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Abstract
The problem of radial localization of kinetically excited Alfven-type waves in the terrestial magnetosphere is examined using WKB approximations in the radial direction. These modes have been called drift Alfven ballooning modes (DABM) by CHEN and HASEGAWA, (1991)$\sp1$ and are the prime candidates to explain Pc4-Pc5 waves observed during storms. Pc4-5 type geomagnetic oscillations are long-lasting pulsations with large amplitudes and periods on the order of 500 sec. They are typically observed in the inner magnetosphere. Up to now, work on the theory of these pulsations has been done in one dimension, along the equilibrium magnetic field. In this dissertation, we include the effects of both parallel and perpendicular plasma inhomogeneities and investigate the issue of whether such a wave can be radially localized. In the first part, we formulate the theoretical approach neglecting the wave-particle resonances and using the one-fluid MHD limit. A local dispersion relationship is found on each flux surface of the equilibrium, and a global quantization condition is derived. To each flux surface correspond certain characteristic frequencies, (determined as eigenvalues of appropriate one-dimensional problems along the equilibrium magnetic field), and if the appropriate frequency matches the global mode frequency, then this surface is called resonant. In the picture developed here, the global mode is trapped at the outer side of a storm-time ring current by a steep pressure gradient. At the same time, energy from it tunnels through a barrier, and gets absorbed at its corresponding resonant flux surface, which in space physics terminology is called field line resonance. This energy absorption would lead to the damping of the mode, in the absence of an excitation mechanism. A strong dependence of the damping rate on the azimuthal wave number m is established, as well as on the equilibrium profile. First, it is found that the equilibrium pressure gradient has to be steeper than a certain threshold in order to be able to confine radially an Alfvenic mode. Second, the damping rate increases sharply with decreasing m, and a minimum azimuthal mode number can be found for the DABM to be radially trapped. This minimum m is lower for steeper gradients, while for gentler gradients it rises. Third, the higher the number of radial nodes a mode has, the higher the minimum m is. Fourth, the trapping mechanism favors modes with low parallel mode numbers and lastly the higher the m is, the narrower the localization area is. Finally, in the second part of the present work we include the excitation mechanism, which for the case of the DABM is the bounce-drift resonance of highly energetic protons. The kinetic effects are introduced using quadratic forms, and are treated perturbatively. The lowest order results are those found from the single-fluid analysis in the first part of the thesis. ftn$\sp1$CHEN, L. and HASEGAWA, A. (1991). Kinetic theory of geomagnetic pulsations 1. Internal excitations by energetic particles. Journal of Geophysical Research 96, 1503-1512.
