Abstract. 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.

[1] Grad-Shafranov reconstruction is a data analysis tool for the reconstruction of two-dimensional (2-D) coherent field and flow structures from data collected as the structures move past an observing platform. To date, the method has been applied with good success to reconstruct magnetohydrostatic structures in Earth's magnetopause, in the solar wind, and in the geomagnetic tail, as the structures move past one or more observing spacecraft. However, with suitable modification, the reconstruction method can be extended to other applications, three of which are presented here: 2-D magneto-hydrodynamic structures in which dynamically important field-aligned flow is present, 2-D flow transverse to the magnetic field in the magnetospheric low-latitude boundary layer, and 2-D ordinary gasdynamic/hydrodynamic flow. We develop the fundamental equations required in the reconstructions, both for isotropic pressure and, in Appendix A, for the case where the pressures parallel and perpendicular to the magnetic field are described by the double-polytropic laws. Applications to actual or simulated data are discussed but not included in the present paper.

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We present a two‐dimensional, force‐balanced magnetic field model in which flux tubes have constant pVγ throughout an extended region of the nightside plasma sheet, between approximately 36 RE geocentric distance and the region of the inner edge of the plasma sheet. We have thus demonstrated the theoretical existence of a steady state magnetic field configuration that is force‐balanced and also consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD (isotropic pressure, perfect conductivity). The numerical solution was constructed for a two‐dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The primary characteristics of our steady state convection solution are (1) a pressure maximum just tailward of the inner edge of the plasma sheet and (2) a deep, broad minimum in equatorial magnetic field strength Bze, also just tailward of the inner edge. Our results are consistent with Erickson's (1985) convection time sequences, which exhibited analogous pressure peaks and Bze minima. Observations do not indicate the existence of a Bze minimum, on the average. We suggest that the configurations with such deep minima in Bze may be tearing‐mode unstable, thus leading to substorm onset in the inner plasma sheet.

The properties of small‐amplitude waves propagating in a homogeneous anisotropic plasma are investigated using an MHD double‐polytropic model that incorporates the CGL double‐adiabatic model in one extreme and the isothermal model in the other. It is found that the properties of fast and intermediate mode waves remain qualitatively the same as in ordinary MHD but that, in certain parameter regimes, three inversions occur for slow‐mode waves: (1) their phase speed exceeds that of intermediate waves; (2) they behave like fast‐mode waves in that, across them, the plasma density and magnetic field increase or decrease together; (3) rarefaction waves rather than compression waves steepen.

We have constructed two new two‐dimensional equilibrium magnetic field models for the Earth's magnetotail, in which flux tubes have nearly constant pV5/3 between the outer boundary of the Alfvén layers and 36 RE geocentric distance. These models, corresponding to different values of pV5/3, are constructed for magnetospheres with rectangular magnetopauses and nonflaring tails. These results thus confirm the speculation made in our earlier paper (Hau et al., 1989) that, within the limit of ideal MHD, there exists a family of steady state convection solutions, corresponding to various degrees of magnetotail inflation. Like our previous steady state solution, each of these models also exhibits a broad minimum in equatorial magnetic field strength Bze tailward of the inner edge region between 10 and 20 RE. However, these new steady state magnetic field models possess higher values of flux tube content pV5/3 and thus have more stretched tail configurations and smaller minimum values of Bze than those in the original model. For a model that has Bze/Blobe ≈ 0.15 at 36 RE, which is close to observed averages, the ratio Bze/Blobe is about 0.029 at 13 RE.

The magnetosheath plasma is usually neither isotropic nor adiabatic. This paper contains an attempt to decribe its thermodynamic properties in terms of two polytropic laws, p⟂/ρBγ⟂−1 = C⟂ and p∥Bγ∥−1 / ργ∥ = C∥, such that for γ⟂ = 2, γ∥ = 3 the usual Chew‐Goldberger‐Low double‐adiabatic expressions are recovered and for γ⟂ = 1, γ∥ = 1 double‐isothermal conditions are obtained. Using data from the AMPTE/IRM spacecraft, we 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 γ⟂ = 0.94 ± 0.10 and γ∥ =1.14 ± 0.13 for the 29 cases we have examined.

[1] The strong magnetic field B y component (in GSM coordinates) has been increasingly noticed to play an important role in the dynamics of tail current sheet (CS). The distribution profile of strong B y components in the tail CS (i.e., those with guide field), however, is not well known. In the present work, by using the simultaneous multipoint observations of Cluster satellites, the profile of a strong B y component in tail current sheets is explored, through detailed case studies, as well as in a statistical study. It is discovered that around the midnight meridian, the strength of the strong B y component, i.e., |B y |, is basically enhanced at the center of the CS relative to that in the CS boundaries and lobes and forms a north-south symmetric distribution about the center of CS. Generally, however, for strong guide field cases in the non-midnight meridian, the profile of B y strength basically becomes north-south asymmetric, the strength of the B y component in the northern side of the CS is found to be either stronger or weaker than that in the counterpart southern side. By considering the modulation of the tail flaring magnetic field with magnetic local time, we propose an interpretation to account for the variation of the B y -profile, which is supported by the statistical survey. These results offer an observation basis for further studies.