Flapping of the magnetotail current sheet in a global 6D hybrid-Vlasov simulation.

Flapping waves are large-scale oscillations of the Earth's magnetotail current layer propagating in a cross-tail direction. In the current study, we investigate the plasma sheet flapping waves observed in a global 6D hybrid-Vlasov simulation of the Earth’s magnetosphere obtained with the Vlasiator code. Applying the timing analysis for 4 virtual spacecraft located in the near tail around X=-14 Re (where Re=6371 km is the Earth radius), we find that the phase velocity of the waves is directed duskwards and has a magnitude comparable to the ion drift velocity in the current sheet centre. We analyse the spatio-temporal characteristics of the waves by the ad-hoc technique of current sheet extremum tracing and we find that the average period of the flapping waves is T~40 s, and the typical wavelength λ=1.6 Re. The necessity to develop a specific technique arises from the large inaccuracy of the timing analysis output for the different positions of the virtual spacecraft constellation. We clearly observe that the area of most intense growth of the flapping oscillations coincides with the vicinity of the ion diffusion region of magnetic reconnection. In order to clarify the origin of the flapping waves, we calculate the dispersion relation for the ion-kink instability, taking the parameters of different ion distributions observed nearby with the reconnection X-line at the different time steps. Notably, the ion distribution has a specific crescent-type shape revealing the meandering motion of ions in the reconnecting current sheet that we identify as ions carrying the non-adiabatic current which is required for the development of the current layer instabilities. The agreement between the predicted values of the frequency and wave vectors and those observed in the simulation gives us evidence that flapping waves in the global hybrid-Vlasov simulation arise due to the development of the ion kink instability in the reconnecting current layer.