Kelvin-Helmholtz driven modes of the magnetosphere

Abstract

Ultralow frequency (ULF) waves in the magnetosphere are thought to be driven by disturbances of the magnetopause caused by the flow in the magnetosheath. In this paper a model showing how the trapping and excitation of these modes depends upon the shear flow and propagation angle is presented. The ideal magnetohydrodynamics (MHD) equations are used and the perturbations are assumed to be linear. A bounded, uniform magnetospheric cavity, with a finite plasma beta, separated by a vortex sheet from a semi-infinite, field-free, flowing magnetosheath is considered. It is shown that the bounded model allows the trapping and excitation of both fast and slow cavity modes, and that unstable surface modes may also exist. Slow surface modes are unstable only for a small interval of flow speed, becoming fast surface modes for higher flows. Slow cavity modes have small growth rates and are unlikely to be significant observationally. It is shown that fast modes propagating quasiparallel to the flow may be excited for realistic flow speeds, but that for nonparallel modes, much higher flows are required. Finally, an exact method for predicting the onset of instability for fast modes is derived and is shown to occur at the coalescence of modes of opposite energy.