Magnetic variance analysis for small‐amplitude waves and flux transfer events on a current sheet

Abstract

The properties of the magnetic variance matrix M in the context of remote sensing of two‐dimensional (2‐D) coherent flux transfer events and waves on the magnetopause or other current sheets are investigated. It is known from previous work that, in theory, the smallest eigenvalue of M should be zero and that the corresponding eigenvector should lie in the plane tangent to the unperturbed current layer, forming a certain, theoretically predictable angle, θ N , with the invariant direction (or axis) of the event. For a certain class of events, we now demonstrate the following additional properties: (1) The direction of the vector normal to the unperturbed current layer should coincide with either the maximum or the intermediate variance eigenvector, depending on the Mach numbers of the plasma; and (2) the ratio of maximum to intermediate eigenvalue of M is related in a simple manner to the so‐called stretching factor R and to the angle θ N , permitting both to be determined without use of the Hubert‐transform fitting technique and the trial‐and‐error approach to finding θ N previously employed [ Walthour et al ., 1993]. Magnetopause events from the spacecraft AMPTE/CCE, AMPTE/IRM, and ISEE are used to illustrate the new results.