Ionospheric Alfvén Resonator (IAR) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 145

The same cavity can serve as a resonator for the shear Alfvén waves, which
propagate along the geomagnetic field lines. The ionospheric Alfvén resonator
(IAR) arises due to the Alfvén wave reflection at the point of intersection between
the magnetic field lines and the boundaries of the resonator as sketched in Fig. 5.3 .
The energy of the shear Alfvén wave can get trapped inside the IAR thereby exciting
standing waves into the resonator. To summarize we note that the IAR is referred to
as the class of field line resonances for shear Alfvén waves.
The idea of IAR was originally suggested by Polyakov ( 1976 ) and has been
extensively studied by a number of authors (see Polyakov and Rapoport 1981 ;
Belyaev et al. 1987 , 1990 ; Lysak 1991 ; Trakhtengertz and Feldstein 1991 ). The
existence of the IAR was well documented by ground-based observations in low lat-
itudes (Hickey et al. 1996 ; Bösinger et al. 2002 ), in middle latitudes (Polyakov and
Rapoport 1981 ; Belyaev et al. 1987 , 1990 ; Hickey et al. 1996 ; Bösinger et al. 2002 ,
2004 ; Molchanov et al. 2004 ; Hebden et al. 2005 ), and even high latitudes (Belyaev
et al. 1999 ; Demekhov et al. 2000 ; Yahnin et al. 2003 ; Semenova and Yahnin 2008 ).
Based on Freja and FAST satellite onboard observations the IAR occurrence was
also identified in space (e.g., Grzesiak 2000 ; Chaston et al. 1999 , 2002 , 2003 ).
To study the structure and mechanisms of the IAR excitation in more detail, we
need to construct a suitably idealized model of the medium that is a reasonable
approximation to the altitude variations of the plasma conductivity and the Alfvén
speed. The ionospheric resonance cavity is localized at altitudes below 1-2 the Earth
radius. When considering Alfvén waves propagating between the IAR walls at such
distances, the magnetic field line curvature is of little importance and thus can be
neglected. On the contrary, the plasma number density, the collision frequencies,
the plasma conductivity, and other ionospheric parameters exhibit strong variations
inside the IAR. On account of local character of the examined effect we shall
consider a simplified plane-stratified model of the system Earth-atmosphere-
ionosphere-magnetosphere, widely used in the studies of electromagnetic coupling
between geospheres (e.g., Fujita and Tamo 1988 ; Pokhotelov et al. 2000 ; Surkov et
al. 2004 ). For the sake of simplicity we adopt the model of the vertical external
magnetic field in order to avoid the complexities connected with magnetic field
inclination. A schematic drawing of our model is shown in Fig. 5.4 . In this model,
the conductive Earth, neutral atmosphere, E- and F -layers of the ionosphere, and
magnetosphere, are assumed to be plane-stratified slabs of a constant thickness. The
origin of the coordinate system is at the bottom of the ionosphere and z -axis is
vertically upward. The gyrotropic E-layer of the ionosphere is shown with shaded
area in Fig. 5.4 . Furthermore, the plasma is assumed to be uniform within each layer
in the direction perpendicular to the external magnetic field.

5.1.1 Model of Alfvén Speed Height Profile in the Exosphere

We start with the region above the Alfvén speed minimum, that has been termed
the exosphere. In this region, the Alfvén speed height profile based on tabulated