A general approach to the generation of ion cyclotron harmonic waves o
bserved on board the Akebono satellite in the deep plasmasphere is pre
sented. It is shown that during quiet magnetic conditions the developm
ent of the hydrodynamic Cyclotron instability with growth rate gamma p
roportional to n(i)(1/2), where n(i) is the number density of the hot
heavy ions, is suppressed by the field-aligned inhomogeneity of the di
pole magnetic field. The instability is, in this case, controlled by t
he weak resonant interaction of the waves and the trapped particles wi
th growth rate gamma proportional to n(i). The waves are generated by
a kinetic instability involving hot helium ions with a ring-like distr
ibution. Such ions are present in the magnetosphere during quiet magne
tic conditions. A simple analytical model of this instability accounti
ng for the inhomogeneity of the ambient magnetic field is used. It is
shown that the ULF wave observations during quiet times on board the A
kebono satellite are in a reasonable agreement with the present theore
tical approach.