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We conduct 3D magnetohydrodynamic simulations of decaying turbulence in the context of the solar wind. To account for the spherical expansion of the solar wind, we implement the expanding box model. The initial turbulence comprises uncorrelated counterpropagating Alfvén 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 σ _c and compressibility. The spherical expansion facilitates this process. The resulting residual energy is primarily distributed in the perpendicular direction, with S _2 ( b ) − S _2 ( u ) ∝ l _⊥ or equivalently $-{E}_{r}\propto {k}_{\perp }^{-2}$ . Here S _2 ( b ) and S _2 ( u ) are second-order structure functions of magnetic field and velocity respectively. In most runs, S _2 ( b ) develops a scaling relation ${S}_{2}({\boldsymbol{b}})\propto {l}_{\perp }^{1/2}$ ( ${E}_{b}\propto {k}_{\perp }^{-3/2}$ ). In contrast, S _2 ( u ) is consistently shallower than S _2 ( 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, depend on the initial σ _c and are strongly affected by the expansion effect. 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, the causal relation between them seems to be weak, possibly because they are generated on different scales.

Numerical simulations have been an increasingly important tool in space physics. Here, we introduce an open-source three-dimensional compressible Hall-Magnetohydrodynamic (MHD) simulation code LAPS (UCLA-Pseudo-Spectral, https://github.com/chenshihelio/LAPS). The code adopts a pseudo-spectral method based on Fourier Transform to evaluate spatial derivatives, and third-order explicit Runge-Kutta method for time advancement. It is parallelized using Message-Passing-Interface (MPI) with a “pencil” parallelization strategy and has very high scalability. The Expanding-Box-Model is implemented to incorporate spherical expansion effects of the solar wind. We carry out test simulations based on four classic (Hall)-MHD processes, namely, 1) incompressible Hall-MHD waves, 2) incompressible tearing mode instability, 3) Orszag-Tang vortex, and 4) parametric decay instability. The test results agree perfectly with theory predictions and results of previous studies. Given all its features, LAPS is a powerful tool for large-scale simulations of solar wind turbulence as well as other MHD and Hall-MHD processes happening in space.

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 3D 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 ( β ) is smaller than one, the switchback is more stable as β increases. However, when β is greater than 1, 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.

Large amplitude Alfvénic fluctuations, sometimes leading to localized inversions of the magnetic field, called switchbacks, are a common but poorly understood phenomenon in the solar wind. In particular, their origin(s), evolution, and stability within solar wind conditions are yet to be fully understood. Simulations modeling switchbacks have previously studied their stability in 2D. Here, we investigate the decay process of Alfvén wave packets via MHD simulations in 3D by characterizing the effects of system size, aspect ratio, and propagation angle on the decay rate. We show that the initial wave packet is unstable to parametric instabilities that develop compressible and Alfvénic secondary modes in the plane of, and transverse to, the initial wave packet propagation direction. The growth of transverse modes, absent in 2D simulations, increases the decay rate of the wave packet. We finally discuss the implications of our results for lifetime estimates of switchbacks and wave energy conversion in the solar wind.

The parametric decay instability of Alfvén waves has been widely studied, but few investigations have examined wave packets of finite size and the effect of different boundary conditions on the growth rate. In this paper, we perform a linear analysis of circular and arc-polarized wave trains and wave packets in periodic and open boundary systems in a low- β plasma. We find that both types of wave are 3–5 times more stable in open boundary conditions compared to periodic. Additionally, once the wave packet width ℓ becomes smaller than the system size L , the growth rate decreases nearly with a power law γ ∝ ℓ / L . This study demonstrates that the stability of a pump wave cannot be separated from the laboratory settings, and that the growth rate of daughter waves depends on the conditions downstream and upstream of the pump wave and on the fraction of volume it fills. Our results can explain simulations and experiments of localized Alfvén waves. They also suggest that Alfvénic fluctuations in the solar wind, including sharp impulses known as switchbacks, can be more stable than traditional theory suggests depending on wind conditions.

Parker Solar Probe and Solar Orbiter data are used to investigate the radial evolution of magnetic turbulence between 0.06 ≲ R ≲ 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, α _B = −3/2, independent of plasma parameters. The inertial range grows with distance, progressively extending to larger spatial scales, while steepening toward a α _B = −5/3 scaling. It is observed that spectra for intervals with large magnetic energy excesses and low Alfvénic content steepen significantly with distance, in contrast to highly Alfvénic 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 Alfvénicity.

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 evaluate tearing stability criterion for the events identified via our neural network outlier method, and 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.

The heating and acceleration of the solar wind remains one of the unsolved fundamental 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 anticorrelation 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 the proton temperature and the wind speed and a negative correlation between the electron temperature and the wind speed. One year (2019) of WIND data confirm that the proton temperature is positively correlated with the 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 1D Alfvén-wave-driven solar wind model with different proton and electron temperatures, we find, for the first time, that if most of the dissipated Alfvén wave energy heats the ions instead of the 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 the radial distance to the Sun, such that the negative correlation gradually turns positive. The model results show that Alfvén waves are one of the possible explanations for the observed evolution of the proton and electron temperatures in the solar wind.

Large amplitude, turbulent Alfvénic fluctuations have been commonly observed in the solar wind since the first in situ measurements. An important but still unexplained property of such nonlinear fluctuations seen typically in the fastest streams is that, despite the large excursion of the magnetic field fluctuations, the magnitude of the total magnetic field remains nearly constant, a condition that corresponds to spherical polarization. How is this Alfvénic turbulent state achieved in the solar wind remains a fundamental open question in space physics. Although nonlinear Alfvénic fluctuations have been studied for several decades, most of previous work has considered a plasma in thermodynamic equilibrium. The solar wind however displays many non-thermal features and here we discuss how non-thermal effects, in particular pressure anisotropy, and nonlinearities affect the stability and nonlinear evolution of Alfvénic fluctuations with constant total magnetic field magnitude in different plasma-β regimes. [ABSTRACT FROM AUTHOR]

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 , with S as the Lundquist number defined by the half-length L of the current sheet (of a thickness of 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. [ABSTRACT FROM AUTHOR]

A double adiabatically expanding solar wind would quickly develop large parallel to perpendicular temperature anisotropies in electrons and ions that are not observed. One reason is that firehose instabilities would be triggered, leading to an ongoing driving/saturation evolution mechanism. We verify this assumption here for the first time for the electron distribution function and the electron firehose instability (EFI), using fully kinetic simulations with the Expanding Box Model. This allows the self-consistent study of onset and evolution of the oblique, resonant EFI in an expanding solar wind. We characterize how the competition between EFI and adiabatic expansion plays out in high- and low-beta cases, in high- and low-speed solar wind streams. We observe that, even when competing against expansion, the EFI results in perpendicular heating and parallel cooling. These two concurrent processes effectively limit the expansion-induced increase in temperature anisotropy and parallel electron beta. We show that the EFI goes through cycles of stabilization and destabilization: when higher wave number EFI modes saturate, lower wave number modes are destabilized by the effects of the expansion. We show how resonant wave/ particle interaction modifies the electron velocity distribution function after the onset of the EFI. The simulations are performed with the fully kinetic, semi-implicit expanding box code EB-iPic3D. [ABSTRACT FROM AUTHOR]

We address the challenges that come with fully kinetic Particle-In-Cell (PIC) simulations of the expanding solar wind by introducing a semi-implicit, Expanding Box Model (EBM) approach to the study of solar wind kinetic physics. Plasma propagation and expansion are dealt with via the variable change of the EBM. In this way the large separation between scales of interest and domain size is addressed by including solar wind propagation and expansion as time-dependent coupling terms and coordinate stretching. The semi-implicit discretization, in the widely used Implicit Moment Method (IMM) flavor, promises to increase the simulated domain size and duration with respect to explicit discretization. The EBM IMM equations are derived and tested against expected behavior of expanding plasma. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic simulations have shown that a nonunique critical Lundquist number Sc exists, hovering around Sc ∼ 104, 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 nonuniversality 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 ≤ 104). 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 that begin at any given wavelength can remain unstable, rendering the instability nonexponential. We find that the linear theory based on the expanding-wavelength assumption works well for S larger than ∼1000. However, we also find that the inflow and location of the initial perturbation also affect the stability threshold. [ABSTRACT FROM AUTHOR]

We study the stability of large-amplitude, circularly polarized Alfvén 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 Alfvén wave parametric decay in magnetohydrodynamics (MHD). Anisotropy allows instability over a much wider range of values of parallel plasma beta (β∥) when ξ = p0⊥/p0∥ > 1. When the pressure anisotropy exceeds a critical value, ξ ≥ ξ* with ξ* ≃ 2.7, there is a new regime in which the parametric instability is no longer quenched at high β∥, and in the limit β∥ ≫ 1, the growth rate becomes independent of β∥. In the opposite case of ξ < ξ*, 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 (ξ, β∥) parameter space and discuss possible implications for Alfvénic turbulence in the solar wind. [ABSTRACT FROM AUTHOR]

One of the main questions in magnetic reconnection is the origin of triggering behavior with on/off properties that, once it is activated, accounts 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 . As shown by Pucci & Velli, at , the timescale for the instability to develop becomes of the order of the Alfvén 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 that are comparable to the ion inertial length di. When this occurs, Hall currents produce a three-dimensional quadrupole structure of the 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 , at which point the instability growth rate becomes Alfvénic and does not depend on either of the (small) parameters . We discuss the implications of this generalized triggering aspect ratio for recently developed phase diagrams of magnetic reconnection. [ABSTRACT FROM AUTHOR]

Alfvénic 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-Alfvénic 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 Alfvén wave propagation across the Alfvén critical point. [ABSTRACT FROM AUTHOR]

This paper studies the growth rate of reconnection instabilities in thin current sheets in the presence of both resistivity and viscosity. In a previous paper, Pucci & Velli, it was argued that at sufficiently high Lundquist number S it is impossible to form current sheets with aspect ratios that scale as with because the growth rate of the tearing mode would then diverge in the ideal limit . Here we extend their analysis to include the effects of viscosity, always present in numerical simulations along with resistivity, and which may play a role in the solar corona and other astrophysical environments. A finite Prandtl number allows current sheets to reach larger aspect ratios before becoming rapidly unstable in pileup-type regimes. Scalings with Lundquist and Prandtl numbers are discussed, as well as the transition to kinetic reconnection. [ABSTRACT FROM AUTHOR]