Modelling, numerical simulation and optimal control of the plasma configurations for the tokamak NET and for the future generation of fusions reactors

The plasma is maintained inside the tokamak by electrical currents flowing external coils. The optimization of the position of the plasma is made by adjusting the currents. The first chapter gives the partial differential equations that govern the behaviour of a plasma inside a tokamak. In the second chapter, the plasma equilibrium issue is considered and solved by a finite element method combined with a Newton algorithm. The control of the plasma position implies to determine the electrical currents in the coils so that the plasma matches a fixed configuration. In order to do that, we define a Lagrangian, we derive an optimality system we solve by using a conjugate gradient algorithm. In the third chapter we develop a model for simulating the changes in a plasma configuration during a discharge. The last chapter is dedicated to the control of the evolution of a plasma configuration. The question is to find the laws governing the changes in current intensity and voltage necessary to get a right evolution of the plasma. The feasibility of a feedback law of PID type that could servo-controlled the shape of the plasma is considered. (A.C.)