In previous chapters the cyclotron interaction of charged particles with whistler (or Alfvén) mode waves of a given amplitude was considered, as was the amplification of monochromatic waves and wavelets using a linear approach. At the same time, such important questions as the dynamics of the radiation belts, pitch-angle diffusion and the precipitation of energetic charged particles, their acceleration, the origin of different types of electromagnetic emissions in the Earth's and other magnetospheres demand the development of a self-consistent approach to the problem of wave–particle interactions; this should be based on a nonlinear theory of the cyclotron instability. This theory includes the influence of feedback of the waves generated on the energetic charged particle distribution. The formulation of such a nonlinear theory is non-trivial in the case of space CMs.

Experiments show a huge diversity of wave generation regimes in CMs, including both noise-like and quasi-monochromatic regimes, and complicated interactions between these two regimes. A general theory which permits us to describe this diversity of generation regimes from a single point of view does not yet exist.

However, it is helpful to classify the observed natural electromagnetic signals into one of two groups – noise-like emissions or signals with a discrete frequency spectrum. A dominant example of the first group is ELF or VLF hiss; representatives of the second group are ELF or VLF chorus. Similar groupings exist in the ion cyclotron frequency range; these are the short-period geomagnetic pulsations of IPDP (irregular pulsations of diminishing period) and Pc1 types, respectively.