Resonances of the Thin‐Shell Model of the Earth‐Ionosphere Cavity With a Dipolar Magnetic Field

Abstract

A coupled multimode analysis technique is applied to a model of the earth‐ionosphere cavity at ELF in which the ionosphere is replaced by a thin, anisotropic shell. The unique feature of the analy. sis is that it is capable of illustrating the effects of a dipolar form of geomagnetic field. Numerical values of the cavity resonant frequencies and quality factors for several values of electron density and collision frequency are presented for both a homogeneous and a dipolar magnetic field configuration. The main purpose of the paper is to demonstrate that a coupled multimode analysis is applicable to such nonsymmetrical configurations.

Resonances of a cylindrical Earth-ionosphere cavity model with a dipolar magnetic field

“…Table 3 shows results from the cylindrical model that are reasonably close to measurement. As in the case of a differently idealized model with a dipolar field [Large and Wait, 1967], the theoretical resonant frequencies are higher than the measured values, and the Q's are lower. As indicated in Tables I and 2, the constant field model with induction equal to the average of the dipolar field yields resonances very near to the dipolar model.…”

“…A considerable amount of work in the past few years has been directed toward a better understanding of the extremely low frequency (ELF) resonant oscillations of the electromagnetic cavity formed by the region between the earth and the lower ionosphere. Various models have been employed, each having particular usefulness in studying different aspects of the actual earthionosphere system [Madden and Thompson, 1965;Galejs, 1965;Large and Wait, 1967]. One aspect of the cavity that is of interest is the influence of the geomagnetic field upon the resonances.…”

Theory of electromagnetic coupling phenomena in the Earth-ionosphere cavity

“…The procedure was proposed on an earlier occasion [Wait, 1963], but the explicit derivation was not given. When the electrical properties of the outer cavity boundary are allowed to vary with location in a general way, the total field must be ex- Z c.,,h,, sin O' ,, (cos 0)½'" -•-Z Z a.,,e,,P,, (cos Resonant frequencies and quality factors may then be found by tech-niques developed earlier [Large and Wait, 1967c]. This approach is likely, however, to be quite time consuming, since the dimension of the determinantal equation will be large.…”

“…This step is easily performed and the result is the formal solution for the coefiqcients a• from which the magnetic field H• can be calculated by means of expression 28. Note that, if the source vanishes (i.e.identical to the modal equation used in the source-free problem[Large, 196.6;Large and Wait, 1967c]. Ia the following sections, (29) is evaluated for specified forms of the impedance tensor.…”

Line splitting in the Schumann resonance oscillations

“…The presence of the magnetic field violates the equivalence of the eastward and westward propagation (in magnetic coordinates), and the waves corresponding to distinct eigenfunctions acquire different phase speeds. The degeneracy is therefore removed, the resonance frequencies are split, and elliptical polarization appears [ Wait , 1962; Large and Wait , 1966, 1967a, 1967b, 1968; Bliokh et al , 1968, 1971, 1977, 1980; Sentman , 1987, 1989, 1995; Nickolaenko and Hayakawa , 2002].…”