Nonlinear Phenomena in a Pure Electron Plasma Studied with a 2-D Fluid Code

Citation

Bachman, David Alan (1998) Nonlinear Phenomena in a Pure Electron Plasma Studied with a 2-D Fluid Code. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/72z8-gm50. https://resolver.caltech.edu/CaltechETD:etd-01232008-081243

Abstract

This thesis presents a new computational tool for studying cylindrical pure electron plasmas. Previous research used linear methods to describe the evolution of small plasma perturbations. This new tool numerically solves the nonlinear two- dimensional (2-D) fluid equations in cylindrical coordinates, allowing the exploration of many phenomena that have been observed experimentally in these plasmas. Most experimentally observed phenomena are large in amplitude and follow nonlinear dynamics. Clearly, codes based on the linearized equations can not reproduce these nonlinear phenomena. The plasma was first studied for small amplitude perturbations using the nonlinear fluid code, producing results that agree with linearized calculations. The perturbed electric field decays in time, due to shear in the flow of density perturbations at different radii, which results in the total contribution to the perturbed electric field phase mixing away. At higher amplitudes, the decay envelope becomes modulated, which is a result that has been observed experimentally and is also reproduced by this fluid code. The modulation is caused by nonlinear trapping of fluid elements within the wave, which is illustrated in images of the perturbed density. For two applied pulses separated in time, a third echo response is observed after the responses to the two applied pulses have decayed away. Echoes have been observed experimentally in neutral plasmas, but have not yet been observed experimentally in non-neutral plasmas. At very high amplitudes, a nonlinear decay instability occurs. A high amplitude wave decays into a wave with lower azimuthal symmetry number due to an interaction occurring at the beat frequency between the two waves. The beat-wave decay instability has been observed experimentally, and is also observed using the 2-D nonlinear fluid code. The 2-D cylindrical nonlinear fluid code is capable of reproducing a wide range of non-neutral plasma phenomena, and is an important new tool for future research on non-neutral plasmas. This research is also relevant to ordinary fluids, since the equations describing a non-neutral plasma are analogous to the 2-D Euler equations for an inviscid fluid.

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