Stability Analysis of Magnetically Confined Plasmas

The major problem confronting researchers who wish to obtain power from controlled thermonuclear reactions is the necessity to contain a completely ionized plasma of sufficiently high density and temperature. The time duration of confinement has to be long enough so that the energy released by the fusion process is greater than that required for creating and maintaining the plasma. Because of the temperature of the plasma, the containment can not be performed solely with material walls. Since all of the particles in the plasma are electrically charged, electromagnetic forces are used to confine the plasma to one place and also to isolate it from the surrounding material environment. The problem with suggested confinement schemes is that they are unstable and the plasma tends to escape. Research is needed to study the stability of plasma containment devices and to find ways of making them stable. The plasma stability problem is approached in this dissertation using some new extensions of Liapunov stability theory to partial differential equations that have emanated from research on the control of distributed parameter systems. This theory can be applied to a more general model of a thermonuclear plasma than could be used by previous investigators of plasma stability. With this approach, stability criteria for the equilibrium states have been obtained for both the linear and the non-linear resistive plasma models. Besides producing results that are much more general than existing criteria, the developed theory indicates possible corrective action. Additional results included the determination of an estimate on transient behavior for the linear model and the region of asymptotic stability for the non-linear plasma model. The theory presented in the dissertation is illustrated by an example