Reconnection Diffusion Research Articles

Magnetospheric Multiscale Science Mission Profile and Operations

Abstract The Magnetospheric Multiscale (MMS) mission and operations are designed to provide the maximum reconnection science. The mission phases are chosen to investigate reconnection at the dayside magnetopause and in the magnetotail. At the dayside, the MMS orbits are chosen to maximize encounters with the magnetopause in regions where the probability of encountering the reconnection diffusion region is high. In the magnetotail, the orbits are chosen to maximize encounters with the neutral sheet, where reconnection is known to occur episodically. Although this targeting is limited by engineering constraints such as total available fuel, high science return orbits exist for launch dates over most of the year. The tetrahedral spacecraft formation has variable spacing to determine the optimum separations for the reconnection regions at the magnetopause and in the magnetotail. In the specific science regions of interest, the spacecraft are operated in a fast survey mode with continuous acquisition of burst mode data. Later, burst mode triggers and a ground-based scientist in the loop are used to determine the highest quality data to downlink for analysis. This operations scheme maximizes the science return for the mission.

Observation of directional change of core field inside flux ropes within one reconnection diffusion region in the Earth’s magnetotail

Two consecutive magnetic flux ropes, sepa- rated by less than 30 s (Dt \ 30 s), are observed within one magnetic reconnection diffusion region without strong guide field in the Earth's magnetotail by Cluster multi- spacecraft. The flux ropes are characterized by bipolar signatures of the south-north magnetic field component Bz accompanied with strong core magnetic field By, intense current J and density depletions inside of them. In spite of the small but non-trivial global scale negative guide field (-By), there exists a directional change of the core fields of two flux ropes, i.e., -By for the first one, and ?By for the second one. The directions of the core fields are the same as the ambient cross-tail magnetic field component (By) just outside of flux ropes. Therefore, we suggest that the core field of flux ropes is formed by compression of the local preexisting By and that the directional change of core field is due to the change of local preexisting By. Such a change in ambient By might be caused by some microscale physics.

Superdiffusion revisited in view of collisionless reconnection

Abstract. The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail during reconnection is reexamined making use of the division of particle orbits into waiting orbits and break-outs into ballistic motion lying at the bottom, for instance, of Lévy flights. The rms average displacement in this case increases with time, describing superdiffusion, though faster than classical, is still a weak process, being however strong enough to support fast reconnection. Referring to two kinds of numerical particle-in-cell simulations we determine the anomalous diffusion coefficient, the anomalous collision frequency on which the diffusion process is based, and construct a relation between the diffusion coefficients and the resistive scale. The anomalous collision frequency from electron pseudo-viscosity in reconnection turns out to be of the order of the lower-hybrid frequency with the latter providing a lower limit, thus making similar assumptions physically meaningful. Tentative though not completely justified use of the κ distribution yields κ ≈ 6 in the reconnection diffusion region and, for the anomalous diffusion coefficient, the order of several times Bohm diffusivity.

COMPLEXITY AND DIFFUSION OF MAGNETIC FLUX SURFACES IN ANISOTROPIC TURBULENCE

The complexity of magnetic flux surfaces is investigated analytically and numerically in static homogeneous magnetic turbulence. Magnetic surfaces are computed to large distances in magnetic fields derived from a reduced magnetohydrodynamic model. The question addressed is whether one can define magnetic surfaces over large distances when turbulence is present. Using a flux surface spectral analysis, we show that magnetic surfaces become complex at small scales, experiencing an exponential thinning that is quantified here. The computation of a flux surface is of either exponential or nondeterministic polynomial complexity, which has the conceptual implication that global identification of magnetic flux surfaces and flux exchange, e.g., in magnetic reconnection, can be intractable in three dimensions. The coarse-grained large-scale magnetic flux experiences diffusive behavior. The link between the diffusion of the coarse-grained flux and field-line random walk is established explicitly through multiple scale analysis. The Kubo number controls both large and small scale limits. These results have consequences for interpreting processes such as magnetic reconnection and field-line diffusion in astrophysical plasmas.

Observation and analysis of whistler-mode wave and electrostatic solitary waves within density depletion near magnetic reconnection X-line

The PWI/WFC data onboard Geotail during one burst time interval when Geotail is skimming a magnetic reconnection diffusion region in the near-Earth magnetotail is carefully analyzed. Both the whistler-mode wave and the electrostatic solitary wave are found within the region with density depletion on the boundary layer near the magnetic reconnection X-line. The whistler-mode wave is electromagnetic whistler wave propagating quasi-parallel to the ambient field with a small angle between the wave vector and the ambient magnetic field. The whistler-mode wave associated with ESWs suggests that enhanced electromagnetic whistler-mode fluctuations can also be generated after the decay of the ESWs, which is different from the 2-D PIC simulation results.

Reconnection Diffusion in Turbulent Fluids and Its Implications for Star Formation

Astrophysical fluids are turbulent a fact which changes the dynamics of many key processes, including magnetic reconnection. Fast reconnection of magnetic field in turbulent fluids allows the field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. Plasma associated with a given magnetic field line at one instant is distributed along a different set of magnetic field lines at the next instant. This diffusion of plasmas and magnetic field is enabled by reconnection and therefore is termed “reconnection diffusion”. The astrophysical implications of this concept include heat transfer in plasmas, advection of heavy elements in interstellar medium, magnetic field generation etc. However, the most dramatic implications of the concept are related to the star formation process. The reason is that magnetic fields are dynamically important for most of the stages of star formation. The existing theory of star formation has been developed ignoring the possibility of reconnection diffusion. Instead, it appeals to the decoupling of mass and magnetic field arising from neutrals drifting in respect to ions entrained on magnetic field lines, i.e. through the process that is termed “ambipolar diffusion”. The predictions of ambipolar diffusion and reconnection diffusion are very different. For instance, if the ionization of media is high, ambipolar diffusion predicts that the coupling of mass and magnetic field is nearly perfect. At the same time, reconnection diffusion is independent of the ionization but depends on the scale of the turbulent eddies and on the turbulent velocities. In the paper we explain the physics of reconnection diffusion both from macroscopic and microscopic points of view, i.e. appealing to the reconnection of flux tubes and to the diffusion of magnetic field lines. We make use of the Lazarian and Vishniac (Astrophys. J. 517:700, 1999) theory of magnetic reconnection and show that this theory is applicable to the partially ionized gas. We quantify the reconnection diffusion rate both for weak and strong MHD turbulence and address the problem of reconnection diffusion acting together with ambipolar diffusion. In addition, we provide a criterion for correctly representing the magnetic diffusivity in simulations of star formation. We discuss the intimate relation between the processes of reconnection diffusion, field wandering and turbulent mixing of a magnetized media and show that the role of the plasma effects is limited to “breaking up lines” on small scales and does not affect the rate of reconnection diffusion. We address the existing observational results and demonstrate how reconnection diffusion can explain the puzzles presented by observations, in particular, the observed higher magnetization of cloud cores in comparison with the magnetization of envelopes. We also outline a possible set of observational tests of the reconnection diffusion concept and discuss how the application of the new concept changes our understanding of star formation and its numerical modeling. Finally, we outline the differences of the process of reconnection diffusion and the process of accumulation of matter along magnetic field lines that is frequently invoked to explain the results of numerical simulations.

Dipolarization fronts as a consequence of transient reconnection: In situ evidence

Dipolarization fronts (DFs) are frequently detected in the Earth's magnetotail from XGSM = −30 RE to XGSM = −7 RE. How these DFs are formed is still poorly understood. Three possible mechanisms have been suggested in previous simulations: (1) jet braking, (2) transient reconnection, and (3) spontaneous formation. Among these three mechanisms, the first has been verified by using spacecraft observation, while the second and third have not. In this study, we show Cluster observation of DFs inside reconnection diffusion region. This observation provides in situ evidence of the second mechanism: Transient reconnection can produce DFs. We suggest that the DFs detected in the near‐Earth region (XGSM > −10 RE) are primarily attributed to jet braking, while the DFs detected in the mid‐ or far‐tail region (XGSM < −15 RE) are primarily attributed to transient reconnection or spontaneous formation. In the jet‐braking mechanism, the high‐speed flow “pushes” the preexisting plasmas to produce the DF so that there is causality between high‐speed flow and DF. In the transient‐reconnection mechanism, there is no causality between high‐speed flow and DF, because the frozen‐in condition is violated.

THE COLLAPSE OF TURBULENT CORES AND RECONNECTION DIFFUSION

For a molecular cloud clump to form stars some transport of magnetic flux is required from the denser, inner regions to the outer regions of the cloud, otherwise this can prevent the collapse. Fast magnetic reconnection which takes place in the presence of turbulence can induce a process of reconnection diffusion (RD). Extending earlier numerical studies of reconnection diffusion in cylindrical clouds, we consider more realistic clouds with spherical gravitational potentials and also account for the effects of the gas self-gravity. We demonstrate that within our setup RD is efficient. We have also identified the conditions under which RD becomes strong enough to make an initially subcritical cloud clump supercritical and induce its collapse. Our results indicate that the formation of a supercritical core is regulated by a complex interplay between gravity, self-gravity, the magnetic field strength and nearly transonic and trans-Alfv\'enic turbulence, confirming that RD is able to remove magnetic flux from collapsing clumps, but only a few of them become nearly critical or supercritical, sub-Alfv\'enic cores, which is consistent with the observations. Besides, we have found that the supercritical cores built up in our simulations develop a predominantly helical magnetic field geometry which is also consistent with observations. Finally, we have evaluated the effective values of the turbulent reconnection diffusion coefficient and found that they are much larger than the numerical diffusion, especially for initially trans-Alfv\'enic clouds, ensuring that the detected magnetic flux removal is due to to the action of the RD rather than to numerical diffusivity.

Explosive Turbulent Magnetic Reconnection

We report simulation results for turbulent magnetic reconnection obtained using a newly developed Reynolds-averaged magnetohydrodynamics model. We find that the initial Harris current sheet develops in three ways, depending on the strength of turbulence: laminar reconnection, turbulent reconnection, and turbulent diffusion. The turbulent reconnection explosively converts the magnetic field energy into both kinetic and thermal energy of plasmas, and generates open fast reconnection jets. This fast turbulent reconnection is achieved by the localization of turbulent diffusion. Additionally, localized structure forms through the interaction of the mean field and turbulence.

Statistics of the tripolar electrostatic solitary waves within magnetic reconnection diffusion region in the near‐Earth magnetotail

In this paper, we report the observations and statistical characteristics of tripolar electrostatic solitary waves (ESWs) along the plasma sheet boundary layer near the magnetic reconnection X line in the near‐Earth magnetotail. Within reconnection diffusion region, the tripolar ESWs are ample and are continuously observed during one burst interval (8.75 s) of the Geotail/WaveForm Capture in the neutral plasma sheet where β > 1 on 10:20 UT, 2 February 1996. The tripolar ESW is suggested to be one kind of steady‐going solitary structure. More than 200 waveforms with clear tripolar characteristics are differentiated for statistical analysis, and result shows that (1) their amplitude is within 100–>500 μV/m, with an average amplitude of about 254 μV/m; (2) the pulse width of the tripolar ESWs is 0.5–1.0 ms, with an average value of about 0.75 ms; (3) it is asymmetrical in both the amplitude and pulse width of the tripolar ESWs: most part of the tripolar ESWs (about 76.5%) are asymmetrical in the amplitude of one hump and the other one, and more than 75% (about 177 amount the 236 waveforms) of the tripolar ESWs are asymmetrical in the time duration of the two humps in the waveform; (4) most of the tripolar ESWs are with the potential humps of 10–60 mV, small ratio of them with potential humps larger than 100 mV. The tripolar ESWs with net potential drop of about 10–50 mV can be interpreted as “weak” double layers. The possible generation mechanism of tripolar ESWs and their role in reconnection are discussed by studying the particle distribution during which the tripolar ESWs are continuously observed. The observation of tripolar ESWs presents evidence of complex structure of electron holes within the reconnection diffusion region and is helpful to the understanding of the energy release process of reconnection.

Slow magnetosonic waves detected in reconnection diffusion region in the Earth's magnetotail

We studied the ULF waves with a period of 30 s in the ion diffusion region of reconnection observed by Cluster satellites on 21 August 2002. The fast convective tailward ion flow accompanied with a large southward magnetic field component, a strong Hall magnetic field, and a Hall electric field demonstrates that the Cluster satellites are located in the ion diffusion region of reconnection. The analyses of wave properties using minimum variance analysis and timing method indicate that this wave is an obliquely propagating slow magnetosonic wave which is characterized by the anti phase relation between the magnitude of the magnetic field and the ion number density and by a propagation angle of around 130° with respect to the ambient magnetic field. This wave is generated by periodic magnetic reconnection. The periodic oscillations in the By and Bx components are driven by the periodic Hall current system, while the oscillation in the Bz component is driven by quasiperiodic convective tailward ion flows. The slow magnetosonic wave significantly influences the frequency of whistler waves and low hybrid waves excited by magnetic reconnection by changing the magnitude of the local magnetic field and subsequently the electron cyclotron frequency.

Mapping HF waves in the reconnection diffusion region

We study in detail high‐frequency (HF) plasma waves between the electron cyclotron and plasma frequencies within a reconnection diffusion region (DR) encountered by Cluster in the magnetotail using continuous electric field waveforms. We identify three wave types, all observed within the separatrix regions: Langmuir waves (LW), electrostatic solitary waves (ESWs), and electron cyclotron waves (ECWs). This is the first time the ECWs have been observed inside this region. Direct comparison between waveforms and electron distributions are made at the timescale of one energy sweep of the electron detector (125 ms). Based on the wave and electron distribution characteristics, we find that the separatrix region has a stratified spatial structure. The outer part of the region is dominated by LW emissions related to suprathermal electron beams propagating away from the X‐line. Furthest in, nearest to the current sheet, we observe ESWs associated with counterstreaming electron populations. Studying HF waveforms allows for a precise mapping of kinetic boundaries in the reconnection region and helps to improve our understanding of the electron dynamics in the DR.

Propagation and dispersion of whistler waves generated by fast reconnection onset

The role of whistler mode during the onset of magnetic reconnection (MR) has been widely suggested, but the manifestations of its highly dispersive and anisotropic propagation properties in reconnection events remain largely unclear. Comparing results from a recently developed theoretical model for reconnection in terms of whistler's dispersive behavior with those reported from laboratory experiments on fast spontaneous magnetic reconnection, we demonstrate that the onset of fast reconnection in electron current layers (ECLs) emits whistler wave packets. The time scale of the explosively fast reconnection events are inversely related to the whistler mode frequencies at the lower end of the whistler frequency band. The wave packets in this frequency band have a characteristic angular dispersion, which marks the initial opening of the reconnection exhaust angle. The multidimensional propagation of the whistler for the reconnection with a strong guide magnetic field is investigated, showing that the measured propagation velocities of the reconnection electric field along the guide field in the Versatile Toroidal Facility at MIT quantitatively compare with the group velocities of the whistler wave packets. The whistler mode dispersive properties measured in laboratory experiments without a guide magnetic field in the magnetic reconnection experiments at Princeton also compare well with the theoretically predicted dispersion of the wave packets depending on the ECL width. Fast normalized reconnection rates extending to ∼0.35 at the MR onset in thin ECLs imply whistler wave propagation away from the onset location. We also present evidences for the whistler wave packets being emitted from reconnection diffusion region as seen in simulations and satellite observations.

Disc formation in turbulent cloud cores: is magnetic flux loss necessary to stop the magnetic braking catastrophe or not?

Recent numerical analysis of Keplerian disc formation in turbulent, magnetized cloud cores by Santos-Lima et al. demonstrated that reconnection diffusion is an efficient process to remove the magnetic flux excess during the buildup of a rotationally supported disc. This process is induced by fast reconnection of the magnetic fields in a turbulent flow. In a similar numerical study, Seifried et al. concluded that reconnection diffusion or any other non-ideal magnetohydrodynamic effects would not be necessary and turbulence shear alone would provide a natural way to build up a rotating disc without requiring magnetic flux loss. Their conclusion was based on the fact that the mean mass-to-flux ratio (μ) evaluated over a spherical region with a radius much larger than the disc is nearly constant in their models. In this paper, we compare the two sets of simulations and show that this averaging over large scales can mask significant real increases of μ in the inner regions where the disc is built up. We demonstrate that turbulence-induced reconnection diffusion of the magnetic field happens in the initial stages of the disc formation in the turbulent envelope material that is accreting. Our analysis is suggestive that reconnection diffusion is present in both sets of simulations and provides a simple solution for the ‘magnetic braking catastrophe’ which is discussed in the literature in relation to the formation of protostellar accretion discs.

Large Bi-Polar Signature in a Perpendicular Electric Field of Two-Dimensional Electrostatic Solitary Waves Associated with Magnetic Reconnection: Statistics and Discussion

More than 300 electrostatic solitary waves (ESWs) with a large perpendicular component which is a bi-polar waveform structure are observed in the boundary layer within the magnetic reconnection diffusion region in the near-Earth magnetotail. Such ESWs are called two-dimensional ESWs. A Singe-reconnection-based-statistical study of two-dimensional ESWs shows that: (1) ESWs can be continuously observed in the plasma sheet boundary layer (PSBL) associated with the magnetic reconnection diffusion region, and their amplitude ranges are mainly from several tens to hundreds of μV/m; (2) both one-dimension-like ESWs (very small magnitude on E⊥) and two-dimension-like ESWs (large magnitude on E⊥, which are even comparable to that in the E‖) are observed within a small time interval; (3) within the observation time spans, more than 61% of ESWs are regarded as two-dimensional ESWs for the I2D > 20%. We discuss the bi-polar structure in E⊥. The observation of ESWs with a large bi-polar structure in the perpendicular electric field gives evidence that the unique waveform differs from previous understanding from observations and simulations which suggests that it should be a uni-polar waveform structure in the E⊥ of ESWs.

MAGNETIZATION OF CLOUD CORES AND ENVELOPES AND OTHER OBSERVATIONAL CONSEQUENCES OF RECONNECTION DIFFUSION

Recent observational results for magnetic fields in molecular clouds reviewed by Crutcher (2012) seem to be inconsistent with the predictions of the ambipolar diffusion theory of star formation. These include the measured decrease in mass to flux ratio between envelopes and cores, the failure to detect any self-gravitating magnetically subcritical clouds, the determination of the flat PDF of the total magnetic field strengths implying that there are many clouds with very weak magnetic fields, and the observed scaling $B \propto \rho^{2/3}$ that implies gravitational contraction with weak magnetic fields. We consider the problem of magnetic field evolution in turbulent molecular clouds and discuss the process of magnetic field diffusion mediated by magnetic reconnection. For this process that we termed "reconnection diffusion" we provide a simple physical model and explain that this process is inevitable in view of the present day understanding of MHD turbulence. We address the issue of the expected magnetization of cores and envelopes in the process of star formation and show that reconnection diffusion provides an efficient removal of magnetic flux that depends only on the properties of MHD turbulence in the core and the envelope. As a result, the magnetic flux trapped during the collapse in the envelope is being released faster than the flux trapped in the core, resulting in much weaker fields in envelopes than in cores, as observed. We provide simple semi-analytical model calculations which support this conclusion and qualitatively agree with the observational results. We argue that magnetic reconnection provides a solution to the magnetic flux problem of star formation that agrees better with observations than the long-standing ambipolar diffusion paradigm.

Electron acceleration in the reconnection diffusion region: Cluster observations

We present one case study of magnetic islands and energetic electrons in the reconnection diffusion region observed by the Cluster spacecraft. The cores of the islands are characterized by strong core magnetic fields and density depletion. Intense currents, with the dominant component parallel to the ambient magnetic field, are detected inside the magnetic islands. A thin current sheet is observed in the close vicinity of one magnetic island. Energetic electron fluxes increase at the location of the thin current sheet, and further increase inside the magnetic island, with the highest fluxes located at the core region of the island. We suggest that these energetic electrons are firstly accelerated in the thin current sheet, and then trapped and further accelerated in the magnetic island by betatron and Fermi acceleration.

Magnetotail dipolarization front and associated ion reflection: Particle‐in‐cell simulations

For the Earth magnetotail, the Svenes et al. (2008) statistical study infers the lobe density to be highly variable, in the range of 0.007–0.092 cm−3. Such lobe density variation modifies reconnection diffusion region physical processes and reconnection rate drastically. This letter addresses observable reconnection signatures in the vicinity of the X‐line that are to be affected by the dynamic changes of reconnection. Using a 2.5D particle‐in‐cell (PIC) code, we find the dipolarization front (DF) a moving ram that pushes the initial equilibrium plasma sheet in front of it. The DF propagation velocity scales with the upstream Alfvén speed, leading to faster, steeper, and more compressed DFs with strongerBz at low lobe densities. These DFs reflect plasma sheet ions in a streaming manner. The streaming ions create a bipolar magnetic field straddling the central plasma sheet and can excite various instabilities.

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

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

Electron pitch angle distribution during magnetic reconnection diffusion region observations in the Earth's magnetotail

Abstract. The Earth's magnetosphere provides an excellent laboratory for magnetic reconnection research. In particular, the magnetotail current sheet that is formed between the interface of the similar Northern and Southern Hemispheres of the magnetotail provides a relatively stable symmetric reconnection configuration that can be used to study basic aspects of the reconnection process. Of particular importance is the manner in which electrons are processed by the reconnection. Simulations and satellite data analyses of the ion diffusion region have suggested that the fluxes of electrons in the inflow regions of reconnection are greater in the directions parallel and anti-parallel to the magnetic field (field-aligned) whereas the electron flux in the outflow region is distributed more isotropically. However, this has only been studied experimentally on a case-by-case basis. In this paper, we investigate this claim by analyzing the degree of bulk electron field alignment in the outflow and inflow regions during encounters of the magnetic reconnection ion diffusion region by the Cluster spacecraft in the years 2001–2006. We demonstrate that while the median electron flux in the inflow region is indeed more field aligned than in the outflow region during some ion diffusion region encounters, the variation of the signature across events is so large that it cannot be said to be a general feature of magnetic reconnection in the Earth's magnetotail.