Impact of toroidal and poloidal mode spectra on the control of non-axisymmetric fields in tokamaks

In several tokamaks, non-axisymmetric magnetic field studies show that applied magnetic fields with a toroidal harmonic n = 2 can lead to disruptive n = 1 locked modes. In Ohmic plasmas, n = 2 magnetic reconnection thresholds in otherwise stable discharges are readily accessed at edge safety factors q similar to 3, low density, and low rotation. Similar to previous studies with n = 1 fields, the thresholds are correlated with the "overlap" field computed with the IPEC code. The overlap field quantifies the plasma-mediated coupling of the external field to the resonant field. Remarkably, the "critical overlap fields" at which magnetic islands form are similar for applied n = 1 and 2 fields. The critical overlap field increases with plasma density and edge safety factor but is independent of the toroidal field. Poloidal harmonics m> nq dominate the drive for resonant fields while m < nq harmonics have a negligible impact. This contrasts with previous results in H-mode discharges at high plasma pressure in which the toroidal angular momentum is sensitive to low poloidal harmonics. Together, these results highlight unique requirements for n > 1 field control including the need for multiple rows of coils to control selected plasma parameters for specific functions (e.g., rotation control or ELM suppression).