Exjobbsförslag från företag

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Förslaget inkom 2007-12-18

Modelling and identification for physical analysis in thermonuclear fusion

The main objective of this project is to develop some new modeling and identification tools for the understanding and analysis of complex physical phenomenon that occur in thermonuclear fusion. Indeed, recent developments in control theory and fusion research are naturally leading to research topics of common interest that are particularly challenging for both scientific communities. The representation (qualitative and quantitative) of the particles transport at the plasma edge is an example of such topics and motivates this project, focused on the particles source identification from electron density profiles in Tore Supra Tokamak. Most of the research will take place in the Automatic Control Department of GIPSA-lab (Grenoble, France). This department is the largest group of researchers specialized in systems and control theory in France, and has a leading position in modeling, identification and control of complex processes. Depending on the student’s desires, the initial literature studies and the final writing of the report can be carried at the Alfvèn lab in Stockholm.

Tore Supra Tokamak is equipped with Lower Hybrid antennas to heat the plasma and create the toroidal current. The power is coupled with the plasma by approaching the antenna to the confined plasma. During the wave propagation to the core plasma, a small but significant part will be absorbed at the edge in an area where the plasma is not confined and therefore cold. A possible effect of this absorption is the gas ionization, which results in an increased electron density. This ionization is localized and occurs only in magnetic flux tubes passing through in front of the antenna. On Tore Supra, the electron density is measured by using a microwave reflectometer which has both a good spatial (?r~1cm) and temporal resolution (?t~2ms for the experiments considered).

The aim of this master project is to develop an identification algorithm for determining the 'source term', i.e. the number of electrons created per unit time and volume, when the HF heating is switched on, and the particles diffusion coefficient. To achieve this, we will use a simple particle transport model in the area of non-confined plasma (plasma edge) and develop an appropriate parametric identification method for distributed systems. The emphasis will be on the robustness of the identification method with respect to perturbed measurements, as well as on the distinction between modeling and discretisation errors. The spatial localization (according to the distance to the center of the plasma) of the measurements is an important element to take into account.

The identification algorithm will be validated on Tore Supra shots that have been specifically set for this determination. The evaluation of – possibly very large – model uncertainties will also be considered.

Summary: The student will develop a new identification method based on a simple analytical model and experimental (electronic density profiles) or theoretical (connection lengths, electrons/ions temperature) data. The resulting algorithm will be validated on multiple Tore Supra shots, the data being provided by CEA-Cadarache.


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