General formulation of the resistive wall mode coupling equations.

A theoretical framework to describe the magnetic coupling of the toroidal plasma with the resistive wall and other sources of the field asymmetry is formulated. This is done for general toroidal geometry without restrictions on the plasma, while the wall is considered as a thin shell. Mathematically, the approach here exploits the Chance concept [M. S. Chance, Phys. Plasmas 4, 2161 (1997)], but with an essential difference: each source of the magnetic perturbation b (plasma, wall, external currents) is treated separately with account of their differences in space and nature. This allows much simpler formulation of the problem than was known before. The final equation couples the normal component of ∂b/∂t at the wall to the perturbation at the plasma surface. Step by step reduction of this first-principle equation is performed with demonstration of its main features, starting from the known problem of singularities. This also includes the reduction to axially symmetric geometry, large-aspect-ratio, and the cylindrical limits. In the latter case, the known “cylindrical” equation is reproduced, but now from the full “toroidal” equations. [ABSTRACT FROM AUTHOR]