8.4.1 The magnetopause as an MHD discontinuity
The magnetohydrodynamic (MHD) description of the magnetopause layer should be applicable when its thickness is many ion gyroradii, as is often the case (see the thickness histogram in Figure 8.10). When no reconnection effects are present, the magnetopause can be represented as a tangential discontinuity (TD), in which the normal magnetic field component is identically zero; plasma flow across the layer, from the magnetosheath side to the magnetosphere side, could be present only as a result of diffusion. During reconnection, however, the normal magnetic field component is nonzero, and it is accompanied by plasma flow across the discontinuity from the magnetosheath into the magnetosphere, where it appears as a boundary layer on open field lines adjacent to the magnetopause. The detailed structure of the magnetopause, away from the reconnection site, may involve more than one MHD wave structure: rotational discontinuities (RDs) or intermediate shocks, or slow shocks and expansion fans; the RD is often the dominant feature. For this reason, the magnetopause is commonly designated either as an RD, which indicates the local presence of reconnection signatures, or as a TD, when such signatures are locally absent.
The RD is a large-amplitude Alfven wave in which the flow, seen in the HT frame, is field aligned and Alfvenic. This feature has led to a simple test of the presence or absence of local signatures of reconnection. This test is referred to as the Walen test. It consists of plotting measured plasma velocity components, transformed into the HT frame, against the corresponding components of the measured Alfven velocity. It is important that the data be properly chosen and that the entire magnetopause structure be included. A regression line slope of +1 or -1, with high correlation coefficient, indicates Alfvenic flow and therefore RD structure. The interpretation is that reconnection is occurring somewhere on the magnetopause, away from the observation point and that, locally, a magnetic field component normal to the magnetopause must be present, even if it is too small to allow direct determination from minimum variance analysis of the magnetic field. This normal component in turn allows local plasma flow across the magnetopause. An example of such a Walen scatter plot, where the slope of the regression line is near +1 and the correlation coefficient is high, will be given the in the next Section (Figure 8.21).
The sign of the regression line slope in the Walen scatter plot is significant: A positive slope indicates flow (as seen in the HT frame) that is parallel to the field, whereas a negative slope indicates anti-parallel flow. If one assumes that the flow is always from the magnetosheath into the magnetosphere, then the sign of the slope indicates whether the normal magnetic field points inward (positive slope) or outward (negative slope). This information in turn tells us on what side of the reconnection site (X line) the observations were made. Experience has shown that only
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