Tearing mode stability in tokamaks with shaped plasma cross-sections

In tokamaks, magnetic perturbations with different poloidal mode numbers are coupled together via toroidicity, pressure, and the shaping of equilibrium flux-surfaces. The quantities Δ which determine the resistive layer response to tearing perturbations at each rational surface in the plasma are interrelated via a matrix equation. The most general form for the tearing mode dispersion relation is (Δ - E)Ψ = C, where Δ is the diagonal matrix of the Δ quantities at each of the N (say) rational surfaces in the plasma, E is an N x N real symmetric matrix usually referred to as the E-Matrix, Ψ is a 1 x N and C is a 1 x N vector dependent on externally applied resonant magnetic perturbations. The recently developed T7 code determines the elements of the E-Matrix and C-Vector by standard shooting techniques for a large aspect-ratio tokamak with non-circular flux-surfaces. Both free boundary and fixed boundary calculations are possible. Toroidicity, pressure, and plasma shaping are all found to reinforce the destabilizing tendency of a free boundary (i.e. no wall) with respect to a fixed boundary (i.e. a perfectly conducting wall at the edge of the plasma). This is particularly the case if the free boundary plasma lies close to the ideal stability boundary for external kink modes. Thus, at realistic aspect-ratios locked modes (which do not open-quote see close-quote the wall) may be significantly more unstable than rotating modes (which do). This is a possible explanation for the JET observation that a relatively small (2, 1) error field can drive a far larger (2, 1) locked mode once the rotation of the tearing frame at q = 2 has been arrested