Hydromagnetic eigen-oscillations in the dipolar field

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MHD equations in the dipolar coordinates are analyzed for an idealized model in which the earth surface is assumed to be a perfect conductor. For the case of standing resonance waves, i. e., the guided toroidal and the guided poloidal waves, the eigenperiods are determined mainly by the mass density near the equatorial plane in the magnetosphere. The eigenperiods of the standing waves importantly depend on the mass density of the heavy ions outside the plasmapause. The resonance oscillations are expected to occur only on a field line having L-values within a narrow range, since a displacement of MHD fluid in the equatorial plane is of the order of 0.1 R_E for a perturbed electric field ∿2mV/m near L=10. The relation of the electric field wave amplitude (δE) of the standing oscillation to the displacement ((δξ)_<eq>) is represented by |δE|=B_0(L)^<-3>・(δξ)_<eq> near the magnetic equator. The magnetic perturbation fields of the standing oscillations in the equatorial plane are one order smaller than those in the ionosphere for a case of perfect reflection. The conditions of the coupling oscillations of an Alfven wave and a compressional wave are theoretically discussed for the special case of highly asymmetric modes.
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