B. U. Ö. Sonnerup

Magnetic-field re-connexion in a highly conducting incompressible fluid

Model for magnetic field-line reconnection in conducting incompressible fluid, determining maximum reconnection rate entirely by null point conditions

Two‐dimensional coherent structures in the magnetopause: Recovery of static equilibria from single‐spacecraft data

A new technique for recovering magnetic field maps that describe two-dimensional, coherent field structures observed in space is documented, benchmarked, and then applied to four magnetopause crossings by the spacecraft AMPTE/IRM (Active Magnetospheric Particle Tracer Explorers/Ion Release Module) in which the basic observed signatures were those associated with a tangential discontinuity. The calculations required for the recovery consist of the numerical solution of the Grad-Shafranov equation, using as initial values magnetic field and plasma data collected by a single spacecraft along a straight-line trajectory, produced when structures are convected past it. The integration proceeds in small spatial steps in both directions away from the trajectory. The integration domain, which is rectangular, is limited in the transverse direction by the appearance of numerically generated singularities. Nevertheless, the method offers a substantial field of view of the region surrounding the trajectory, within which the accuracy is a few percent. For the magnetopause events examined, it is found that the simple tangential-discontinuity structure is modified by embedded strings of magnetic islands, separated by X-type nulls in the transverse field. These configurations are interpreted as being the result of the tearing mode after it has reached its saturated state. Two or more islands contained within larger islands are observed, indicating that, during the active phase of the tearing mode, the reconnection rate was not the same at all X points. The possibility exists that one dominant X point produces a pair of narrow channels of open flux, connecting the magnetosphere to the magnetosheath. Even without such open flux, the presence of the islands should allow flow of plasma along magnetic field lines, from the outermost (magnetosheath) to the innermost (magnetosphere) parts of the magnetopause current layer, thus facilitating the overall plasma transport across the layer.

Low‐latitude dayside magnetopause and boundary layer for high magnetic shear: 2. Occurrence of magnetic reconnection

Quantitative comparisons of the flow velocity change across the magnetopause (MP) with the prediction from local tangential stress balance in a one-dimensional time-stationary rotational discontinuity, that is, with the Walen relation, have been performed on 69 Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) low-latitude ( 45°) MP crossings. It is found that in 61% of the crossings the observed flow changes agree with the prediction to better than 50%. No dependence of the occurrence of reconnection flows on local magnetic shear, local time/latitude, local tangential magnetosheath flow speed, and local magnetosheath Alfven Mach number is found. We confirm an earlier result that the agreement with the Walen relation becomes worse with increasing magnetosheath plasma β (β is the ratio of plasma pressure to magnetic pressure) but find that the velocity change itself, predicted by the Walen relation, decreases with increasing β. Moreover, the motion and thickness of the boundary also depend on β: the higher the β value, the faster the speed and the smaller the thickness. These effects combine to make velocity changes in high β events more difficult to measure accurately, which may contribute to the poor agreement with the Walen relation in these events. The 42 events which exhibit plasma flows in reasonable agreement with the Walen relation include 21 cases where the flow direction is inconsistent with a single X line hinged at the subsolar point. The discrepancies between the former result arid dayside X line locations reported earlier may be due to a bias in selection of reconnection events in earlier studies. An average (dimensionless) reconnection rate that is substantially lower than 0.1 is inferred for the 42 events.

Reconstruction of magnetic flux ropes in the solar wind

We recover two-dimensional magnetic structures of small-scale flux ropes in the solar wind from WIND spacecraft data by solving the plane Grad-Shafranov equation as a spatial initial value problem. The cross-sections of two recovered flux ropes show nested non-circular loops of transverse field lines rather than concentric circles. The expected helical structure is recovered, albeit with significant distortions from axial symmetry. The rope structures are self-consistent, non-force free, magnetohydrostatic equilibria. Their orientations are determined by a novel technique.

The Magnetospheric Sash and the Cross‐Tail S

As revealed in MHD simulation, the magnetospheric sash is a band of weak magnetic field that, for the usual case in which the IMF is approximately perpendicular to the geomagnetic dipole, runs tailward along the high-latitude magnetopause flanks from one dayside cusp to the other, closing via the cross-tail neutral sheet. On the magnetopause flanks, it contains the magnetic separator line, at which all three topological types of field lines meet. Seen in a cross-sectional plane through the near-Earth tail, the magnetospheric sash takes the form of the cross-tail S, a weak-field feature comprised of the tail neutral sheet with diagonally symmetric extensions along the magnetopause flanks connecting it to the separator line. The cross-tail S is evident in the MHD results and in cross-sectional maps based on IMP 8 data. The magnetopause expression of the sash is latent in prior works that described the geometry of antiparallel fields across the magnetopause and the consequent cancellation of the fields within the magnetopause layer. The sash picture bears a strong resemblance to antiparallel merging geometry.

Error estimates for minimum variance analysis

Analytical estimates of errors, associated with random statistical noise in magnetic field and other data to which the minimum/maximum variance analysis technique is commonly applied, are derived from first principles. A systematic expansion procedure is used in which the expansion parameter is proportional to the noise amplitude and inversely proportional to the square root of the number of vector data samples, K. The two special cases where the signal-to-noise ratio is large and small are considered for arbitrary noise distributions. The ideal case of small errors and isotropic Gaussian noise allows determination of uncertainty cones of elliptic cross section for all three eigenvectors, x1, x2, x3, and uncertainty intervals for all three eigenvalues, λ1, λ2, λ3, of the variance matrix, all in terms of the eigenvalues themselves and the number of data points. Denoting the angular standard deviation (in radians) of vector xi toward or away from vector xj by Δϕij these results are Δϕij = ±[λ3(λi + λj − λ3)/(K − 1)(λi − λj)2]1/2 and Δλi = ±[2λ3(2λi − λ3)/(K − 1)]1/2 where λ3 is the smallest eigenvalue. The predictions from these formulas compare favorably with results from simple bootstrap numerical error analysis. Applications to maximum variance analysis of electric field data and to the study of anisotropic plasma pressure tensors are discussed as special cases.

Global role of E ‖ in magnetopause reconnection: An explicit demonstration

We use a global MHD simulation to compute the distribution of E‖ on the face of the magnetopause as represented by the last closed field line surface. In MHD codes, E‖ is a proxy for magnetic reconnection. Integrating E‖ along the topological separator line between open and closed magnetic field lines gives the global reconnection rate at the magnetopause. In the case studied here, where the interplanetary magnetic field (IMF) is precisely duskward, we find the global reconnection rate to be ∼49 kV, comparable to potentials inferred from measurements made in the polar cap. The exercise demonstrates an application of a general reconnection theorem that, in effect, equates reconnection with E‖. It prepares the way for MHD imaging of reconnection in terms of contours of E‖ on the magnetopause. The result also illustrates a property of parallel potentials in the global context that is not generally recognized. Nearly the full magnetopause reconnection voltage exists on some closed field lines between the northern and southern polar caps, so that they leave the dawn, southern hemisphere with a sizable positive polarity and enter the dusk, northern hemisphere with a sizable negative polarity. An unexpected finding is a substantial parallel potential (between 10 and 15 kV) between the magnetopause and the ionosphere in northern dawn and southern dusk sectors. (Interchange “dawn” and “dusk” for dawnward IMF.) This potential has the polarity that accelerates electrons into the ionosphere in the dusk sector and, so, might be the origin of the “hot spot” seen there in precipitating electrons.

Double‐polytropic closure in the magnetosheath

The magnetosheath plasma is usually neither isotropic nor adiabatic. This paper contains an attempt to describe its thermodynamic properties in terms of two polytropic laws, p[perpendicular]/[rho]B[sup [gamma][sub [perpendicular]][minus]1] = C[sub [perpendicular]] and p[sub [parallel]]B[sup [gamma][sub [perpendicular]][minus]1]/[rho][sub [perpendicular]]= C[sub [parallel]], such that for [gamma][sub [perpendicular]]=2, [gamma][sub [parallel]] = 3 the usual Chew-Goldberger-Low double-adiabatic expressions are recovered and for [gamma][sub [perpendicular]] = 1, [gamma][sub [parallel]] = 1 double-isothermal conditions are obtained. Using data from the AMPTE/IRM spacecraft, the authors show that the subsolar magnetosheath plasma may be better described by the double-polytropic laws than by the mirror instability threshold, in particular in the low beta region near the magnetopause. The inferred polytropic exponents vary from event to event but are typically in the ranges of [gamma][sub [perpendicular]] = 0.94 [+-] 0.10 and [gamma][sub [parallel]] = 1.14. [+-] 0.13 for the 29 cases they have examined.

Orientation and motion of current layers: minimization of the Faraday residue

A simple analytical solution is presented for a minimization problem encountered by Terasawa et al. [1996] in analyzing electromagnetic (EM) field and plasma data series acquired by a spacecraft traversing a one-dimensional (1D) current layer. Their analysis was developed to infer the direction of spatial variation, n, and velocity, un, along n of a 1D EM structure such as the bowshock, the magnetopause, or the geotail current sheet. We show that the optimization procedure of Terasawa et al., which involved a numerical search, in fact reduces to solving a 3 × 3 eigen-problem for a certain matrix Q defined in terms of the data. A step-by-step outline is given of the operations needed to predict n and un in this manner from an actual data set. Statistical estimates of uncertainty are given. Two magnetopause crossings by the spacecraft AMPTE/IRM are used to illustrate the procedure and to compare the results with those obtained by other methods.

Fluid and kinetics signatures of reconnection at the dawn tail magnetopause: Wind observations

We report an accelerated plasma flow event detected by Wind at the low-latitude dawn tail magnetopause (xGSE≈−10 RE) when the local magnetic shear across the magnetopause was high (∼180°) and the GSM y component of the interplanetary magnetic field was positive and much larger than the z component. High time resolution (3 s) three-dimensional ion and electron distributions were obtained for this event. We have performed rigorous tests of fluid and particle predictions of reconnection. Consistent with reconnection, we observed at the magnetopause (1) jetting of plasma, with a flow speed, measured in the deHoffmann-Teller frame, at 98% of the Alfven speed; (2) mixing of a nearly isotropic hot plasma sheet ion distribution with a field-aligned magnetosheath distribution having a low-energy cutoff at the predicted deHoffmann-Teller velocity; (3) opposite streaming of magnetosheath and plasma sheet electrons consistent with open field topology; and (4) a finite inward (earthward) directed normal magnetic field (BN<0) at and an associated earthward plasma flow (at 94% of the normal Alfven speed) across the magnetopause. The combined fluid and particle signatures provide a comprehensive set of evidence for reconnection at the magnetopause. These reconnection signatures were observed in the tail flank magnetopause, where the presence of fast plasma flow (at almost twice the local Alfven speed) in the adjacent magnetosheath has been predicted to suppress reconnection. The sense of the flow enhancement, the direction of the electron heat flux, and the polarity of BN are all consistent with each other and with the spacecraft being located tailward and northward of the reconnection site. Our analysis places the reconnection site ∼7 Earth radii south of the magnetic equator. The dimensionless reconnection rate at this flank magnetopause is estimated to be in the range of 0.1 to 0.2, which is similar to values reported for the subsolar region. In essence, the present event provides unambiguous evidence for reconnection and shows that reconnection signatures at the tail flank magnetopause are not noticeably different from those predicted and observed in the subsolar region.