Oscillations of the Earth's Outer Atmosphere and Micropulsations

Summary In recent years many workers have considered hydromagnetic oscillations of the Earth's outer atmosphere as a possible cause of geomagnetic micropulsations. Almost all of them use the equations derived by Dungey (1954b) for calculating the eigenperiods of the system. Because of the complexity of the equations the coupling terms, which in spherical polar coordinates contain ∂/∂φ, are usually neglected. For this reason the equations of small hydromagnetic oscillations are here derived in cylindrical coordinates with the main magnetic field lying in the plane perpendicular to the axis of the cylinder. Since the structure of the equations in this system is somewhat simpler than in spherical polar coordinates, it is possible to obtain the eigenperiods of toroidal oscillations as a function of co-latitude without making any approximations. Using an electronic computer it is possible to extend the calculations to the case of a non-uniform plasma density distribution, as used by Dessler (1958) in his studies on the geomagnetic field. In the past most workers have assumed the Earth's field to be a geocentric dipole. As a result of recent studies, however, it appears that the geomagnetic field does not extend as far into outer space as was assumed but that to a first approximation it is confined to a cavity (Dungey 195413, Parker 1958). For this reason the equation of toroidal oscillations is applied to a compressed dipole field. Assuming both a constant and a variable plasma density distribution the eigenperiods of the deformed magnetic lines of force are obtained.