Secondary Islands Research Articles

Electron Acceleration in a Dynamically Evolved Current Sheet Under Solar Coronal Conditions

Electron acceleration in a drastically evolved current sheet under solar coronal conditions is investigated via the combined 2.5-dimensional (2.5D) resistive magnetohydrodynamics (MHD) and test-particle approaches. Having a high magnetic Reynolds number (105), the long, thin current sheet is torn into a chain of magnetic islands, which grow in size and coalesce with each other. The acceleration of electrons is explored in three typical evolution phases: when several large magnetic islands are formed (phase 1), two of these islands are approaching each other (phase 2), and almost merging into a “monster” magnetic island (phase 3). The results show that for all three phases electrons with an initial Maxwell distribution evolve into a heavy-tailed distribution and more than 20 % of the electrons can be accelerated higher than 200 keV within 0.1 second and some of them can even be energized up to MeV ranges. The lower-energy electrons are located away from the magnetic separatrices and the higher-energy electrons are inside the magnetic islands. The most energetic electrons have a tendency to be around the outer regions of the magnetic islands or to appear in the small secondary magnetic islands. It is the trapping effect of the magnetic islands and the distributions of Ep that determine the acceleration and spatial distributions of the energetic electrons.

Generation of X-points and secondary islands in 2D magnetohydrodynamic turbulence

We study the time development of the population of X-type critical points in a two-dimensional magnetohydrodynamic model during the early stages of freely decaying turbulence. At sufficiently high magnetic Reynolds number Rem, we find that the number of neutral points increases as Rem3/2, while the rates of reconnection at the most active sites decrease. The distribution of rates remains approximately exponential. We focus in particular on delicate issues of accuracy, which arise in these numerical experiments, in that the proliferation of X-points is also a feature of under-resolved simulations. The “splitting” of neutral points at high Reynolds number appears to be a fundamental feature of the cascade that has important implications for understanding the relationship between reconnection and turbulence, an issue of considerable importance for the Magnetospheric Multiscale and Solar Probe missions as well as observation of reconnection in the solar wind.

Out-of-plane electron currents in magnetic islands formed during collisionless magnetic reconnection

[1] Secondary islands are considered to play a crucial role in collisionless magnetic reconnection. Based on 2-D particle-in-cell simulations, we investigate the characteristics of the out-of-plane electron currents in magnetic islands formed during collisionless magnetic reconnection with an initial guide field. In a primary island (formed simultaneously with the appearance of the X lines), due to the acceleration of the trapped electrons, the direction of the formed out-of-plane electron current is reverse to the original one. In the secondary island (formed in the vicinity of the X-line), the out-of-plane electron current is generated due to the accelerated electrons by the reconnection electric field in the vicinity of the X line. In such a way, the direction of the out-of-plane electron current in a secondary island is found to be opposite to that in a primary island. Such characteristics are found to be related to the evolution of the magnetic islands and then electron dynamics in the islands, which are proposed in this paper to be a possible criterion to identify a secondary island formed during collisionless magnetic reconnection, especially in the magnetotail.

IMPACT OF TEMPERATURE-DEPENDENT RESISTIVITY AND THERMAL CONDUCTION ON PLASMOID INSTABILITIES IN CURRENT SHEETS IN THE SOLAR CORONA

In this paper we investigate, by means of two-dimensional magnetohydrodynamic simulations, the impact of temperature-dependent resistivity and thermal conduction on the development of plasmoid instabilities in reconnecting current sheets in the solar corona. We find that the plasma temperature in the current sheet region increases with time and it becomes greater than that in the inflow region. As secondary magnetic islands appear, the highest temperature is not always found at the reconnection $X$-points, but also inside the secondary islands. One of the effects of anisotropic thermal conduction is to decrease the temperature of the reconnecting $X-$points and transfer the heat into the $O-$points, the plasmoids, where it gets trapped. In the cases with temperature-dependent magnetic diffusivity, $\eta \sim T^{-3/2}$, the decrease in plasma temperature at the $X-$points leads to: (i) increase in the magnetic diffusivity until the characteristic time for magnetic diffusion becomes comparable to that of thermal conduction; (ii) increase in the reconnection rate; and, (iii) more efficient conversion of magnetic energy into thermal energy and kinetic energy of bulk motions. These results provide further explanation of the rapid release of magnetic energy into heat and kinetic energy seen during flares and coronal mass ejections. In this work, we demonstrate that the consideration of anisotropic thermal conduction and Spitzer-type, temperature-dependent magnetic diffusivity, as in the real solar corona, are crucially important for explaining the occurrence of fast reconnection during solar eruptions.

Anomalous Resistivity Associated with Secondary Islands in the Reconnection Region

We calculate the anomalous resistivity (AR) due to electrostatic waves, including possibly the lower hybrid wave and electron beam mode, around the secondary islands in the reconnection region observed by the Cluster spacecraft. Our main findings are: AR is important on the reconnection separatrix layer but heavily suppressed at the central current sheet where Bx ∼ 0. Moreover, there is a highly asymmetric pattern of AR across the island along the outflow direction, with much larger AR on one side of island than on the other side. Our results may be helpful in understanding the role of AR in reconnection.

Secondary Magnetic Islands Generated by the Kelvin-Helmholtz Instability in a Reconnecting Current Sheet

Magnetic islands or flux ropes produced by magnetic reconnection have been observed on the magnetopause, in the magnetotail, and in coronal current sheets. Particle-in-cell simulations of magnetic reconnection with a guide field produce elongated electron current layers that spontaneously produce secondary islands. Here, we explore the seed mechanism that gives birth to these islands. The most commonly suggested theory for island formation is the tearing instability. We demonstrate that in our simulations these structures typically start out, not as magnetic islands, but as electron flow vortices within the electron current sheet. When some of these vortices first form, they do not coincide with closed magnetic field lines, as would be the case if they were islands. Only after they have grown larger than the electron skin depth do they couple to the magnetic field and seed the growth of finite-sized islands. The streaming of electrons along the magnetic separatrix produces the flow shear necessary to drive an electron Kelvin-Helmholtz instability and produce the initial vortices. The conditions under which this instability is the dominant mechanism for seeding magnetic islands are explored.

Electric field structure inside the secondary island in the reconnection diffusion region

Secondary islands have recently been intensively studied because of their essential role in dissipating energy during reconnection. Secondary islands generally form by tearing instability in a stretched current sheet, with or without guide field. In this article, we study the electric field structure inside a secondary island in the diffusion region using large-scale two-and-half dimensional particle-in-cell (PIC) simulation. Intense in-plane electric fields, which point toward the center of the island, form inside the secondary island. The magnitudes of the in-plane electric fields Ex and Ez inside the island are much larger than those outside the island in the surrounding diffusion region. The maximum magnitudes of the fields are about three times the B0VA, where B0 is the asymptotic magnetic field strength and VA is the Alfvén speed based on B0 and the initial current sheet density. Our results could explain the intense electric field (~100 mV/m) inside the secondary island observed in the Earth’s magnetosphere. The electric field Ex inside the secondary island is primarily balanced by the Hall term (j × B)/ne, while Ez is balanced by a combination of (j × B)/ne, −(vi × B), and the divergence of electron pressure tensor, with (j × B)/ne term being dominant. This large Hall electric field is due to the large out-of-plane current density jy inside the island, which consists mainly of accelerated electrons forming a strong bulk flow in the –y direction. The electric field Ey shows a bipolar structure across the island, with negative Ey corresponding to negative Bz and positive Ey corresponding to positive Bz. It is balanced by (j × B)/ne and the convective electric field. There are significant parallel electric fields, forming a quadrupolar structure inside the island, with maximum amplitude of about 0.3B0VA.

Strong Nonlinear Effects in the Dynamics of Tearing Modes Controlled by Electron Cyclotron Current Drive

The 2-D time-dependent response of a tearing mode magnetic island to a radio frequency (RF)-driven current may lead to strong nonlinear effects. An extended magnetohydrodynamics model shows first the prompt appearance of current sheets tending to shield the RF current effect and, subsequently, a nonlinear filamentation of the island structure that eventually proceeds in the coalescence of secondary islands.

The evolution of electron current sheet and formation of secondary islands in guide field reconnection

Abstract. Two-dimensional (2-D) particle-in-cell (PIC) simulations are performed to investigate the evolution of the electron current sheet (ECS) in guide field reconnection. The ECS is formed by electrons accelerated by the inductive electric field in the vicinity of the X line, which is then extended along the x direction due to the imbalance between the electric field force and Ampere force. The tearing instability is unstable when the ECS becomes sufficiently long and thin, and several seed islands are formed in the ECS. These tiny islands may coalesce and form a larger secondary island in the center of the diffusion region.

Numerical simulations of high Lundquist number relativistic magnetic reconnection

We present the results of two-dimensional and three-dimensional magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of the plasma in a Petschek-type configuration with high Lundquist numbers, S\sim 10^5-10^8. The numerical scheme adopted, allowing for unprecedented accuracy for this type of calculations, is based on high order finite volume and discontinuous Galerkin methods as recently proposed by \citet{Dumbser2009}. The possibility of producing high Lorentz factors is discussed, showing that Lorentz factors close to \sim 4 can be produced for a plasma parameter \sigma_m=20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S > S_c = 10^8, much larger than what is reported in the Newtonian regime. Finally, the effects of a mildly anisotropic Ohm law are considered in a configuration with a guide magnetic field. Such effects produce only slightly faster reconnection rates and Lorentz factors of about 1% larger with respect to the perfectly isotropic Ohm law.

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth dη≡SL-1/2LνA/γ, where SL is the Lundquist number, L, the length of the current sheet, νA, the Alfvén speed, and γ, the growth rate. Modifications to a recent resistive MHD analysis [N. F. Loureiro et al., Phys. Plasmas 14, 100703 (2007)] arise when collisions are sufficiently weak that dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (di/L)6/13SL7/13νA/L and the number of plasmoids as (di/L)1/13SL11/26, compared to SL1/4νA/L and S3/8, respectively, in resistive MHD.

Electron dynamics in collisionless magnetic reconnection

Magnetic reconnection provides a physical mechanism for fast energy conversion from magnetic energy to plasma kinetic energy. It is closely associated with many explosive phenomena in space plasma, usually collisionless in character. For this reason, researchers have become more interested in collisionless magnetic reconnection. In this paper, the various roles of electron dynamics in collisionless magnetic reconnection are reviewed. First, at the ion inertial length scale, ions and electrons are decoupled. The resulting Hall effect determines the reconnection electric field. Moreover, electron motions determine the current system inside the reconnection plane and the electron density cavity along the separatrices. The current system in this plane produces an out-of-plane magnetic field. Second, at the electron inertial length scale, the anisotropy of electron pressure determines the magnitude of the reconnection electric field in this region. The production of energetic electrons, which is an important characteristic during magnetic reconnection, is accelerated by the reconnection electric field. In addition, the different topologies, temporal evolution and spatial distribution of the magnetic field affect the accelerating process of electrons and determine the final energy of the accelerated electrons. Third, we discuss results from simulations and spacecraft observations on the secondary magnetic islands produced due to secondary instabilities around the X point, and the associated energetic electrons. Furthermore, progress in laboratory plasma studies is also discussed in regard to electron dynamics during magnetic reconnection. Finally, some unresolved problems are presented.

Emerging Parameter Space Map of Magnetic Reconnection in Collisional and Kinetic Regimes

In large-scale systems of interest to solar physics, there is growing evidence that magnetic reconnection involves the formation of extended current sheets which are unstable to plasmoids (secondary magnetic islands). Recent results suggest that plasmoids may play a critical role in the evolution of reconnection, and have raised fundamental questions regarding the applicability of resistive MHD to various regimes. In collisional plasmas, where the thickness of all resistive layers remain larger than the ion gyroradius, simulations results indicate that plasmoids permit reconnection to proceed much faster than the slow Sweet-Parker scaling. However, it appears these rates are still a factor of ∼10× slower than observed in kinetic regimes, where the diffusion region current sheet falls below the ion gyroradius and additional physics beyond MHD becomes crucially important. Over a broad range of interesting parameters, the formation of plasmoids may naturally induce a transition into these kinetic regimes. New insights into this scenario have emerged in recent years based on a combination of linear theory, fluid simulations and fully kinetic simulations which retain a Fokker-Planck collision operator to allow a rigorous treatment of Coulomb collisions as the reconnection electric field exceeds the runaway limit. Here, we present some new results from this approach for guide field reconnection. Based upon these results, a parameter space map is constructed that summarizes the present understanding of how reconnection proceeds in various regimes.

Unidirectional resonance modes supported by secondary islands in a microcavity comprised of two half-ellipses

We propose a simple and robust mechanism to achieve unidirectional emission in a microcavity comprised of two half-ellipses. The microcavity has two geometrical parameters, two eccentricities, which permit a control of the directional emissions. For the microcavity with two small eccentricities, the positions of secondary islands near primary islands in the survival probability distributions determine the directionality of emissions. We obtain the optimized values of the eccentricities for unidirectional emission.

Magnetic Reconnection for Coronal Conditions: Reconnection Rates, Secondary Islands and Onset

Magnetic reconnection may play an important role in heating the corona through a release of magnetic energy. An understanding of how reconnection proceeds can contribute to explaining the observed behavior. Here, recent theoretical work on magnetic reconnection for coronal conditions is reviewed. Topics include the rate that collisionless (Hall) reconnection proceeds, the conditions under which Hall reconnection begins, and the effect of secondary islands (plasmoids) both on the scaling and properties of collisional (Sweet-Parker) reconnection and on the onset of Hall reconnection. Applications to magnetic energy storage and release in the corona are discussed.

Numerical study about the nonlinear instability of the Sweet-Parker thin current sheet with shearing flows

以Harris Sheet作为初始条件, 使用数值模拟的方法, 研究了二级磁岛不稳定重联的一些性质. 在模拟中随着初始扰动的加入, Harris Sheet将演化到非线性阶段, 形成更薄的有剪切速度的电流片, 并伴有一级磁岛产生. 当Lundquist数大于或等于10⁵时, 非均匀剪切速度的Sweet-Parker电流片开始不稳定, 并有二级磁岛出现. 不稳定Sweet-Parker电流片对应的临界长宽比为65. Lundquist数越大, 演化形成的Sweet-Parker电流片越薄, 更多的二级磁岛将出现, 且沿电流片两边向外喷出, 随时间变大, 相互合并. 二级磁岛的出现使重联率增大, 并与Lundquist数之间不再满足S^-1/2的关系, 而似乎对它的依赖关系不明显.

Fast magnetic reconnection in low-density electron-positron plasmas

Two-dimensional particle-in-cell simulations have been performed to study magnetic reconnection in low-density electron-positron plasmas without a guide magnetic field. Impulsive reconnection rates become of the order of unity when the background density is much smaller than 10% of the density in the initial current layer. It is demonstrated that the outflow speed is less than the upstream Alfvén speed, and that the time derivative of the density must be taken into account in the definition of the reconnection rate. The reconnection electric fields in the low-density regime become much larger than the ones in the high-density regime, and it is possible to accelerate the particles to high energies more efficiently. The inertial term in the generalized Ohm’s law is the most dominant term that supports a large reconnection electric field. An effective collisionless resistivity is produced and tracks the extension of the diffusion region in the late stage of the reconnection dynamics, and significant broadening of the diffusion region is observed. Because of the broadening of the diffusion region, no secondary islands, which have been considered to play a role to limit the diffusion region, are generated during the extension of the diffusion region in the outflow direction.

“Island surfing” mechanism of electron acceleration during magnetic reconnection

One of the key unresolved problems in the study of space plasmas is to explain the production of energetic electrons as magnetic field lines “reconnect” and release energy in an explosive manner. Recent observations suggest possible roles played by small‐scale magnetic islands in the reconnection region, but their precise roles and the exact mechanism of electron energization have remained unclear. Here we show from two‐dimensional particle‐in‐cell simulations that secondary islands generated in the reconnection region indeed produce energetic electrons. We found that when electrons are trapped inside the islands, they are energized continuously by the reconnection electric field prevalent in the reconnection diffusion region. Applications to observations in the Earth's magnetotail are briefly discussed.

Flushing effect in reconnection: Effects of minority species of oxygen ions

Effects of O + ions on magnetic reconnection in the magnetotail are examined in a Harris equilibrium using a combination of linear Vlasov theory and large-scale driven and non-driven two-dimensional fully kinetic particle simulations. Linear theory of multiple species plasma indicates that the growth rate is rather insensitive to the composition of the background (lobe) or its temperature but more sensitive to the properties of the current carriers. Thus O + can affect significant changes to the linear growth rate of tearing mode only as a current carrier. However, it is demonstrated that in the nonlinear stage reconnection can effectively move trace material from the lobes into the current sheet proper. If the supply of lobe markers (like O +) is sufficiently permanent in the lobe, an initially proton-dominated current sheet can be virtually replaced by the marker ions through this “flushing effect”. The dominance of marker ions introduces finite Larmor radius signatures with marker gyroradii scales rather than that of the protons. In this way, the presence of heavier marker species in the lobe can lead to (i) reduced efficiency of energy conversion, (ii) reduction in the number and repetition frequency of secondary islands, (iii) broadening of the quadrupole magnetic structure, (iv) slowing down of the coalescence process and (v) modification of the composition of the ion current carriers. Using Cluster observations, we show the evidence for the “flushing effect” in the data. Detailed comparison with observations is planned for future work.

Comparison of Secondary Islands in Collisional Reconnection to Hall Reconnection

Large-scale resistive Hall-magnetohydrodynamic simulations of the transition from Sweet-Parker (collisional) to Hall (collisionless) magnetic reconnection are presented; the first to separate secondary islands from collisionless effects. Three main results are described. There exists a regime with secondary islands but without collisionless effects, and the reconnection rate is faster than Sweet-Parker, but significantly slower than Hall reconnection. This implies that secondary islands do not cause the fastest reconnection rates. The onset of Hall reconnection ejects secondary islands from the vicinity of the X line, implying that energy is released more rapidly during Hall reconnection. Coronal applications are discussed.