Nonlinear ion cyclotron resonance in electromagnetic wave with non-uniform amplitude

The cyclotron motion of ion in a nonuniform electromagnetic wave is analysed using the multiple-time-scale-expansion method. A set of nonlinear equations which describes the evolutions of the gyroradius ρ, the gyrophase β, and the average velocity along the magntic field B 0 is obtained. The set is found exactly integrable and three conservation relations are obtained for an arbitrary harmonic among ρ, β, and the drift coordinates perpendicular to B 0 . The theory includes the one obtained for the fundamental harmonic and a uniform amplitude wave and is also applied to ion acceleration in a non-uniform field near an antenna used in an ion-cyclotron-range-of-frequencies (ICRF) wave heating. Thus the theory seems to be more rigorous and general than the previous ones.