Geoscience Reference
In-Depth Information
6
FLR in Plasma Configurations
6.1 Introduction
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 sys-
tem 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 Alfven waves has been derived for the dipole case by Dungey [17], Cum-
mings 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 semi-
kinetic approaches (see [2], [9], [25], [26], [27], [31], [35], [49], [51], [55], [59],
[64], [65] and references therein).
A general method for analyzing singularities near resonance magnetic
shells is based on expansion of the wave field into series over the distance
to a resonance field line
x
x
0
. The series may include power and logarithmic
singularities ([40], [59], [65]). This method is in fact a direct generalization of
the Frobenius method (see, e.g., [6], [63]) applied to multidimensional systems.
The method enables the field structure to be studied allowing for a number of
additional factors, i.e. inhomogeneous plasma distribution, variable curvature
of magnetic field-lines, both the Hall and Pedersen conductivities of plasma
boundaries (conjugate ionospheres). In particular, the axially symmetric case
with field-lines orthogonal to the ionospheres was considered in ([40], [65])
and for inclined lines in [21].
Another approach to the construction of the FLR-theory is based on the
presentation of wave fields as superposed oscillations of field line harmonics.
Amplitudes of the harmonics are determined by the infinite system of coupled
−
Search WWH ::
Custom Search