An Alpha Loss-Cone Instability in the Central Cell of a Tandem Mirror Reactor
Ho, Shu Kay
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https://hdl.handle.net/2142/70908
Description
Title
An Alpha Loss-Cone Instability in the Central Cell of a Tandem Mirror Reactor
Author(s)
Ho, Shu Kay
Issue Date
1987
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Fluid and Plasma
Abstract
D-T fusion-born alpha particles are mirror-confined in the central cell of a tandem mirror reactor. The resulting anisotropic loss-cone distribution of the alpha particles in velocity space is capable of destabilizing low frequency plasma waves, thus affecting the energy balance in a tandem mirror plasma.
The low frequency waves of a cold, cylindrical, sharp-boundary, D-T plasma are studied. Techniques have been developed to trace the wave propagation regions and search the wave eigenfrequencies. Three branches of waves are found, namely the Alfven, hybrid, and fast waves; but only the Alfven wave is destabilized by the alpha loss-cone instability. The modeling of the alpha distribution function for the linear and quasi-linear instability calculations is done by a diffusion-front method and a numerical finite difference method, respectively. Their validity is established by comparing them with a converged 80-term Legendre function expansion model of the alpha distribution. The growth rate of the instability is basically determined by the alpha number density, the loss-cone angle, and the polarization of the wave. These quantities are in turn mainly affected by the density and temperature of the plasma ions and electrons, the mirror ratio, and the plasma radius.
A stability boundary in the n-T plane is constructed to locate the stable and unstable regions. The instability is found to occur with moderate values of plasma density and temperature.
A $1{1\over2}$-D quasi-linear diffusion code is developed to study the non-linear evolution of the alpha distribution function due to enhanced diffusion in velocity space and radial position driven by the unstable Alfven wave. It is found that velocity-space diffusion pitch-angle scattering of the resonant alphas into the loss-cone causes significant losses while radial diffusion driven leakage is negligible for a reactor-size plasma.
For a typical tandem mirror reactor design (e.g. the MARS design), the added alpha density and energy losses due to the instability are 36% and 47%, respectively. As a result, the alpha plasma heating is greatly reduced that ignition in the central cell cannot not be achieved. For MARS, an additional heating power of about 200 MW is required to compensate for the alpha loss due to the instability.
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