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How to distinguish between kink and sausage modes in flapping oscillations?

Flapping waves are most noticeable large‐scale perturbations of the magnetotail current sheet, whose nature is still under discussion. They represent rather slow (an order of magnitude less than typical Alfven speed) waves propagating from the center of the sheet to its flanks with a typical speed of 20–60 km/s, amplitude of 1–2 Re and quasiperiod of 2–10 min. The double‐gradient MHD model, which was elaborated in Erkaev et al. (2007) predicts two (kink and sausage) modes of the flapping waves with differences in their geometry and propagation velocity, but the mode structure is hard to resolve observationally. We investigate the possibility of mode identification by observing the rotation of magnetic field and plasma velocity vectors from a single spacecraft. We test theoretical results by analyzing the flapping oscillations observed by Time History of Events and Macroscale Interactions during Substorms spacecraft and confirm that character of observed rotation is consistent with kink mode determination made by using multispacecraft methods. Also, we checked how the existence of some obstructive conditions, such as noise, combined modes, and multiple sources of the flapping oscillations, can affect on the possibility of the modes separation with suggested method.