Coalescence Of Magnetic Islands Research Articles

New Aspects of Energy Conversion in Magnetic Island Dynamics: Particle-in-cell Simulation of Multiple Island Coalescence and MMS Observations

Coalescence of multiple magnetic islands is recognized as an effective process to energize particles during magnetic reconnection, while its energy conversion process still remains unclear. Here, a two-dimensional fully kinetic simulation of multiple island coalescence with a small reconnection guide field is studied. In the analysis of energy conversion within a magnetic island, the dot product of is a useful quantity to compare with j · E = w 2, since the average work done by the Lorentz force on the circulating particles is negligible in the island and . A bipolar pattern of w 1 is found at a secondary island when the electrons are in circular motion inside the island. Significant energy dynamo (w 3 < 0) resulting from j ∥ E ∥ is found at the secondary island, which has not been reported before, where the parallel electric field E ∥ is highly correlated with w 3. Moreover, significant energy dissipation (w 3 > 0) due to is seen in the merging region between two coalescing islands. Both types of energy conversions are accompanied by enhancements in j ∥ and the parallel electron temperature T e∥. Three ion-scale magnetic islands (FR1, FR2, and FR3) observed by the Magnetospheric Multiscale spacecraft are compared favorably with the simulated signatures of energy dynamo and dissipation of an evolving secondary island. In particular, FR1 displayed a similar energy dynamo signature as that simulated in an early stage of the secondary island. FR2 and FR3 showed a dominant energy conversion similar to that obtained in a later stage of the secondary island.

Spatial and time scaling of coalescing multiple magnetic islands

Magnetic reconnection is a key fundamental process in collisionless plasmas, which converts magnetic energy to plasma kinetic energy. Past observation and simulation studies suggested that this process causes an efficient energy conversion through the formation and coalescence of multiple magnetic islands. In this study, based on a large-scale two-dimensional fully kinetic simulations of coalescing multiple islands with a moderate guide magnetic field, we first examined the spatial dimensions of the internal structures of the coalescing islands. The results show that the dimensions of the structures in the directions normal to and along the initial current sheet depend on the initial thickness of the current sheet and the number of coalescing islands. We then found that the horizontal dimension of the structures controls the evolution time scale of the island coalescence process. We further found that when the vertical dimension of the structures, which corresponds to the length of the reconnection X-line in the reconnection outflow direction at the merging point between the two coalescing islands, is sufficiently longer than the ion inertial length, reconnection in the merging current sheet can well mature and both ions and electrons can be effectively heated around the merging X-line. The obtained scaling predicts that such a strong heating by well-matured reconnection in the island coalescence process would be seen in various plasma environments, such as the Earth's magnetotail and solar flares.

Numerical study of magnetic island coalescence using magnetohydrodynamics with adaptively embedded particle-in-cell model

Collisionless magnetic reconnection typically requires kinetic treatment that is, in general, computationally expensive compared to fluid-based models. In this study, we use the magnetohydrodynamics with an adaptively embedded particle-in-cell (MHD-AEPIC) model to study the interaction of two magnetic flux ropes. This innovative model embeds one or more adaptive PIC regions into a global MHD simulation domain such that the kinetic treatment is only applied in regions where the kinetic physics is prominent. We compare the simulation results among three cases: (1) MHD with adaptively embedded PIC regions, (2) MHD with statically (or fixed) embedded PIC regions, and (3) a full PIC simulation. The comparison yields good agreement when analyzing their reconnection rates and magnetic island separations as well as the ion pressure tensor elements and ion agyrotropy. In order to reach good agreement among the three cases, large adaptive PIC regions are needed within the MHD domain, which indicates that the magnetic island coalescence problem is highly kinetic in nature, where the coupling between the macro-scale MHD and micro-scale kinetic physics is important.

Scaling of reconnection parameters in magnetic island coalescence: Role of in-plane shear flow

A 2D incompressible viscoresistive-MHD model [Mahapatra et al., Phys. Plasmas 28, 072103 (2021)] is used to study the scaling of reconnection parameters in the magnetic island coalescence problem under two interesting scenarios. First, the effect of changing island half-width at a fixed system size is investigated. As the island half-width increases, the total magnetic flux content of the islands increases, resulting in an increase in upstream magnetic field, upstream velocity field, and unnormalized reconnection rate. However, the downstream magnetic field, current sheet length and normalized reconnection rate (normalized to the upstream magnetic field and upstream Alfvénic velocity) remain independent of it. Interestingly, the reconnection rate is found to be different from the upstream to downstream velocity ratio as well as from the aspect ratio of the current sheet, as opposed to the findings of the Sweet–Parker model. Second, the in-plane shear flow effects are studied, keeping the island width and system size fixed. Here, thickness and length of the current sheet, the upstream magnetic and velocity field components, reconnection rate and time, current sheet inclination angle with shear flow length scale, and amplitude are calculated. Interestingly, the inclination angle of the current sheet and the diffusion region are found to be different, and the differences are more in stronger shear flows. These results are significantly different from the Harris sheet setup with shear flow.

Electron‐Only Magnetic Reconnection: Lessons Learned From Magnetic Island Coalescence

AbstractElectron‐only magnetic reconnection, in which ions do not couple, has recently been observed in turbulent magnetosheath and magnetotail, and in association with magnetic flux rope coalescence. This study reproduces the electron‐only reconnection during magnetic island coalescence via 2.5‐D particle‐in‐cell simulations. We find that the degree of ion coupling is not sensitive to the spatial scale of the merging current sheet but is determined by the persistent time of the coalescence, which suggests that the electron‐only reconnection is the early stage of the coalescence. During the electron‐only reconnection, ions are affected by the reconnection electric field though the ion bulk outflow is absent. It is revealed that the pre‐existing inflows and Hall electric field Ez from the adjacent main reconnection impede the formation of ion outflow during coalescence. This study provides in‐depth knowledge of electron‐only reconnection through the perspective of ion kinetics.

Statistical description of coalescing magnetic islands via magnetic reconnection

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as$\tilde {t}^{-1}$, the number of islands decreases as$\tilde {t}^{-1}$and the averaged area of islands grows as$\tilde {t}$, where$\tilde {t}$is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.

Effect of in-plane shear flow on the magnetic island coalescence instability

Using a 2D Viscoresistive Reduced MagnetoHydroDynamic model, the magnetic island coalescence problem is studied in the presence of in-plane, parallel shear flows. Extending the analytical work of Waelbroeck et al. [Phys. Plasmas 14, 022302 (2007)] and Throumoulopoulos et al., [J. Phys. A 42, 335501 (2009)] in the sub-Alfvénic flow shear regime for Fadeev equilibrium, the super-Alfvénic regime is studied for the first time numerically. A wide range of values of shear flow amplitudes and shear scale lengths have been considered to understand the effect of sub-Alfvénic and super-Alfvénic flows on the coalescence instability and its nonlinear fate. We find that for flow shear length scales greater than the magnetic island size, the maximum reconnection rate decreases monotonically from sub-Alfvénic to super-Alfvénic flow speeds. For scale lengths smaller than the island size, the reconnection rate decreases up to a critical value v0c, beyond which the shear flow is found to destabilize the islands. The value of v0c decreases with a decrease in the value of shear flow length scale. Interestingly, for our range of parameters, we find suppression of the Kelvin–Helmholtz instability in super-Alfvénic flows even when the shear scale length is smaller than the island width. Observation of velocity streamlines shows that the plasma circulation inside the islands has a stabilizing influence in strong shear flow cases. Plasma circulation is also found to be responsible for the decrease in upstream velocity, causing less pileup of magnetic flux on both sides of the reconnection sheet.

Fast Radio Bursts from Reconnection in a Magnetar Magnetosphere

Abstract The nearly 100% linear polarization has been reported for a few fast radio bursts (FRBs). This finding places severe limits on the emission mechanism. I argue that the completely polarized radiation could be generated in the course of relativistic magnetic reconnection in the outer magnetosphere of the magnetar. At the onset of the magnetar flare, a large-scale magnetic perturbation forms a magnetic pulse, which propagates from the flare cite outward. The pulse strongly compresses magnetospheric plasma and pushes it away. The high-frequency MHD waves are generated when the magnetic pulse reaches the current sheet separating, just beyond the light cylinder, the oppositely directed magnetic fields. Coalescence of magnetic islands in the reconnecting current sheet produces magnetosonic waves, which propagate away on the top of the magnetic pulse and escape in the far zone of the wind as radio waves polarized along the rotational axis of the magnetar. I estimate parameters of the outgoing radiation and show that they are compatible with the observed properties of FRBs.

Magnetic island merger as a mechanism for inverse magnetic energy transfer

Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: magnetic energy decays as $\tilde t^{-1}$, where $\tilde t$ is time normalized to the (appropriately defined) reconnection timescale; and the correlation length of the field grows as $\tilde t^{1/2}$. The magnetic energy spectrum is self-similar, and evolves as $\propto \tilde t ^{-3/2}k^{-2}$, where the $k$-dependence is imparted by the formation of thin current sheets.

Radio emission of the Crab and Crab-like pulsars

The pulsar radio emission is commonly associated with the plasma outflow in the open field line tube; then a pencil beam is emitted along the pulsar magnetic axis. Observations suggest that there is an additional radio emission mechanism specific for pulsars with high magnetic field at the light cylinder. These pulsars are known to be strong sources of non-thermal high energy radiation, which could be attributed to reconnection in the current sheet separating, just beyond the light cylinder, the oppositely directed magnetic fields. Pulsars with the highest magnetic field at the light cylinder (>100 kG) exhibit also radio pulses in phase with the high energy pulses. Moreover, giant radio pulses are observed in these pulsars. I argue that the reconnection process that produces high energy emission could also be responsible for the radio emission. Namely, coalescence of magnetic islands in the sheet produces magnetic perturbations that propagate away in the form of electro-magnetic nano-shots. I estimate the parameters of this emission and show that they are compatible with observations.

Study of magnetic reconnection in large-scale magnetic island coalescence via spatially coupled MHD and PIC simulations

We study the process of magnetic reconnection in a coalescing magnetic island setup by means of numerical simulation. This process mimics flux tube merging which can take place in the solar corona, laboratory, and astrophysical objects. Simulations are performed with magnetohydrodynamics (MHD), Hall-MHD, and a newly developed Coupled MHD and Particle-In-Cell (PIC) model (CMAP). This model treats the global simulation domain with MHD, while the region around the reconnection zone is treated with PIC. This CMAP code allows us to simulate larger-scale domains with lesser computing power compared to fully PIC simulations. CMAP reproduces the dynamics of fully kinetic simulations which Hall-MHD does not capture, as seen in the Hall magnetic field and the reconnecting current sheet structure. For large islands in kinetic simulations, the current sheet does not form smoothly and shows chaotic behavior, and the magnetic islands also bounce and slosh. The current sheet thickness, length, and aspect ratios are calculated. They show that in the CMAP model, the thickness remains close to the ion skin depth, while the length changes weakly with the system size, giving a steady aspect ratio for the two largest system size simulations. The pressure tensor also shows large deviations from isotropy and gyrotropy near the current sheet. The CMAP simulations for smaller system sizes are compared to fully kinetic simulations, and we find that a minimum fraction of area has to be provided PIC feedback in the CMAP simulations in order to produce reconnection rates and dynamics similar to fully kinetic simulations. The reconnection rate reduces with the increasing island size. For the CMAP model, this reduction is steeper compared to MHD and Hall-MHD initially, but for larger system sizes, the reconnection rates in CMAP simulations show a steady behavior.

Temperature gradient driven heat flux closure in fluid simulations of collisionless reconnection

Recent efforts to include kinetic effects in fluid simulations of plasmas have been very promising. Concerning collisionless magnetic reconnection, it has been found before that damping of the pressure tensor to isotropy leads to good agreement with kinetic runs in certain scenarios. An accurate representation of kinetic effects in reconnection was achieved in a study by Wang et al. (Phys. Plasmas, vol. 22, 2015, 012108) with a closure derived from earlier work by Hammett and Perkins (Phys. Rev. Lett., vol. 64, 1990, 3019). Here, their approach is analysed on the basis of heat flux data from a Vlasov simulation. As a result, we propose a new local closure in which heat flux is driven by temperature gradients. This way, a more realistic approximation of Landau damping in the collisionless regime is achieved. Previous issues are addressed and the agreement with kinetic simulations in different reconnection set-ups is improved significantly. To the authors’ knowledge, the new fluid model is the first to perform well in simulations of the coalescence of large magnetic islands.

Two-way coupled MHD-PIC simulations of magnetic reconnection in magnetic island coalescence

We present simulations of magnetic reconnection with a newly developed coupled MHD-PIC code. In this work a global magnetohydrodynamic (MHD) simulation receives kinetic feedback within an embedded region that is modeled by a kinetic particle-in-cell (PIC) code. The PIC code receives initial and boundary conditions from the MHD simulation, while the MHD solution is updated with the PIC state. We briefly describe this coupling mechanism. This method is suitable for simulating magnetic reconnection problems, as we show with the example of reconnection in the coalescence of magnetic islands. We compare the MHD, Hall-MHD, fully PIC and coupled MHD-PIC simulations of the magnetic island coalescence. We find that the kinetic simulations are very different from the MHD and Hall-MHD results, while the coupled MHD-PIC simulations can remedy this discrepancy while saving computing time. The diffusion region is well resolved in the kinetic simulations, which is also captured by the coupled MHD-PIC model. The coupled simulation also reproduces the kinetic Hall magnetic fields correctly. We calculate the reconnection rates and find differences between the MHD and kinetic results. We find that the coupled MHD-PIC code can reasonably reproduce the kinetic reconnection rate when a larger PIC feedback region is used, while still saving significant computing time.

On the role of system size in Hall MHD magnetic reconnection

We study the effects of the Hall electric field on magnetic island coalescence in the large island limit and find evidence for both an elongated electron current sheet layer with a Sweet-Parker-like reconnection rate and a collapsed, Petschek-like electron sheet with a peak reconnection rate approaching the 0.1vAB0 Hall MHD rate. The state observed in our simulations appears to depend on the grid scale. Furthermore, even at the largest system sizes, we find that flux-pileup effects cause the islands to “bounce” despite the presence of a collapsed current sheet allowing fast instantaneous reconnection. The average reconnection rate in the large island limit is slow though the peak reconnection rate is fast.

Particle Acceleration during Magnetic Reconnection in a Low-beta Plasma

Abstract Magnetic reconnection is a primary mechanism for particle energization in space and astrophysical plasmas. By carrying out two-dimensional (2D) fully kinetic simulations, we study particle acceleration during magnetic reconnection in plasmas with different plasma β (the ratio between the thermal pressure and the magnetic pressure). For the high-β cases, we do not observe significant particle acceleration. In the low-β regime ( β &lt; 0.1 ), we find that reconnection is efficient at energizing both electrons and ions. While the distribution of accelerated particles integrated over the whole simulation box appears highly non-thermal, it is actually the superposition of a series of distributions in different sectors of a 2D magnetic island. Each of those distributions has only a small non-thermal component compared with its thermal core. By tracking a large number of particles, we show that particles get energized in X-line regions, contracting magnetic islands, and magnetic island coalescence regions. We obtain the particle energization rate j · E by averaging over particle drift motions and find that it agrees well with the particle kinetic energy change. We quantify the contribution of curvature drift, gradient drift, polarization drift, magnetization, non-gyrotropic effect, and parallel electric field in different acceleration regions. We find that the major energization is due to particle curvature drift along the motional electric field. The other particle motions contribute less but may become important in different acceleration regions. The highly efficient particle energization in low-β plasmas may help us understand the strong particle energization in solar flares and accretion disk coronae.

Impact of compressibility and a guide field on Fermi acceleration during magnetic island coalescence

Previous work has shown that Fermi acceleration can be an effective heating mechanism during magnetic island coalescence, where electrons may undergo repeated reflections as the magnetic field lines contract. This energization has the potential to account for the power-law distributions of particle energy inferred from observations of solar flares. Here, we develop a generalized framework for the analysis of Fermi acceleration that can incorporate the effects of compressibility and non-uniformity along field lines, which have commonly been neglected in previous treatments of the problem. Applying this framework to the simplified case of the uniform flux tube allows us to find both the power-law scaling of the distribution function and the rate at which the power-law behavior develops. We find that a guide magnetic field of order unity effectively suppresses the development of power-law distributions.

On the electron agyrotropy during rapid asymmetric magnetic island coalescence in presence of a guide field

AbstractWe present an analysis of the properties of the electron velocity distribution during island coalescence in asymmetric reconnection with and without guide field. In a previous study, three main domains were identified, in the case without guide field, as X, D, and M regions featuring different reconnection evolutions. These regions are also identified here in the case with guide field. We study the departure from isotropic and gyrotropic behavior by means of different robust detection algorithms proposed in the literature. While in the case without guide field these metrics show an overall agreement, when the guide field is present, a discrepancy in the agyrotropy within some relevant regions is observed, such as at the separatrices and inside magnetic islands. Moreover, in light of the new observations from the Multiscale MagnetoSpheric mission, an analysis of the electron velocity phase‐space in these domains is presented.

Plasma physics of magnetic island coalescence during magnetic reconnection

AbstractA large‐scale two‐dimensional electromagnetic particle‐in‐cell simulation was employed to study the magnetic island coalescence/merging process during magnetic reconnection with guide field. The merged island after coalescence is characterized by strong core field and plasma density dip at the island center. We found that the core field enhancement is caused by the out‐of‐plane magnetic field pileup, as well as the field line twisting due to Hall effect. There is an in‐plane electric current loop, which is mainly carried by electrons, circumventing the enhanced core field region. Total force points away or tangentially to the surface of density dip within the merged island, which prevents electrons from higher‐density region entering the lower density region between two merging islands. This is contrary to the force in the secondary island, inside which the total force points toward the island center and constrains plasma there. The coalescence process involves a reconnection at the merging sheet between two islands. Electron frozen‐in condition is violated locally along the merging sheet. It is contributed by both the divergence of electron pressure tensor and electron inertial. Energy dissipation is concentrated on the merging line during coalescence, while a train of dynamo (j′ · E′ &lt; 0) and dissipation (j′ · E′ &gt; 0) regions are distributed along the merging sheet after coalescence. Electrons and ions within the density dip at the island center are accelerated antiparallel to the ambient magnetic field, i.e., along the out‐of‐plane direction. The resultant distribution can excite the Buneman instability and two‐streaming instability, which probably account for the electrostatic solitary waves observed by satellite.

Resistive magnetohydrodynamic reconnection: Resolving long-term, chaotic dynamics

In this paper, we address the long-term evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (grid-adaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shock-capturing, conservative, grid-adaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco-)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shock-capturing, high order finite differences, and particle in cell-like methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.

A review of recent studies on coronal dynamics: Streamers, coronal mass ejections, and their interactions

In this article I present a review of recent studies on coronal dynamics, including research progresses on the physics of coronal streamers that are the largest structure in the corona, physics of coronal mass ejections (CMEs) that may cause a global disturbance to the corona, as well as physics of CME-streamer interactions. The following topics will be discussed in depth: (1) acceleration of the slow wind flowing around the streamer considering the effect of magnetic flux tube curvature; (2) physical mechanism accounting for persistent releases of streamer blobs and diagnostic results on the temporal variability of the slow wind speed with such events; (3) force balance analysis and energy release mechanism of CMEs with a flux rope magnetohydrodynamic model; (4) statistical studies on magnetic islands along the coronal-ray structure behind a CME and the first observation of magnetic island coalescence with associated electron acceleration; and (5) white light and radio manifestations of CME-streamer interactions. These studies shed new light on the physics of coronal streamers, the acceleration of the slow wind, the physics of solar eruptions, the physics of magnetic reconnection and associated electron acceleration, the large-scale coronal wave phenomenon, as well as the physics accounting for CME shock-induced type II radio bursts.