Coupling of tearing modes in tokamaks

The simultaneous presence of tearing modes of different helical pitches leads to the destruction of magnetic surfaces, which has been suggested as the mechanism leading to the onset of the disruptive instability in tokamaks. For current profiles in which the m=2 mode is unstable, but the m=3 is stable, the coupling of the m=3 to the m=2 through the poloidal variation of the toroidal field can drive the m=3 amplitude ψ3 to order ψ2 times the inverse aspect ratio. Detailed calculations, including nonlinear effects, have been performed for two models for the equilibrium and m=2 mode structure. A slab model and incompressible m=3 perturbations are assumed. The m=3 amplitude increases with shear, up to a point, showing that as the current channel shrinks, overlap of resonances becomes more likely. Our results also apply qualitatively to other m, m±1 interactions.