Secondary Islands Research Articles

Annihilation of Magnetic Islands at the Top of Solar Flare Loops

Abstract The dynamics of magnetic reconnection in the solar current sheet (CS) is studied by high-resolution 2.5-dimensional MHD simulation. With the commencing of magnetic reconnection, a number of magnetic islands are formed intermittently and move quickly upward and downward along the CS. Upon collision with the semi-closed flux of the flare loops, the downflow islands cause a second reconnection with a rate comparable with that in the main CS. Though the time-integrated magnetic energy release is still dominated by the reconnection in the main CS, the second reconnection can release substantial magnetic energy, annihilating the main islands and generating secondary islands with various scales at the flare loop top. The distribution function of the flux of the secondary islands is found to follow a power law varying from f ψ ∼ ψ − 1 (small scale) to ψ −2 (large scale), which seems to be independent to background plasma β and thermal conduction (TC). However, the spatial scale and the strength of the termination shocks driven by the main reconnection outflows or islands decrease if β increases or if TC is included. We suggest that the annihilation of magnetic islands at the flare loop top, which is not included in the standard flare model, plays a nonnegligible role in releasing magnetic energy to heat flare plasma and accelerate particles.

Investigation of annular/central collapse events triggered by the double tearing modes in EAST

Annular/central collapses of electron temperature have been investigated in the EAST tokamak. The precursor modes are excited before the annular/central collapse events, and the coexistence of multi magnetic island chains can be observed synchronously for the core concentration of high-Z impurities. The primary magnetic islands for the two cases are located in the same region of 0.25 ⩽ ρ(r/a) ⩽ 0.35, while the secondary magnetic islands for central and annular cases are located inside (ρ ≈ 0.1) and outside (ρ ≈ 0.4) respectively. The similar simulation has been performed by the toroidal resistive MHD code CLT (Zhang et al 2020 Phys. Plasmas 27 122509), and the annular/central collapse events can be reproduced by the magnetic reconnection of m/n = 2/1 double tearing modes, m and n are the poloidal and toroidal mode numbers respectively. The combination of lower hybrid current driven and off-axis electron cyclotron resonance heating is an essential condition for the establishment of reversed magnetic shear. The different penetration depth of high-Z impurity density plays an important role for excitation of the annular/central collapse events, e.g. the steeper gradient of T e-profile can be formed accordingly in the annular region of 0.1 ⩽ ρ ⩽ 0.4, together with excitation of the precursor modes.

Dissipation measures in weakly collisional plasmas

ABSTRACT The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include interparticle collisions: the fully kinetic particle-in-cell vpic, the fully kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov–Maxwell (HVM) code. We differentiate between (i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and (ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is an overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of interparticle collisions on these parameters is finally discussed.

Surface morphology evolution and underlying defects in homoepitaxial growth of GaAs (110)

The evolution of the surface morphology and underlying pyramidal defects in homoepitaxial GaAs (110) layers was investigated with respect to the layer thickness up to 1 µm. Ga and As atoms coexisting in a one-to-one atomic ratio on the (110)-oriented GaAs surface exhibit different incorporation rates and adatom migration rates, giving rise to local As atomic disordering in the epitaxial layer. Accordingly, this disordering triggers distinctive shapes of three-dimensional surface islands composed of specific facets and underlying microtwins. Single triangular-shaped islands initially appear at an early stage of epitaxial growth. With increasing layer thickness, all of the single triangular islands suddenly become paired triangular islands by forming secondary single triangular islands nearby, like decalcomania. A further increase of the layer thickness induces a complete transformation into four-legged starfish shapes containing directional side edges. At this stage, the underlying pyramidal defects of the surface islands are filled with {111} microtwins. Surprisingly, the evolutions of island shapes and underlying twin formation are closely associated with the strain relaxation in the thick GaAs (110) layers, which is unexpected in any homoepitaxial system. We found that a higher growth temperature retards the shape evolution of surface islands, leading to suppression of compressive strain.

Nonlinear evolution and secondary island formation of the double tearing mode in a hybrid simulation

Double tearing modes (DTMs), induced by double current sheet configurations or two neighboring rational surfaces with the same safety factor in tokamaks, are widely observed in solar, space, and fusion plasmas. In this paper, the evolution of DTMs without a guide field is investigated numerically using a hybrid model (electron fluid + ion PIC). The overall evolution processes of DTMs are qualitatively consistent with previous works using other models. The particle dynamics during the evolution of DTMs is analyzed in detail. Behaviors of ions and electrons present different characteristics around the reconnection region which gives rise to Hall effects producing the out-of-plane quadrupole magnetic field. In the explosive reconnection process with interactions between two DTMs islands, the asymmetric drive and the thin current layer feature lead to the emergence of secondary magnetic islands which develop with the late evolution of the DTMs.

Evolution of Three-dimensional Coherent Structures in Hall Magnetohydrodynamics

Abstract This work extends the computational model EULAG-MHD to include Hall magnetohydrodynamics (HMHD)—important to explore physical systems undergoing fast magnetic reconnection at the order of the ion inertial length scale. Examples include solar transients along with reconnections in magnetosphere, magnetotail, and laboratory plasmas. The paper documents the results of two distinct sets of implicit large-eddy simulations in the presence and absence of the Hall forcing term, initiated with an unidirectional sinusoidal magnetic field. The HMHD simulation while benchmarking the code also emphasizes the complexity of three-dimensional (3D) evolution over its two-dimensional counterpart. The magnetic reconnections onset significantly earlier in HMHD. Importantly, the magnetic field generated by the Hall term breaks any inherent symmetry, ultimately making the evolution 3D. The resulting 3D reconnections develop magnetic flux ropes (MFRs) and magnetic flux tubes. Projected on the reconnection plane, the ropes and tubes appear as magnetic islands, which later break into secondary islands, and finally coalesce to generate an X-type neutral point. These findings are in agreement with the theory and contemporary simulations of HMHD, and thus verify our extension of the EULAG-MHD model. The second set explores the influence of the Hall forcing on generation and ascend of an MFR from sheared magnetic arcades—a novel scenario instructive in understanding the coronal transients. The rope evolves through intermediate complex structures, ultimately breaking locally because of reconnections. Interestingly, the breakage occurs earlier in the presence of the Hall term, signifying faster dynamics leading to magnetic topology favorable for reconnections.

Energy conversion during multiple X-lines reconnection

Magnetic reconnection efficiently converts magnetic energy into kinetic and thermal energy of plasmas. It is recently found that energy conversion mainly occurs at reconnection fronts (characterized by the enhancement of the reconnected magnetic field component Bz) and the reconnection exhaust during single X-line reconnection. However, magnetic islands are produced in multiple X-line reconnection. These islands can coalesce, which complicates the energy conversion process relative to the single X-line reconnection. Using 2.5D particle-in-cell simulation, we examine the energy conversion in multiple X-line reconnection. It is found that the magnetic energy releases predominantly through primary islands and second at X-lines. The contributions of secondary islands and merging current sheets to magnetic energy conversion are much less than those by the primary islands. The presence of the guide field reduces the energy conversion rate but increases the proportion of the electron energy gain. We further find that island coalescence increases the energy conversion in magnetic islands.

Particle-in-cell Simulations of Secondary Magnetic Islands: Ion-scale Flux Ropes and Plasmoids

Abstract Ion-scale flux ropes and plasmoids are secondary magnetic islands produced during magnetic reconnection in various heliospheric plasma environments. Here we study the structure of secondary islands and the particle dynamics within them using particle-in-cell simulations. Ion-scale flux ropes (secondary islands with a strong core field) are formed in a strong guide field regime, whereas ion-scale plasmoids (secondary islands with a weak core field) are formed in a weak guide field regime. Currents in both types of secondary islands are carried primarily by electrons. Both types of secondary islands have a magnetic tension force pointing radially inward toward their center. In the flux rope type, this inward tension force is balanced by an outward magnetic pressure gradient of the strong core field; in the plasmoid type, it is countered by an outward thermal pressure gradient caused by electron and ion energizations. The transition between these two types occurs when B g /B 0 = 0.1–0.2 (B g is the guide field, and B 0 is the asymptotic magnetic field).

Connecting the dots in databases of endangered species: a Bayesian hierarchical imputation strategy for missing Peary caribou (Rangifer tarandus pearyi) population data

Peary caribou (Rangifer tarandus pearyi) is listed as Endangered under Canada's Species at Risk Act. Studying rare and endangered species can be particularly challenging due to the constraints posed by incomplete datasets owing to poor weather conditions, lack of technology, organizational deficiencies, and high survey costs in remote areas. A defensible way to remedy data gaps and thus improve the robustness of any given modelling exercise is through imputation schemes, which are typically selected on the basis of missing data patterns. In this study, we develop a regression-based imputation method aiming to identify the linkages among available population records in time and space. One of the fundamental assumptions of our imputation model is that there is a subset of primary islands that act as the core areas from where the Peary caribou populations migrate to secondary or satellite islands. Specifically, we delineated six distinct geographic clusters (Banks, Axel Heiberg, Bathurst, Boothia, Melville and Mackenzie King) across the Canadian Arctic Archipelago, and within each cluster Peary caribou seasonal inter-island movements take place in any given year. Parameterized with Bayesian inference techniques, our imputation modelling strategy has a flexible structure that can accommodate non-monotonic spatiotemporal patterns, and was thus able to capture more than 65% of the variability in our dataset. The two islands (Banks and Northwest Victoria) of the Banks island complex exhibited an average decline rate of 6% per year over the past four decades, which collectively reflects the dramatic population decrease from the early 1970s until the late 1990s, as well as the distinct recovery after the early 2000s. Similar “wax-and-wane” cycles characterize the Peary caribou population patterns on Melville and Bathurst island complexes. Our analysis provides evidence of positive rate of change of the population trends on Axel Heiberg and Ellesmere Islands, which likely stems from pockets on those islands, where favorable climatic/geomorphological conditions, and rich vegetation prevail. In stark contrast, overharvesting, higher predation, adverse climatic conditions, and human-induced forage shortage have led to a dramatic decline, nearing their extirpation, on the Boothia island complex.

The Critical Role of Collisionless Plasma Energization on the Structure of Relativistic Magnetic Reconnection

Abstract During magnetically dominated relativistic reconnection, inflowing plasma depletes the initial relativistic pressure at the x-line and collisionless plasma heating inside the diffusion region is insufficient to overcome this pressure loss. The resulting significant pressure drop causes a collapse at the x-line, essentially a localization mechanism of the diffusion region necessary for fast reconnection. The extension of this low-pressure region (into the outflow) further explains the bursty nature of antiparallel reconnection because a once opened outflow exhaust can also collapse, which repeatedly triggers secondary tearing islands. However, a stable single x-line reconnection can be achieved when an external guide field exists, since the reconnecting magnetic field component rotates out of the reconnection plane at outflows, providing additional magnetic pressure to keep the exhaust open.

Spectral signatures of recursive magnetic field reconnection

ABSTRACT We use 2.5D magnetohydrodynamic simulations to investigate the spectral signatures of the non-linear disruption of a tearing unstable current sheet via the generation of multiple secondary current sheets and magnetic islands. During the non-linear phase of tearing mode evolution, there develops a regime in which the magnetic energy density shows a spectrum with a power law close to B(k)2 ∼ k−0.8. Such an energy spectrum is found in correspondence of the neutral line, within the diffusion region of the primary current sheet, where energy is conveyed towards smaller scales via a ‘recursive’ process of fast tearing-type instabilities. Far from the neutral line, we find that magnetic energy spectra evolve towards slopes compatible with the ‘standard’ Kolmogorov spectrum. Starting from a self-similar description of the non-linear stage at the neutral line, we provide a model that predicts a reconnecting magnetic field energy spectrum scaling as k−4/5, in good agreement with numerical results. An extension of the predicted power law to generic current sheet profiles is also given and possible implications for turbulence phenomenology are discussed. These results provide a step forward to understand the ‘recursive’ generation of magnetic islands (plasmoids), which has been proposed as a possible explanation for the energy release during flares, but which, more in general, can have an impact on the subsequent turbulent evolution of unstable sheets that naturally form in the high Lundquist number and collisionless plasmas found in most of the astrophysical environments.

Turbulence and Particle Acceleration in Collisionless Magnetic Reconnection: Effects of Temperature Inhomogeneity across Pre-reconnection Current Sheet

Abstract Magnetic reconnection is an important process in various collisionless plasma environments because it reconfigures the magnetic field and releases magnetic energy to accelerate charged particles. Its dynamics depend critically on the properties of the pre-reconnection current sheet. One property in particular, cross-sheet temperature inhomogeneity, which is ubiquitous throughout the heliosphere, has been shown to increase reconnection outflow speed, energy conversion efficiency, and secondary island formation rate using two-dimensional particle-in-cell simulations. Here we expand upon these findings, considering two cases with a long, thin current sheet, one with homogeneous temperature and one with inhomogeneous temperature across the current sheet. In the inhomogeneous temperature case, numerous secondary islands form continuously, which increases current sheet turbulence (well-developed cascade power spectra) at large wavenumbers. Current density, energy conversion, dissipation, and acceleration of high-energy particles are also enhanced relative to the homogenous temperature case. Our results suggest that inhomogeneous temperature profiles, which are realistic, need to be incorporated into studies of turbulence and particle acceleration in collisionless magnetic reconnection.

Numerical study on nonlinear growth of m/n = 3/1 double tearing mode in high Lundquist number regime

The nonlinear growth of the m/n = 3/1 double tearing mode (DTM) is numerically investigated in cylinder geometry with non-monotonic radial profiles of the equilibrium safety factor, having two q = 3 surfaces. The formation of plasmoids is found in high Lundquist number regime in such configurations for the first time. During the nonlinear growth of DTM, long and thin Sweet–Parker current sheets are formed near the original inner and outer rational surfaces and become tearing unstable for a large enough Lundquist number, leading to secondary and tertiary magnetic islands which accelerate the magnetic reconnection. The plasmoids also affect the magnetic topology at nonlinear mode saturation. The system can eventually saturate at a quasi-stationary state with small island pairs. The simulation results show that the Lundquist number and the distance between two rational surfaces have important effects on plasmoids formation.

Small‐Scale Flux Transfer Events Formed in the Reconnection Exhaust Region Between Two X Lines

AbstractWe report MMS observations of the ion‐scale flux transfer events (FTEs) that may involve two main X lines and tearing instability between the two X lines. The four spacecraft detected multiple isolated regions with enhanced magnetic field strength and bipolar Bn signatures normal to the nominal magnetopause, indicating FTEs. The currents within the FTEs flow mostly parallel to B, and the magnetic tension force is balanced by the total pressure gradient force. During these events, the plasma bulk flow velocity was directed southward. Detailed analysis of the magnetic and electric field and plasma moments variations suggests that the FTEs were initially embedded within the exhaust region north of an X line but were later located southward/downstream of a subsequent X line. The cross sections of the individual FTEs are in the range of ~2.5–6.8 ion inertial lengths. The observations suggest the formation of multiple secondary FTEs. The presence of an X line in the exhaust region southward of a second X line results from the southward drift of an old X line and the reformation of a new X line. The current layer between the two X lines is unstable to the tearing instability, generating multiple ion‐scale flux‐rope‐type secondary islands.

Numerical studies of the Kelvin-Hemholtz instability in a coronal jet

Kelvin-Hemholtz (K-H) instability in a coronal EUV jet is studied via 2.5D MHD numerical simulations. The jet results from magnetic reconnection due to the interaction of the newly emerging magnetic field and the pre-existing magnetic field in the corona. Our results show that the Alfvén Mach number along the jet is about 5–14 just before the instability occurs, and it is even higher than 14 at some local areas. During the K-H instability process, several vortex-like plasma blobs with high temperature and high density appear along the jet, and magnetic fields have also been rolled up and the magnetic configuration including anti-parallel magnetic fields forms, which leads to magnetic reconnection at many X-points and current sheet fragments inside the vortex-like blob. After magnetic islands appear inside the main current sheet, the total kinetic energy of the reconnection outflows decreases, and cannot support the formation of the vortex-like blob along the jet any longer, then the K-H instability eventually disappears. We also present the results about how the guide field and flux emerging speed affect the K-H instability. We find that a strong guide field inhibits shock formation in the reconnecting upward outflow regions but helps secondary magnetic islands appear earlier in the main current sheet, and then apparently suppresses the K-H instability. As the speed of the emerging magnetic field decreases, the K-H instability appears later, the highest temperature inside the vortex blob gets lower and the vortex structure gets smaller.

Physics of the saturation of particle acceleration in relativistic magnetic reconnection

We investigate the saturation of particle acceleration in relativistic reconnection using two-dimensional particle-in-cell simulations at various magnetizations \sigma. We find that the particle energy spectrum produced in reconnection quickly saturates as a hard power law that cuts off at \gamma~4\sigma, confirming previous work. Using particle tracing, we find that particle acceleration by the reconnection electric field in X-points determines the shape of the particle energy spectrum. By analyzing the current sheet structure, we show that physical cause of saturation is the spontaneous formation of secondary magnetic islands that can disrupt particle acceleration. By comparing the size of acceleration regions to the typical distance between disruptive islands, we show that the maximum Lorentz factor produced in reconnection is \gamma ~ 5 \sigma, which is very close to what we find in our particle energy spectra. We also show that the dynamic range in Lorentz factor of the power law spectrum in reconnection is < 40. The hardness of the power law combined with its narrow dynamic range implies that relativistic reconnection is capable of producing the hard narrowband flares observed in the Crab Nebula but has difficulty producing the softer broadband prompt GRB emission.

Post-test characterization of a solid oxide fuel cell stack operated for more than 30,000 hours: The cell

A four-layer solid oxide fuel cell stack with planar anode-supported cells was operated galvanostatically at 700 °C and 0.5Acm−2 for nearly 35,000 h. One of the four planes started to degrade more rapidly after ∼28,000 h and finally more progressively after ∼33,000 h. The stack was then shut down and a post-test analysis was carefully performed. The cell was characterized with respect to cathodic impurities and clarification of the reason(s) for failure. Wet chemical analysis revealed very low chromium incorporation into the cathode. However, SEM and TEM observations on polished and fractured surfaces showed catastrophic failure in the degraded layer. The cathode–barrier–electrolyte cell layer system delaminated from the entire cell over large areas. The source of delamination was the formation of a porous, sponge-like secondary phase consisting of zirconia, yttria and manganese (oxide). Large secondary phase islands grew from the electrolyte–anode interface towards the anode and cracked the bonding between both layers. The manganese originated from the contact or protection layers used on the air side. This stack result shows that volatile species – in this case manganese – should be avoided, especially when long-term applications are envisaged.

Effect of plasmoids on nonlinear evolution of double tearing modes

The nonlinear evolution of the double tearing mode is numerically investigated in 2D geometry. Long and thin current sheets are found to be formed and become tearing unstable in the high Lundquist number regime during the fast reconnection phase, leading to the onset of the secondary and tertiary islands (plasmoids). Eventually the system saturates at a quasi-stationary state with those islands coexisting in two pairs. Interestingly, a new evolution process, characterized by two fast reconnection phases, is also discovered for an intermediate distance between the two resonant surfaces due to the evolution of current ribbons associated with the secondary island. These results are obtained only when the symmetry of magnetic configuration is strictly guaranteed in numerical calculations.

Electron acceleration in a secondary magnetic island formed during magnetic reconnection with a guide field

Secondary magnetic islands may be generated in the vicinity of an X line during magnetic reconnection. In this paper, by performing two-dimensional (2-D) particle-in-cell simulations, we investigate the role of a secondary magnetic island in electron acceleration during magnetic reconnection with a guide field. The electron motions are found to be adiabatic, and we analyze the contributions of the parallel electric field and Fermi and betatron mechanisms to electron acceleration in the secondary island during the evolution of magnetic reconnection. When the secondary island is formed, electrons are accelerated by the parallel electric field due to the existence of the reconnection electric field in the electron current sheet. Electrons can be accelerated by both the parallel electric field and Fermi mechanism when the secondary island begins to merge with the primary magnetic island, which is formed simultaneously with the appearance of X lines. With the increase in the guide field, the contributions of the Fermi mechanism to electron acceleration become less and less important. When the guide field is sufficiently large, the contribution of the Fermi mechanism is almost negligible.

Multiple secondary islands formation in nonlinear evolution of double tearing mode simulations

A new numerical code solving the conservative perturbed resistive magnetohydrodynamic (MHD) model is developed. Numerical tests of the ideal Kelvin-Helmholtz instability and the resistive double tearing mode (DTM) show its capability in solving linear and nonlinear MHD instabilities. The nonlinear DTM evolution in 2D geometry is numerically investigated with low guiding field Bz0, short half-distance y0 between the equilibrium current sheets, and small resistivity η. The interaction of islands on the two initial current sheets may generate an unstable flow driven current sheet with a high length-to-thickness aspect ratio (α), and multiple secondary islands can form. In general, the length-to-thickness aspect ratio α and the number of secondary islands increase with decreasing guide field Bz0, decreasing half-distance y0, and increasing Lundquist number of the flow driven current sheet SL although the dependence may be non-monotonic. The reconnection rate dependence on SL, Bz0, and y0 is also investigated.