Time-dependent Magnetic Reconnection Research Articles

Analytical solutions for time-dependent kinematic three-dimensional magnetic reconnection.

Magnetic reconnection is a process that can rapidly convert magnetic field energy into plasma thermal energy and kinetic energy, and it is also an important energy conversion mechanism in space physics, astrophysics and plasma physics. Research related to analytical solutions for time-dependent three-dimensional magnetic reconnection is extremely difficult. For decades, several mathematical descriptions have been developed regarding different reconnection mechanisms, in which the equations based on magnetohydrodynamics theory outside the reconnection diffusion region are widely accepted. However, the equation set cannot be analytically solved unless specified constraints are imposed or the equations are reduced. Based on previous analytical methods for kinematic stationary reconnection, here the analytical solutions for time-dependent kinematic three-dimensional magnetic reconnection are discussed. In contrast to the counter-rotating plasma flows that existed in steady-state reconnection, it is found that spiral plasma flows, which have never been reported before, can be generated if the magnetic field changes exponentially with time. These analyses reveal new scenarios for time-dependent kinematic three-dimensional magnetic reconnection, and the deduced analytical solutions could improve our understanding of the dynamics involved in reconnection processes, as well as the interactions between the magnetic field and plasma flows during magnetic reconnection.

Onset of 2D magnetic reconnection in the solar photosphere, chromosphere, and corona

Aims. We aim to investigate the onset of 2D time-dependent magnetic reconnection that is triggered using an external (non-local) velocity driver located away from, and perpendicular to, an equilibrium Harris current sheet. Previous studies have typically utilised an internal trigger to initiate reconnection, for example initial conditions centred on the current sheet. Here, an external driver allows for a more naturalistic trigger as well as the study of the earlier stages of the reconnection start-up process. Methods. Numerical simulations solving the compressible, resistive magnetohydrodynamic (MHD) equations were performed to investigate the reconnection onset within different atmospheric layers of the Sun, namely the corona, chromosphere and photosphere. Results. A reconnecting state is reached for all atmospheric heights considered, with the dominant physics being highly dependent on atmospheric conditions. The coronal case achieves a sharp rise in electric field (indicative of reconnection) for a range of velocity drivers. For the chromosphere, we find a larger velocity amplitude is required to trigger reconnection (compared to the corona). For the photospheric environment, the electric field is highly dependent on the inflow speed; a sharp increase in electric field is obtained only as the velocity entering the reconnection region approaches the Alfvén speed. Additionally, the role of ambipolar diffusion is investigated for the chromospheric case and we find that the ambipolar diffusion alters the structure of the current density in the inflow region. Conclusions. The rate at which flux enters the reconnection region is controlled by the inflow velocity. This determines all aspects of the reconnection start-up process, that is, the early onset of reconnection is dominated by the advection term in Ohm’s law in all atmospheric layers. A lower plasma-β enhances reconnection and creates a large change in the electric field. A high plasma-β hinders the reconnection, yielding a sharp rise in the electric field only when the velocity flowing into the reconnection region approaches the local Alfvén speed.

Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD

The nonlinear, extended-magnetohydrodynamic (MHD) code NIMROD is benchmarked with the theory of time-dependent forced magnetic reconnection induced by small resonant fields in slab geometry in the context of visco-resistive MHD modeling. Linear computations agree with time-asymptotic, linear theory of flow screening of externally applied fields. The inclusion of flow in nonlinear computations can result in mode penetration due to the balance between electromagnetic and viscous forces in the time-asymptotic state, which produces bifurcations from a high-slip state to a low-slip state as the external field is slowly increased. We reproduce mode penetration and unlocking transitions by employing time-dependent externally applied magnetic fields. Mode penetration and unlocking exhibit hysteresis and occur at different magnitudes of applied field. We also establish how nonlinearly determined flow screening of the resonant field is affected by the square of the magnitude of the externally applied field. These results emphasize that the inclusion of nonlinear physics is essential for accurate prediction of the reconnected field in a flowing plasma.

On the periodicity of oscillatory reconnection

Oscillatory reconnection is a time-dependent magnetic reconnection mechanism that naturally produces periodic outputs from aperiodic drivers. This paper aims to quantify and measure the periodic nature of oscillatory reconnection for the first time. We solve the compressible, resistive, nonlinear MHD equations using 2.5D numerical simulations. We identify two distinct periodic regimes: the impulsive and stationary phases. In the impulsive phase, we find the greater the amplitude of the initial velocity driver, the longer the resultant current sheet and the earlier its formation. In the stationary phase, we find that the oscillations are exponentially decaying and for driving amplitudes 6.3 - 126.2 km/s, we measure stationary-phase periods in the range 56.3 - 78.9 s, i.e. these are high frequency (0.01 - 0.02 Hz) oscillations. In both phases, we find that the greater the amplitude of the initial velocity driver, the shorter the resultant period, but note that different physical processes and periods are associated with both phases. We conclude that the oscillatory reconnection mechanism behaves akin to a damped harmonic oscillator.

Reconstruction of the reconnection rate from Cluster measurements: Method improvements

[1] A remote-sensing method for reconstructing the reconnection rate and the location of X-line from single-spacecraft observations developed recently is extended to a compressible plasma and an asymmetric magnetic field configuration. The method is based on the two-dimensional analytical model of time-dependent Petschek-type magnetic reconnection. The reconstruction technique is applied to a nightside flux transfer event recorded by Cluster spacecraft in the near-Earth magnetotail on 26 September 2005. The reconnection rate is found to be 3.7–4.8 mV/m; the reconnection distance is around 9–11 Re in the tail.

Internal Shocks in the Magnetic Reconnection Jet in Solar Flares: Multiple Fast Shocks Created by the Secondary Tearing Instability

Space solar missions such as Yohkoh and RHESSI observe the hard X- and gamma-ray emission from energetic electrons in impulsive solar flares. Their energization mechanism, however, is unknown. In this Letter, we suggest that the internal shocks are created in the reconnection jet and that they are possible sites of particle acceleration. We examine how magnetic reconnection creates the multiple shocks by performing two-dimensional resistive magnetohydrodynamic simulations. In this Letter, we use a very small grid to resolve the diffusion region. As a result, we find that the current sheet becomes thin due to the tearing instability, and it collapses to a Sweet-Parker sheet. The thin sheet becomes unstable to the secondary tearing instability. Fast reconnection starts by the onset of anomalous resistivity immediately after the secondary tearing instability. During the bursty, time-dependent magnetic reconnection, the secondary tearing instability continues in the diffusion region where the anomalous resistivity is enhanced. As a result, many weak shocks are created in the reconnection jet. This situation produces turbulent reconnection. We suggest that multiple fast shocks are created in the jet and that the energetic electrons can be accelerated by these shocks.

A numerical model of the ionospheric signatures of time-varying magneticreconnection: I. ionospheric convection

Abstract. This paper presents a numerical model for predicting the evolution of the pattern of ionospheric convection in response to general time-dependent magnetic reconnection at the dayside magnetopause and in the cross-tail current sheet of the geomagnetic tail. The model quantifies the concepts of ionospheric flow excitation by Cowley and Lockwood (1992), assuming a uniform spatial distribution of ionospheric conductivity. The model is demonstrated using an example in which travelling reconnection pulses commence near noon and then move across the dayside magnetopause towards both dawn and dusk. Two such pulses, 8min apart, are used and each causes the reconnection to be active for 1min at every MLT that they pass over. This example demonstrates how the convection response to a given change in the interplanetary magnetic field (via the reconnection rate) depends on the previous reconnection history. The causes of this effect are explained. The inherent assumptions and the potential applications of the model are discussed. Key words. Ionosphere (ionosphere-magnetosphere interactions; plasma convection) – Magnetospheric physics (magnetosphere-ionosphere interactions; solar wind-magnetosphere interactions)

Time-dependent magnetic reconnection in two-dimensional periodic geometry

We compare the predictions of incompressible, analytic reconnection theory with numerical simulations performed using a time-dependent, doubly periodic code. The properties of the simulated current sheets are shown to be in good quantitative agreement with recent planar analytic reconnection solutions based on X-point merging driven by sheared incompressible flows. We conclude that the analytic treatment is not seriously compromised by assuming an open flow geometry and a one-dimensional current layer. The analytic models, when augmented by nonlinear saturation arguments, are also shown to provide resistive scaling laws that accord well with computed merging rates. By way of contrast, we have found no computational evidence for the osculation of separatrices in current sheets, even for the case of classical head-on reconnection in which all shearing flows are absent. We attribute this to the dynamic nature of the simulated current sheet. Our simulations provide some evidence that dynamic current sheets can break up into magnetic islands, but whether this fragmentation can be attributed to the tearing mode instability remains unclear.

Modified Magnetohydrodynamic Model of Magnetic Reconnection

This paper presents the modified magnetohydrodynamic (MHD) model and simulations of solar wind-magnetosphere interactions. We use the two-dimensional and three-component, compressible, resistive, ion gyroviscous and Hall MHD model, i.e., including the ion finite Larmor radius (FLR) and Hall MHD effects, but neglecting the electron inertia and electron FLR effects. The composed dynamic pressure pulses (shear variations in the flow velocity) in the solar wind form gusts that continually buffet the magnetosphere and cause the time-dependent magnetic reconnection at the magnetopause. The results show that the magnetic field and the flow velocity components perpendicular to the reconnection plane can be generated in magnetopause current layer. The vortical flow structures can also occur in the magnetospheric side region. These results are responsible for non-ideal MHD properties of the plasma fluid, i.e., ion FLR and Hall MHD effects.

Nonlinear evolution of magnetic islands in the magnetopause current sheet

Nonlinear evolution of magnetic islands produced by time-dependent magnetic reconnection in the magnetopause current sheet is studied. It is shown that the magnetic islands are unstable against the interference from external disturbances. Their structure can be destroyed by medium and small-scale solar wind turbulences, leading to stochastic magnetic reconnection and the formation of irregular small-scale structures in magnetospheric boundary regions.

Flux transfer events at the dayside magnetopause: Transient reconnection or magnetosheath dynamic pressure pulses?

The suggestion is discussed that characteristic particle and field signatures at the dayside magnetopause, termed “flux transfer events” (FTEs), are, in at least some cases, due to transient solar wind and/or magnetosheath dynamic pressure increases, rather than time‐dependent magnetic reconnection. It is found that most individual cases of FTEs observed by a single spacecraft can, at least qualitatively, be explained by the pressure pulse model, provided a few rather unsatisfactory features of the predictions are explained in terms of measurement uncertainties. The most notable exceptions to this are some “two‐regime” observations made by two satellites simultaneously, one on either side of the magnetopause. However, this configuration has not been frequently achieved for sufficient time, such observations are rare, and the relevant tests are still not conclusive. The strongest evidence that FTEs are produced by magnetic reconnection is the dependence of their occurrence on the north‐south component of the interplanetary magnetic field (IMF) or of the magnetosheath field. The pressure pulse model provides an explanation for this dependence (albeit qualitative) in the case of magnetosheath FTEs, but this does not apply to magnetosphere FTEs. The only surveys of magnetosphere FTEs have not employed the simultaneous IMF, but have shown that their occurrence is strongly dependent on the north‐south component of the magnetosheath field, as observed earlier/later on the same magnetopause crossing (for inbound/outbound passes, respectively). This paper employs statistics on the variability of the IMF orientation to investigate the effects of IMF changes between the times of the magnetosheath and FTE observations. It is shown that the previously published results are consistent with magnetospheric FTEs being entirely absent when the magnetosheath field is northward: all crossings with magnetosphere FTEs and a northward field can be attributed to the field changing sense while the satellite was within the magnetosphere (but close enough to the magnetopause to detect an FTE). Allowance for the IMF variability also makes the occurrence frequency of magnetosphere FTEs during southward magnetosheath fields very similar to that observed for magnetosheath FTEs. Conversely, the probability of attaining the observed occurrence frequencies for the pressure pulse model is 10−14. In addition, it is argued that some magnetosheath FTEs should, for the pressure pulse model, have been observed for northward IMF: the probability that the number is as low as actually observed is estimated to be 10−10. It is concluded that although the pressure model can be invoked to qualitatively explain a large number of individual FTE observations, the observed occurrence statistics are in gross disagreement with this model.

Time-dependent magnetic reconnection: Two- and three-dimensional MHD simulations

Observations of flux transfer events (FTEs) at the earth magnetospause and plasmoids in the magnetotail indicate that magnetic reconnections in the earth magnetosphere are time-dependent. Motivated by the observed flux transfer events, Lee and Fu proposed a multiple X-line reconnection (MXR) model for the dayside magnetopause. The multiple X-line reconnection is intrinsically a time-dependent process and is different from the classical single X-line reconnection (SXR) process. As a consequence of MXR, plasmoids or magnetic flux ropes are intermittently formed and convected out of the reconnection region. Two- and three-dimensional MHD simulations have been carried out to study the time-dependent magnetic reconnection process. The 2-D simulation results show that the time-dependent multiple X-line process tends to occur when the system length is long and the resistivity is small. Otherwise, the quasi-steady single X-line process takes place. It is found that the occurrence of multiple reconnection sites in the current sheet may be due to either (1) the development of tearing mode instability in the local slab model, or (2) the nonuniformity of the current sheet in the global model. In the three-dimensional case, the multiple X-line reconnection process leads to the formation of magnetic flux tubes or magnetic ropes. In the three-dimensional case, the field line topology at the ends of the magnetic rope is very complicated. The simulation shows that magnetic ropes formed through the MXR process usually have “frayed” ends. In addition, a strong tube-aligned plasma flow is observed during the formation of magnetic flux tubes in the 3-D simulation.