High-.beta. equilibria which are stable to all ideal MHD modes are found by optimizing the plasma shape and current profile for doublets, up-down asymmetric dees, and symmetric dees. The ideal MHD stability of these equilibria for low toroidal mode number n is analyzed with a global MHD stability code, GATO. The stability to high-n modes is analyzed with a localized ballooning code, BLOON. The attainment of high .beta. is facilitated by an automated optimization search on shape and current parameters. The equilibria are calculated with a free-boundary equilibrium code using coils appropriate for the Doublet III experimental device. The optimal equilibria are characterized by broad current profiles with values of .beta./sub poloidal/ approx. =1. Experimental realization of the shapes and current profiles giving the highest .beta. limits is explored with a 1 1/2-D transport code, which simulates the time evolution of the 2-D MHD equilibrium while calculating consistent current profiles from a 1-D transport model. Transport simulations indicate that nearly optimal shapes may be obtained provided that the currents in the field-shaping coils are appropriately programmed and the plasma current profile is sufficiently broad. Obtaining broad current profiles is possible by current ramping, neutral beam heating, and electron cyclotron heating. With combinations of these techniques it is possible to approach the optimum .beta. predicted by the MHD theory.

This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.

The ideal MHD stability properties of a special class of vertically asymmetric tokamak equilibria are examined. The calculations confirm that no major new physical effects are introduced and the modifications can be understood by conventional arguments. The results indicate that significant departures from up-down symmetry can be tolerated before the reduction in .beta. becomes important for reactor operation.

Achieving very high [beta] and high [beta]{sub p} simultaneously in tokamaks generally implies that the second stability region against ballooning modes must be accessed. We describe several approaches for doing this, which are characterized by the choice of constraints imposed on the equilibrium profiles and the cross-sectional shape of the plasma. The combination of high toroidal beta, restricting the current density to vanish at the edge of the plasma and maintaining a monotonic q profile, proves to be the most stringent. Consideration of equilibria with high [epsilon][beta]{sub p} but low [beta] facilitates accessibility with peaked pressure profiles and high values of q0. Allowing the pressure gradient and, hence, the current density to be finite at the plasma edge allows all surfaces to lie within the second stability regime. For free boundary plasmas with divertors, the divertor stabilized edge region remains in the first stability regime while the plasma core reaches into the second regime. Careful tailoring of the profiles must be used to traverse the unstable barrier commonly seen near the edge of these plasmas. The CAMINO code allows us to compute s-[alpha] curves for general tokamak geometry. These diagrams enable us to construct equilibria whose profiles are only constrained, at worst, to be marginally stable everywhere, but do not necessarily satisfy the constraints on the current or [beta]. There are theoretical indications that under certain conditions the external kinks possess a second region of stability at high q0 that is analogous to that of the ballooning modes. It is found that extremely accurate numerical means must be developed and applied to confidently establish the validity of these results. 14 refs., 5 figs., 1 tab.