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In this paper, we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfvén, and fast wave eigenmodes, and the entropy and field-divergence pseudoeigenmodes. First, the mathematical formalism is introduced, where it is illustrated how the ideal-MHD eigensystem can be used to construct a decomposition of the time variation of the total energy density into contributions from the eigenmodes. The decomposition method is then demonstrated by applying it to the output of three separate nonlinear MHD simulations. The analysis of the simulations confirms that the component wave modes of a composite wavefield are uniquely identified by the method. The slow, Alfvén, and fast energy densities are shown to evolve in exactly the way expected from comparison with known linear solutions and nonlinear properties, including processes such as mode conversion. Along the way, some potential pitfalls for the numerical implementation of the decomposition method are identified and discussed. We conclude that the exact, nonlinear decomposition method introduced is a powerful and promising tool for understanding the nature of the decomposition of MHD waves as well as analyzing and interpreting the output of dynamic MHD simulations.

Energy conversion by reconnection-powered nanoflare heating is one of the leading explanations for the heating of the solar chromosphere and corona. The aim of this paper is to shed light on this mechanism by exploring the magnetic Reynolds-number dependence of the energy-conversion process. To do this we employ boundary-driven, magnetohydrodynamic, flux-braiding simulations at different magnetic Reynolds numbers (Rm) and explore in detail the properties of the individual magnetic energy-release events. The properties of the reconnecting current sheets that mediate the energy release are shown to depend on Rm. For increasing Rm, the current sheets become thinner, more intense, and more numerous. For sufficiently large Rm, the current sheets fragment along their length, leading to a sharp cutoff in the current-sheet length distribution. The cutoff is consistent with the threshold for nonlinear tearing/plasmoid instability. For increasing Rm the magnetic field lines become increasingly tangled, the mean and peak values of the magnetic-field strength increase, and the Poynting flux into the domain increases, implying that the heating rate also increases. The global reconnection rate is essentially independent of Rm. These results support the braiding mechanism as a viable way to effectively heat the internal portions of coherent flux tubes in the corona.

Physical insight into plasma evolution in the magnetohydrodynamic (MHD) limit can be revealed by decomposing the evolution according to the characteristic modes of the system. In this paper we explore aspects of the eigenenergy decomposition method (EEDM) introduced in an earlier study (ApJ, 967:80). The EEDM provides an exact decomposition of nonlinear MHD disturbances into their component eigenenergies associated with the slow, Alfvén, and fast eigenmodes, together with two zero-frequency eigenmodes. Here we refine the EEDM by presenting globally analytical expressions for the eigenenergies. We also explore the nature of the zero-frequency “pseudoadvective (PA) modes” in detail. We show that in evolutions with pure advection of magnetic and thermal energy (without propagating waves), a part of the energy is carried by the PA modes. Exact expressions for the error terms associated with these modes—commonly encountered in numerical simulations—are also introduced. The new EEDM equations provide a robust tool for the exact and unique decomposition of nonlinear disturbances governed by homogeneous quasi-linear partial differential equations, even in the presence of local or global degeneracies.

Precise tracking and measurement of the energy carried by the individual magnetohydrodynamic (MHD) modes has important implications and utility in both astrophysical and laboratory plasmas. Previously, this was only achievable in limited linear MHD cases in the β ≪ 1 or β ≫ 1 regimes. In a series of papers, of which this is the third, we introduced the Eigenenergy Decomposition Method (or EEDM) and derived exact analytical expressions for the modal energy components—called eigenenergies—of nonlinear 3D disturbances governed by the homogeneous ideal MHD equations. Here we extend the method to inhomogeneous ideal MHD by introducing a source term accounting for gravity, and we provide detailed guidelines for applying the decomposition scheme to any general inhomogeneous quasi-linear partial differential equations that possess a globally conserved quantity, beyond the realm of MHD. Furthermore, we show that the eigenenergies can be used to locate and measure nonlinear mode conversions, which is an additional feature of the method. Finally, we provide well-categorized context for the application of the method to simulations and discuss the possible numerical inaccuracies that may inevitably arise owing to discretization. This paper provides a more mature description of the method and its interpretation and is recommended as the starting point for readers unfamiliar with the method.

Fast-mode magnetohydrodynamic waves in the solar corona are often known to be produced by solar flares and eruptive prominences. Here, we simulate the effect of the interaction of an external perturbation on a magnetic null in the solar corona, which results in the formation of a current sheet (CS). Once the CS undergoes a sufficient extension in its length and squeezing of its width, it may become unstable to the formation of multiple impulsive plasmoids. Eventually, the plasmoids merge with one another to form larger plasmoids and/or are expelled from the sheet. The formation, motion, and coalescence of plasmoids with each other and with magnetic Y-points at the outer periphery of the extended CS are found to generate wavelike perturbations. An analysis of the resultant quasiperiodic variations of pressure, density, velocity, and magnetic field at certain locations in the model corona indicates that these waves are predominantly fast-mode magnetoacoustic waves. For typical coronal parameters, the resultant propagating waves carry an energy flux of 105 erg cm−2 s−1 to a large distance of at least 60 Mm away from the CS. In general, we suggest that both waves and reconnection play a role in heating the solar atmosphere and driving the solar wind and may interact with one another in a manner that we refer to as a “symbiosis of waves and reconnection.”

In the present paper, using MPI-AMRVAC, we perform a 2.5D numerical magnetohydrodynamic simulation of the dynamics and associated thermodynamical evolution of an initially force-free Harris current sheet subjected to an external velocity perturbation under the condition of uniform resistivity. The amplitude of the magnetic field is taken to be 10 G, typical of the solar corona. We impose a Gaussian velocity pulse across this current sheet that mimics the interaction of fast magnetoacoustic waves with a current sheet in the corona. This leads to a variety of dynamics and plasma processes in the current sheet, which is initially quasi-static. The initial pulse interacts with the current sheet and splits into a pair of counterpropagating wavefronts, which form a rarefied region that leads to an inflow and a thinning of the current sheet. The thinning results in Petschek-type magnetic reconnection followed by a tearing instability and plasmoid formation. The reconnection outflows containing outward-moving plasmoids have accelerated motions with velocities ranging from 105 to 303 km s−1. The average temperature and density of the plasmoids are found to be 8 MK and twice the background density of the solar corona, respectively. These estimates of the velocity, temperature, and density of the plasmoids are similar to values reported from various solar coronal observations. Therefore, we infer that the external triggering of a quasi-static current sheet by a single-velocity pulse is capable of initiating magnetic reconnection and plasmoid formation in the absence of a localized enhancement of resistivity in the solar corona.

Magnetic reconnection and magnetohydrodynamic waves may well be both playing a role in coronal heating. In this paper, we simulate reconnection in the corona as a response to the convergence of opposite-polarity magnetic sources at the base of the corona. A current sheet forms at a magnetic null and undergoes impulsive bursty reconnection, which drives natural modes of oscillation of the current sheet by a process of symbiosis. These are leaky surface sausage modes, which cause the length of the current sheet to oscillate. Interaction of the oscillations and reconnection outflows with the magnetic Y-points at the ends of the sheet acts as sources for magnetoacoustic waves. Fast-mode waves propagate outward into the coronal environment, while slow-mode waves propagate along the separatrices extending from the ends of the current sheet. The periodicities for sausage oscillations of the current sheet, for the current sheet length, and for the propagating large-scale magnetoacoustic waves are all estimated to be approximately 91 s for the parameters of our experiment.

Multiwavelength observations of the propagating disturbances (PDs), discovered by Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO), are analyzed to determine their driving mechanism and physical nature. Two magnetic strands in the localized corona are observed to approach and merge with each other, followed by the generation of brightening, which further propagates in a cusp-shaped magnetic channel. Differential emission measure analysis shows an occurrence of heating in this region of interest. We extrapolate potential magnetic field lines at coronal heights from the observed Helioseismic and Magnetic Imager vector magnetogram via Green’s function method using MPI-AMRVAC. We analyze the field to locate magnetic nulls and quasi-separatrix layers (QSLs), which are preferential locations for magnetic reconnection. Dominant QSLs including a magnetic null are found to exist and match the geometry followed by PDs; therefore, this provides conclusive evidence of magnetic reconnection. In addition, spectroscopic analysis of Interface Region Imaging Spectrograph Si iv λ1393.77 line profiles show a rise of line width in the same time range depicting the presence of mass motion in the observed cusp-shaped region. PDs are observed to exhibit periodicities of around 4 minutes. The speeds of PDs measured by the surfing transform technique are close to each other in four different SDO/AIA bandpasses, i.e., 304, 171, 193, and 131 Å, excluding the interpretation of PDs in terms of slow magnetoacoustic waves. We describe comprehensively the observed PDs as quasiperiodic plasma flows generated as a result of periodic reconnection in the vicinity of a coronal magnetic null.

The Sun’s open–closed flux boundary (OCB) separates closed and open magnetic field lines, and is the site for interchange magnetic reconnection processes thought to be linked to the origin of the slow solar wind (SSW). We analyze the global magnetic field structure and OCB from 2010 December to 2019 December using three coronal magnetic field models: a potential-field source-surface (PFSS) model, a static equilibrium magnetofrictional model, and a time-dependent magnetofrictional model. We analyze the model and cycle dependence of the OCB length on the photosphere, as well as the magnetic flux in the vicinity of the OCB. Near solar maximum, the coronal magnetic field for each model consists predominantly of long, narrow coronal holes, and nearly all the open flux lies within 1 supergranule diameter (25 Mm) of the OCB. By comparing to interplanetary scintillation measurements of SSW speeds, we argue that the fraction of open flux within this 25 Mm band is a good predictor of the amount of SSW in the heliosphere. Importantly, despite its simplicity, we show that the PFSS model estimates this fraction as well as the time-dependent model. We discuss the implications of our results for understanding SSW origins and interchange reconnection at the OCB.

The Sun’s outer atmosphere, the corona, is maintained at mega-Kelvin temperatures and fills the heliosphere with a supersonic outflowing wind. The dissipation of magnetic waves and direct electric currents are likely to be the most significant processes for heating the corona, but a lively debate exists on their relative roles. Here, we suggest that the two are often intrinsically linked, since magnetic waves may trigger current dissipation, and impulsive reconnection can launch magnetic waves. We present a study of the first of these processes by using a 2D physics-based numerical simulation using the Adaptive Mesh Refined Versatile Advection Code. Magnetic waves such as fast magnetoacoustic waves are often observed to propagate in the large-scale corona and interact with local magnetic structures. The present numerical simulations show how the propagation of magnetic disturbances toward a null point or separator can lead to the accumulation of the electric currents. Lorentz forces can laterally push and vertically stretch the magnetic fields, forming a current sheet with a strong magnetic field gradient. The magnetic field lines then break and reconnect and so contribute toward coronal heating. Numerical results are presented that support these ideas and support the concept of a symbiosis between waves and reconnection in heating the solar corona.