The Velocity-Space Particle Loss in Field-Reversed Theta Pinches
Hsiao, Ming-Yuan
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https://hdl.handle.net/2142/70894
Description
Title
The Velocity-Space Particle Loss in Field-Reversed Theta Pinches
Author(s)
Hsiao, Ming-Yuan
Issue Date
1983
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)
Engineering, Nuclear
Abstract
A field-reversed theta pinch (FRTP) is a compact device for magnetic fusion. It has attracted much attention in recent years since encouraging experimental results have been obtained. However, the definite causes for the observed particle loss rate and plasma rotation are not well known. In this work, we study the velocity-space particle loss (VSPL), i.e., particle loss due to the existence of a loss region in velocity space, in FRTP's in order to have a better understanding about the characteristics of this device.
Based on two constants of motion, H and P(,(theta)), where H is the total energy of a particle and P(,(theta)) is the canonical angular momentum, particle confinement criteria are derived, which impose constraints on H and P(,(theta)). It is found that only a portion of (H,P(,(theta))) space, or equivalently, of velocity space, is for confinement. A loss region in velocity space is found.
Effects of this loss region in velocity space are investigated. The velocity-space particle loss due to collisions is calculated from the Fokker-Planck equation. The scaling law for particle confinement is obtained. Without assuming any instability, the particle confinement time based on VSPL theory alone can account for the experimentally observed particle confinement time. This shows the importance of the velocity-space particle loss.
For the velocity distribution in collisional equilibrium, a simple analytical expression, V(,0), is verified to be a good representation of the actual velocity distribution in the presence of the loss region in velocity space. In steady-state, simple analytical approximate solutions for the whole particle distribution function, f(r,v), are obtained, from which the characteristics of the FRTP plasmas can be known.
It is shown that the VSPL model can account for the experimental observation in density profiles, particle confinement time, occurrence and spin-up of plasma rotation. Therefore, the VSPL has the possibility to be the dominant particle loss mechanism and the sole cause responsible for the observed plasma rotation in FRTP's.
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