Plasmoid Formation Research Articles

Effects of Cross‐Sheet Density and Temperature Inhomogeneities on Magnetotail Reconnection

AbstractProperties of magnetic reconnection in Earth's magnetotail are determined by prereconnection current sheet characteristics. Although spacecraft observations have revealed that the spatial profiles of two important parameters, density and temperature, across the prereconnection magnetotail current sheet are inhomogeneous, the effects of the inhomogeneities on reconnection processes have received insufficient attention. Using Time History of Events and Macroscale Interactions during Substorm (THEMIS) and Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) observations, we show that the inhomogeneities are ubiquitous throughout the magnetotail. Using particle‐in‐cell simulations, we demonstrate that strong density inhomogeneity increases magnetotail reconnection rate, and strong temperature inhomogeneity further increases reconnection outflow speed (although reconnection rate does not change significantly). Overall, these inhomogeneities expedite energy conversion efficiency and secondary plasmoid formation during reconnection. As the current sheet density and temperature characteristics vary considerably with geocentric distance and time under different geospace conditions, a large variety of reconnection and postreconnection dynamics results from this dependence.

Plasmoid instability in the semi-collisional regime

We investigate analytically and numerically the semi-collisional regime of the plasmoid instability, defined by the inequality $\unicode[STIX]{x1D6FF}_{\text{SP}}\gg \unicode[STIX]{x1D70C}_{s}\gg \unicode[STIX]{x1D6FF}_{\text{in}}$, where $\unicode[STIX]{x1D6FF}_{\text{SP}}$ is the width of a Sweet–Parker current sheet, $\unicode[STIX]{x1D70C}_{s}$ is the ion sound Larmor radius and $\unicode[STIX]{x1D6FF}_{\text{in}}$ is the width of the boundary layer that arises in the plasmoid instability analysis. Theoretically, this regime is predicted to exist if the Lundquist number $S$ and the length of the current sheet $L$ are such that $(L/\unicode[STIX]{x1D70C}_{s})^{14/9}<S<(L/\unicode[STIX]{x1D70C}_{s})^{2}$ (for a sinusoidal-like magnetic configuration; for a Harris-type sheet the lower bound is replaced with $(L/\unicode[STIX]{x1D70C}_{s})^{8/5}$). These bounds are validated numerically by means of simulations using a reduced gyrokinetic model (Zocco & Schekochihin, Phys. Plasmas, vol. 18 (10), 2011, 102309) conducted with the code Viriato. Importantly, this regime is conjectured to allow for plasmoid formation at relatively low, experimentally accessible, values of the Lundquist number. Our simulations obtain plasmoid instability at values of $S$ as low as ${\sim}250$. The simulations do not prescribe a Sweet–Parker sheet; rather, one is formed self-consistently during the nonlinear evolution of the initial tearing mode configuration. This proves that this regime of the plasmoid instability is realizable, at least at the relatively low values of the Lundquist number that are accessible to current dedicated experiments.

Evolution of energy spectra of the electronic component for plasmoids generated under autoresonance conditions in a long magnetic mirror

We performed a 3D numerical simulation of plasmoid generation with a relativistic electron component under gyromagnetic autoresonance conditions in a long mirror trap. We studied the process of plasmoid formation, the spaciotemporal dynamics and the evolution of the energy spectra of the electron component of the plasma and the efficiency of electron trapping as a function of the experimental parameters.

Global Three‐Dimensional Simulation of the Earth's Magnetospheric and Ionospheric Responses to Small‐Scale Magnetic Flux Ropes in the Solar Wind

AbstractThe orientation of magnetic flux ropes in the solar wind is an important component that affects interactions with the Earth's magnetosphere and ionosphere. In this study, we performed global magnetohydrodynamic (MHD) simulations on the responses of the magnetosphere and ionosphere to the impact of small‐scale magnetic flux ropes (SMFRs). We considered four types of SMFR structures according to the alignment direction of the flux rope axis in the plane perpendicular to the Sun‐Earth line. The flux rope axis of the two types is oriented in the north‐south direction, while the flux rope axis of the other two types is oriented along the dusk‐dawn direction. Accordingly, the By and Bz profiles of the SMFR types vary as the SMFR passes through the Earth. The main features of the response are as follows: (i) The magnetic reconnection on both the dayside and nightside is well organized by the specific profiles of By and Bz. (ii) One type of SMFRs where Bz turns from south to north and By remains duskward leads to plasmoid formation in the tail, distinguishing it from the other types. (iii) The temporal responses of the tail plasma flow, cross‐tail electric field, tail plasma pressure, and cross‐polar cap potential depend on the specific profiles of By and Bz, causing different response times. (iv) The evolution of ionospheric convection pattern sensitively depends on the magnetic field variation within SMFRs. (v) The peak value of cross‐polar cap potential ranges from 25 kV to >50 kV, providing energy storage suitable for substorm expansion.

An experimental platform for pulsed-power driven magnetic reconnection

We describe a versatile pulsed-power driven platform for magnetic reconnection experiments, based on the exploding wire arrays driven in parallel [Suttle et al., Phys. Rev. Lett. 116, 225001 (2016)]. This platform produces inherently magnetised plasma flows for the duration of the generator current pulse (250 ns), resulting in a long-lasting reconnection layer. The layer exists for long enough to allow the evolution of complex processes such as plasmoid formation and movement to be diagnosed by a suite of high spatial and temporal resolution laser-based diagnostics. We can access a wide range of magnetic reconnection regimes by changing the wire material or moving the electrodes inside the wire arrays. We present results with aluminium and carbon wires, in which the parameters of the inflows and the layer that forms are significantly different. By moving the electrodes inside the wire arrays, we change how strongly the inflows are driven. This enables us to study both symmetric reconnection in a range of different regimes and asymmetric reconnection.

Magnetohydrodynamic Turbulence in the Plasmoid-mediated Regime

Abstract Magnetohydrodynamic turbulence and magnetic reconnection are ubiquitous in astrophysical environments. In most situations these processes do not occur in isolation but interact with each other. This renders a comprehensive theory of these processes highly challenging. Here we propose a theory of magnetohydrodynamic turbulence driven at a large scale that self-consistently accounts for the mutual interplay with magnetic reconnection occurring at smaller scales. Magnetic reconnection produces plasmoids (flux ropes) that grow from turbulence-generated noise and eventually disrupt the sheet-like structures in which they are born. The disruption of these structures leads to a modification of the turbulent energy cascade, which in turn exerts a feedback effect on the plasmoid formation via the turbulence-generated noise. The energy spectrum in this plasmoid-mediated range steepens relative to the standard inertial range and does not follow a simple power law. As a result of the complex interplay between turbulence and reconnection, we also find that the length scale that marks the beginning of the plasmoid-mediated range and the dissipation length scale do not obey true power laws. The transitional magnetic Reynolds number above which the plasmoid formation becomes statistically significant enough to affect the turbulent cascade is fairly modest, implying that plasmoids are expected to modify the turbulent path to dissipation in many astrophysical systems.

Experimental Study of a Long-Living Plasmoid Using High-Speed Filming

This paper describes the time evolution of ball plasmoids generated by millisecond atmospheric discharge in contact with water. The aim of this paper was to clarify an initiation and a formation mechanism of an atmospheric ball plasmoid. The use of a higher frame rate of filming and shorter exposition time, in comparison with past experiments, allows us to observe the fast processes that occur during a plasmoid evolution. We assert that an initial electrical breakdown in a cathode ceramic tube filled by a conductive liquid is essential for further plasmoid formation. It generates a shock wave resulting in a blast of conductive liquid. The resulting expansion of water vapor and bubbles with an addition of weekly ionized plasma serves as a main source of matter for plasmoid formation. We also note that an electrical arc generated after the breakdown transforms to a plasma jet. This jet accelerates plasma to the plasmoid.

Non-linear growth of double tearing mode: Explosive reconnection, plasmoid formation, and particle acceleration

The nonlinear evolution of double tearing modes (DTMs) is investigated within the framework of resistive magnetohydrodynamic (MHD) simulations in a two-dimensional Cartesian geometry. We have explored the explosive reconnection phase associated with the growth of the secondary structure-driven instability for a range of resistivity values. The time scale of the explosive phase (that is of order of a few Alfvénic time scales) is shown to be quasi-independent of the resistivity, even when fast growing plasmoids develop for the highest enough Lundquist number cases. Test particle accelerations are performed using the MHD explosive simulations as input parameters. Our results show that reconnection DTM dynamics is able to provide an efficient process for accelerating charged particles far beyond characteristic thermal velocities within the reconnection layers. The main acceleration mechanism is attributed to the strong inductive electric field generated by the island structure-driven instability, with an additional smaller contribution due to the presence of plasmoids. Finally, our results are used to discuss some features of the accelerated particle spectra during flaring activity in the solar corona.

Transformation of the ordered internal structures during the acceleration of fast charged particles in a dense plasma focus

The paper concerns important differences in the evolution of plasma column structures during the production of fusion neutrons in the first and subsequent neutron pulses, as observed for plasma-focus discharges performed with the deuterium filling. The first neutron pulse, of a more isotropic distribution, is usually produced during the formation of the first big plasmoid. The next neutron pulses can be generated by the fast deuterons moving dominantly in the downstream direction, at the instants of a disruption of the pinch constriction, when other plasmoids are formed during the constriction evolution. In both cases, the fusion neutrons are produced by a beam-target mechanism, and the acceleration of fast electron- and deuteron-beams can be interpreted by transformation and decay of the magnetic field associated with a filamentary structure of the current flow in the plasmoid.

Anomalous Heating and Plasmoid Formation in a Driven Magnetic Reconnection Experiment

We present a detailed study of magnetic reconnection in a quasi-two-dimensional pulsed-power driven laboratory experiment. Oppositely directed magnetic fields (B=3 T), advected by supersonic, sub-Alfvénic carbon plasma flows (V_{in}=50 km/s), are brought together and mutually annihilate inside a thin current layer (δ=0.6 mm). Temporally and spatially resolved optical diagnostics, including interferometry, Faraday rotation imaging, and Thomson scattering, allow us to determine the structure and dynamics of this layer, the nature of the inflows and outflows, and the detailed energy partition during the reconnection process. We measure high electron and ion temperatures (T_{e}=100 eV, T_{i}=600 eV), far in excess of what can be attributed to classical (Spitzer) resistive and viscous dissipation. We observe the repeated formation and ejection of plasmoids, consistent with the predictions from semicollisional plasmoid theory.

Dynamo-driven plasmoid formation from a current-sheet instability

Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal guide field. As helicity is injected, two types of current sheets are formed from (1) the oppositely directed field lines in the injector region (primary reconnecting current sheet), and (2) the poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetric fluctuations arising from the current-sheet instability isolated near the plasma edge have tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate by breaking up the current sheet. Second, for the first time, a dynamo poloidal flux amplification is observed at the reconnection site (in the region of the oppositely directed magnetic field). This fluctuation-induced flux amplification increases the local Lundquist number, which then triggers a plasmoid instability and breaks the primary current sheet at the reconnection site. The plasmoids formation driven by large-scale flux amplification, i.e., a large-scale dynamo, observed here has strong implications for astrophysical reconnection as well as fast reconnection events in laboratory plasmas.

Visco-resistive plasmoid instability

The plasmoid instability in visco-resistive current sheets is analyzed in both the linear and nonlinear regimes. The linear growth rate and the wavenumber are found to scale as S1/4(1+Pm)−5/8 and S3/8(1+Pm)−3/16 with respect to the Lundquist number S and the magnetic Prandtl number Pm. Furthermore, the linear layer width is shown to scale as S−1/8(1+Pm)1/16. The growth of the plasmoids slows down from an exponential growth to an algebraic growth when they enter into the nonlinear regime. In particular, the time-scale of the nonlinear growth of the plasmoids is found to be τNL∼S−3/16(1+Pm)19/32τA,L. The nonlinear growth of the plasmoids is radically different from the linear one, and it is shown to be essential to understand the global current sheet disruption. It is also discussed how the plasmoid instability enables fast magnetic reconnection in visco-resistive plasmas. In particular, it is shown that the recursive plasmoid formation can trigger a collisionless reconnection regime if S≳Lcs(ϵclk)−1(1+Pm)1/2, where Lcs is the half-length of the global current sheet and lk is the relevant kinetic length scale. On the other hand, if the current sheet remains in the collisional regime, the global (time-averaged) reconnection rate is shown to be 〈dψ/dt|X〉≈ϵcvA,uBu(1+Pm)−1/2, where ϵc is the critical inverse aspect ratio of the current sheet, while vA,u and Bu are the Alfvén speed and the magnetic field upstream of the global reconnection layer.

Nonlinear instability and intermittent nature of magnetic reconnection in solar chromosphere

Abstract The recent observations of Singh et al. (2012, ApJ, 759, 33) have shown multiple plasma ejections and the intermittent nature of magnetic reconnection in the solar chromosphere, highlighting the need for fast reconnection to occur in highly collisional plasma. However, the physical process through which fast magnetic reconnection occurs in partially ionized plasma, like the solar chromosphere, is still poorly understood. It has been shown that for sufficiently high magnetic Reynolds numbers, Sweet–Parker current sheets can become unstable leading to tearing mode instability and plasmoid formation, but when dealing with a partially ionized plasma the strength of coupling between the ions and neutrals plays a fundamental role in determining the dynamics of the system. We propose that as the reconnecting current sheet thins and the tearing instability develops, plasmoid formation passes through strongly, intermediately, and weakly coupled (or decoupled) regimes, with the time scale for the tearing mode instability depending on the frictional coupling between ions and neutrals. We present calculations for the relevant time scales for fractal tearing in all three regimes. We show that as a result of the tearing mode instability and the subsequent non-linear instability due to the plasmoid-dominated reconnection, the Sweet–Parker current sheet tends to have a fractal-like structure, and when the chromospheric magnetic field is sufficiently strong the tearing instability can reach down to kinetic scales, which are hypothesized to be necessary for fast reconnection.

Computational extended magneto-hydrodynamical study of shock structure generated by flows past an obstacle

The magnetized shock problem is studied in the context where supersonic plasma flows past a solid obstacle. This problem exhibits interesting and important phenomena such as a bow shock, magnetotail formation, reconnection, and plasmoid formation. This study is carried out using a discontinuous Galerkin method to solve an extended magneto-hydrodynamic model (XMHD). The main goals of this paper are to present a reasonably complete picture of the properties of this interaction using the MHD model and then to compare the results to the XMHD model. The inflow parameters, such as the magnetosonic Mach number Mf and the ratio of thermal pressure to magnetic pressure β, can significantly affect the physical structures of the flow-obstacle interaction. The Hall effect can also significantly influence the results in the regime in which the ion inertial length is numerically resolved. Most of the results presented are for the two-dimensional case; however, two three-dimensional simulations are presented to make a connection to the important case in which the solar wind interacts with a solid body and to explore the possibility of performing scaled laboratory experiments.

RESISTIVE MAGNETOHYDRODYNAMICS SIMULATIONS OF THE IDEAL TEARING MODE

We study the linear and nonlinear evolution of the tearing instability on thin current sheets by means of two-dimensional numerical simulations, within the framework of compressible, resistive magnetohydrodynamics. In particular we analyze the behavior of current sheets whose inverse aspect ratio scales with the Lundquist number S as S 1=3 . This scaling has been recently recognized to yield the threshold separating fast, ideal reconnection, with an evolution and growth which are independent of S provided this is high enough, as it should be natural having the ideal case as a limit for S! 1. Our simulations conrm that the tearing instability growth rate can be as fast as 0:6 A 1 , where A is the ideal Alfv enic time set by the macroscopic scales, for our least diusive case with S = 10 7 . The expected instability dispersion relation and eigenmodes are also retrieved in the linear regime, for the values of S explored here. Moreover, in the nonlinear stage of the simulations we observe secondary events obeying the same critical scaling with S, here calculated on the local, much smaller lengths, leading to increasingly faster reconnection. These ndings strongly support the idea that in a fully dynamic regime, as soon as current sheets develop, thin and reach this critical threshold in their aspect ratio, the tearing mode is able to trigger plasmoid formation and reconnection on the local (ideal) Alfv enic timescales, as required to explain the explosive aring activity often observed in solar and astrophysical plasmas. Subject headings: plasmas { MHD { methods: numerical.

Plasmoids Formation During Simulations of Coaxial Helicity Injection in the National Spherical Torus Experiment.

The formation of an elongated Sweet-Parker current sheet and a transition to plasmoid instability has for the first time been predicted by simulations in a large-scale toroidal fusion plasma in the absence of any preexisting instability. Plasmoid instability is demonstrated through resistive MHD simulations of transient coaxial helicity injection experiments in the National Spherical Torus Experiment (NSTX). Consistent with the theory, fundamental characteristics of the plasmoid instability, including fast reconnection rate, have been observed in these realistic simulations. Motivated by the simulations, experimental camera images have been revisited and suggest the existence of reconnecting plasmoids in NSTX. Global, system-size plasmoid formation observed here should also have strong implications for astrophysical reconnection, such as rapid eruptive solar events.

Extended theory of the Taylor problem in the plasmoid-unstable regime

A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid phase. An expression for the threshold perturbation amplitude required to trigger the plasmoid phase is derived, as well as an analytical expression for the reconnection rate in the plasmoid-dominated regime. Visco-resistive magnetohydrodynamic simulations complement the analytical calculations. The plasmoid formation plays a crucial role in allowing fast reconnection in a magnetohydrodynamical plasma, and the presented results suggest that it may occur and have profound consequences even if the plasma is tearing-stable.

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.

外部平衡磁場分布を用いた電流シート内のプラズモイド生成実験

外部平衡磁場分布を用いた電流シート内のプラズモイド生成実験

Nonlinear evolution of three-dimensional instabilities of thin and thick electron scale current sheets: Plasmoid formation and current filamentation

Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =de=c/ωpe), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheets (half thickness ∼5 de), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.