Real-time control of the plasma density profile on ASDEX upgrade

The tokamak concept currently is the most promising approach to future power generation by controlled thermonuclear fusion. The spatial distribution of the particle density in the toroidally confined fusion plasma is of particular importance. This thesis work therefore focuses on the question as to what extent the shape of the density profile can be actively controlled by a feedback loop in the fusion experiment ASDEX Upgrade. There are basically two essential requirements for such feedback control of the density profile, which has been experimentally demonstrated within the scope of this thesis work: On the one hand, for this purpose the density profile must be continuously calculated under real-time constraints during a plasma discharge. The calculation of the density profile is based on the measurements of a sub-millimeter interferometer, which provides the line-integrated electron density along 5 chords through the plasma. Interferometric density measurements can suffer from counting errors by integer multiples of 2π when detecting the phase difference between a probing and a reference beam. As such measurement errors have severe impact on the reconstructed density profile, one major part of this work consists in the development of new readout electronics for the interferometer, which allows for detection of such measurement errors in real-time with high reliability. A further part of this work is the design of a computer algorithm which reconstructs the spatial distribution of the plasma density from the line-integrated measurements. This algorithm has to be implemented on a computer which communicates the measured data to other computers in real-time, especially to the tokamak control system. On the other hand, a second fundamental requirement for the successful implementation of a feedback controller is the identification of at least one actuator which enables a modification of the density profile. Here, electron cyclotron resonance heating (ECRH) has been chosen, which permits a very localized power deposition in the plasma center. As a coupling mechanism between temperature profile and density profile exists, central heating effects a central flattening or peaking of the density profile, depending on the type of discharge. This effect was successfully exploited for feedback control of the shape of the density profile. The last part of this thesis work investigates this coupling mechanism between temperature and density in more detail, especially with respect to the temporal behavior in response to sudden changes in the central heating power. Here, a hysteresis loop in the local density-temperature diagram is observed. With the help of a simple numerical model, it is finally shown that, based on the transport equations for heat and particles, the occurrence of such a hysteresis loop is expected. In particular, the results indicate a temperature dependence of the particle inwards drift. (orig.)