to thickness) which may be reached for current sheets with a macroscopic length L, the limit being provided by the fact that the tearing mode growth time becomes of the same order as the Alfven time calculated on the macroscopic scale. For current sheets with a smaller aspect ratio than critical the normalized growth rate tends to zero with increasing Lundquist number S, while for current sheets with an aspect ratio greater than critical the growth rate diverges with S. Here we carry out a similar analysis but with electron inertia as the term violating magnetic flux conservation: previously found scalings of critical current sheet aspect ratios with the Lundquist number are generalized to include the dependence on the ratio d 2 e ∕L 2 , where d e is the electron skin depth, and it is shown that there are limiting scalings which, as in the resistive case, result in reconnecting modes growing on ideal time scales. Finite Larmor radius effects are then included, and the rescaling argument at the basis of " ideal " reconnection is proposed to explain secondary fast reconnection regimes naturally appearing in numerical simulations of current sheet evolution.

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 for which the tearing mode becomes fast, or ideal. In the decoupled regime the standard tearing mode is recovered with a small correction that depends 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. In the coupled regime, the growth rate depends on the density ratio between ions and neutrals through the collision frequency between these two species.

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 use 2.5D magnetohydrodynamic simulations to investigate the spectral signatures of the non-linear disruption of a tearing unstable current sheet via the generation of multiple secondary current sheets and magnetic islands. During the non-linear 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 ∼ 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 non-linear 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

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 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.

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.

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.