We study the parametric decays of left-hand polarized electromagnetic
ion cyclotron waves, propagating parallel to the external magnetic fie
ld, in the magnetosphere. We show that the presence of He+ ions and a
mixed population of thermal and hot protons give rise to new wave coup
lings. These couplings lead to a number of new instabilities. Some of
the instabilities involve sound waves carried mainly by the He+ ions,
which can be very efficient in heating up the bulk of the He+ ions via
Landau damping. Other instabilities involve the branch of the left-ha
nd polarized electromagnetic ion cyclotron waves which has a resonance
at the He+ ion gyrofrequency. These instabilities can also play a rol
e in the energy transfer from the pump wave to the He+ ions through re
sonance absorption, preferably in the direction perpendicular to the e
xternal magnetic field. The new couplings give rise to several types o
f parametric instabilities such as ordinary decay instabilities, beat
wave instabilities, and modulational instabilities. There are also cou
plings where the pump wave decays into two electromagnetic sideband wa
ves.