On the propagation of MHD eigenmodes in a 2-D-magnetotail

The propagation of MHD kink/sausage low frequency waves in the magnetotail with a finite normal Bz component is addressed. The general idea is to investigate how a finite Bz may affect the propagation of MHD eigenmodes in the plasma sheet. The standard MHD equations are linearized and solved numerically in a modified Harris sheet. Boundary conditions are chosen such that energy flows outward of the frame box (free propagating system). An initial perturbation is set up in the pressure gradient term and the wave energy is then traced in the system. While a pure 1-D-Harris sheet constitutes an efficient wave guide for MHD eigenmodes, the introduction of a finite Bz in the zero-order geometry changes significantly the propagation of MHD fluctuations: the eigenmodes propagate much more slowly and carry little energy whereas a pure sound wave is excited and propagates isotropically in the system. The presence of a finite Bz thus tends to inhibit the MHD propagation of energy along the plasma sheet. It tends rather to spread the energy throughout the magnetotail. As an application of the above study, the role of a permanent X-point structure on MHD propagation in the plasma sheet is also explored.