Plasma drift waves and instabilities
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The work of this thesis is concerned with the investigation of the propagation of waves in a magnetized plasma containing various parameter gradients, and with the stability of ion acoustic waves in a weakly collisional plasma with a strong temperature gradient. The thesis is divided into three sections. In the first section the intention is to derive in a compact and unambiguous tensor form the dispersion relation describing the propagation of waves in a magnetized plasma containing three-dimensional density and temperature gradients, an E̲⏜ B̲ drift, and differing temperatures parallel and perpendicular to the magnetic field. This is achieved by introducing and extending the polarized co-ordinate system first proposed by Buneman in 1961, and then carrying through the standard procedure of integration along unperturbed trajectories. The "local" approximation of Krall and Rosenbluth is used in order that an analytic result may be derived. The dispersion relation obtained includes certain moment tensors whose elements may be evaluated independently of the gradients involved in the problem. These elements may then be listed and the list referred to in order to obtain the elements required for a specific problem. The second section is concerned with the use of the theory and results of J.P. Dougherty to show that in the high-frequency regime the introduction of a small amount of collisions into a plasma is sufficient to disrupt the gyro-resonances which allow the existence of Bernstein waves at multiples of the gyro-frequencies perpendicular and near- perpendicular to the magnetic field. It is shown that a collision frequency v such that (k 𝜌) ⁻² ≲ v/Ω < (k 𝜌) ⁻¹ where k 𝜌 >> 1 is sufficient to do this; k is the wave-number, 𝜌 the Larmor radius, and the gyro-frequency. It is also shown that in this case the ion-acoustic dispersion relation is valid even for propagation perpendicular to the magnetic field. In the final section the result of the second section is used to derive a dispersion relation for high-frequency wave propagation in a weakly-collisional plasma containing an electron temperature gradient. The dispersion relation is solved numerically for various electron-ion temperature ratios and electron temperature gradient drift velocities. Earlier predictions, based on analytic calculations for small temperature ratios and drift velocities, are confirmed and some new results presented. In particular, it is shown that a temperature gradient is a more effective destabilizing agent then a simple drift between ions and electrons. Dispersion plots are given, along with analytic and physical explanations of their form; finally neutral stability curves are presented. The thesis concludes with a summary of the results obtained.
Thesis, PhD Doctor of Philosophy
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