FLR in Plasma Configurations

In Chapter 5 the FLR-theory was formulated within the framework of a 'plasma box' model: with 1D inhomogeneity across straight field-lines. Despite the seeming simplicity of the model, the spectral properties of the relevant system of MHD equations turned out to be non-trivial. Such a magnetospheric model is a rare example of a spatially confined physical system in which a continuous spectrum appears. The eigenmode equation for standing toroidal shear Alfvén waves has been derived for the dipole case by Dungey [17], Cummings et al. [14] and by many other authors. Basic ideas of FLR-theory that guided much of the subsequent research of the FLR in complex plasma con- figurations can be found in ([7], [50]), the basic mathematics is given in [30]. Numerous papers are devoted to consideration of 2-D and 3-D cases and semikinetic approaches (see [2], [9], [25], [26], [27], [31], [35], [49], [51], [55], [59], [64], [65] and references therein).