Eddy currents and error fields in the toroidally segmented shell configuration aka Armadillo

Abstract

A stream function formulation for the calculation of the eddy current distribution in a toroidally segmented conducting shell (Armadillo) is presented and verified. The governing Poisson-like equation is solved spectrally via a Discrete Sine Transform, which enforces the zero-current boundary condition at each gap exactly by construction, and the related radial magnetic field at the plasma surface is obtained by Biot-Savart integration. The toroidal eddy current flows in the same direction on every sector with a cosine-like poloidal distribution, while the poloidal return current, required by current continuity, peaks near each gap and reverses sign between adjacent sectors. The scaling of both components with the number of gaps is governed by the competition between the poloidal geometric scale of the shell and the toroidal segmentation scale. The transition between the two regimes is set by the aspect ratio of the device, around eight gaps for an RFX-mod2-like geometry, as predicted by the analytical wall time model of the Armadillo configuration. At the gap, the poloidal return current produces a radial field of opposite sign to the value far from the gap; the resulting non-axisymmetric error field peaks near this transition and becomes negligible for highly segmented shells. These results provide a first characterisation of the eddy currents and error fields of the Armadillo configuration, needed for future resistive wall mode and tearing mode stability analyses.