Effect of a static external magnetic perturbation on resistive mode stability in tokamaks

The influence of a general static external magnetic perturbation on the stability of resistive modes in a tokamak plasma is examined. There are three main parts to this investigation. First, the vacuum perturbation is expanded as a set of well‐behaved toroidal ring functions, and is, thereafter, specified by the coefficients of this expansion. Second, a dispersion relation is derived for resistive plasma instabilities in the presence of a general external perturbation, and finally, this dispersion relation is solved for the amplitudes of the tearing and twisting modes driven in the plasma by a specific perturbation. It is found that the amplitudes of driven tearing and twisting modes are negligible until a certain critical perturbation strength is exceeded. Only tearing modes are driven in low‐β plasmas with εβ_p≪1. However, twisting modes may also be driven if εβ_p≳1. For error‐field perturbations made up of a large number of different poloidal and toroidal harmonics the critical strength to drive locked modes has a ‘‘staircase’’ variation with edge‐q, characterized by strong discontinuities as coupled rational surfaces enter or leave the plasma. For single harmonic perturbations, the variation with edge‐q is far smoother. Both types of behavior have been observed experimentally. The critical perturbation strength is found to decrease strongly close to an ideal external kink stability boundary. This is also in agreement with experimental observations.