  This work investigates the short wavelength stability of the magnetopause
between a rapidly-rotating, supersonic, dense accretion disc and a
slowly-rotating low-density magnetosphere of a magnetized star. The
magnetopause is a strong shear layer with rapid changes in the azimuthal
velocity, the density, and the magnetic field over a short radial distance and
thus the Kelvin-Helmholtz (KH) instability may be important. The plasma
dynamics is treated using non-relativistic, compressible (isentropic)
magnetohydrodynamics. It is necessary to include the displacement current in
order that plasma wave velocities remain less than the speed of light. We focus
mainly on the case of a star with an aligned dipole magnetic field so that the
magnetic field is axial in the disc midplane and perpendicular to the disc flow
velocity. However, we also give results for cases where the magnetic field is
at an arbitrary angle to the flow velocity. For the aligned dipole case the
magnetopause is most unstable for KH waves propagating in the azimuthal
direction perpendicular to the magnetic field which tends to stabilize waves
propagating parallel to it. The wave phase velocity is that of the disc matter.
A quasi-linear theory of the saturation of the instability leads to a
wavenumber ($k$) power spectrum $\propto k^{-1}$ of the density and temperature
fluctuations of the magnetopause, and it gives the mass accretion and angular
momentum inflow rates across the magnetopause. For self-consistent conditions
this mass accretion rate will be equal to the disc accretion rate at large
distances from the magnetopause.
