Open versus closed magnetosphere

Let us, for a moment, consider the consequences of a hypothetical model, which describes the solar wind/magnetosphere interaction by ideal MHD, including MHD discontinuities (Section 3.9). As the Earth's dipole field is an obstacle in the supersonic solar wind, a fast MHD shock wave, the bow shock, stands in front of the magnetosphere. The magnetopause is a tangential discontinuity, confining the geomagnetic field. It is a necessary element of the initial value problem (an analogous case was discussed in Section 11.2.6); the magnetized solar and magnetospheric plasmas cannot mix, because magnetic line conservation (Section 3.8.2), which holds in our hypothetical model, would be violated. The solar wind, when switched on, would sweep the magnetospheric medium toward the Earth until pressure equilibrium is reached. The magnetosphere would be completely closed and, as the magnetopause would separate media of different origin, we can expect the magnetopause to carry a current (Section 8.6.2).

In spite of the fundamental deficiencies of such a model, which are described below, it is not completely off the mark; it can explain global features such as the positions of the bow shock and of the frontside magnetopause reasonably well (Spreiter et al., 1966). It drastically fails, however, in other respects. For example, for a closed magnetosphere the interaction with the solar wind would be independent of a reversal of the directions of the interplanetary magnetic and electric fields. It follows from the structure of the ideal MHD equations (Section 3.3.2) that this reversal would not affect the hydrodynamic variables and the magnitude of the magnetic field B. In particular the total pressure (p + B2/2^0) at the magnetopause remains unchanged. Since in MHD, besides vanishing normal velocity and magnetic field components, total pressure balance is the only condition for a tangential discontinuity, the field reversal has no consequences for the interaction.

The closed magnetosphere is in conflict with both observational facts and theoretical results. Observationally, one finds that magnetospheric dynamics, and in particular substorm dynamics, is strongly correlated with the sign of the z-component of the interplanetary magnetic field (IMF). This is based on an impressive history of studies investigating the correlation between interplanetary signatures with geomagnetic disturbances in the auroral zones (e.g., Bargatze et al., 1985, 1999). In one of the earlier studies

Arnoldy (1971) correlated the AE index, a quantitative measure of auroral zone magnetic activity (Davis and Sugiura, 1966), with Bs, which is set to zero for IMF Bz > 0 and to \Bz\ for southward orientation of Bz. On the basis of hourly averages a correlation coefficient of 0.8 was obtained, while other solar wind variables produced coefficients < 0.4. Further studies introduced more refined coupling expressions (e.g., Perreault and Akasofu, 1978; Bargatze et al., 1985); for instance, Bs was replaced by the dawn-dusk electric field component FswBs (Burton et al., 1975), where Fsw is the solar wind velocity. All studies, although varying in details, confirmed that the southward directed IMF component plays a central role in determining the strength of energy coupling between the solar wind and the terrestrial magnetosphere (Bargatze et al., 1999), so that these (as many other) observations are in conflict with the closed magnetosphere model.

A conceptual model of an open magnetosphere by Dungey (1961) removes this difficulty, at least qualitatively. The magnetic topology and the resulting flow pattern are illustrated in Fig. 13.1 for a southward-pointing IMF. If the IMF was northward the structure would be quite different, as discussed later. So, in this model the magnetospheric structure is strongly influenced by the direction of the IMF ¿-component.

Clearly, Dungey's model involves magnetic reconnection (Section 11.2.1). (In fact, the term magnetic reconnection was suggested by Dungey in this

Open Magnetosphere
Fig. 13.1 Sketch of magnetic field lines of Dungey's open magnetosphere in the non-midnight meridian plane; the plasma flow is indicated by the open arrows.

context.) In the midnight meridian plane shown in Fig. 13.1 there is a reconnection site at the front side and one at the night side of the magnetosphere. As reconnection involves nonideal processes, the open topology violates ideal MHD, consistent with the above reasoning.

What do the theoretical tools teach us about the issue of closed versus open magnetosphere? An important fact is that a collisionless current sheet like the magnetopause can become the site of magnetic reconnection. The collisionless tearing instability (Section 10.4) occurs under a variety of circumstances. Although single modes might saturate at small amplitudes, mode coupling can lead to further growth; more details are given below. Also, external driving by local perturbations can speed up the instability, so that a nonlinear reconnection pattern would arise (Section 11.3.3). This scenario would have the consequence that an initially closed magnetopause would open by magnetic reconnection. The details would depend on the effectiveness of the opening and on the orientation of the interplanetary field. Intuitively, one expects most efficient reconnection for southward interplanetary field orientation, when the magnetospheric and interplanetary fields are antiparallel at the subsolar magnetopause region. These arguments give strong support to Dungey's field topology. For an MHD model of a complete open magnetotail boundary see Siscoe and Sanchez (1987).

On purely theoretical reasoning, the opening of the magnetosphere, although fairly plausible, cannot be considered as rigorously established. Therefore, it seems advisable to test it by looking at in situ observations of reconnection at the magnetopause.

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