Spectrum of hydromagnetic waves in the exosphere

Abstract

A disturbance in the exosphere generates waves in three partially separable modes. The modes are described by considering the vorticity about a line of force, the two-dimensional divergences of velocity in the plane perpendicular to the line of force, and the component of velocity along the line of force. The propagation of vorticity is one-dimensional and there is no geometrical attenuation. It is suggested that this mode is associated with the sudden commencement of a magnetic storm. The propagation of the longitudinal component velocity is almost one-dimensional, but it is heavily damped at high frequencies. In a gravitational field, the medium is no longer uniform, and at low frequencies the modes are coupled in a complicated way. The influence of gravity is characterized by the frequency of oscillation of a small parcel of fluid when displaced from its zero-order position in the gravitational field. For parallel magnetic and gravitational fields the vorticity mode is still separable, and gravity leads to anisotropic dispersion in the other modes. The propagation at low frequencies is no longer cylindrically symmetrical if the lines of force are at an arbitrary angle to the direction of gravity. Detailed investigations of the influence of the gravitational field on hydromagnetic wave propagation is carried out for the case where the sound velocity is small compared to the Alfven wave velocity. The principal aim of the study is an attempt to provide a background for the separation of source effects from those of the medium as an aid to the spectral study of magnetic records. The relative proportion of the three modes generated by a specific source is estimated. Consideration of the regions of allowed solutions in frequency-wave number space show that the vorticity mode will have a narrow spectrum. It is suggested that high-frequency micropulsations are associated with vorticity mode propagation. Examples of vorticity generating sources include the turbulent region in the vicinity of a finite amplitude wave, the outgassing of a rocket motor, and a wake of a satellite in the lower exosphere. Energy may be trapped within the exosphere in various free vorticity mode oscillations. The free periods of these oscillations are comparable to the periods observed in the low frequency micropulsations. The limiting conditions for the propagation of the various modes in the exosphere are considered. Because of the long-range nature of the Coulomb forces, the charged particle may travel distances short compared with its mean free path and still exchange a substantial proportion of its momentum. For representative models of the exosphere, disturbances at several earth radii must have a length scale large compared with several kilometers for the propagation of the longitudinal component of velocity. The limiting conditions on the vorticity and transverse modes involve the ratio of the length scale of the disturbance to the Larmor radius. These modes are propagated if the disturbances have length scales of some hundreds of meters in the outer regions of the exosphere.