Variational methods for studying the evolution of a plasma. Application to Tokamak

In the first part of the text, a variational principle is converted into a directly usable form to monitor the evolution of a hot confined plasma. It is shown that the standard form can be be extended to the increasingly complex situations encountered in practice while retaining a simple expression. The very important situation in which a perturbation produces stochastic trajectories is envisaged. It is obvious that useful information on the phenomena associated with stochastic processes can be obtained by applying the preceeding variational principles to the situation in question, provided that certain basic hypotheses are modified. The application of these variational principles was limited to Tokamak. Any magnetic configuration, however, confining hot plasma can be studied using the same standard form delta M by introducing the appropriate angular variables and action. Applications of this method other than those listed for Tokamak are possible. In particular, all the neoclassical phenomena occurring can be dealt with in a relatively simple manner. Non-linear effects with respect to density and temperature gradients could for example be investigated. As far as turbulence theory is concerned, the principles studied can be applied in order to obtain dispersion relations, to calculate transport coefficients and even saturation levels under these complex conditions. Finally, the results of these calculations have led to modifications in experiments associated with projected Tokamak and suggestions for further experiments. The level of ripple that can be admitted for strongly heated machines was examined. The rotating of the plasma in order to decontaminate it by removing heavy impurities was considered together with the practical means necessary to realize this operation. Two divertor schemas were also examined: an H.F. electric field divertor, an ergodic divertor