A general approach to the generation of ion cyclotron harmonic waves observed on board the Akebono satellite in the deep plasmasphere is presented. It is shown that during quiet magnetic conditions the development of the hydrodynamic cyclotron instability with growth rate &ggr;∝ni1/2, where ni is the number density of the hot heavy ions, is suppressed by the field-aligned inhomogeneity of the dipole magnetic field. The instability is, in this case, controlled by the weak resonant interaction of the waves and the trapped particles with growth rate &ggr;∝ni. The waves are generated by a kinetic instability involving hot helium ions with a ring-like distribution. Such ions are present in the magnetosphere during quiet magnetic conditions. A simple analytical model of this instability accounting for the inhomogeneity of the ambient magnetic field is used. It is shown that the ULF wave observations during quiet times on board the Akebono satellite are in a reasonable agreement with the present theoretical approach. ¿ 1998 American Geophysical Union