Ion Velocity Distributions in Inhomogeneous and Time-dependent Auroral Situations

Aurorae often break down into elongated filaments parallel to the geomagnetic field lines (B) with cylindrically symmetric structures. The object of this thesis is to study the ion distribution function and transport properties in response to the sudden introduction of a radial electric field (E) in such a cylindrical geometry. Both collision-free and collisional situations are considered. The thesis starts by solving a collision-free problem where the electric field is constant in time but increases linearly with radius, while the initial ion density is uniform in space. The attendant Boltzmann equation is solved by tracking the ions back in time, thereby using the temporal link between the initial position and velocity of an ion and its position and velocity at an arbitrary time and place. Complete analytical solutions show that the ion distribution function is a pulsating Maxwellian in time, and all transport parameters (e.g., bulk speed, temperature, etc.) oscillate in time but independent of radius. If the ion-neutral collisions are taken into account by employing a simple relaxation model, analytical solutions are also obtained. In this case, the ion distribution function can be driven to horseshoe shapes which are symmetric with respect to the ExB direction. The bulk parameters evolve in a transition period of the order of one collision time as they go from oscillating to the non-oscillating steady state. In more realistic electric field structures which are spatially inhomogeneous but still constant in time, a generalized semi-numerical code is developed under collision-free conditions. This code uses a backmapping approach to calculate the ion velocity distribution and bulk parameters. With arbitrarily selected electric field rofiles, calculations reveal various shapes of ion velocity distribution functions (e.g., tear-drop, core-halo, ear-donut, etc). The associated transport properties are also obtained and discussed. Under both collision-free and collisional conditions, the effect of the density inhomogeneities at the initial time is studied in an electric field which is proportional to radius and constant in time. With two profiles of the initial ion density for the collision-free case, and one profile for the collisional case, complete analytical solutions are obtained. The results reveal that the distribution function and the bulk properties are now strongly dependent on radial position. If the radial electric field is unable to stay constant with time but modulated by in-coming charged particles, a fluid formalism is used to study the excitation of several plasma waves under different kinds of initial conditions. These identified waves include the ion cyclotron oscillation, the ion and electron upper-hybrid oscillations, and the lower-hybrid oscillation. The results of this thesis are expected to be applicable to high-resolution observations. Future work should also include the mirror effect and the formation of conics in velocity space. Finally, the velocity distributions obtained in this thesis could trigger various plasma instabilities, and this topic should also be looked at in the future