Ionospheric Alfvén Resonator (IAR) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 156

and

s D .k ? L/ C k ? tanh .k ? d/

k ? C tanh .k ? d/ I LJ 2 :

(5.35)

It is clear that all the components of the electromagnetic perturbations at the
ground surface are proportional to the factor ‰. d/ given by Eq. ( 5.32 ). In this
notation, the zeros of the factor q in the denominator of Eq. ( 5.32 ) define the
resonance structure of the IAR spectrum. We return to this point later.
Depending on the neutral wind velocity, v , the function F 0 plays a role of forcing
functions/sources for the IAR excitation. In contrast to Eqs. ( 5.14 ) and ( 5.16 ) where
the shear Alfvén and compressional modes are uncoupled, Eq. ( 5.32 ) describes the
interference of these two modes by virtue of the Hall conductivity H . Indeed, only
if Ǜ H D 0, the set of boundary equations ( 5.120 ) and ( 5.121 ) is split into two
independent equations for the shear Alfvén .A;dž/ and compressional .‰/ modes.
As we shall see, this mode coupling plays a significant role in the IAR excitation
and thus cannot be neglected. Furthermore, it is worth mentioning that Eqs. ( 5.120 )
and ( 5.121 ) describe the coupling of the ionospheric MHD modes with neutral wind
motions in the ionosphere. To understand the forcing function F 0 in more detail,
however, we need to consider the role of other sources of the IAR excitation such as
the thunderstorm activity. We return to this matter in Sect. 5.3 .
The denominator in Eq. ( 5.32 ) contains the factor LJ 3 ( 5.31 ) which increases
strongly if k ? d 1 because of the presence of the function exp .k ? d/,so
that the signals become practically undetectable owing to their smallness on the
ground. This means that only large-scale perturbations with typical horizontal sizes
k 1

? d 100 km make a main contribution to the IAR spectrum observed on
the ground. Before discussing this problem in any detail, we need to understand a
little about the IAR dispersion relation and the IAR eigenfrequencies.

5.2 IAR Eigenfrequencies

5.2.1 Dispersion Relation of the IAR

The IAR is referred to as a class of magnetic field resonances for shear Alfvén
waves. The resonance frequencies of the IAR are determined by the length, L,of
the segment of magnetic field line, which is bounded from above and from below by
the resonator sides. Based on the plane-stratified model of the IAR (Plyasov et al.
2012 ) have shown that the vertical electromagnetic structure inside IAR has a form
of the standing mode: electric components have their anti-nodes in the vicinity of the
magnetic nodes. Assuming that the integer number of the Alfvén half-wavelength
keeps within L, the characteristic IAR eigenfrequencies can be estimated as f n
V A n=.2L/, where V A is the Alfvén wave speed and n is integer value. Taking the