The velocity shear of an ion beam interacting with a background plasma is shown to excite low-frequency electrostatic Kelvin--Helmholtz instabilities and ion cyclotron instability propagating nearly transverse to the magnetic field Bo. In the plasma sheet boundary layer region, the noise generated by velocity shear instabilities is broadband with frequencies from 10-4 Hz to 4 Hz and the transverse wavelengths ranging from 30 km to 2400 km. The low-frequency noise can efficiently scatter electrons and the beam ions and is expected to affect significantly the stability of the plasma sheet against ion tearing mode instability. In the polar cusp regions, the velocity shear instabilities can generate a low-frequency broadband electrostatic noise from 2 Hz to 35 Hz provided the temperature of background electrons is ~100 eV. ¿ American Geophysical Union 1987