Doctoral Dissertations
Date of Award
6-1983
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Engineering Science
Major Professor
J. Milton Bailey
Committee Members
Joseph M. Googe, Marshall O. Pace, J. Reece Roth, William T. Snyder
Abstract
A brief history of the beginnings of nuclear fusion research involving toroidal closed-system magnetic plasma containment is presented in Section 1.
In Section 2 a tokamak machine is defined mathematically for the purposes of plasma equilibrium position perturbation analysis.
The perturbation equations of a tokamak plasma equilibrium position are developed in Section 3.
Solution of the approximated perturbation equations of a tokamak plasma equilibrium position is carried out in Section 4. A unique, simple, and useful plasma displacement dynamics transfer function of a tokamak is developed. The dominant time constants of the dynamics transfer function are determined in a symbolic form. This symbolic form of the dynamics transfer function makes it possible to study the stability of a tokamak's plasma equilibrium position. Knowledge of the dynamics transfer function permits systematic syntheses of the required plasma displacement feedback control systems.
The major parameters governing the plasma equilibrium position stability of a tokamak are shown to be (1) external magnetic field decay index, (2) transformer iron core effect, (3) plasma current, (4) radial rate-of-change inductance parameter, (5) vertical rate-of-change inductance parameter, and (6) vacuum vessel eddy-current time constant. An important and unique result is derived, showing that for a vacuum vessel eddy-current time constant exceeding a certain value the vertical plasma equilibrium position is stable, in spite of an intentional vertical instability design represented by a negative decay index.
It is shown that a tokamak design having a theoretical set of positive decay index, negative radial rate-of-change inductance parameter, and positive vertical rate-of-change inductance parameter is expected to have a better plasma equilibrium position stability tolerance than a tokamak design having the same set with the signs reversed.
In Section 5 a tokamak plasma displacement feedback control design is considered, Linear Optimal Control and the Optimality Condition are discussed, and a minimal hardware tokamak plasma displacement feedback control system is presented.
The ISX-A tokamak high-frequency oscillations and low-frequency dynamics functions are given numerically in Section 6, using the ISX-A tokamak numerical data given in the Appendix.
The results of an actual hardware ISX-A tokamak plasma displacement feed back control system design are presented in Section 7. It is shown that a theoretical design computer simulation and the actual hardware step function responses of the radial plasma displacement feedback control system are practically identical. The actual hardware vertical plasma displacement feedback control system performed just as well. Experimental results support all of the analytical developments.
Recommended Citation
Burenko, Oleg, "Dynamics and feedback control of plasma equilibrium position in a Tokamak. " PhD diss., University of Tennessee, 1983.
https://trace.tennessee.edu/utk_graddiss/13013