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One of the most promising concepts for future fusion reactors is the tokamak. In these devices, a hot ionized plasma is confined with the use of large magnetic fields. The subject of this thesis is the study of a particular type of tokamak instabilities with MagnetoHydroDynamic (MHD) simulations. The code JOREK-STARWALL is adapted and applied to the simulation of the so-called free-boundary instabilities. The investigation of this type of instabilities requires a special treatment for the plasma boundary conditions, where the interaction of the plasma with the vacuum and the surrounding conducting structures needs to be taken into account. In this work, the modelling of the electromagnetic plasma-wall-vacuum interaction is reviewed and generalized for the so-called halo currents. The adapted JOREK-STARWALL code is applied in order to study the physics of two particular free-boundary instabilities: Edge Localized Modes (ELMs) triggered by vertical position oscillations and Vertical Displacement Events (VDEs). Two major results are obtained: 1. The triggering of ELMs during vertical position oscillations is for the first time reproduced with self-consistent simulations. These allow for the investigation of the physical mechanism underlying this phenomenon. The simulations reveal that for the international ITER project, a large-scale tokamak, these triggered ELMs are mainly due to an increase in the plasma edge current due to the vertical plasma motion. 2. For VDEs, several benchmarks are performed with other existing MHD codes showing a good agreement and therefore allowing the performance of ITER simulations to estimate the expected amount of halo currents in ITER.
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.
We analyze the magnetohydrodynamic (MHD) stability of the axisymmetric system consisting of a free boundary, non-circular cross-section tokamak plasma, finite resistivity passive conductors, and an active feedback system with magnetic flux pickup loops, a proportional amplifier with gain G, and current carrying poloidal field coils. Numerical simulation of a system that is unstable with G = 0 shows that for some placements of the pickup loops, the system will remain unstable for all values of G, while for other placements of the loops, the system will be stable for G> G/sub crit/. This behavior is explained by analysis using an extended energy principle, and it is shown to result from the deformability of the plasma cross section. 9 refs., 5 figs.
Comprehensive, self-contained, and clearly written, this book describes the macroscopic equilibrium and stability of high temperature plasmas.
Extensive numerical studies of ideal MHD instabilities have been carried out to gain insight into the parametric dependence of critical .beta.'s in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical .beta. has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate for both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that for aspect ratio R/a approximately equal to 3, critical .beta.'s are of the order of 2% for circular cross sections and 5% for plasmas with elongation K approximately equal to 2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analyzed to compare critical .beta. as a function of toroidal mode number n. We conclude that the infinite-n analytic ballooning theory provides a sufficient condition for ideal MHD internal mode stability. Low-n free boundary modes appear to set a lower limit.
Magnetohydrodynamics, the study of the motion of electrically conducting fluids in magnetic fields, is an important area in plasma physics. The effects of instabilities in such electrical fluids are very difficult to calculate and this is the first book to deal with the subject as a whole in a detailed manner. MHD and Microinstabilities in Confined Plasma starts from first principles and builds up to a full understanding of MHD. It features a number of topics not covered in other books on plasma, including non-linear theory, anomalous transport and magnetic reconnection.