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Title:
Theory of Resistive Magnetohydrodynamic Instabilities Excited by Energetic Trapped Particles in Large-Size Tokamaks.
Authors:
Biglari, Hamid
Affiliation:
PRINCETON UNIVERSITY.
Publication:
Thesis (PH.D.)--PRINCETON UNIVERSITY, 1987.Source: Dissertation Abstracts International, Volume: 47-11, Section: B, page: 4560.
Publication Date:
00/1987
Category:
Physics: Fluid and Plasma
Origin:
UMI
Abstract Copyright:
(c) 1987: UMI Company
Bibliographic Code:
1987PhDT........96B

Abstract

A theory describing excitation of resistive magnetohydrodynamic instabilities due to a population of energetic particles, trapped in region of adverse curvature in tokamaks, is presented. Theory's principal motivation is observation that high magnetic field strengths and large geometric dimensions characteristic of present-generation thermonuclear fusion devices, places them in a frequency regime whereby precessional drift frequency of auxiliary hot ion species, in order of magnitude, falls below a typical inverse resistive interchange time scale, so that inclusion of resistive dissipation effects becomes important. Destabilization of resistive internal kink mode by these suprathermal particles is first topic under investigation. Using variational techniques, generalized dispersion relation governing such modes, which recovers ideal theory in its appropriate limit, is derived and analyzed using Nyquist diagrammatic techniques. Important implication of theory for present-generation fusion devices is that they will be stable to "fishbone" activity. Interaction of energetic particles with resistive interchange-ballooning modes is taken up. A population of hot particles, deeply -trapped on adverse curvature side in tokamaks, can resonantly destabilize resistive interchange mode, which is stable in their absence because of favorable average curvature. Both modes are different from their usual resistive magnetohydrodynamic counterparts in their destabilization mechanism, and in that they have a real component to their frequency comparable to drift frequency of rapidly-precessing energetic species. Corresponding growth rates and threshold conditions for this trapped -particle driven instability are then derived, and finite banana width effects are shown to have a stabilizing influence on mode. Ballooning/tearing dispersion relation is generalized to include hot particles, so that both the ideal and resistive modes are derivable in the appropriate limits. Linear picture having thus emerged, a weak turbulence theory is proposed to seek mode's saturated amplitude in nonlinear phase. Adopting a single-helicity approach, a set of coupled nonlinear equations describing interaction of a high-frequency (fundamental) mode with a low-frequency (virtual) mode is derived. In analyzing nonlinear dispersion relation, it is found that except for limit of strong wave-particle interaction, modes are explosively unstable. The inclusion of viscosity is shown not to alter these conclusions.
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