Space Plasma Dynamics : Instabilities, Coherent Vortices and Covariant Parametrization

Abstract: The magnetospheric cusps are two funnel-like regions of Earth's magnetosphere where solar wind plasma can have direct access to the ionosphere. The cusps are very dynamic regions where wave-particle interactions continuously take place and redistribute energy among different particle populations. In this thesis, both low and high frequency plasma waves in the cusp have been studied in detail using data from the Cluster spacecraft mission. The waves were studied with respect to frequency, Poynting flux and polarization. Wavelengths have also been estimated using multi-spacecraft techniques. At low frequencies, kinetic Alfvén waves and nonpotential ion cyclotron waves are identified and at high frequencies, electron cyclotron waves, whistler waves, upper-hybrid and RX-waves are observed. A common generation mechanism called the shell-instability is proposed for several of the wave modes present in the cusp, both at low and high frequencies. The plasma in the cusp is shown to be strongly inhomogeneous. In an inhomogeneous low-frequency magnetoplasma, kinetic Alfvén waves couple to drift-waves. Such drift-kinetic Alfvén waves have long been believed to nonlinearly self-interact and form coherent structures in the form of drift-kinetic Alfvén vortices. In this thesis the first unambiguous direct measurements confirming the existence of such vortices in a turbulent space plasma are presented. Some of the crucial parameters such as the vortex radius are determined. Plasma theory is electrodynamics applied to a large collection of charged particles. In this thesis a new way of looking at the fundamental Maxwell tensor is presented. A covariant spectral density tensor containing information on electromagnetic waves is formed. This tensor is then decomposed into irreducible components by using the spinor formalism for an arbitrary metric. The obtained fundamental tensors are shown to correspond both to well known tensors in Maxwell's theory, as well as several physically interesting new tensors.