Time‐dependent magnetic annihilation at a stagnation point

The basic plasma processes associated with magnetic reconnection in the Earth's magnetosphere are studied in our proposed project. In the past year, several problems associated with the 2-D and 3-D nonlinear reconnection processes were investigated. A new theory for nonlinear fast steady-state magnetic reconnection is proposed. The inflow region possesses highly curved magnetic field lines, which differs from that in the classical model of Petschek. A separatrix jet of plasma is ejected from the central diffusion region along the magnetic separatrix. Two types of outflow are studied, the simplest one possessing a potential outflow magnetic field and the other containing weak standing shock waves attached to the ends of the diffusion region. Across the separatrix jet, the outflow can be either slowed down by the fast-mode shocks or speeded up by the slow-mode shocks, depending on the downstream boundary conditions. In the 3-D MHD simulations, frayed magnetic flux ropes are found to be formed during the dayside magnetic reconnection process. Strong flux rope-aligned plasma flows are observed. Simulations of the driven reconnection process also indicate that the focusing of the Poynting flux has an important effect on the onset of reconnection and the location of reconnection sites.

A new theory for fast steady-state magnetic reconnection is proposed that includes many features of recent numerical experiments. The inflow region differs from that in the classical model of Petschek (1964) and the unified linear solutions of Priest & Forbes (1986) in possessing highly curved magnetic field lines rather than ones that are almost straight. A separatrix jet of plasma is ejected from the central diffusion region along the magnetic separatrix. Two types of outflow are studied, the simplest possessing an outflow magnetic field that is potential. The other contains weak standing shock waves attached to the ends of the diffusion region and either slowing down the flow (fast-mode shock) after it crosses the separatrix jet or speeding it up (slow-mode), depending on the downstream boundary conditions. A spike of reversed current slows down the plasma that emerges rapidly from the diffusion region into the more slowly moving downstream region, and diverts most of it along the separatrix jets. In the simplest case the outflow possesses no vorticity over most of the downstream region. The models demonstrate that both upstream and downstream boundary conditions are important in determining which regime of reconnection is produced from a wide variety of possibilities.

Magnetic reconnection is a fundamental plasma process responsible for the sometimes explosive release of magnetic energy in space and laboratory plasmas. Inside the diffusion regions of magnetic reconnection, the plasma becomes demagnetized and decouples from the magnetic field, enabling the change in magnetic topology necessary to power the energy release over larger scales. Since it was launched in 2015, the Magnetospheric MultiScale (MMS) mission has significantly advanced the understanding of the particle dynamics key to magnetic reconnection by providing high-resolution, in-situ measurements able to resolve ion and electron kinetic scales that have confirmed theoretical predictions, revealed new phenomena, and refined existing models. These breakthroughs are critical for understanding not only space plasmas but also laboratory and astrophysical plasmas where magnetic reconnection occurs. In this talk, we give a brief review and present some recent results of selected topics related to the ion and electron dynamics occurring within the diffusion regions.

<p>The localized crustal magnetic anomalies scattered across the surface Mars create a unique, hybrid magnetosphere. Over regions of strong crustal magnetism (100-1000 nT at the surface), the crustal anomalies protrude up to thousands of kilometers in space and a create a “mini-magnetospheric” interaction with the draped interplanetary magnetic field (IMF). One consequence of this interaction is the occurrence of discrete aurora on the nightside of Mars via electron precipitation and energy deposition into the planet’s atmosphere stimulating light emission (<em>Bertaux et al.,</em> 2005). Discrete auroral emissions from electron impact with atmospheric CO<sub>2</sub> in the mid ultra-violet have been observed via the Imaging Ultra-Violet Spectrograph (IUVS) instrument onboard the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft. These emissions have been preferentially observed over the region of strong crustal magnetism in the southern hemisphere (~153°-213° E longitude, 30°S-70°S latitude) and favor “open” magnetic field lines (i.e., one end connected to the IMF, the other connected to the planet) (<em>Schneider et al., </em>2021). These trends suggest discrete aurora at Mars may form via magnetic reconnection between the strong crustal anomalies and the draped IMF around the planet. Magnetic reconnection is a process that can “open-up” the closed crustal magnetic fields at Mars and accelerate electrons along these magnetic field lines. However, there has yet to be a study that links these two phenomena directly, and as a result, our understanding of discrete auroral formation at Mars remains poorly understood.</p> <p><img src="" alt="" /></p> <p>In this study, we uncover the relationship between magnetic reconnection and discrete aurora at Mars by analyzing the draped magnetic field conditions during 78 discrete auroral emissions observed via nadir observations taken by the IUVS within the region of strong crustal fields. First, we simplify the crustal field region into its two primary constituents: one crustal anomaly that is positioned in the northern half of the region and closes northward, and one crustal anomaly that is positioned in the southern half of the region and closes southward (Figure <strong>1</strong>). We note that the discrete auroral emissions tend to fall on the “footprints” of the two crustal anomalies where the dominant component of the crustal magnetic field points radially into or out of the planet. Two plasma regimes are more susceptible to reconnection when their magnetic field orientations are anti-parallel to one another. Therefore, we hypothesize that if crustal field-draped IMF magnetic reconnection plays a role in discrete auroral formation over the strong crustal anomalies at Mars, then a southward draped IMF would activate auroral emissions over the northern crustal anomaly and a northward draped IMF would activate auroral emissions over the southern crustal anomaly.</p> <p><img src="" alt="" /></p> <p>We estimate the orientation of the draped magnetic field over this region of strong crustal magnetism using data obtained from the magnetometer instrument onboard MAVEN along the same orbit in a discrete auroral emission was detected by IUVS. We find that the estimated orientation of the draped magnetic field associated with each discrete auroral event shows a regional dependence consistent with our hypothesis: discrete auroral emissions over the footprints of the northern anomaly are associated with southward draped fields, and emissions over the footprints of the southern anomaly are associated with northward draped fields (Figure <strong>2</strong>). We also demonstrate that these findings hold implications for other trends reported in previous studies of discrete aurora over this region of crustal fields, namely a trend in local time and upstream IMF conditions. This study is the first to more definitively link magnetic reconnection to discrete aurora formation on the nightside of Mars.</p> <p>Bertaux, J., F. Leblanc, O. Witasse, E. Quemerais, J. Lilensten, S. Stern, B. Sandel, and O. Korablev (2005), Discovery of an aurora on Mars, Nature, 435(7043), 790-794.</p> <p>Schneider, N., et al. (2021), Discrete Aurora on Mars: Insights Into Their Distribution and Activity From MAVEN/IUVS Observations, Journal of Geophysical Research-Space Physics, 126(10).</p>

The question about the interpretation of numerical experiments on magnetic reconnection in solar flares is considered. A correspondence between the standard classification of magnetohydrodynamic discontinuities and the parameters characterizing the mass flux through a discontinuity and the magnetic field configuration has been established within a classical formulation of the problem on discontinuous magnetohydrodynamic flows. A pictorial graphical representation of the relationship between the angles of the magnetic field vector relative to the normal to the discontinuity plane on both its sides has also been found. The relations between the parameters of a two-dimensional discontinuous flow have the simplest form in a frame of reference where the magnetic field lines (B) are parallel to the matter velocity (u)—the deHoffmann-Teller frame. The question about the transformation of the magnetic field configuration when passing to a “laboratory” frame of reference where (v · B) ≠ 0, i.e., an electric field is present, is considered in this connection. The result is applied to the analytical solution of the problem on the magnetic field structure in the vicinity of a reconnecting current sheet obtained previously by Bezrodnykh et al. The regions of nonevolutionary shocks are shown to appear near the endpoints of a current sheet with reverse currents.

A magnetic field embedded in a perfectly conducting fluid preserves its topology for all times. Although ionized astrophysical objects, like stars and galactic disks, are almost perfectly conducting, they show indications of changes in topology, magnetic reconnection, on dynamical time scales. Reconnection can be observed directly in the solar corona, but can also be inferred from the existence of large scale dynamo activity inside stellar interiors. Solar flares and gamma ray busts are usually associated with magnetic reconnection. Previous work has concentrated on showing how reconnection can be rapid in plasmas with very small collision rates. Here we present numerical evidence, based on three dimensional simulations, that reconnection in a turbulent fluid occurs at a speed comparable to the rms velocity of the turbulence, regardless of the value of the resistivity. In particular, this is true for turbulent pressures much weaker than the magnetic field pressure so that the magnetic field lines are only slightly bent by the turbulence. These results are consistent with the proposal by Lazarian & Vishniac (1999) that reconnection is controlled by the stochastic diffusion of magnetic field lines, which produces a broad outflow of plasma from the reconnection zone. This work implies that reconnection in a turbulent fluid typically takes place in approximately a single eddy turnover time, with broad implications for dynamo activity and particle acceleration throughout the universe. In contrast, the reconnection in 2D configurations in the presence of turbulence depends on resistivity, i.e. is slow.

This work analyzes the Hall magnetohydrodynamics (HMHD) and magnetohydrodynamics (MHD) numerical simulations of a flaring solar active region as a test bed while idealizing the coronal Alfvén speed to be less by two orders of magnitude. HMHD supports faster magnetic reconnection and shows richer complexity in magnetic field line evolution compared to the MHD. The magnetic reconnections triggering the flare are explored by numerical simulations augmented with relevant multiwavelength observations. The initial coronal magnetic field is constructed by non-force-free extrapolation of photospheric vector magnetic field. Magnetic structure involved in the flare is identified to be a flux rope, with its overlying magnetic field lines constituting the quasi-separatrix layers (QSLs) along with a three-dimensional null point and a null line. Compared to the MHD simulation, the HMHD simulation shows a higher and faster ascent of the rope together with the overlying field lines, which further reconnect at the QSL located higher up in the corona. The footpoints of the field lines match better with the observations for the HMHD case, with the central part of the flare ribbon located at the chromosphere. Additionally, field lines are found to rotate in a circular pattern in the HMHD, whereas no such rotation is seen in the MHD results. Interestingly, plasma is also observed to be rotating in a cospatial chromospheric region, which makes the HMHD simulation more credible. Based on the aforementioned agreements, HMHD simulation is found to agree better with observations and thus opens up a novel avenue to explore.

Some comments are made about how to determine the speed with which magnetic flux is carried towards an X-type neutral point and reconnected. Conditions in the diffusion region near the neutral point are also investigated, with the conclusion that the streamlines and magnetic field lines cannot both be locally hyperbolic. Instead, two distinct modes may be possible. In the first, the magnetic field lines are straight, and the diffusion region does not differ greatly from that described by Parker (1963). In the second, the fluid velocity components increase cubically away from the neutral point with the result that, for a given reconnection rate, the diffusion region is typically five times greater than in the Parker model.

A topological model with magnetic reconnection at two separators in the corona is used to account for the recently discovered changes of the photospheric magnetic field in the active region NOAA 9077 during the July 14, 2000 flare. The model self-consistently explains the following observed effects: (1) the magnetic field strength decreases on the periphery of the active region but increases in its inner part near the neutral line of the photospheric magnetic field; (2) the center-of-mass positions of the fields of opposite (northern and southern) polarities converge; and (3) the magnetic flux of the active region decreases after the flare. The topological model gives not only a qualitative interpretation of the flare phenomena (the structure of the interacting magnetic fluxes in the corona, the location of the energy sources, the shape of the flare ribbons and kernels in the chromosphere and photosphere), but also correct quantitative estimates of the large-scale processes that form the basis for solar flares. The electric field emerging in the flare during large-scale reconnection is calculated. The electric field strength correlates with the observed intensity of the hard X-ray bremsstrahlung, suggesting an electron acceleration as a result of reconnection.

Magnetic reconnection is a fundamental process that is important for the dynamical evolution of highly conducting plasmas throughout the Universe. In such highly conducting plasmas the magnetic topology is preserved as the plasma evolves, an idea encapsulated by Alfvén’s frozen flux theorem. In this context, “magnetic topology” is defined by the connectivity and linkage of magnetic field lines (streamlines of the magnetic induction) within the domain of interest, together with the connectivity of field lines between points on the domain boundary. The conservation of magnetic topology therefore implies that magnetic field lines cannot break or merge, but evolve only according to smooth deformations. In any real plasma the conductivity is finite, so that the magnetic topology is not preserved everywhere: magnetic reconnection is the process by which the field lines break and recombine, permitting a reconfiguration of the magnetic field. Due to the high conductivity, reconnection may occur only in small dissipation regions where the electric current density reaches extreme values. In many applications of interest, the change of magnetic topology facilitates a rapid conversion of stored magnetic energy into plasma thermal energy, bulk-kinetic energy, and energy of non-thermally accelerated particles. This energy conversion is associated with dynamic phenomena in plasmas throughout the Universe. Examples include flares and other energetic phenomena in the atmosphere of stars including the Sun, substorms in planetary magnetospheres, and disruptions that limit the magnetic confinement time of plasma in nuclear fusion devices. One of the major challenges in understanding reconnection is the extreme separation between the global system scale and the scale of the dissipation region within which the reconnection process itself takes place. Current understanding of reconnection has developed through mathematical and computational modeling as well as dedicated experiments in both the laboratory and space. Magnetohydrodynamic (MHD) reconnection is studied in the framework of magnetohydrodynamics, which is used to study plasmas (and liquid metals) in the continuum approximation.

In previous work we used a semi‐analytical treatment to describe accelerated magnetosheath flows caused by the draping of interplanetary magnetic field (IMF) lines around the magnetosphere. Here, we use the same approach, i.e., modeling the magnetic field lines as elastic strings, to examine how the magnetic tension force, one of the two agents responsible for producing these flows, varies along field lines away from the equatorial plane. The bend in the field line caused by the draping mechanism propagates as two oppositely‐directed waves to higher latitudes. For a due northward IMF ‐ the case we consider here ‐ these propagate symmetrically north/south of the equatorial plane. As a result, a two‐peaked latitude velocity profile develops as we go further downtail and the velocity peaks migrate along the magnetic field line to higher latitudes. We examine this velocity‐profile for two Alfvén Mach numbers (MA = 8 and 3), representative of conditions in the solar wind at 1 AU (“normal” solar wind and solar transients). Qualitatively, the picture is the same but quantitatively there are important differences: (i) the flows reach higher values for the lower MA (maximum V/VSW = 1.6) than for the higher MA (V/VSW= 1.3); (ii) asymptotic values are reached farther downstream of the dawn‐dusk terminator for the lowerMA (∼−50 RE vs −15 RE); (iii) For the lower MAthe highest speeds are reached away from the equatorial plane. We predict two channels of fast magnetosheath flow next to the magnetopause at off‐equatorial latitudes that exceed the solar wind speed.

In two or three dimensions, magnetic reconnection may occur at neutral points and is accompanied by the transport of magnetic field lines across separatrices, the field lines (or flux surfaces in three dimensions) at which the mapping of field lines is discontinuous. Here we show that reconnection may also occur in three dimensions in the absence of neutral points at so‐called “quasi‐separatrix layers,” where there is a steep gradient in field line linkage. Reconnection is a global property, and so, in order to determine where it can occur, the first step is to enclose the volume being considered by a boundary (such as a spherical surface). Then the mapping of field lines from one part of the boundary to another is determined, and quasi‐separatrix layers may be identified as regions where the gradient of the mapping or its inverse is very much larger than normal. The most effective measure of the presence of such layers is the norm of the displacement gradient tensor; their qualitative location is robust and insensitive to the particular surface that is chosen. Reconnection itself occurs when there is a breakdown of ideal MHD and a change of connectivity of plasma elements, where the field line velocity becomes larger than the plasma velocity, so that the field lines slip through the plasma. This breakdown can occur in the quasi‐separatrix layers with an electric field component parallel to the magnetic field. In three dimensions the electric field E (and therefore the field line velocity v⊥) depends partly on the imposed values of E (or v⊥) at the boundary and partly on the gradients of the inverse mapping function. We show that the inverse mapping determines the location of the narrow layers where the breakdown of ideal MHD can occur, while the imposed boundary values of v⊥ determine mainly the detailed flow pattern inside the layers. Thus, in general, E (and therefore v⊥) becomes much larger than its boundary values at locations where the gradients of the inverse mapping function are large. An example is given of a sheared X field, where a slow smooth continuous shear flow imposed on the boundary across one quasi‐separatrix produces a flipping of magnetic field lines as they slip rapidly through the plasma in the other quasi‐separatrix layer. It results in a strong plasma jetting localized in, and parallel to, the separatrix layers.

We study student understanding of the direction of the magnetic force experienced by a charged particle moving through a homogeneous magnetic field in both the magnetic pole and field line representations of the magnetic field. In five studies, we administer a series of simple questions in either written or interview format. Our results indicate that although students begin at the same low level of performance in both representations, they answer correctly more often in the field line representation than in the pole representation after instruction. This difference is due in part to more students believing that charges are attracted to magnetic poles than believing that charges are pushed along magnetic field lines. Although traditional instruction is fairly effective in teaching students to answer correctly up to a few weeks following instruction, especially for the field line representation, some students revert to their initial misconceptions several months after instruction. The responses reveal persistent and largely random sign errors in the direction of the force. The sign errors are largely nonsystematic and due to confusion about the direction of the magnetic field and the execution and choice of the right-hand rule and lack of recognition of the noncommutativity of the cross product.

We consider stochastic reconnection in a magnetized, partially ionized medium. Stochastic reconnection is a generic effect, due to field line wandering, in which the speed of reconnection is determined by the ability of ejected plasma to diffuse away from the current sheet along magnetic field lines, rather than by the details of current sheet structure. We consider the limit of weak stochasticity, so that the mean magnetic field energy density is greater than either the turbulent kinetic energy density or the energy density associated with the fluctuating component of the field. We consider field line stochasticity generated through a turbulent cascade, which leads us to consider the effect of neutral drag on the turbulent cascade of energy. In a collisionless plasma, neutral particle viscosity and ion-neutral drag will damp mid-scale turbulent motions, but the power spectrum of the magnetic perturbations extends below the viscous cutoff scale. We give a simple physical picture of the magnetic field structure below this cutoff, consistent with numerical experiments. We provide arguments for the reemergence of the turbulent cascade well below the viscous cut-off scale and derive estimates for field line diffusion on all scales. We note that this explains the persistence of a single power law form for the turbulent power spectrum of the interstellar medium, from scales of tens of parsecs down to thousands of kilometers. We find that under typical conditions in the ISM stochastic reconnection speeds are reduced by the presence of neutrals, but by no more than an order of magnitude.

In three dimensions, magnetic reconnection may take place in a sheared magnetic field at any singular field line, where the nearby field has X‐type topology in planes perpendicular to the field line and where an electric field is present parallel to the field line. In the ideal region around the singular line there will, in general, be singularities in the plasma flow and electric field, both at the singular line and at “magnetic flipping layers,” which are remnants of local magnetic separatrices. In the absence of a three‐dimensional magnetic neutral point or null point, reconnection of field lines can still occur by a process of magnetic flipping, in which the plasma crosses the flipping layers but the field lines rapidly flip along them by magnetic diffusion. Depending on the boundary conditions, there may be two or four flipping layers which converge on the singular line. A boundary layer analysis of a flipping layer is given, in which the magnetic field parallel to the layer decreases as one crosses it while the plasma pressure (or magnetic pressure associated with the field along the singular line) increases. The width of the flipping layer decreases with distance from the singular line.