Abstract

Abstract We explore the three‐dimensional structure of ion‐kinetic instabilities in a thin current layer using a hybrid‐Vlasov simulation of the Earth's magnetosphere. The simulation shows the simultaneous growth of tearing and kinking instabilities, which develop in the Sun‐Earth and dawn‐dusk directions, respectively, within the magnetotail current sheet. The formation of flux ropes indicates the development of the tearing instability, while flapping‐type cross‐tail oscillations arise from the kink instability. We consider both instabilities as independent polarizations, albeit sharing a common source: demagnetized ions forming crescent‐shape distributions at the center of the current layer. These oscillations exhibit spatiotemporal characteristics within the proton‐scale range, featuring a growth time on the order of 40–80 proton gyroperiods and a wavelength of approximately 15–30 proton skin depths.