A general description of ion acceleration by the ponderomotive forces of circularly polarized electromagnetic waves with arbitrary frequency in magnetized plasmas is presented. The time derivative parallel ponderomotive force turns out to play an important role for nonstationary ion acceleration. Our results can be useful in understanding the acceleration of escaping ions in the presence of intense electromagnetic waves in the auroral zone of the Earth's ionosphere.
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Shukla et al. (1996) studied this question.