A New Approach to Flapping Oscillations in the Magnetotail Current Sheet

In the Earth`s magnetotail there exists a current sheet, which is found to be frequently moving in the north-south direction. Such a motion is referred to as flapping motion or oscillation. Early interpretations associated these flapping motions with kink-like perturbations propagating in the dawn-dusk direction. Cluster observations and statistical studies confirm such a view of this phenomenon and suggest that the source of these waves is located in the centre of the magnetotail. Recent investigations point at a connection between so-called "Bursty Bulk Flows" (BBFs) and the flapping oscillations. It seems that flapping oscillations are closely related to fast plasma flows, which can be generated by magnetic reconnection in the magnetotail. This Joint Project proposes a new mechanism of magnetohydrodynamic (MHD) waves in the current sheet, which are connected to a gradient of the normal component of the magnetic field. Depending upon the direction of the gradient, a small disturbance either leads to an instability or to waves propagating in dawn-dusk direction. The main objectives of the proposed Joint Project are (1) to study the properties and dynamics of the flapping oscillations in the Earth`s magnetotail for different current sheet conditions and thicknesses and (2) to clarify the question of the generation mechanism of the kink-like perturbations and possible ionospheric disturbances due to these processes. These aims will be achieved by theoretical studies as well as by the analysis of observations. Two nonlinear, three-dimensional MHD models will be developed in the course of this project: one in one-fluid ideal MHD and one in multi-fluid MHD including finite Larmor radius (FLR) and Hall effects. The results of both models will be compared in order to estimate the influence of the particle dynamics (FLR and Hall effects) and of the current sheet thickness. Further, a three-dimensional, semi-analytical, time-dependent magnetic reconnection model will be developed in order to be able to study the role of magnetic reconnection for flapping oscillations. Hence, the models will be used to investigate the following chain of causality: magnetic reconnection -> accelerated magnetic flux tubes and BBFs -> flapping oscillations -> ionospheric phenomena. Apart from Cluster observations, which provide the opportunity to resolve spatial and temporal processes, observations by the THEMIS mission will also be included in the data analysis part of this project. The THEMIS measurements offer the possibility to study the time history between reconnection, appearances of BBFs and magnetic flux tubes and flapping oscillations. Thus, this project proposes a comprehensive approach, which combines theoretical studies and data analysis.

This project addressed the origin and evolution of the so-called flapping oscillations, which are sausage-type or kink-type quasi-periodic perturbations, registered in the Earth magnetotail current sheet (also in the Saturn and Jupiter magnetospheres) in numerous in-situ observations. The occurrence of such oscillations shortly before the substorm onset is known well enough. Typically (for the Earth magnetotail conditions), flapping waves are observed in the central part of the midtail at the distances of 10 30 Earth radii from the Earth, propagating toward the flanks with the speed of tens km/s, amplitude and wavelength of several Earth radii and quasiperiod of several minutes.The main questions we were focused within the project were: which properties of the magnetotail current sheet are favorable / unfavorable for the flapping mode and what can stabilize / destabilize the mode?We found out that several factors are of high importance in this regard.The most influential one is the growth direction of the normal to ecliptic plane magnetic com- ponent, Bz. Arbitrary fluctuations of the magnetic field and plasma parameters may grow in time ex- ponentially (flapping instability), when Bz increases tailward, and then propagate toward the current sheet flanks (flapping wave), when direction of the Bz growth reverses. This mechanism of excitation seems to be rather usual for flapping motions, as growth direction of the Bz component in the midtail is known to be fluctuating with time-scale ~10 min before the substorm onset.However, flapping oscillations are not observed so often, as it could be supposed from the pre- vious paragraph. One of effective stabilizing mechanisms is related to the so-called guide field magnetic field component in the direction (y) perpendicular to the line Sun-Earth (x) and to the normal to ecliptic plane (z). Small non-zero guide field By reduces the growth rate of the flapping instability, introducing the typical (fastest-growing) wavelength of the order of the current sheet width. Total de- cay of the mode is expected for By ~ 0.5 of the magnetic field value far above (below) the ecliptic plane.Another factor of importance is a curvature radius of the magnetic field lines, Rc, which should not be too large, in order to flapping oscillations could develop. In more detail, magnetic flux tubes should be elongated enough to provide for existence of the flapping wavelength range, which is estimated as Rc < l < L, where L is the typical size of the current sheet in the x direction and l is the wave- length. Enlarging of Rc yields substantial stabilization of the mode.Finally, inhomogeneous accelerated plasma flows may initiate flapping motions both in the center of the current sheet and at the flanks. In the central part of the sheet, such flows are produced by non-steady magnetotail reconnection, and at the current sheet flanks they may be caused by draping of interplanetary magnetic field lines around the magnetosphere or by magnetopause reconnection.Obtained results are relevant for any plasma physics objects exhibiting elongated current sheets with local sheet thinning regions, such as planet magnetospheres (own or induced), solar corona, magnetodisks, etc.