Dynamo action in the ionosphere and motions of the magnetospheric plasma

Abstract

This thesis presents a study of the dynamic interaction which takes place between the magnetospheric plasma and the underlying neutral atmosphere; it is hoped thus to gain a better understanding of the effects of this interaction upon the steady state configuration of the magnetosphere. The neutral portion of the atmosphere (the neutrosphere) and the overlying ionized regions (the upper atmosphere and magnetosphere) may be regarded as two distinct dynamic domains that interact in a region of transition occurring between 100 and 150 km over the earth. The neutrosphere because of its greater mass will dominate the motion, and the magnetospheric plasma can be expected to undergo motions related to those of the upper neutrosphere and transition region. However, the geomagnetic field restricts the motion of the magnetospheric plasma to a particular class, allowing one to consider the magnetospheric motion to be constrained. Motions in the transition region of the class not permitted the magnetospheric plasma will give rise to forces against the constraint. The reaction of the constraint on the atmosphere of the transition region takes the form of a Lorentz force J x B where J is the current responsible for the well known solar quiet day daily magnetic variation (Sq). The explanation for the production of this current in the transition region has traditionally been presented in terms of a dynamo-like electromotive force generated by motions of the conducting atmosphere through the magnetic field, whence the transition region is aptly named the dynamo region. The Lorentz force represented by this current constitutes a significant term in the equation of motion for the dynamo region. Another important term arises from eddy viscous stresses immediately below the dynamo region. The equation of motion for the dynamo region must thus include such forces as well as the pressure gradient and Coriolis terms. However, our almost total ignorance of the eddy viscous stress field at the lower surface of the dynamo layer at present precludes our deducing the entire dynamo layer winds from the observed Sq magnetic variation. The kinematics of the dynamo layer are discussed and the motion or the dynamo layer is divided into a symmetric and an antisymmetric part. The term symmetric is here used to describe winds in the northern and southern hemisphere that are the mirror images of each other with respect to the equatorial plane. It is demonstrated that the symmetric component gives rise to electrostatic fields transverse to the field lines, but to no currents along the field lines, while the antisymmetric case produces the converse effects. The symmetric and antisymmetric winds are further divided into components according to the horizontal electromotive force they produce. (a) Symmetric Wind. In the case of the symmetric wind, only the portion of the wind producing the solenoidal component of the horizontal dynamo electromotive force is effective in producing ionospheric currents. It is demonstrated that only this current producing wind system acts against the constraints imposed by the geomagnetic field on magnetospheric motions. The motion of the magnetospheric plasma driven by each such wind system is discussed. The earlier treatments of the dynamo theory consider the dynamo region to be a single layer in which the wind system and the electric conductivity are assumed to be uniform in height. A new, more general derivation of the layer's dynamo action is given in which no restrictions are placed upon the vertical distributions. An effective wind is defined which permits the use of the earlier equations relating the current function, the electrostatic field, and the scalar field describing the current producing part of the effective wind. The equation relating the electrostatic field and the current function is essentially that employed by Maeda (1956), allowing his solution for the portion of the electrostatic field associated with the current producing wind to remain unaffected by the stratification of the wind system. Mathematical techniques for solving the dynamo equations for the electrostatic field are developed. These allow for a quite general conductivity distribution over the globe, only requiring that it be expressible in surface harmonics. The effect of undetected zonal currents upon the solution for the electrostatic field is discussed. It is suggested that a considerable diurnal component of electrostatic field and other components as well may be hidden from us by our inability to detect the prevailing magnetic perturbations produced by zonal currents. The electrostatic field associated with the non-current producing components of the symmetric wind is likewise hidden from us. (b) Antisymmetric Wind. The equations for the current driven by the antisymmetric component of wind are derived, and some of the effects of such currents are discussed. It is found that the conduction of current along the field lines from one hemisphere to the other is associated with an interhemispheric stress between geomagnetically conjugate points of order 3 x 10⁻⁷ newtons/meter². In addition it is found that an antisymmetric layer current density of 5 amperes/km into the polar cap region (across the 75° latitude circle) might give rise to a displacement of about 150 km in the relative position of the conjugate points defined by field lines of the magnetospheric tail. It is suggested that the dynamo action in the 100 to 150 km height plays a role in determining the manner in which the magnetosphere divides itself into the corotating region and the magnetospheric tail.