Control of the magnetic topology and plasma exhaust in the edge region of Wendelstein 7-X. A numerical study

Nuclear fusion is the energy source of the stars and has the potential of being the main energy source for mankind in the future. The research on fusion energy focuses primarily on magnetic confinement, where hot plasma - with temperatures on the order of 100 million degrees Celsius - are confined by specially designed toroidal magnetic topology. The main candidates for magnetic confinement are the tokamak and the stellarator. The tokamak concept is further developed than the stellarator concept, but the stellarator concept has some intrinsic and potentially very important advantages and is therefore also actively pursued. The Wendelstein 7-X (W7-X) stellarator will be the world's leading stellarator experiment. It is about to go into operation in Greifswald, Germany. This thesis delves into some very important scientific challenges for the stellarator concept as a whole and W7-X in particular, namely, how one effectively interfaces the hot plasma with the material walls of the experiment, in special how the plasma heat and particle fluxes are controlled. The fundamental concept that will be used in W7-X for particle and heat exhaust is the island divertor. Although the divertor concept at a stellarator was invented by Lyman Spitzer back in the 1950s, the stellarator island divertor still needs to be experimentally tested at fusion-relevant heat loads and temperatures in steady-state. W7-X is the first experiment that will be able to do so. A number of theoretical and numerical studies have been performed to guide the design of the divertor components. The actual divertor components are in series production at this time, and are largely compatible with the expected heat loads. However, with the sophisticated codes now available, it has become clear that there are some, otherwise very attractive, operational scenarios that could lead to overloading of the W7-X divertors. At least one mitigation strategy was proposed but was until now not analyzed in sufficient detail. In this thesis, state-of-the-art codes are used to analyze this previously proposed mitigation strategy; they are also used to develop several alternative mitigation schemes, which may in the end be advantageous. The work performed here shows not only that it is conceivable to solve this already identified problem in new and arguably better ways but also that the W7-X coil set has enough degrees of freedom that many important long-pulse plasma e.ects can be e.ectively mimicked in short-pulse operation. This opens up a rich research program in the early phases of operation and may therefore lead to a significant acceleration of the scientific program to control and optimize the divertor operation in W7-X. The main scientific challenge for the island divertor operation in W7-X is that, since the divertor geometry is now fixed, the magnetic field structure must be adjusted to the divertor geometry, or additional plasma-facing components must be manufactured and installed. Well before this thesis work was done, such additional plasma-facing components were proposed. These are called scraper elements (SEs). As a part of this work, computer simulations were performed in order to obtain a better knowledge base regarding the SEs. To analyze the e.ect of the SE, edge plasma physics simulation code EMC3-Eirene, was used, in combination with state-of-the-art magneto hydrodynamic (MHD) equilibrium codes. This combination was computationally non-trivial and new, and it has led to important insights. One main result of this study is that the SEs significantly reduce the particle exhaust capabilities in steady state operation; this is a concern for W7-X. To test and further quantify this deleterious effect, physics experiments with a prototype SE should be performed as soon as possible, ideally in the first operation campaigns before the approximately two-year break needed to complete W7-X for steady-state operation. In this first operation phase, however, the necessary combination of plasma parameters, heating power, and achievable pulse length is not accessible. This means, on the one hand, that the problem described will not be present in the first operation phase; on the other hand, the physics implications of installing an SE would appear not to be experimentally testable in that phase. One major finding of this thesis is that the coil system of W7-X is flexible enough to allow such an early experimental test. Different stages of high performance long-pulse discharge can be effectively mimicked in the experiment by a targeted use of the available coil sets. Thus, even in the early phases of the W7-X program one can assess both the protection capabilities of the SEs and their effects on particle exhaust and plasma performance in general. These mimic scenarios also have the potential to test other possibilities for divertor protection besides the SE. Such strategies are addressed in this thesis. The two most promising strategies identified here can be classified as plasma shift and iota control. Both adjust the edge magnetic field to better fit the divertor geometry. This is done slowly but dynamically - i.e. during a long plasma discharge. The differences between iota control and plasma shift can be quickly summarized as follows: In iota control, the edge magnetic field topology is kept constant by negating the effects of evolving plasma currents through changes in external coil currents. The external field changes needed for this strategy are substantial. The plasma shift approach lets the plasma edge topology evolve as the plasma currents evolve but nonetheless allows a safe divertor operation by shifting the location of the plasma.