Plasma boundary control in tokamaks

Plasma MHD equilibrium and stability play a key role in tokamak engineering since they have far reaching consequences in the design and operation of present and future fusion devices. Here the problem of the control of the plasma boundary is addressed and solved by a two-steps procedure. Firstly the fixed plasma equilibrium problem is solved inside a pre-assigned region and the external eideali flux necessary to keep such equilibrium is derived. Then a linear formula is given for the deviation of the plasma boundary from the ideal shape given the error in matching the external eideali flux. We apply this formula to the ITER quasi-static and dynamic plasma boundary control problem. In the quasi-static problem we aim at computing the optimal equilibrium currents that maintain a desired plasma equilibrium. The external flux is matched at the plasma boundary trading-off accuracy and cost. In the dynamic problem, the plasma equilibrium and external currents are known and we derive a linear model describing the (unstable) plasma vertical dynamics. The method proposed presents several advantages: it is computationally cheap since it requires only the mesh of the plasma region. It is remarkably robust since it requires solving an elliptic, fixed boundary problem plus the computation and SVD of the mutual inductance matrix coils-plasma boundary nodes, therefore avoiding the solution of the numerically more delicate free-boundary problem. It computes important equilibrium features (e.g. instability growth rate) and is naturally suited to include the presence of 3D eddy currents in the surrounding metallic structures.