Experimental data show that the generation of ELF/VLF waves and energetic charged particle dynamics in the magnetosphere are non-stationary processes. They operate over different time scales ranging from a fraction of a second up to some tens or even hundreds of seconds. This time interval includes the characteristic period of bounce oscillations, TB, of energetic electrons between magnetic mirror points in the northern and southern hemispheres, as well as the period of a whistler-mode wave packet, Tg, between reflection points (the conjugate ionospheres); both of these are of the order of 1 s and or a few seconds. It is clear that the quantitative description of these non-stationary processes demands different approaches in the CM theory.

In particular, for slow processes with a characteristic time τ » (TB, Tg), we can use the system of quasi-linear equations (8.34) and (8.41). Fast processes in CMs, for which τ ≤ (TB, Tg), as a rule are associated with discrete ELF/VLF emissions having a narrow dynamic frequency spectrum. In this case the nonlinear theory of wave–particle interactions, developed in Chapters 5 and 6, is more suitable. An example of such an approach is the nonlinear theory of the BWO generator, developed in Chapter 5. Here we shall concentrate our attention on the slow dynamics of CMs in the frame of quasi-linear theory, following in the main the review by Bespalov and Trakhtengerts (1986b) and later papers by Trakhtengerts et al. (1986), Demekhov and Trakhtengerts (1994), Trakhtengerts et al. (1996) and Pasmanik et al. (2002).