Magneto-hydrodynamic Waves in the Ionosphere and their Application to Giant Pulsations

In magneto-hydrodynamics conservation of energy leads to the adiabatic relation, du = pdϱ/ϱ², between the internal energy u per unit mass, the pressure p, and the density ϱ. The relation is valid for arbitrary amplitudes in a non-dissipative medium. The Hall current modifies the properties of magneto-hydrodynamic waves in an ionized gas. The compressive modes and the Alfvén mode earlier discussed by van de Hulst are shown to be coupled by means of the Hall current. The dissipation of slightly damped waves is expressed in terms of the effective conductivity σ₃ = σ₁ + σ₃²/σ₁ earlier introduced by Cowling. The theory is applied to magneto-hydrodynamic oscillations in the layers of the ionosphere. The possible periods of the waves are consistent with the periods of “giant pulsations” which have been observed as a type of perturbation in the earth's magnetic field in the auroral zone. The results indicate that magneto-hydrodynamic waves in the E-, F₁-, and F₂-layers may explain the existence of giant pulsations as well as the occurrence of rapid vibrations in the terrestrial magnetic field.