Bent current sheet: A possible catalyzer to trigger substorm onset

It is generally accepted that some sort of instability in Earths cross-tail current sheet (CS) in the transition region of tail-like to dipole-like magnetic field line configuration plays a crucial role in the onset of substorms. Candidates for this instability are the Ballooning/Interchange Instability (BICI) and Double-Gradient Instability (DGI). So far, investigations of these instabilities were conducted under the assumption of a symmetric CS. However, the interplanetary magnetic field, solar wind and geomagnetic dipole tilt angle influence the geometry of the CS. Under realistic conditions, the CS is mainly bent and not symmetric. This effect was not taken into account so far. This project aims to investigate the effect of a bent CS on substorm onset and the formation and evolution of BICI and DGI. For this purpose, we want to answer the following scientific questions: (1) Does a bending of the CS favor the formation of instabilities? (2) Can instabilities grow faster in a bent CS? (3) Do bent CSs favor substorm onset? (4) Is magnetic reconnection catalyzing the growth of instabilities? Hence, we want to investigate a bending of the CS in terms of (1) its stability (2) the interplay of different modes (3) its relation to substorms (4) the influence of reconnection on the evolution of instabilities. These goals will be achieved by the means of analytical, numerical and observational investigations in close collaboration with our international partners. In order to resolve the importance of electron currents and kinetic effects during the evolution of instabilities, we will use an analytical Hall-MHD (HMHD) model of DGI in symmetric and bent CS configurations and non-linear 3D MHD and HMHD simulations complemented by and compared to 3D PIC simulations. The non-linear DGI/BICI evolution in symmetric and bent CSs will be studied by implementation of all aforementioned 3D simulations (MHD/HMHD/PIC). The interplay between kink and sausage modes will be investigated also by using the magnetic filament approach to study their temporal co-evolution and possible dominance of one specific mode. For investigations on the interplay of reconnection with instabilities, a 2.5D electron HMHD model will be used to investigate the stability of realistic magnetotail configurations and reconstruct the electron CS. The analytical and numerical investigations are supplemented by observations of the THEMIS and MMS missions. These multi-spacecraft missions allow us to observe instability features simultaneously from different observational points and on different scales, ranging from the electron to the MHD scale. Thus, this project proposes a comprehensive approach, which combines data analysis with theoretical and numerical studies under a realistic magnetotail configuration that was not taken into account by previous studies. This may shed light in the formation and evolution of substorm relevant instabilities and the role of a bent CS for substorm onset.

Due to the solar wind streaming from the Sun into the interplanetary medium, the Earth's magnetosphere, which is the region around Earth where its magnetic field is present, gets compressed on the sunside and elongated into a tail, the so-called magnetotail, on the nightside. Inside this magnetotail, the Earth's magnetosphere is separated into a northern and southern hemisphere by a cross-tail current sheet. To study the dynamics of the Earth's magnetotail, including substorms, the current sheet is usually considered to be plane for simplicity. However, in reality, the current sheet is bent due to the Earth's dipole tilt angle and deviations of the solar wind stream from a purely radial propagation direction. In this project, we investigated the influence of current sheet bending on its stability to the transversal mode and on the onset of substorms. For this purpose we use analytical, numerical and observational methods. We obtained the following results: (1) The growth rate of an instability is more than two times larger in a bent current sheet than in a plane current sheet. Hence, current sheet bending is found to be a significant destabilizing factor. (2) The so-called double gradient instability corresponds to the compressible ballooning mode in the strongly stretched magnetotail. (3) While in a plane current sheet perturbations can be either symmetric ("kink") or anti-symmetric ("sausage"), both kink and sausage modes coexist in a bent current sheet. (4) Over the course of time, a concurrence of stable and unstable modes can be found in our simulations. In a plane current sheet, the unstable mode dominates after about 1.5 to 2 hours, which is long compared to substorm onset timescales. However, in bent current sheets, the unstable mode dominates much faster, after about 5 minutes, which is consistent with substorm onset time scales. (5) Magnetic reconnection, a process during which magnetic energy is getting converted into plasma energy, enhances the instability growth rate for a factor of two. (6) Entropy does not affect the current sheet stability with respect to the considered mode. (7) A generalized instability criterion was derived, which is applicable not only in the strongly stretched region of the magnetotail, but also in the near-Earth region and for bent current sheets. This generalization allowed us to understand that the instability is controlled by second derivatives of the total pressure. (8) It was found that neither a wave nor an instability with a wave vector pointing toward the Earth/magnetotail can develop. These findings explain why flapping waves are observed predominantly in the orthogonal direction. (9) It was found that the phase velocity as function of wave number can have a local maximum - contrary to simple analytical models. Such behavior was confirmed by observations.