Control of Nonaxisymmetric Magnetic Field Perturbations in Tokamaks

The theory of control of nonaxisymmetric perturbations is dominated by the wide sensitivity range of a tokamak plasma to externally produced magnetic perturbations. External perturbations are characterized by their normal magnetic field [italic B with right arrow above]_x[italic n with circumflex accent] on the unperturbed plasma surface. The first spatial distribution of [italic B with right arrow above]_x[italic n with circumflex accent] on the unperturbed plasma surface in a sensitivity series is that distribution that at the smallest amplitude has a significant effect on plasma properties. The second distribution of [italic B with right arrow above]_x[italic n with circumflex accent] in that series is the distribution to which the plasma has greatest sensitivity while being orthogonal to the first. Two distributions are orthogonal if the integral of their product over the unperturbed plasma surface is zero. Only a limited number of distributions in the sensitivity series can be driven to an unacceptable amplitude by credible construction errors in ITER. Essentially any external coil set that produces a nonaxisymmetric magnetic field of adequate strength with a controllable toroidal phase can null the drive for the distribution of highest plasma sensitivity. However, the simultaneous nulling of not only the first but also of a number of other distributions in the sensitivity series is far more difficult. It is the properties of these distributions of secondary importance that determine both the machine tolerances that are required for successful control and the adequacy of a given set of error field control coils. Nonaxisymmetric fields can also have beneficial effects such as the control of edge-localized modes. Implementation requires driving a normal field distribution to which the beneficial effect is sensitive while not driving detrimental distributions of high plasma sensitivity.