EVOLUTION OF ION CYCLOTRON INSTABILITY IN THE PLASMA CONVECTION SYSTEM OF THE MAGNETOSPHERE.

Liouville's theorem and approximate but extremely accurate expressions which reflect the invariance of mu and J can be used to determine analytically the evolution of an adiabatically convecting energetic particle distribution. The energy dependence of the injection yields upper and lower cutoffs to the distribution within the plasmasphere, and only an upper cutoff outside. This approach is used to study the evolution of ion cyclotron waves in a convecting particle distribution, and it is found that the upper cutoff to the distribution restricts the growth of these waves, both on and off the geomagnetic equator, to a narrow range of frequencies which grow only inside the plasmasphere. In addition, it is found that the upper cutoff limits wave growth to a few hours in either side of dusk. The results are examined for two source distributions, a power law and a Maxwellian, and it is found that for distributions with equivalent mean energies the power law is unstable over a greater range of frequencies and radial distances than the Maxwellian.