Topic/Type: 1.2 Fusion Plasmas (magnetic & inertial confinement), Poster

Response of a resistive wall with holes to an external kink mode in a tokamak

C.V. Atanasiu1, A. Moraru2, L.E. Zakharov3

1 Association MEdC-EURATOM, Bucharest, Romania
2 University POLITEHNICA of Bucharest, Bucharest, Romania
3 Princeton University, Plasma Physics Laboratory, PO Box 451, Princeton NJ 08543, USA

Starting from the expression for the potential energy in terms of the perturbation of the flux function, a system of ordinary differential equations in that perturbation has been obtained [1], by performing an Euler minimization. This system of equations describes an external kink mode if the resonance surface is situated at the plasma boundary. It is known that the external modes are stabilized by the presence of a close-fitting perfectly conducting wall but become destabilized when the wall is assumed to have finite resistivity. For a toroidal geometry with a separatrix, natural boundary conditions for the perturbed flux function, just at the plasma boundary have been determined by using the concept of a surface current [2], replacing the vanishing boundary conditions at infinity. By adding the wall, in its thin approximation, but with the real geometry of a tokamak with a realistic wall containing holes, new boundary conditions for the external kink mode, now a resistive wall mode, due to the field produced by the eddy currents in the wall and due to feedback coils have been determined.
Special attention has been given to obtain a very fast and reliable numerical tool to calculate the influence of the eddy currents on the boundary conditions of the system of equations describing the RWM. In place of the usually used magnetic vector potential, we have developed a model by defining a scalar potential (stream function) for the induced surface currents. For a wall with holes, we have developed a new extremely fast numerical method (for example, on 151 x 151 grid points, 14 seconds where necessary only to solve the whole problem on a dual core PC at 64 bits). Both magnetic fields have been considered: the exciting field due to the external kink mode and the magnetic field produced by the surface currents themselves. To check the accuracy of our method, we have used Stokes theorem by performing some line integrals and verifying the corresponding surface integrals. At sufficiently high number of grid points, an excellent agreement between both integrals has been found ? overlapping up to the 5th significant digit. Besides this checking, we have imagined some simple cases permitting an analytical solution. The singularities due to sharp corners in the boundary (holes) have been treated with the help of conformal transforms [3].

[1] C.V. Atanasiu, S. G?nter, K. Lackner, A. Moraru, L.E. Zakharov, Phys. Plasmas 11, 5580 (2004).

[2] C.V. Atanasiu, A.H. Boozer, L.E. Zakharov, A.A. Subbotin, Phys. Plasmas 6, 2781 (1999).

[3] A. Moraru, Rev. Roum. Sci. Techn. ? Electrotechn. et Energ. 52, 2 (2007).