Secondary Islands Research Articles

Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D

Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with relativistic test particle methods. We propose a system with two parallel, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and separation on Alfv\'enic timescales, forming secondary islands and (up to tearing unstable) current sheets in which non-thermal energy distributions are expected to develop. Using the recently developed particle module of our open-source grid-adaptive MPI-AMRVAC software, we simulate MHD evolution combined with test particle treatments in MHD snapshots. We explore under which plasma-$\beta$ conditions the fastest reconnection occurs in two-and-a-half dimensional (2.5D) scenarios and in these settings test particles are evolved. We quantify energy distributions, acceleration mechanisms, relativistic corrections to the particle equations of motion and effects of resistivity in magnetically dominated proton-electron plasmas. Due to large resistive electric fields and indefinite acceleration of particles in the infinitely long current channels, hard energy spectra are found in 2.5D configurations. Solutions to these numerical artifacts are proposed for both 2.5D setups and future 3D work. We discuss the magnetohydrodynamics of an additional kink instability in 3D setups and the expected effects on energy distributions. The obtained results hold as a proof-of-principle for test particle approaches in MHD simulations, relevant to explore less idealised scenarios like solar flares and more exotic astrophysical phenomena, like black hole flares, magnetar magnetospheres and pulsar wind nebulae.

Retraction of "Thermodynamic Self-Limiting Growth of Heteroepitaxial Islands Induced by Nonlinear Elastic Effect".

We investigate nonlinear elastic effect (NLEF) on the growth of heteroepitaxial islands, a topic of both scientific and technological significance for their applications as quantum dots. We show that the NLEF induces a thermodynamic self-limiting growth mechanism that hinders the strain relaxation of coherent island beyond a maximum size, which is in contrast to indefinite strain relaxation with increasing island size in the linear elastic regime. This self-limiting growth effect shows a strong dependence on the island facet angle, which applies also to islands inside pits patterned in a substrate surface with an additional dependence on the pit inclination angle. Consequently, primary islands nucleate and grow first in the pits and then secondary islands nucleate at the rim around the pits after the primary islands reach the self-limited maximum size. Our theory sheds new lights on understanding the heteroepitaxial island growth and explains a number of past and recent experimental observations.

HEATING MECHANISMS IN THE LOW SOLAR ATMOSPHERE THROUGH MAGNETIC RECONNECTION IN CURRENT SHEETS

ABSTRACT We simulate several magnetic reconnection processes in the low solar chromosphere/photosphere; the radiation cooling, heat conduction and ambipolar diffusion are all included. Our numerical results indicate that both the high temperature (≳8 × 104 K) and low temperature (∼104 K) magnetic reconnection events can happen in the low solar atmosphere (100–600 km above the solar surface). The plasma β controlled by plasma density and magnetic fields is one important factor to decide how much the plasma can be heated up. The low temperature event is formed in a high β magnetic reconnection process, Joule heating is the main mechanism to heat plasma and the maximum temperature increase is only several thousand Kelvin. The high temperature explosions can be generated in a low β magnetic reconnection process, slow and fast-mode shocks attached at the edges of the well developed plasmoids are the main physical mechanisms to heat the plasma from several thousand Kelvin to over 8 × 104 K. Gravity in the low chromosphere can strongly hinder the plasmoid instability and the formation of slow-mode shocks in a vertical current sheet. Only small secondary islands are formed; these islands, however, are not as well developed as those in the horizontal current sheets. This work can be applied to understand the heating mechanism in the low solar atmosphere and could possibly be extended to explain the formation of common low temperature Ellerman bombs (∼104 K) and the high temperature Interface Region Imaging Spectrograph (IRIS) bombs (≳8 × 104) in the future.

The structures of magnetic islands formed during collisionless magnetic reconnections in a force-free current sheet

In this paper, with a two-dimensional particle-in-cell simulation model, we compare the structures of a primary magnetic island to those of a secondary magnetic island, and these islands are formed during collisionless magnetic reconnection in a force-free current sheet. The out-of-plane magnetic field By is enhanced in the center of both the primary and secondary islands; however, a quadrupole structure of By with a good symmetry may be formed at the ends of the primary island. The in-plane electric field also exists in both the primary and secondary islands. The electric field Ex has a positive value in the left and a negative value in the right of the islands, while the electric field Ez has a positive value in the upper part and a positive value in the lower part of the islands. However, the in-plane electric field exists in the outer part of the primary island, while it exists in the center of the secondary island.

THE COMPLEX STRUCTURE OF MAGNETIC FIELD DISCONTINUITIES IN THE TURBULENT SOLAR WIND

ABSTRACT Using high-resolution Cluster satellite observations and a multi-dimensional intermittency technique, we show that the magnetic discontinuities in the turbulent solar wind are connected through the spatial scales, going from proton down to electron scales. In some circumstances, their structure resembles the Harris equilibrium profile in plasmas. Observations are consistent with a scenario where many current layers develop in turbulence and where the outflow of these reconnection events are characterized by complex sub-proton networks of secondary islands, in a self-similar way. Although in the past these pictures have been speculated to be separately ubiquitous, through theories and simulations, the present work confirms that “reconnection in turbulence” and “turbulent reconnection” coexist in space plasmas.

Thermodynamic Self-Limiting Growth of Heteroepitaxial Islands Induced by Nonlinear Elastic Effect.

We investigate nonlinear elastic effect (NLEF) on the growth of heteroepitaxial islands, a topic of both scientific and technological significance for their applications as quantum dots. We show that the NLEF induces a thermodynamic self-limiting growth mechanism that hinders the strain relaxation of coherent island beyond a maximum size, which is in contrast to indefinite strain relaxation with increasing island size in the linear elastic regime. This self-limiting growth effect shows a strong dependence on the island facet angle, which applies also to islands inside pits patterned in a substrate surface with an additional dependence on the pit inclination angle. Consequently, primary islands nucleate and grow first in the pits and then secondary islands nucleate at the rim around the pits after the primary islands reach the self-limited maximum size. Our theory sheds new lights on understanding the heteroepitaxial island growth and explains a number of past and recent experimental observations.

In-situ observations of flux ropes formed in association with a pair of spiral nulls in magnetotail plasmas

Signatures of secondary islands are frequently observed in the magnetic reconnection regions of magnetotail plasmas. In this paper, magnetic structures with the secondary-island signatures observed by Cluster are reassembled by a fitting-reconstruction method. The results show three-dimensionally that a secondary island event can manifest the flux rope formed with an As-type null and a Bs-type null paired via their spines. We call this As-spine-Bs-like configuration the helically wrapped spine model. The reconstructed field lines wrap around the spine to form the flux rope, and an O-type topology is therefore seen on the plane perpendicular to the spine. Magnetized electrons are found to rotate on and cross the fan surface, suggesting that both the torsional-spine and the spine-fan reconnection take place in the configuration. Furthermore, detailed analysis implies that the spiral nulls and flux ropes were locally generated nearby the spacecraft in the reconnection outflow region, indicating that secondary reconnection may occur in the exhaust away from the primary reconnection site.

Magnetic reconnection: from the Sweet–Parker model to stochastic plasmoid chains

Magnetic reconnection is the topological reconfiguration of the magnetic field in a plasma, accompanied by the violent release of energy and particle acceleration. Reconnection is as ubiquitous as plasmas themselves, with solar flares perhaps the most popular example. Other fascinating processes where reconnection plays a key role include the magnetic dynamo, geomagnetic storms and the sawtooth crash in tokamaks.Over the last few years, the theoretical understanding of magnetic reconnection in large-scale fluid systems has undergone a major paradigm shift. The steady-state model of reconnection described by the famous Sweet–Parker (SP) theory, which dominated the field for ∼50 years, has been replaced with an essentially time-dependent, bursty picture of the reconnection layer, dominated by the continuous formation and ejection of multiple secondary islands (plasmoids). Whereas in the SP model reconnection was predicted to be slow, a major implication of this new paradigm is that reconnection in fluid systems is fast (i.e. independent of the Lundquist number), provided that the system is large enough. This conceptual shift hinges on the realization that SP-like current layers are violently unstable to the plasmoid (tearing) instability—implying, therefore, that such current sheets are super-critically unstable and thus can never form in the first place. This suggests that the formation of a current sheet and the subsequent reconnection process cannot be decoupled, as is commonly assumed.This paper provides an introductory-level overview of the recent developments in reconnection theory and simulations that led to this essentially new framework. We briefly discuss the role played by the plasmoid instability in selected applications, and describe some of the outstanding challenges that remain at the frontier of this subject. Amongst these are the analytical and numerical extension of the plasmoid instability to (i) 3D and (ii) non-magnetohydrodynamics (MHD) regimes. New results are reported in both cases.

NUMERICAL EXPERIMENTS ON THE DETAILED ENERGY CONVERSION AND SPECTRUM STUDIES IN A CORONA CURRENT SHEET

In this paper, we study the energy conversion and spectra in a corona current sheet by 2.5-dimensional MHD numerical simulations. Numerical results show that many Petschek-like fine structures with slow-mode shocks mediated by plasmoid instabilities develop during the magnetic reconnection process. The termination shocks can also be formed above the primary magnetic island and at the head of secondary islands. These shocks play important roles in generating thermal energy in a corona current sheet. For a numerical simulation with initial conditions close to the solar corona environment, the ratio of the generated thermal energy to the total dissipated magnetic energy is around $1/5$ before secondary islands appear. After secondary islands appear, the generated thermal energy starts to increase sharply and this ratio can reach a value about $3/5$. In an environment with a relatively lower plasma density and plasma $\beta$, the plasma can be heated to a much higher temperature. After secondary islands appear, the one dimensional energy spectra along the current sheet do not behave as a simple power law and the spectrum index increases with the wave number. The average spectrum index for the magnetic energy spectrum along the current sheet is about $1.8$. The two dimensional spectra intuitively show that part of the high energy is cascaded to large $kx$ and $ky$ space after secondary islands appear. The plasmoid distribution function calculated from numerical simulations behaves as a power law closer to $f(\psi) \sim \psi^{-1}$ in the intermediate $\psi$ regime. By using $\eta_{eff} = v_{inflow}\cdot L$, the effective magnetic diffusivity is estimated about $10^{11}\sim10^{12}$~m$^2$\,s$^{-1}$.

Evolution of electron current sheets in collisionless magnetic reconnection

An electron current sheet embedded in an ion scale current sheet is an inherent feature of collisionless magnetic reconnection. Such thin electron current sheets are unstable to tearing mode and produce secondary magnetic islands modulating the reconnection rate. In this work, 2-D evolution of tearing mode at multiple reconnection sites in an electron current sheet is studied using electron-magnetohydrodynamic (EMHD) model. It is shown that growth of the perturbations can make reconnection impulsive by suddenly enhancing the reconnection rate and also forms new structures in the presence of multiple reconnection sites, one of which is dominant and others are secondary. The rise of the reconnection rate to a peak value and the time to reach the peak value due to tearing instability are similar to those observed in particle-in-cell simulations for similar thicknesses of the electron current sheet. The peak reconnection rate scales as 0.05/ϵ1.15, where ϵ is half thickness of the current sheet. Interactions of electron outflows from the dominant and secondary sites form a double vortex sheet inside the magnetic island between the two sites. Electron Kelvin-Helmholtz instability in the double vortex sheet produces secondary vortices and consequently turbulence inside the magnetic island. Interaction of outflow from the dominant site and inflows to the adjacent secondary sites launches whistler waves which propagate from the secondary sites into the upstream region at Storey angle with the background magnetic field. Due to the wave propagation, the out-of-plane magnetic field has a nested structure of quadrupoles of opposite polarities. A numerical linear eigen value analysis of the EMHD tearing mode, valid for current sheet half-thicknesses ranging from ϵ<de=c/ωpe (strong electron inertia) to ϵ>de (weak electron inertia), is presented.

Magnetic islands formed due to the Kelvin‐Helmholtz instability in the outflow region of collisionless magnetic reconnection

AbstractWe carry out large‐scale particle‐in‐cell kinetic simulations to demonstrate that a super‐Alfvénic electron shear flow across the current layer can be spontaneously generated in the outflow region of magnetic reconnection, which is unstable to the electron Kelvin‐Helmholtz (K‐H) instability. The resulted K‐H vortex structures continuously drive the secondary magnetic reconnection and formation of secondary magnetic islands, which leads to strong electron energization in the outflow region.

SMALL-SCALE MAGNETIC ISLANDS IN THE SOLAR WIND AND THEIR ROLE IN PARTICLE ACCELERATION. I. DYNAMICS OF MAGNETIC ISLANDS NEAR THE HELIOSPHERIC CURRENT SHEET

Increases of ion fluxes in the keV-MeV range are sometimes observed near the heliospheric current sheet (HCS) during periods when other sources are absent. These resemble solar energetic particle (SEP) events, but the events are weaker and apparently local. Conventional explanations based on either shock acceleration of charged particles or particle acceleration due to magnetic reconnection at interplanetary current sheets are not persuasive. We suggest instead that recurrent magnetic reconnection occurs at the HCS and smaller current sheets in the solar wind (Zharkova & Khabarova 2012), of which a consequence is particle energization by the dynamically evolving secondary current sheets and magnetic islands (Zank et al. 2014; Drake et al. 2006a). The effectiveness of the trapping and acceleration process associated with magnetic islands depends in part on the topology of the HCS. We show that the HCS possesses ripples superimposed on the large-scale flat or wavy structure. We conjecture that the ripples can efficiently confine plasma and provide tokamak-like conditions that are favorable for the appearance of small-scale magnetic islands that merge and/or contract. Particles trapped in the vicinity of merging islands and experiencing multiple small-scale reconnection events are accelerated by the induced electric field, and experience first-order Fermi acceleration in contracting magnetic islands (Zank et al. 2014). We present multi-spacecraft observations of magnetic island merging and particle energization in the absence of other sources, providing support for theory and simulations that show particle energization by reconnection related processes of magnetic island merging and contraction.

Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection. I. Macroscopic effects of the electron flows

In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (bg). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (βi = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (bg ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (bg ≳ 5). Kinetic PIC simulations using guide fields bg ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (βi = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (bg ≲ 3).

FAST MAGNETIC RECONNECTION IN THE SOLAR CHROMOSPHERE MEDIATED BY THE PLASMOID INSTABILITY

Magnetic reconnection in the partially ionized solar chromosphere is studied in 2.5-dimensional magnetohydrodynamic simulations including radiative cooling and ambipolar diffusion. A Harris current sheet with and without a guide field is considered. Characteristic values of the parameters in the middle chromosphere imply a high magnetic Reynolds number of $\sim10^{6}\mbox{--}10^7$ in the present simulations. Fast magnetic reconnection then develops as a consequence of the plasmoid instability without the need to invoke anomalous resistivity enhancements. Multiple levels of the instability are followed as it cascades to smaller scales, which approach the ion inertial length. The reconnection rate, normalized to the asymptotic values of magnetic field and Alfv\'en velocity in the inflow region, reaches values in the range $\sim0.01\mbox{--}0.03$ throughout the cascading plasmoid formation and for zero as well as for strong guide field. The out-flow velocity reaches $\approx40$~km\,s$^{-1}$. Slow-mode shocks extend from the $X$-points, heating the plasmoids up to $\sim 8\times10^4$~K. In the case of zero guide field, the inclusion of ambipolar diffusion and radiative cooling both cause a rapid thinning of the current sheet (down to $\sim30$~m) and early formation of secondary islands. Both of these processes have very little effect on the plasmoid instability for a strong guide field. The reconnection rates, temperature enhancements, and upward out-flow velocities from the vertical current sheet correspond well to their characteristic values in chromospheric jets.

Drift resonance effect on stochastic runaway electron orbit in the presence of low-order magnetic perturbations

During major disruptions, an induced loop voltage accelerates runaway electrons (REs) towards high energy, being in the order of 1–100 MeV in present tokamaks and ITER. The stochastization mechanisms of such high-energy RE drift orbits are investigated by three-dimensional (3D) orbit following in tokamak plasmas. Drift resonance is shown to play an important role in determining the onset of stochastic drift orbits for different electron energies, particularly in cases with low-order perturbations that have radially global eigenfunctions of the scale of the plasma minor radius. The drift resonance due to the coupling between the cross-field drift motion with radially global modes yields a secondary island structure in the RE drift orbit, where the width of the secondary drift islands shows a square-root dependence on the relativistic gamma factor γ. Only for highly relativistic REs (γ ≫ 1), the widths of secondary drift islands are comparable with those of magnetic islands due to the primary resonance, thus the stochastic threshold becoming sensitive to the RE energy. Because of poloidal asymmetry due to toroidicity, the threshold becomes sensitive not only to the relative amplitude but also to the phase difference between the modes. In this paper, some examples of 3D orbit-following calculations are presented for analytic models of magnetic perturbations with multiple toroidal mode numbers, for both possibilities that the drift resonance enhances and suppresses the stochastization being illustrated.

Instability of the current sheet in the Earth's magnetotail with normal magnetic field

Instability of a current sheet in the Earth's magnetotail has been investigated by two-dimensional fully kinetic simulations. Two types of magnetic configuration have been studied; those with uniform normal magnetic field along the current sheet and those in which the normal magnetic field has a spatial hump. The latter configuration has been proposed by Sitnov and Schindler [Geophys. Res. Lett. 37, L08102 (2010)] as one in which ion tearing modes might grow. The first type of configuration exhibits electron tearing modes when the normal magnetic field is small. The second type of configuration exhibits an instability which does not tear or change the topology of magnetic field lines. The hump in the initial configuration can propagate Earthward in the nonlinear regime, leading to the formation of a dipolarization front. Secondary magnetic islands can form in regions where the normal magnetic field is very weak. Under no conditions do we find the ion tearing instability.

Kinetic simulations of electric field structure within magnetic island during magnetic reconnection and their applications to the satellite observations

AbstractMagnetic islands are considered to play a crucial role in collisionless magnetic reconnection. We use particle‐in‐cell simulations to investigate electric field Ez structure in the magnetic islands (including primary and secondary islands) with and without a guide field during magnetic reconnection. It is found that the electric field has multilayers in the primary island and a large bipolar structure in the secondary island in the absence of guide field. The electric field is provided by the Hall term (J × B)z (mainly), the divergence of electron pressure tensor, and the convective term (Vi × B)z in the outer and the inner region of primary island, while the electric field is much smaller (~0) in the middle and the core region of primary island due to the cancelation of the three terms. The single bipolar electric field is primarily provided by the Hall term in the secondary island. In the presence of a guide field, the electric field has multiple layers in the primary island (similar to zero guide field case) and the secondary island. However, there still exists one single large sharp bipolar structure of electric field in the central region of the secondary island. The differences of electric field in the primary and secondary islands are essentially due to the variations of the current Jy. These features can be used as the observational criteria to identify different types of magnetic islands in the magnetosphere using the data of future mission, such as the Magnetospheric Multiscale mission.

Formation of plasmoids during sawtooth crashes

The nonlinear growth of the internal kink mode is studied numerically using reduced magnetohydrodynamic equations in cylinder geometry. For low Lundquist numbers, S < 107, the already well-known results have been reproduced: a m/n = 1/1 magnetic island (m: poloidal, n: toroidal mode number) grows while the original core shrinks until full reconnection is achieved. For higher S values, however, the dynamics is found to be qualitatively different from the well-known Kadomtsev's model (Kadomtsev 1975 Sov. J. Plasma Phys. 1 389). The growth of the 1/1 island causes the development of a very thin current sheet which becomes tearing unstable. The current sheet is thus broken up and secondary islands (plasmoids) form. These plasmoids strongly speed up the reconnection and eventually coalesce into one secondary island. The formation of a large secondary island stops the fast reconnection process, leading even to a partial reversal of this process. The final state of sawtooth reconnection is thus no longer an axis-symmetric equilibrium as in the case of complete reconnection for low S values, but a helical equilibrium with two coexisting magnetic islands.

Do dispersive waves play a role in collisionless magnetic reconnection?

Using fully kinetic simulations, we demonstrate that the properly normalized reconnection rate is fast ∼0.1 for guide fields up to 80× larger than the reconnecting field and is insensitive to both the system size and the ion to electron mass ratio. These results challenge conventional explanations of reconnection based on fast dispersive waves, which are completely absent for sufficiently strong guide fields. In this regime, the thickness of the diffusion layer is set predominantly by the electron inertial length with an inner sublayer that is controlled by finite gyro-radius effects. As the Alfvén velocity becomes relativistic for very strong guide fields, the displacement current becomes important and strong deviations from charge neutrality occur, resulting in the build-up of intense electric fields which absorb a portion of the magnetic energy release. Over longer time scales, secondary magnetic islands are generated near the active x-line while an electron inertial scale Kelvin-Helmholtz instability is driven within the outflow. These secondary instabilities give rise to time variations in the reconnection rate but do not alter the average value.

Out-of-plane shear flow effects on fast magnetic reconnection in a two-dimensional hybrid simulation model

The effects of out-of-plane shear flows on fast magnetic reconnection are numerically investigated by a two-dimensional (2D) hybrid model in an initial Harris sheet equilibrium with flows. The equilibrium and driven shear flows out of the 2D reconnection plane with symmetric and antisymmetric profiles respectively are used in the simulation. It is found that the out-of-plane flows with shears in-plane can change the quadrupolar structure of the out-of-plane magnetic field and, therefore, modify the growth rate of magnetic reconnection. Furthermore, the driven flow varying along the anti-parallel magnetic field can either enhance or reduce the reconnection rate as the direction of flow changes. Secondary islands are also generated in the process with converting the initial X-point into an O-point.