Collisionless Reconnection Research Articles

Particle-in-cell simulations of magnetosphere electrodynamics

This paper reviews the basic principles and techniques involved in formulating particle-in-cell (PIC) simulation models which can be used to address medium- and large-scale problems in magnetosphere electrodynamics. The limitations imposed by the underlying kinetic physics of a plasma are emphasized, and representative algorithms are described for full particle and hybrid (particle ions, fluid electrons) models. Issues related to the choice of initial and boundary conditions and the implementation of PIC models on massively parallel computers are discussed. Explicit examples involving the diffusion region in collisionless reconnection, plasma sheet convection, and large scale structure in magnetic reconnection are presented to illustrate the current capabilities of PIC models.

Basic physics of collisionless three-dimensional reconnection in the solar corona related to Yohkoh observations

New results concerning magnetic reconnection in the solar corona are reviewed. We apply the collisionless 3D reconnection theory — more exactly, the model of a high-temperature turbulent-current non-neutral current sheet — to the coronal conditions derived from the observations with the HXT and SXT onboard Yohkoh. New interpretations are discussed of the Yohkoh data on the site and mechanism of magnetic energy transformation into kinetic and thermal energies of superhot plasmas and accelerated high-energy particles. Open issues are the focus of our attention.

Three-dimensional particle simulation of plasma instabilities and collisionless reconnection in a current sheet

Generation of anomalous resistivity and dynamical development of collisionless reconnection in the vicinity of a magnetically neutral sheet are investigated by means of a three-dimensional particle simulation. For no external driving source, two different types of plasma instabilities are excited in the current layer. The lower hybrid drift instability (LHDI) is observed to grow in the periphery of current layer in an early period, while a drift kink instability (DKI) is triggered at the neutral sheet in a late period as a result of the nonlinear deformation of the current sheet by the LHDI. A reconnection electric field grows at the neutral sheet in accordance with the excitation of the DKI. When an external driving field exists, the convective electric field penetrates into the current layer through the particle kinetic effect and collisionless reconnection is triggered by the convective electric field earlier than the DKI is excited. It is also found that the anisotropic ion distribution is formed through the anomalous ion heating by the DKI.

Hamiltonian magnetic reconnection

Magnetic reconnection in two dimensional (2D), collisionless, non-dissipative regimes is investigated analytically and numerically by means of a finite difference code in the nonlinear regime where the island size becomes macroscopic. The cross-shaped structure of the reconnection region, originally reported by Cafaro et al (1998 Phys. Rev. Lett. 80 20) is analysed as a function of the ratio between the ion sound Larmor radius and the inertial skin depth. This cross shape structure is found to survive in the presence of weak dissipation. Further insight on the quasi-explosive behaviour of the magnetic island width as a function of time and on the spatial structure of the perturbed current density is provided. We confirm that the amount of reconnected flux becomes of order unity on the time scale of the inverse linear growth rate. Results in the collisionless limit are interpreted on the basis of the Hamiltonian properties of the adopted collisionless, 2D, fluid model. Thus, collisionless reconnection is a fast, non-steady-state process, fundamentally different from 2D resistive magnetic reconnection, of which the Sweet-Parker model is the classic paradigm.

Longitudinal and transversal structure functions in two-dimensional electron magnetohydrodynamic flows

Electron magnetohydrodynamic flows have recently attracted considerable interest not only in the field of collisionless reconnection, but also as the first two-dimensional turbulent system showing Kolmogorov-type scaling for the energy spectrum. In this paper, longitudinal and transversal structure functions are calculated for varying Reynolds numbers. The simulations show that the differences between longitudinal and transversal structure functions are finite size effects for this type of flow and vanish in the limit of high Reynolds numbers. In addition, the scaling of structure functions for velocity and current density could be described by assuming a log-Poisson statistics with two atoms, as recently proposed for passive scalar advection.

Experimental studies of magnetic reconnection

Laboratory magnetic reconnection experiments have been performed for nearly 20 years. Elegant experiments by Stenzel and Gekelman [R. L. Stenzel and W. Gekelman, Phys. Rev. Lett. 42, 1055 (1979); W. Gekelman and R. L. Stenzel, Phys. Rev. Lett. 54, 2414 (1985)] focused on the measurement of field quantities with a single movable probe in a highly reproducible plasma. Observations included a very thin current sheet (on the order of c/ωpe), accelerated electrons, and whistler waves. The argon ions were unmagnetized in these experiments. Recent magnetohydrodynamic (MHD) experiments by Yamada and Ono have used merging plasmoids [M. Yamada, Y. Ono, A. Hayakawa, M. Katsurai, and F. W. Perkins, Phys. Rev. Lett. 65, 721 (1990); Y. Ono, M. Yamada, T. Akao, T. Tajima, and R. Matsumoto, Phys. Rev. Lett. 76, 3328 (1996)] and have measured three dimensional effects and ion acceleration. We have observed correlations between magnetic reconnection and energetic ion flow events with merging force free spheromaks at the Swarthmore Spheromak Experiment (SSX) [T. W. Kornack, P. K. Sollins, and M. R. Brown, Phys. Rev. E 58, R36 (1998)]. The reconnection layer is measured with linear and two dimensional probe arrays and ion flow is directly measured with a retarding grid energy analyzer. Flow has been measured both in the plane of the reconnection layer and out of the plane. The outflow velocity is nearly Alfvénic in the reconnection plane and the scale of the magnetic structures is consistent with collisionless reconnection theories (on the order of c/ωpi). Results from the two dimensional array show the formation of magnetic islands correlated with super-Alfvénic ions accelerated normal to the layer.

Collisionless magnetic reconnection in the presence of an external driving flow

The dynamical development of collisionless reconnection and the consequent energy-conversion process in the presence of an external driving flow are investigated by means of a full particle simulation. Magnetic reconnection develops in two steps in accordance with the formation of ion and electron current layers. In the early phase magnetic reconnection is controlled by an ion kinetic effect, while an electron kinetic effect becomes dominant in the late phase. There exist two mechanisms associated with the particle kinetic effects, that break the frozen-in condition of magnetic field and lead to magnetic reconnection in a collisionless plasma, namely a particle inertia effect and a particle thermal orbit effect. It is found that the dominant triggering mechanism in the late phase changes from an electron thermal orbit effect to an electron inertia effect as the longitudinal magnetic field increases. Electron acceleration and heating take place in the reconnection area under the influence of the reconnection electric field, while the energy conversion takes place from electrons to ions through the action of an electrostatic field excited downstream. As a result, the average ion temperature becomes about 1.5 times the average electron temperature.

Reconnection: Space plasma simulations for multi-spacecraft satellite observations in the ISTP Era

In the ISTP era multi-spacecraft measurements have not only become a tool for phenomenological and correlative studies of the solar- terrestrial coupling. They also open new opportunities to test, verify or falsify basic physical concepts. For the use of multi-spacecraft measurements in this sense numerical modelling and simulations are becoming more and more a necessary tool for interpreting the observations correctly. We take the reconnection process as an example. Reconnection is supposed to release magnetic field energy from the sun, to couple the Earth's magnetosphere to the solar wind and to suddenly release previously stored magnetic energy in the course of magnetospheric substorms. Hence, reconnection is a key concept in the solar-terrestrial relationship. On the other hand it is difficult to theoretically grasp collisionless reconnection in space plasmas. This complicates its experimental verification.In this paper we present some selected essentially kinetic features of spontaneous reconnection through collisionless thin current sheets in two and three dimensions: These should be observable, e.g., at the onset of magnetospheric substorm. The kinetic approach is necessary due to the cross-scale coupling, inherent to collisionless reconnection. We demonstrate that microscopic magnetic islands of the Debye length scale are always present through thin current sheets. They are, however, reversible and occur at the level of thermal fluctuations. Macroscopic reconnection and island structure formation starts with irreversible energy transfer from fields to plasma. We demonstrate the different routes to macroscopic merging in two and three dimensions. In two dimensions Landau damping in the potential wells of magnetic islands causes the classical slow tearing mode instability. In three dimensions a sausage mode bulk current instability accelerates the transition to macroscopic reconnection. As a result three-dimensional magnetic islands are formed, which are limited in all three spatial directions. We, finally, demonstrate how multi-spacecraft observations of the ISTP era together with well posed computer simulations can help to understand col lisionless reconnection by means of in situ measurements in the Earth's magnetosphere.

Particle simulation of collisionless reconnection in three dimensions

Generation of anomalous resistivity and dynamical development of collisionless reconnection in the vicinity of a magnetically neutral sheet are investigated by means of a three-dimensional particle simulation. For no external driving source, two different types of plasma instabilities are excited in the current layer in the same way as the two-dimensional case. The lower hybrid drift instability is observed to grow in the periphery of the current layer, but it cannot penetrate into a high-beta region near the neutral sheet. Instead, a low-frequency electromagnetic (EM) instability is excited at the neutral sheet after saturation of the lower hybrid drift wave. Thus, the interaction between this EM wave and charged particles can cause an anomalous resistivity in the neutral sheet. When an external driving flow exists, collisionless reconnection is triggered by the particle kinetic effect and the anisotropic ion distribution is formed through the anomalous ion heating inside the current layer.

Hybrid simulation of magnetotail reconnection

Magnetic reconnection is studied by using a large-scale two-dimensional hybrid simulation code that treats the ions fully kinetically and the electrons as a massless fluid. Reconnection is realised by localising an anomalous resistivity in a kinetic tail equilibrium. Within a distance of about 80 lobe ion inertia lengths tailward from the neutral line the fast reconnection jet is characterised over most of the region by partial shell type ion distributions; i.e., the distribution in the central current sheet is not thermalised. Inward drifting cold lobe ions perform in the centre of the reconnection wedge due to the small magnetic field curvature Speiser-type orbits and are subsequently ejected again onto lobe field lines. This situation is similar to the collisionless reconnection scenario described by Hill (1975). The cross-tail current of the thin current sheet is supported by the drifting ions. This current sheet warps and an instability develops further away from the neutral line, resulting in a filamentation of the cross tail current. The simulation demonstrates that ion kinetic effects are of importance for the large-scale structure of the magne-totail during near-Earth reconnection.

Ion kinetic effects in magnetic reconnection: Hybrid simulations

Magnetic reconnection in a low beta plasma is studied by using a large‐scale two‐dimensional hybrid simulation code that treats the ions fully kinetically and the electrons as a massless fluid. Reconnection is realized by localizing an anomalous resistivity in the the center of a Harris‐type current sheet. The results are applicable to reconnection in the geomagnetic tail. Within a distance of about 200 ion inertial lengths from the neutral line the fast reconnection jet is characterized over most of the region by partial shell type ion distributions; i.e., the distribution in the central current sheet is not thermalized. Inward drifting cold lobe ions perform in the center of the reconnection wedge due to the small magnetic field curvature Speiser‐type orbits and are subsequently ejected again onto lobe field lines. This stadium is similar to the collisionless reconnection scenario described by Hill [1975]. The cross‐tail current of the thin current sheet is supported by the drifting ions. This current sheet warps and an instability develops, which leads further away from the neutral line to a filament ation of the cross tail current. These simulations suggested that after near‐Earth reconnection proceeds to lobe magnetic field lines a postplasmoid plasma sheet with a thin current sheet builds up, which is of a boundary layer type. The thin current sheet is instable. At about 200 ion inertial lengths away from the neutral line the instability has reached a nonlinear state and the cross‐tail current becomes patchy; the incoming and ejected cold lobe ions are isotropized in the ensuing magnetic field and thus constitute a hot plasma sheet distribution. This can then support the occurrence of slow mode shocks at the boundary of the reconnection layer with backstreaming ions upstream of the shocks.

Kinetic quasi‐viscous and bulk flow inertia effects in collisionless magnetotail reconnection

Both electron inertia and nongyrotropic effects were analysed using 2 1/2‐dimensional hybrid simulations of collisionless magnetic reconnection. The traditional hybrid approach which treats ions as particles and electrons as an isotropic massless fluid was modified. In the new model the electron mass dependence was introduced both in the expression for the electric field and in the evolution equation of the full electron pressure tensor. This comprehensive hybrid model includes full ion kinetics, incorporates Hall effects, describes the leading terms in electron dynamics responsible for breaking the frozen magnetic flux constraint and allows to consider arbitrary ion/electron temperature and mass ratios. We demonstrate that the kinetic quasi‐viscous electron inertia associated with nongyrotropic pressure effects dominates over the electron bulk flow inertia in controlling the structure of the dissipation region around the neutral X line. The reconnection electric field based on the nongyrotropic pressure tends to reduce the current density and to relax gradients in the vicinity of the X line (similar to the localized anomalous viscosity). On the other hand, the reconnection electric field based on electron bulk flow inertia tends to require an increased current density, with gradient scales comparable with the electron skin depth. The dependence on the ion/electron temperature ratio and on the current carrier also is discussed. An analytical analysis which supports the results of the numerical simulations is also presented.

Interpretation of particle acceleration in a simulation study of collisionless reconnection

A recent simulation study [Horiuchi and Sato, Phys. Plasmas 4, 277 (1997)] investigated collisionless magnetic reconnection in a sheared magnetic field. Theoretical models for particle acceleration in current sheets are used to interpret some of the simulation results, which are found to be consistent with analytical expressions for values of the electron energy gain, the acceleration time, and the longitudinal magnetic field giving rise to adiabatic particle motion. The simulation also identified an ion acceleration mechanism that will require additional theoretical study.

Collisionless Reconnection and High‐Energy Particle Acceleration in Solar Flares

Observations with the Hard X-Ray Telescope (HXT) and the Soft X-Ray Telescope (SXT) on board Yohkoh show that the reconnection process is common to impulsive and gradual Nares. We apply the collisionless reconnection theoryEmore exactly, the model of a high-temperature turbulent-current sheet (HTTCS)Eto the coronal conditions derived from the Yohkoh data on the site and mechanism of mag- netic energy transformation into kinetic and thermal energies of superhot II plasma and accelerated par- ticles. We consider the reconnecting current sheet as the source of Nare energy and the -rst-step mechanism in a two-step acceleration of electrons and ions to high energies. According to our model, reconnected -eld lines rapidly move out of the HTTCS, being frozen into superhot plasma, and form magnetic loops on the upstream side of a fast oblique collisionless shock (FOCS) situated above the soft X-rayEemitting loops of a strong magnetic -eld. The electrons and ions energized and preaccelerated by the HTTCS are trapped in magnetic loops. The top of each loop moves with a high speed toward the FOCS, while its feet penetrate through the shock front. For these reasons, two mechanismsEthe adiabatic heating inside the collapsing trap and acceleration by the shock front at the two feet of the trapEefficiently increase the particle energy. The lifetime of an individual collapsing trap can be identi-ed with the observed few-second delay to higher energies of hard X-ray and gamma-ray emission. The trap of accelerated electrons can be seen as the coronal hard X-ray above-the-loop-top source.II Precipitation of accelerated electrons from the trap through the FOCS into the chromosphere is responsible for the hard X-ray footpoint sources.II The model explains timing, location, and motion of the hard X-ray sources in solar Nares as well as the observed relative intensity of the coronal and chromospheric hard X-ray sources and other physical properties.

Two-fluid theory of collisionless magnetic reconnection

Theoretical studies of collisionless reconnection in the framework of two-fluid theory are presented. In the high-β case (β≳1) reconnection is controlled by the whistler mode, leading to decoupling of ions from electrons on scales <c/ωpi. Though reconnection requires electron inertia, the reconnection rate is independent thereof, controlled only by ion inertia. Reconnection is hence much faster than in the absence of the Hall term. In the opposite limit of small β the strong axial field suppresses the whistler mode. Hence ions have to follow the electrons in the narrow reconnection layer δ∼c/ωpe, forming a macroscopic current sheet which strongly reduces the reconnection rate. Theoretical scaling laws are confirmed by numerical simulations.

The generalized Ohm’s law in collisionless magnetic reconnection

The generalized Ohm’s law and the force balance near neutral lines in collisionless magnetic reconnection is studied based on two-dimensional full particle simulations in which the ion–electron mass ratio is set to be 1836. The off-diagonal elements of a plasma pressure tensor are found to be responsible for the breakdown of the frozen-in condition in collisionless reconnection. While the off-diagonal elements of the electron pressure tensor are dominant terms in the generalized Ohm’s law near neutral lines, the ion off-diagonal pressure terms are of significant importance when ions are main current carriers. The spatial scale of electron off-diagonal pressure term Pxy(e) is also found to be proportional to the Dungey length scale, (meEy/eβ2)1/3, where β=∂Bz/∂x.

Collisionless reconnection in the magnetotail

Recent developments regarding collisionless reconnection in current sheets with a finite normal magnetic field component ( B z ) are reviewed. In 2-D x, z configurations the ion tearing mode is stabilized by the electron compressibility. When the y dependence is included, cross-field current instabilities can be excited. Of these, the drift kink mode appears to be particularly important. 3-D electromagnetic particle simulations indicate that this mode can act as the precursor to the growth of tearing modes and subsequent reconnection.

Particle simulations of collisionless reconnection in magnetotail configuration including electron dynamics

The role of electron dynamics in collisionless magnetotail reconnection is investigated by using two‐dimensional full particle simulations with ion‐to‐electron mass ratios mi/me set to 1 and 10. The results indicate that the electrons have a stabilizing influence on the ion tearing instability in the sense that growth rates are reduced in runs with the initial electron Larmor radius being sufficiently small in comparison with the ion Larmor radius. A comparison of our results with those obtained by Pritchett [1994] using a significantly different numerical model shows encouraging agreement. The attempt to achieve an approach closer to realistic magnetotail conditions is inhibited by present technical restrictions.

Asymmetry and thermal effects due to parallel motion of electrons in collisionless magnetic reconnection

Fast collisionless reconnection of magnetic flux loops by the macro-particle simulation code shows significant asymmetry of the plasma flow under an ambient toroidal magnetic field. The parallel motion of electrons induced by the reconnection electric field is found to produce large density and toroidal magnetic field inhomogeneities of a quadrupole shape, δn/n0∼0.3, unlike the m=1 mode. The divergence of the plasma flow is locally not identical to zero with each species, ∇⋅V(s)≠0 (s=e,i), due to the electron spatial movement along the magnetic field. This internal structure results in a thick current layer and enhances the reconnection process. A plasmoid that impedes magnetic reconnection is created when the parallel mass diffusivity of electrons arising from their thermal motion is suppressed (the fluid limit). The reconnection rate becomes a smoothly increasing function of the ion mass and an inverse of the toroidal magnetic field, the latter of which being due to the compressional effect. The rate is drastically reduced when the ion Larmor radius far exceeds the ion skin depth.

Ion-controlled collisionless magnetic reconnection.

A theory of fast collisionless reconnection is presented. Because of the Hall term in Ohm's law, electron and ion dynamics decouple on scales smaller than the ion inertial length $\frac{c}{{\ensuremath{\omega}}_{\mathrm{pi}}}$. Though reconnection requires electron inertia to break the frozen-flux constraint, the rate is essentially independent of the electron mass. Instead, ion inertia controls the reconnection rate, which is strongly enhanced compared to previous estimates in which Hall effects were neglected.