Simulations Of Magnetic Reconnection Research Articles

Simultaneous Proton and Electron Energization during Macroscale Magnetic Reconnection

The results of simulations of magnetic reconnection accompanied by electron and proton heating and energization in a macroscale system are presented. Both species form extended power-law distributions that extend nearly three decades in energy. The primary drive mechanism for the production of these nonthermal particles is Fermi reflection within evolving and coalescing magnetic flux ropes. While the power-law indices of the two species are comparable, the protons overall gain more energy than electrons, and their power law extends to higher energy. The power laws roll into a hot thermal distribution at low energy with the transition energy occurring at lower energy for electrons compared with protons. A strong guide field diminishes the production of nonthermal particles by reducing the Fermi drive mechanism. In solar flares, proton power laws should extend down to tens of keV, far below the energies that can be directly probed via gamma-ray emission. Thus, protons should carry much more of the released magnetic energy than expected from direct observations.

Temperature-reducing shocks in optically thin radiative MHD—Analytical and numerical results

Shocks are often invoked as heating mechanisms in astrophysical systems, with both adiabatic compression and dissipative heating that leading to the increase in temperature. While shocks are reasonably well understood for ideal magnetohydrodynamic (MHD) systems, in many astrophysical plasmas, radiation is an important phenomena, which can allow energy to leave the system. As such, energy becomes non-conservative, which can fundamentally change the behavior of shocks. The energy emitted through optically thin radiation post-shock can exceed the thermal energy increase, resulting in shocks that reduce the temperature of the medium, i.e., cooling shocks that have a net decrease in temperature across the interface. In this paper, semi-analytical solutions for radiative shocks are derived to demonstrate that both cooling (temperature decreasing) and heating (temperature increasing) shock solutions are possible across the whole temperature range in optically thin radiative MHD. Numerical simulations of magnetic reconnection for solar-like temperatures and plasma-β with optically thin radiative losses also yield both heating and cooling shocks in roughly equal abundances. The detected cooling shocks feature a significantly lower pressure jump across the shock than their heating counterparts. The compression at the shock front leads to locally enhanced radiative losses, resulting in significant cooling within a few grid cells in the upstream and downstream directions. The presence of temperature-reducing (cooling) shocks is critical in determining the thermal evolution, and heating or cooling, across a wealth of radiative astrophysical plasmas including magnetic reconnection in the solar corona.

Radiative properties of plasmoids and plasmoid mergers in magnetic reconnection

ABSTRACT Magnetic reconnection is often considered as the primary particle acceleration mechanism in a magnetized blazar zone environment. The majority of radiation in the reconnection layer comes from plasmoids and their mergers. In particular, plasmoid mergers can produce strong multiwavelength flares and major variations in synchrotron polarization signatures. However, radiative properties of plasmoid mergers have not been well explored due to difficulties in tracking the merging processes. Here we use an image processing method that combines the magnetic vector potential and density to identify isolated and merging plasmoids. We find that this method can clearly distinguish radiation contributions from isolated plasmoids, merging plasmoids, and the primary current sheet of reconnection. This new method enables us to study the radiative properties of plasmoids and mergers statistically. Our results show that isolated plasmoids have similar emissivity regardless of their sizes, and they generally have non-zero polarization degree (PD) due to their quasi-circular shape. Flares due to plasmoid mergers have relative amplitudes that are antiproportional to the size ratio of the plasmoids participating in the mergers. Finally, only mergers between plasmoids of comparable sizes (width ratio ≲5) can lead to significant spectral hardening and polarization angle (PA) variations; the amplitude of the PA variations is between 0 and 180° and has a mean value of 90°. Our analyses on 2D simulations can pave the way for future analyses and machine learning techniques on radiative properties of 3D magnetic reconnection simulations.

Modeling electron acceleration during the contraction of a magnetic island

Magnetic reconnection releases the magnetic energy through the contraction of multi-magnetic island leading to the electron acceleration as proposed by Drake et. al in 2006. However, how the released magnetic energy is converted into electron’s kinetic energy is still theoretically not well understood. We model in particular the kinetic process assuming the adiabatic contraction of magnetic island that induces electric field which is proportional to the vector potential of the magnetic island and approximate the magnetic island with an ellipse. Under this model, we show that the energy gain is achieved through the work of inductive electric field. We further show that the curvature drift which is along the inductive electric field dominates the energy gain. We compared our model with the magnetic island formed by tearing instability in a 2.5D particle-in-cell simulation of magnetic reconnection and found the results from the model consistent with that of the simulation.

A comparative study of resistivity models for simulations of magnetic reconnection in the solar atmosphere

Context. Plasmoid-mediated reconnection plays a fundamental role in different solar atmospheric phenomena. Numerical reproduction of this process is therefore essential for developing robust solar models. Aims. Our goal is to assess plasmoid-mediated reconnection across various numerical resistivity models in order to investigate how plasmoid numbers and reconnection rates depend on the Lundquist number. Methods. We used the Bifrost code to drive magnetic reconnection in a 2D coronal fan-spine topology, carrying out a parametric study of several experiments with different numerical resolution and resistivity models. We employed three anomalous resistivity models: (1) the original hyper-diffusion from Bifrost, (2) a resistivity proportional to current density, and (3) a resistivity quadratically proportional to electron drift velocity. For comparisons, experiments with uniform resistivity were also run. Results. Plasmoid-mediated reconnection is obtained in most of the experiments. With uniform resistivity, increasing the resolution reveals higher plasmoid frequency with weaker scaling to the Lundquist number, obtaining 7.9–12 plasmoids per minute for SL ∈ [1.8 × 104, 2.6 × 105] with a scaling of SL0.210 in the highest-resolution resistivity cases, transcending into Petschek reconnection in the high-SL limit (where the diffusive effects of the resistivity become small compared to the non-uniform viscosity) and Sweet-Parker reconnection in the low-SL limit. Anomalous resistivity leads to similar results even with lower resolution. The drift-velocity-dependent resistivity excellently reproduces Petschek reconnection for any Lundquist number, and similar results are seen with resistivity proportional to current-density though with slightly lower reconnection rates and plasmoid numbers. Among the different resistivity models applied on the given numerical resolution, the hyper-diffusion model reproduced plasmoid characteristics in closest resemblance to those obtained with uniform resistivity at a significantly higher resolution.

The Scaling of Vortical Electron Acceleration in Thin-current Magnetic Reconnection and Its Implications in Solar Flares

To investigate how magnetic reconnection (MR) accelerates electrons to a power-law energy spectrum in solar flares, we explore the scaling of a kinetic model proposed by Che & Zank (CZ) and compare it to observations. Focusing on thin current sheet MR particle-in-cell (PIC) simulations, we analyze the impact of domain size on the evolution of the electron Kelvin–Helmholtz instability (EKHI). We find that the duration of the growth stage of the EKHI ( tG∼Ωe−1 ) is short and remains nearly unchanged because the electron gyrofrequency Ω e is independent of domain size. The quasi-steady stage of the EKHI (t MR) dominates the electron acceleration process and scales linearly with the size of the simulations as L/v A0, where v A0 is the Alfvén speed. We use the analytical results obtained by CZ to calculate the continuous temporal evolution of the electron energy spectra from PIC simulations and linearly scale them to solar flare observational scales. For the first time, an electron acceleration model predicts the sharp two-stage transition observed in typical soft–hard–harder electron energy spectra, implying that the electron acceleration model must be efficient with an acceleration timescale that is a small fraction of the duration of solar flares. Our results suggest that we can use PIC MR simulations to investigate the observational electron energy spectral evolution of solar flares if the ratio t MR/t G is sufficiently small, i.e., ≲10%.

Comptonization by reconnection plasmoids in black hole coronae – III. Dependence on the guide field in pair plasma

ABSTRACT We perform non-radiative two-dimensional particle-in-cell simulations of magnetic reconnection for various strengths of the guide field (perpendicular to the reversing field), in magnetically dominated electron–positron plasmas. Magnetic reconnection under such conditions could operate in accretion disc coronae around black holes. There, it has been suggested that the transrelativistic bulk motions of reconnection plasmoids containing inverse-Compton-cooled electrons could Compton-upscatter soft photons to produce the observed non-thermal hard X-rays. Our simulations are performed for magnetizations 3 ≤ σ ≤ 40 (defined as the ratio of enthalpy density of the reversing field to plasma enthalpy density) and guide field strengths 0 ≤ Bg/B0 ≤ 1 (normalized to the reversing field strength B0). We find that the mean bulk energy of the reconnected plasma depends only weakly on the flow magnetization but strongly on the guide field strength – with Bg/B0 = 1 yielding a mean bulk energy twice smaller than Bg/B0 = 0. Similarly, the dispersion of bulk motions around the mean – a signature of stochasticity in the plasmoid chain’s motions – is weakly dependent on magnetization (for σ ≳ 10) but strongly dependent on the guide field strength – dropping by more than a factor of two from Bg/B0 = 0 to Bg/B0 = 1. In short, reconnection in strong guide fields (Bg/B0 ∼ 1) leads to slower and more ordered plasmoid bulk motions than its weak guide field (Bg/B0 ∼ 0) counterpart.

Two-fluid reconnection jets in a gravitationally stratified atmosphere

Context. Density decreases exponentially with height in the gravitationally stratified solar atmosphere, and therefore collisional coupling between the ionized plasma and the neutrals also decreases. Reconnection is a process observed at all heights in the solar atmosphere. Aims. Here, we investigate the role of collisions between ions and neutrals in the reconnection process occurring at various heights in the atmosphere. Methods. We performed simulations of magnetic reconnection induced by a localized resistivity in a gravitationally stratified atmosphere, in which we varied the height of the initial reconnection X-point. We compared a magnetohydrodynamic (MHD) model and two two-fluid configurations: one in which the collisional coupling was calculated from local plasma parameters, and another in which the coupling was decreased so that collisional effects would be enhanced. The latter setup has a more representative solar collisionality regime. Results. Simulations in a stratified atmosphere show similar structures in MHD and two-fluid simulations, with strong coupling. However, when collisional effects are increased to attain representative parameter regimes, we find a nonlinear runaway instability, which separates the plasma-neutral densities across the current sheet (CS). With increased collisional effects, the initial decoupling in velocity heats the neutrals and this sets up a nonlinear feedback loop, according to which neutrals migrate outside the CS, replacing charged particles that accumulate toward the center of the CS. Conclusions. The reconnection rate has a maximum value of around 0.1 for both reconnection heights, and is consistent with the locally enhanced resistivity used in all three models. The early-stage plasmoid formation observed near the end of our simulations is influenced by the outflow from the primary reconnection point, rather than by collisions. We synthesized optically thin emission for both MHD and two-fluid models, which can show a very different evolution when the charged-particle density is used instead of the total density. Our simulations have relevance for observed plasmoid features associated with chromospheric to low-coronal flare events.

Energy Dissipation in Magnetic Islands Formed during Magnetic Reconnection

Magnetic reconnection converts magnetic energy into particle kinetic energy, and satellite observations have shown that 20%–50% of magnetic energy is channeled into electron kinetic energy. How such a large amount of magnetic energy is dissipated into electron kinetic energy is in debate. In this paper, by performing a large-scale 2D particle-in-cell simulation of magnetic reconnection with a guide field, we find that there exist both ion and electron shear flows in magnetic islands formed during magnetic reconnection, which are unstable to the ion and electron Kelvin–Helmholtz (K-H) instabilities. With the development of the K-H instabilities, the magnetic field lines are twisted in these magnetic islands, and intensified electron-scale current sheets are consequently generated. We quantitatively analyze the energy dissipation during such a process in magnetic islands and find that electrons obtain kinetic energy from the magnetic field while ion kinetic energy is transferred into magnetic energy. At last, it results that about 42% of magnetic energy is dissipated into electron kinetic energy in the whole process of magnetic reconnection. Our results help us better understand why a large amount of magnetic energy can be dissipated into electron kinetic energy.

A comparative study of resistivity models for simulations of magnetic reconnection in the solar atmosphere

Context. Magnetic reconnection is a fundamental mechanism in astrophysics. A common challenge in mimicking this process numerically in particular for the Sun is that the solar electrical resistivity is small compared to the diffusive effects caused by the discrete nature of codes. Aims. We aim to study different anomalous resistivity models and their respective effects on simulations related to magnetic reconnection in the Sun. Methods. We used the Bifrost code to perform a 2D numerical reconnection experiment in the corona that is driven by converging opposite polarities at the solar surface. This experiment was run with three different commonly used resistivity models: 1) the hyper-diffusion model originally implemented in Bifrost, 2) a resistivity proportional to the current density, and 3) a resistivity proportional to the square of the electron drift velocity. The study was complemented with a 1D experiment of a Harris current sheet with the same resistivity models. Results. The 2D experiment shows that the three resistivity models are capable of producing results in satisfactory agreement with each other in terms of the current sheet length, inflow velocity, and Poynting influx. Even though Petschek-like reconnection occurred with the current density-proportional resistivity while the other two cases mainly followed plasmoid-mediated reconnection, the large-scale evolution of thermodynamical quantities such as temperature and density are quite similar between the three cases. For the 1D experiment, some recalibration of the diffusion parameters is needed to obtain comparable results. Specifically the hyper-diffusion and the drift velocity-dependent resistivity model needed only minor adjustments, while the current density-proportional model needed a rescaling of several orders of magnitude. Conclusions. The Bifrost hyper-diffusion model is as suitable for simulations of magnetic reconnection as other common resistivity models and has the advantage of being applicable to any region in the solar atmosphere without the need for significant recalibration.

Multifluid Simulations of Upper-chromospheric Magnetic Reconnection with Helium–Hydrogen Mixture

Our understanding of magnetic reconnection (MR) under chromospheric conditions remains limited. Recent observations have demonstrated the important role of ion–neutral interactions in the dynamics of the chromosphere. Furthermore, the comparison between the spectral profiles and synthetic observations of reconnection events suggests that current MHD approaches appear to be inconsistent with observations. First, collisions and multithermal aspects of the plasma play a role in these regions. Second, hydrogen and helium ionization effects are relevant to the energy balance of the chromosphere. This work investigates the multifluid multispecies (MFMS) effects on MR in conditions representative of the upper chromosphere using the multifluid Ebysus code. We compare an MFMS approach based on a helium–hydrogen mixture with a two-fluid MHD model based on hydrogen only. The simulations of MR are performed in a Lundquist number regime high enough to develop plasmoids and instabilities. We study the evolution of the MR and compare the two approaches including the structure of the current sheet and plasmoids, the decoupling of the particles, the evolution of the heating mechanisms, and the composition. The presence of helium species leads to more efficient heating mechanisms than the two-fluid case. This scenario, which is out of reach of the two-fluid or single-fluid models, can reach transition region temperatures starting from upper-chromospheric thermodynamic conditions, representative of a quiet Sun scenario. The different dynamics between helium and hydrogen species could lead to chemical fractionation and, under certain conditions, enrichment of helium in the strongest outflows. This could be of significance for recent observations of helium enrichment in the solar wind in switchbacks and coronal mass ejections.

Kinetic energy partitions in electron–ion PIC simulations of ABC fields

Abstract We explore the kinetic energy partitions between electrons and ions in the 2-D magnetostatic equilibria called Arnold–Beltrami–Childress (ABC) fields, using particle-in-cell (PIC) numerical simulations. We cover a wider range of ion–electron temperature combinations and get different results compared to previous studies of the Harris-layer-type magnetic reconnection simulations. We find that the initial ion–electron enthalpy ratio is an important indicator. The particle species that dominates the total enthalpy will also dominate the kinetic energy gains and the momentum distribution peaks, but the other species have higher nonthermal energy fractions because both species show similar maximum energies.

Pressure–strain interaction. III. Particle-in-cell simulations of magnetic reconnection

How energy is converted into thermal energy in weakly collisional and collisionless plasma processes, such as magnetic reconnection and plasma turbulence, has recently been the subject of intense scrutiny. The pressure–strain interaction has emerged as an important piece, as it describes the rate of conversion between bulk flow and thermal energy density. In two companion studies, we presented an alternate decomposition of the pressure–strain interaction to isolate the effects of converging/diverging flow and flow shear instead of compressible and incompressible flow, and we derived the pressure–strain interaction in magnetic field-aligned coordinates. Here, we use these results to study pressure–strain interaction during two-dimensional anti-parallel magnetic reconnection. We perform particle-in-cell simulations and plot the decompositions in both Cartesian and magnetic field-aligned coordinates. We identify the mechanisms contributing to positive and negative pressure–strain interaction during reconnection. This study provides a roadmap for interpreting numerical and observational data of the pressure–strain interaction, which should be important for studies of reconnection, turbulence, and collisionless shocks.

Numerical simulations of the laser-driven Petschek-type magnetic reconnection

This paper describes a numerical study of the magnetic reconnection between two magnetic fields of opposite polarity. The magnetic fields are created by an electric current in a coil connected to two metal disks. One of the disks is irradiated by a strong laser beam, whereby large amounts of free electrons flow toward the other disk, constituting a closed circuit for the electric current flowing through the coil. Two parallel coils are arranged to connect the two disks, and irradiation of the laser beam on one disk results in parallel electric currents in the two coils, inducing two magnetic fields of opposite polarity in the region between them. The magnetic reconnection that occurs in this region is three-dimensional. This three-dimensional magnetic reconnection is investigated via magnetohydrodynamic numerical simulations. The characteristics of the Petschek-type magnetic reconnection are observed for the first time in such numerical simulations of magnetic reconnection. Changes in the shape of the magnetic field lines form the boundary of the dissipation region and the outflow region. Moreover, the thermal plasma generated by reconnection is strongly confined to the region where the reconnecting current sheet and the slow-mode shock are located, and no leaks of thermal plasma are observed. Comparisons with existing laboratory experiment results confirm that our numerical simulations reproduce the experimental outcomes and provide reasonable explanations for the results observed in laboratories.

Acceleration of cold ions in magnetic reconnection

This paper describes the results of 2.5D particle-in-cell kinetic simulations of magnetic reconnection. We consider the case without cold ions (case 0) and with a cold ion flow loaded at two localized positions (cases 1 and 2). The cold ions are loaded on the lower side of the inflow region in cases 1 and 2: along the x-direction, the cold ions are centered at the x location of the X-line in case 1 and are positioned to one side in case 2. Our simulations suggest that cold ions are accelerated and heated near the upper separatrix region in both cases 1 and 2. The gyroradius of the orbit of cold ions increases in the diffusion region owing to the weak magnetic field and then enter the outflow region, where the cold ions pick up the E×B outflow. The cold ions are prevented from crossing the upper separatrix by the Hall electric field, which is negative at the upper exhaust region separatrix. The cold ions are accelerated along the negative z-direction in the upper inflow region by the nonideal electric field (E+vci×B)z for case 1. During this process, the cold ions undergo demagnetization drift association with the finite Larmor radius effect of cold ions. Yet, the reconnection rate decreases after the cold ions flow into the diffusion region. However, the magnetic reconnection rate exhibits no significant changes in case 2.

Polynomial Reconstruction of the Magnetic Field Observed by Multiple Spacecraft With Integrated Velocity Determination

AbstractRecently, a polynomial reconstruction technique has been developed for reconstructing the magnetic field in the vicinity of multiple spacecraft and has been applied to events observed by the Magnetospheric Multiscale (MMS) mission. Whereas previously the magnetic field was reconstructed using spacecraft data from a single time, here we extend the method to allow input over a span of time. This extension increases the amount of input data to the model, improving the reconstruction results and yields an independent estimate of the structure velocity. The effect of this modification, as well as many other options, is explored by comparing reconstructed fields to those of a three‐dimensional particle in cell simulation of magnetic reconnection, using virtual spacecraft data as input. We often find best results using multiple‐time input, a moderate amount of smoothing of the input data, and a model with a reduced set of parameters based on the ordering that the maximum, intermediate, and minimum values of the gradient of the vector magnetic field are well separated. When spacecraft input data are temporally smoothed, reconstructions are representative of spatially smoothed fields. Two MMS events are reconstructed. The first of these was late in the mission when it was not possible to use the current density for MMS4 because of its instrument failure. The second shows a rotational discontinuity without an X or O line. In both cases, the reconstructions yield a visual representation of the magnetic structure that is consistent with earlier studies.

Comptonization by reconnection plasmoids in black hole coronae II: Electron-ion plasma

ABSTRACT We perform 2D particle-in-cell simulations of magnetic reconnection in electron-ion plasmas subject to strong Compton cooling and calculate the X-ray spectra produced by this process. The simulations are performed for trans-relativistic reconnection with magnetization 1 ≤ σ ≤ 3 (defined as the ratio of magnetic tension to plasma rest-mass energy density), which is expected in the coronae of accretion discs around black holes. We find that magnetic dissipation proceeds with inefficient energy exchange between the heated ions and the Compton-cooled electrons. As a result, most electrons are kept at a low temperature in Compton equilibrium with radiation, and so thermal Comptonization cannot reach photon energies $\sim 100\,$ keV observed from accreting black holes. Nevertheless, magnetic reconnection efficiently generates $\sim 100\,$ keV photons because of mildly relativistic bulk motions of the plasmoid chain formed in the reconnection layer. Comptonization by the plasmoid motions dominates the radiative output and controls the peak of the radiation spectrum Epk. We find Epk ∼ 40 keV for σ = 1 and Epk ∼ 100 keV for σ = 3. In addition to the X-ray peak around 100 keV, the simulations show a non-thermal MeV tail emitted by a non-thermal electron population generated near X-points of the reconnection layer. The results are consistent with the typical hard state of accreting black holes. In particular, we find that the spectrum of Cygnus X-1 is well explained by electron-ion reconnection with σ ∼ 3.

Particle Acceleration in Magnetic Reconnection with Ad Hoc Pitch-angle Scattering

Particle acceleration during magnetic reconnection is a long-standing topic in space, solar, and astrophysical plasmas. Recent 3D particle-in-cell simulations of magnetic reconnection show that particles can leave flux ropes due to 3D field-line chaos, allowing particles to access additional acceleration sites, gain more energy through Fermi acceleration, and develop a power-law energy distribution. This 3D effect does not exist in traditional 2D simulations, where particles are artificially confined to magnetic islands due to their restricted motions across field lines. Full 3D simulations, however, are prohibitively expensive for most studies. Here, we attempt to reproduce 3D results in 2D simulations by introducing ad hoc pitch-angle scattering to a small fraction of the particles. We show that scattered particles are able to transport out of 2D islands and achieve more efficient Fermi acceleration, leading to a significant increase of energetic particle flux. We also study how the scattering frequency influences the nonthermal particle spectra. This study helps achieve a complete picture of particle acceleration in magnetic reconnection.

Current-sheet Oscillations Caused by the Kelvin–Helmholtz Instability at the Loop Top of Solar Flares

Current sheets (CSs), long stretching structures of magnetic reconnection above solar flare loops, are usually observed to oscillate; their origins, however, are still puzzled at present. Based on a high-resolution 2.5D MHD simulation of magnetic reconnection, we explore the formation mechanism of CS oscillations. We find that large-amplitude transverse waves are excited by the Kelvin–Helmholtz instability at the highly turbulent cusp-shaped region. The perturbations propagate upward along the CS with a phase speed close to local Alfvén speed thus resulting in the CS oscillations we observe. Though the perturbations damp after propagating for a long distance, the CS oscillations are still detectable. In terms of detected CS oscillations, with a combination of differential emission measure techniques, we propose a new method for measuring the magnetic field strength of the CS and its distribution in height.

Sgr A* X-ray flares from non-thermal particle acceleration in a magnetically arrested disc

ABSTRACT Sgr A* exhibits flares in the near-infrared and X-ray bands, with the luminosity in these bands increasing by factors of 10–100 for ≈60 min. One of the models proposed to explain these flares is synchrotron emission of non-thermal particles accelerated by magnetic reconnection events in the accretion flow. We use the results from particle-in-cell simulations of magnetic reconnection to post-process 3D two-temperature GRMHD simulations of a magnetically arrested disc (MAD). We identify current sheets, retrieve their properties, estimate their potential to accelerate non-thermal particles, and compute the expected non-thermal synchrotron emission. We find that the flux eruptions of MADs can provide suitable conditions for accelerating non-thermal particles to energies γe ≲ 106 and producing simultaneous X-ray and near-infrared flares. For a suitable choice of current-sheet parameters and a simplified synchrotron cooling prescription, the model can simultaneously reproduce the quiescent and flaring X-ray luminosities as well as the X-ray spectral shape. While the near-infrared flares are mainly due to an increase in the temperature near the black hole during the MAD flux eruptions, the X-ray emission comes from narrow current sheets bordering highly magnetized, low-density regions near the black hole, and equatorial current sheets where the flux on the black hole reconnects. As a result, not all infrared flares are accompanied by X-ray ones. The non-thermal flaring emission can extend to very hard (≲ 100 keV) X-ray energies.