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In this paper, the growth rate and eigenmode structures of the streaming sausage and kink instabilities in a current sheet with a super‐Alfvénic flow are studied. Based on the linearized compressible MHD equations, we employ an initial‐value method to obtain the growth rate and eigenmode profiles of the fastest growing mode which is either the streaming sausage mode or kink mode. The streaming sausage and kink instabilities, similar to the Kelvin‐Helmholtz instability, are caused by the sheared plasma flow. The results show that for V0m = 2 VA∞ the sausage mode grows faster than the kink mode when β∞ < 1.5. When β∞ > 1.5, the streaming kink instability has a higher growth rate. Here VA∞ is the Alfvén velocity and β∞ is the ratio between the plasma and magnetic pressures far away from the current layer, and V0m is the maximum velocity of plasma flow at the current sheet. In addition, an analytical dispersion equation is obtained for an ideal four‐layer model of the current sheet in the incompressible limit. In the presence of a finite resistivity, the mixed sausage‐tearing mode or the streaming tearing mode may be excited, which leads to the formation of plasmoids in the magnetotail. As an application to the Earth's magnetotail, where super‐Alfvénic plasma flows are observed in the plasma sheet and β∞ ≃ 0.1–0.3 in the lobes, it is suggested that the streaming sausage and streaming tearing instabilities may occur in the magnetotail. Some of the north‐then‐south or south‐then‐north Bz signatures observed in the distant magnetotail may be associated with the streaming sausage mode or the mixed sausage‐tearing mode. It is also pointed out that kink modes are unlikely to occur in the magnetotail.

The ultraviolet auroral images obtained with the Viking satellite often show spatially periodic bright spots which resemble “beads” or “pearls” aligned on the postnoon auroral oval, which may be due to the coupling of the plasma vortices formed in the boundary layer to the polar ionosphere. Geomagnetic pulsations in the ULF range observed in the cusp region may also be associated with the boundary layer vortices. To explain the observed auroral bright spots and the cusp geomagnetic pulsations, we have developed a model for the plasma dynamics in the low‐latitude boundary layer and its interaction with the polar ionosphere via the field‐aligned current (FAC). In the presence of a driven plasma flow along the magnetopause, the Kelvin‐Helmholtz instability can develop, leading to the formation and growth of plasma vortices in the boundary layer. On the other hand, the finite ionospheric conductivity leads to the decay of these vortices. The competing effect of the formation and decay of vortices leads to the formation of strong vortices only in a limited region. Several enhanced field‐aligned power density regions associated with the boundary layer vortices and the upward FAC filaments can be found along the postnoon auroral oval. These enhanced field‐aligned power density regions may account for the observed auroral bright spots. In addition, we found that the FACs are stronger in the prenoon sector than in the postnoon sector due to the presence of the field‐aligned potential drop in the postnoon sector. The larger prenoon FACs produce stronger cusp pulsations in the prenoon sector, consistent with observations. The frequency spectrum and polarization of the generated pulsations are also discussed. On the other hand, the vortices in the postnoon boundary layer are found to be stronger than those in the prenoon boundary layer.

A three‐dimensional compressible resistive magnetohydrodynamic simulation code, with inclusion of the fully generalized Ohm's law, has been developed to study the nonlinear evolution of field line resonances in Earth's magnetosphere. A simple Cartesian box model of an inhomogeneous plasma with straight geomagnetic field lines is used, and the Alfvén velocity increases monotonically from the magnetopause boundary layer toward Earth. A monochromatic fast mode compressional oblique wave is applied from the direction of the magnetopause boundary layer, pumping energy into the magnetosphere. The fast mode wave, while propagating toward Earth, is partially reflected at the turning point (located at radial distances between 8 and 10 RE in the equatorial plane) and then couples to shear Alfvén waves, leading to the formation of large‐amplitude field line resonances near Earth. The field line resonances are observed to narrow to several electron inertia lengths within several wave periods of the driver wave, and electron inertial effects become important at this stage. Final profiles near the resonance are very similar to Airy functions, indicating that electron inertial effects become important before possible nonlinear effects. The electron inertial effects lead to oscillating parallel electric field which might be potential accelerators for electrons in some types of auroral arcs.