Doctor of Philosophy (Ph.D.)
Experimentally it is observed that the plasma in Elmo Bumpy Torus (EBT) shows discontinuous changes in the electron line density, electron and ion temperatures and fluctuation levels as the ambient gas pressure or electron cyclotron heating is varied continuously. We use the Point Model of Hedrick et al. for the toroidal core plasma in EBT. The Point Model is not a gradient dynamic system. Hence the Elementary Catastrophe Theory is not directly applicable to the Point Model. Nonetheless, the Point Model equilibria will be shown to exhibit properties which are quite akin to the canonical cusp catastrophe. The ambipolar electric field is taken as a control parameter. When electrons are nonresonant, the equilibrium surfaces show only one fold; but when ions are nonresonant, equilibrium surfaces may show single or multiple folds. In the former (electron) case, qualitative agreement with experiments is quite good. For the case of nonresonant ions, predictions are made as to the possible plasma behavior which, when ICRH heating is sufficiently intense, may be checked by experiments. The nonlinear time evolution of the Point Model equations show that the plasma follows the Delay Convention. This simple model of the EBT plasma exhibits rich structure, i.e., equilibrium surfaces with single or multiple folds, attractors, repellors, appearance and disappearance of folds, reversal of direction on equilibrium trajectories, catastrophes, hysterisis, competition between multiple point attractors, and basins of attractors. This leads us to conclude that a simple model of physical systems governed by external parameters can unravel general, complicated qualitative behavior of the system.
© The Author
Punjabi, Alkesh R., "Catastrophes in the Elmo bumpy torus" (1983). Dissertations, Theses, and Masters Projects. Paper 1539623739.