About Forward‐Facing Slow Mode Waves at the Magnetopause

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Abstract
We review a theoretically predicted, hyperbolic MHD feature, exhibited in the field and plasma flow at the magnetopause, namely that of upstream‐traveling, slow‐mode waves, first predicted in the 1950s, but, so far, not identified in spacecraft data. Today's high‐quality observations at Earth's magnetopause now invites a serious attempt to check the prediction. The required theoretical background and analysis methodology is summarized and further developed. The study is limited to elongated disturbance structures, such as bulges, on the magnetopause that are approximately two‐dimensional and, in their proper frame, time independent. Most of the analysis tools are applicable to data from a single spacecraft. Subsequent papers could employ data from multi‐spacecraft missions, such as the four‐spacecraft Magnetospheric Multi‐Scale mission. Such data will permit the study of many additional details. Because they are mathematically intertwined, both elliptic and hyperbolic signatures will be examined. The three key points illustrate the important role played by magnetic‐variance analysis in the study of field perturbations in the vicinity of the magnetopause. Its most common use to date has been for the analysis of the magnetic fields from spacecraft crossings of the magnetopause, where the minimum variance direction can provide an estimate, not always of high quality, of the direction normal to the magnetopause layer. In the present paper, magnetopause traversals play only a secondary role; our primary objective is to analyze field perturbations near the magnetopause, for which we show that the ideal minimum‐variance direction is tangential, rather than normal, to the unperturbed magnetopause surface.

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