Kelvin-Helmholtz Instability in a Dipole Magnetosphere: The Magnetopause as a Tangential Discontinuity

The boundary stability problem is solved for a dipole magnetosphere wrapped by an azimuthal solar wind flow. A simplified equation is obtained describing small-scale fast magnetosonic waves in a dipole magnetosphere. The structure of surface fast magnetosonic waves along magnetic field lines is represented as an expansion into a set of standing (between the magnetoconjugate ionospheres) waves. Over the azimuthal coordinate, along which the plasma is homogeneous, the wave field is decomposed into a set of azimuthal harmonics. It is shown that, in solar wind flows with velocities actually observable near the Earth's magnetosphere, only surface waves corresponding to several first harmonics of these expansions are unstable. The frequency ranges of unstable oscillations do not overlap for harmonics with different wave numbers. As the plasma flow velocity increases, harmonics with higher and higher wave numbers become unstable. The characteristic frequencies of unstable surface waves cover the lowest-frequency, Pc5-Pc6 range of geomagnetic pulsations observed in the magnetosphere. The frequency spectrum of these oscillations corresponds to geomagnetic pulsations at discrete "magic frequencies" occasionally observed in the Earth's magnetosphere.